Interval (music) - Knowledge (XXG)

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inconsistent, as a similar interpretation is impossible for Cm and C+ (in Cm, m cannot possibly refer to the sixth, which is major by definition, and in C+, + cannot refer to the seventh, which is minor). Both approaches reveal only one of the intervals (M3 or M7), and require other rules to complete the task. Whatever is the decoding method, the result is the same (e.g., CM is always conventionally decoded as C–E–G–B, implying M3, P5, M7). The advantage of rule 1 is that it has no exceptions, which makes it the simplest possible approach to decode chord quality.

2507: 7735:. "Lewin posits the notion of musical 'spaces' made up of elements between which we can intuit 'intervals'....Lewin gives a number of examples of musical spaces, including the diatonic gamut of pitches arranged in scalar order; the 12 pitch classes under equal temperament; a succession of time-points pulsing at regular temporal distances one time unit apart; and a family of durations, each measuring a temporal span in time units....transformations of timbre are proposed that derive from changes in the spectrum of partials..." 1754: 1715:

two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (

3334: 2715: 1608: 1180: 2310: 2681:. Helmholtz then designated that two harmonic tones that shared common low partials would be more consonant, as they produced less beats. Helmholtz disregarded partials above the seventh, as he believed that they were not audible enough to have significant effect. From this Helmholtz categorises the octave, perfect fifth, perfect fourth, major sixth, major third, and minor third as consonant, in decreasing value, and other intervals as dissonant. 5291: 8974: 2402: 42: 3128: 1474: 1111: 2860: 6716: 8842: 2563: 1195: 3251:(also skhisma) is the difference between five octaves and eight justly tuned fifths plus one justly tuned major third. It is expressed by the ratio 32805:32768 (2.0 cents). It is also the difference between the Pythagorean and syntonic commas. (A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, F 1249:). This means that interval numbers can also be determined by counting diatonic scale degrees, rather than staff positions, provided that the two notes that form the interval are drawn from a diatonic scale. Namely, B—D is a third because in any diatonic scale that contains B and D, the sequence from B to D includes three notes. For instance, in the B- 6772: 6444:, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7, and the interval from G downward to C is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory. 5256:(augmented fourth or diminished fifth), could have other just ratios; for instance, 7:5 (about 583 cents) or 17:12 (about 603 cents) are possible alternatives for the augmented fourth (the latter is fairly common, as it is closer to the equal-tempered value of 600 cents). The 7:4 interval (about 969 cents), also known as the 5355:

using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle.

153:

between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this

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note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of

3664:

The quality of a compound interval is determined by the quality of the simple interval on which it is based. For instance, a compound major third is a major tenth (1+(8−1)+(3−1) = 10), or a major seventeenth (1+(8−1)+(8−1)+(3−1) = 17), and a compound perfect fifth is a perfect twelfth (1+(8−1)+(5−1)

1303:

Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason, the interval E–E, a perfect unison, is also called a prime (meaning

6933:

According to the two approaches, some may format the major seventh chord as CM (general rule 1: M refers to M3), and others as C (alternative approach: M refers to M7). Fortunately, even C becomes compatible with rule 1 if it is considered an abbreviation of CM, in which the first M is omitted. The

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Notice that staff positions, when used to determine the conventional interval number (second, third, fourth, etc.), are counted including the position of the lower note of the interval, while generic interval numbers are counted excluding that position. Thus, generic interval numbers are smaller by

4140:

and the corresponding symbols 3 and 5 are typically omitted. This rule can be generalized to all kinds of chords, provided the above-mentioned qualities appear immediately after the root note, or at the beginning of the chord name or symbol. For instance, in the chord symbols Cm and Cm, m refers to

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Any compound interval can be always decomposed into one or more octaves plus one simple interval. For instance, a major seventeenth can be decomposed into two octaves and one major third, and this is the reason why it is called a compound major third, even when it is built by adding up four fifths.

6751:

For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference

1714:

defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in

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It is also worth mentioning here the major seventeenth (28 semitones)—an interval larger than two octaves that can be considered a multiple of a perfect fifth (7 semitones) as it can be decomposed into four perfect fifths (7 × 4 = 28 semitones), or two octaves plus a major third (12 + 12 + 4 = 28

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The prefix semi- is typically used herein to mean "shorter", rather than "half". Namely, a semitonus, semiditonus, semidiatessaron, semidiapente, semihexachordum, semiheptachordum, or semidiapason, is shorter by one semitone than the corresponding whole interval. For instance, a semiditonus (3

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General rule 1 achieves consistency in the interpretation of symbols such as CM, Cm, and C+. Some musicians legitimately prefer to think that, in CM, M refers to the seventh, rather than to the third. This alternative approach is legitimate, as both the third and seventh are major, yet it is

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The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered

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The inversion of a major interval is a minor interval, and vice versa; the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval, and vice versa; the inversion of a doubly augmented interval is a doubly diminished interval, and vice

6953:, each spanning 3 semitones (m3 + m3), compatible with the definition of tertian chord. If a major third were used (4 semitones), this would entail a sequence containing a major second (M3 + M2 = 4 + 2 semitones = 6 semitones), which would not meet the definition of tertian chord. 2667:, it makes more sense to speak of consonant and dissonant chords, and certain intervals previously considered dissonant (such as minor sevenths) became acceptable in certain contexts. However, 16th-century practice was still taught to beginning musicians throughout this period. 6318:

Intervals in non-diatonic scales can be named using analogs of the diatonic interval names, by using a diatonic interval of similar size and distinguishing it by varying the quality, or by adding other modifiers. For example, the just interval 7/6 may be referred to as a

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system uses just tones and semitones as building blocks, rather than a stack of perfect fifths, and this leads to even more varied intervals throughout the scale (each kind of interval has three or four different sizes). A more detailed analysis is provided at

3665:= 12) or a perfect nineteenth (1+(8−1)+(8−1)+(5−1) = 19). Notice that two octaves are a fifteenth, not a sixteenth (1+(8−1)+(8−1) = 15). Similarly, three octaves are a twenty-second (1+3×(8−1) = 22), four octaves are a twenty-ninth (1+3×(8-1) = 29), and so on. 6482:

are distinguished. Specific intervals are the interval class or number of semitones between scale steps or collection members, and generic intervals are the number of diatonic scale steps (or staff positions) between notes of a collection or scale.

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points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of

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Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.

7377:, p. 182d: "Just as the coincidences of the two first upper partial tones led us to the natural consonances of the Octave and Fifth, the coincidences of higher upper partials would lead us to a further series of natural consonances." 1528:

Perfect intervals are so-called because they were traditionally considered perfectly consonant, although in Western classical music the perfect fourth was sometimes regarded as a less than perfect consonance, when its function was

208: 5237:. 5-limit tuning was designed to maximize the number of just intervals, but even in this system some intervals are not just (e.g., 3 fifths, 5 major thirds and 6 minor thirds are not just; also, 3 major and 3 minor thirds are 6948:

chords (chords defined by sequences of thirds), and a major third would produce in this case a non-tertian chord. Namely, the diminished fifth spans 6 semitones from root, thus it may be decomposed into a sequence of two

1599:). Conversely, other kinds of intervals have the opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval. 2526:

depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.

1932:. Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number: they are narrower by a chromatic semitone. For instance, an augmented sixth such as E 4153:

of an extra interval is specified immediately after chord quality, the quality of that interval may coincide with chord quality (e.g., CM = CM). However, this is not always true (e.g., Cm = Cm, C+ = C+, CM = CM). See

447: 1893: 1797: 1517: 1493: 1092: 818: 5248:. It is possible to construct juster intervals or just intervals closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular, the 5329:

seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.

1905: 1869: 1857: 1699: 1687: 1505: 1054: 1016: 902: 2658:

usage, perfect fifths and octaves, and major and minor thirds and sixths were considered harmonically consonant, and all other intervals dissonant, including the perfect fourth, which by 1473 was described (by

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For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.

5107:, the intervals are never precisely in tune with each other. This is the price of using equidistant intervals in a 12-tone scale. For simplicity, for some types of interval the table shows only one value (the 3228:

is generally used to mean the difference between three justly tuned major thirds and one octave. It is expressed by the ratio 128:125 (41.1 cents). However, it has been used to mean other small intervals: see

1785: 1627: 1615: 704: 661: 5159:), and their average size is 400 cents. In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε (the difference between the 3539: 1917: 1881: 1845: 1809: 1773: 1675: 1663: 1651: 1639: 1533:. Conversely, minor, major, augmented, or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or near-dissonances. 978: 940: 780: 742: 7577:

Le Istitutione harmoniche ... nelle quali, oltre le materie appartenenti alla musica, si trovano dichiarati molti luoghi di Poeti, d'Historici e di Filosofi, si come nel leggerle si potrà chiaramente vedere

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interval. These names refer just to the individual interval's size, and the interval number need not correspond to the number of scale degrees of a (heptatonic) scale. This naming is particularly common in

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may not necessarily coincide. These two notes are enharmonic in 12-TET, but may not be so in another tuning system. In such cases, the intervals they form would also not be enharmonic. For example, in

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The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.

3659: 3290: 1833: 1821: 854: 306:. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an 2815:

More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the

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In general, a compound interval may be defined by a sequence or "stack" of two or more simple intervals of any kind. For instance, a major tenth (two staff positions above one octave), also called

1761: 1481: 618: 6363:, respectively narrower than a minor or wider than a major interval. The exact size of such intervals depends on the tuning system, but they often vary from the diatonic interval sizes by about a 1928:

Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions): they are wider by a

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The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in

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The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E

5135: ≈ 3.42 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of about 738 cents (700 + 11 4225:(e.g., C = C) and contains, together with the implied major triad, one or more of the following extra intervals: minor 7th, major 9th, perfect 11th, and major 13th (see names and symbols for 6934:

omitted M is the quality of the third, and is deduced according to rule 2 (see above), consistently with the interpretation of the plain symbol C, which by the same rule stands for CM.

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semitones). Intervals larger than a major seventeenth seldom come up, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 19th".

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is only two staff positions above E, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals B—D and D—F

3153: 4184:, the third must be minor. This rule overrides rule 2. For instance, Cdim implies a diminished 5th by rule 1, a minor 3rd by this rule, and a diminished 7th by definition (see below). 2677:. Helmholtz further believed that the beating produced by the upper partials of harmonic sounds was the cause of dissonance for intervals too far apart to produce beating between the 2374:

Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded".

5260:, has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. For further details about reference ratios, see 310:

fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see

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to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding

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scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.

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The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called

7274:(New York: St Martin's Press; London: G. Bell, 1957): , reprinted 1966, 1970, and 1976 by G. Bell, 1971 by St Martins Press, 1981, 1984, and 1986 London: Bell & Hyman. 4141:

the interval m3, and 3 is omitted. When these qualities do not appear immediately after the root note, or at the beginning of the name or symbol, they should be considered

3171:

There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as

1218:) because the notes from B to the D above it encompass three letter names (B, C, D) and occupy three consecutive staff positions, including the positions of B and D. The 2580: 3242:

is the difference between three octaves and four justly tuned perfect fifths plus two justly tuned major thirds. It is expressed by the ratio 2048:2025 (19.6 cents).

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are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be

7671: 7300: 7012: 2868: 4136:

always refer to the interval of the fifth above root. The same is true for the corresponding symbols (e.g., Cm means C, and C+ means C). Thus, the terms third and

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As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (

5207: ≈ 1.96 cents, the difference between the Pythagorean fifth and the average fifth). Notice that here the fifth is wider than 700 cents, while in most 2735:

above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see

4173:) are implied. For instance, a C chord is a C major triad, and the name C minor seventh (Cm) implies a minor 3rd by rule 1, a perfect 5th by this rule, and a 3154: 2691:, in which an interval's strength, consonance, or stability is determined by its approximation to a lower and stronger, or higher and weaker, position in the 1119: 378: 8563: 4230: 4226: 4215: 4155: 4105: 4012: 2890:

spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of

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is a fifth, as it encompasses five staff positions (C, D, E, F, G), and it is diminished, as it falls short of a perfect fifth (such as C-G) by one semitone.

2544:) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the 2325:

or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.

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was used as an official language throughout Europe for scientific and music textbooks. In music, many English terms are derived from Latin. For instance,

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Major 13th (compound major 6th) inverts to a minor 3rd by moving the bottom note up two octaves, the top note down two octaves, or both notes one octave.

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A compound interval is an interval spanning more than one octave. Conversely, intervals spanning at most one octave are called simple intervals (see

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is a third, as it encompasses three staff positions (C, D, E), and it is doubly augmented, as it exceeds a major third (such as C-E) by two semitone.

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is a fourth, as it encompasses four staff positions (C, D, E, F), and it is augmented, as it exceeds a perfect fourth (such as C-F) by one semitone.

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Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called

1214:(lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval B—D is a third (denoted 5835:

semitones, or about 300 cents) is not half of a ditonus (4 semitones, or about 400 cents), but a ditonus shortened by one semitone. Moreover, in

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is the amount that two major thirds of 5:4 and a septimal major third, or supermajor third, of 9:7 exceeds the octave. Ratio 225:224 (7.7 cents).

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is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80 (21.5 cents).

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Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F

7757: 7712: 7684: 7121: 7075: 7025: 5313:. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its 2515: 6323:, since it is ~267 cents wide, which is narrower than a minor third (300 cents in 12-TET, ~316 cents for the just interval 6/5), or as the 4025:

is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (

3088:, these intervals are indistinguishable to the ear, because they are all played with the same two keys. However, in a musical context, the 1368: 185:. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G 4017:

Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the

2867: 7906: 2663:) as dissonant, except between the upper parts of a vertical sonority—for example, with a supporting third below ("6-3 chords"). In the 7622:, edited and translated by Peter M. Lefferts. Greek & Latin Music Theory 7 (Lincoln: University of Nebraska Press, 1991): 193fn17. 352:

have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a

8862: 7602:, abbreviationes et index fontium composuit C. van de Kieft, adiuvante G. S. M. M. Lake-Schoonebeek (Leiden: E. J. Brill, 1976): 955. 7051: 6984: 3406: 2506: 2829:

in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called

7732: 7607: 7563: 7523: 7499: 7478: 7451: 7415: 7374: 7336:, p. 178: "The cause of this phenomenon must be looked for in the beats produced by the high upper partials of such compound tones". 7287: 7279: 7258: 7187: 7155: 1120: 5364:

As shown below, some of the above-mentioned intervals have alternative names, and some of them take a specific alternative name in

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Lissajous Curves: Interactive simulation of graphical representations of musical intervals, beats, interference, vibrating strings

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for seconds, thirds, sixths, and sevenths. This naming convention can be extended to unisons, fourths, fifths, and octaves with

6437:. In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6. 7253:, 16th edition. London: Augener & Co. (facsimile reprint, St. Clair Shores, Michigan: Scholarly Press, 1970), p. 10. 3550: 2405: 45: 7627: 5351:, "unfold a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by 3341: 2722: 1426:). It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in 5415:, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called 181:. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is 5839:(the most commonly used tuning system up to the 16th century), a semitritonus (d5) is smaller than a tritonus (A4) by one 4526: 4054: 2381:

For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.

6375:, in 24-TET is 150 cents, exactly halfway between a minor second and major second. Combined, these yield the progression 2333: 211: 8355: 8335: 122:. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called 8461: 7666: 7309: 7007: 7600:

Mediae latinitatis lexicon minus: Lexique latin médiéval–français/anglais: A Medieval Latin–French/English Dictionary

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Aldwell, E.; Schachter, C.; Cadwallader, A. (11 March 2010), "Part 1: The Primary Materials and Procedures, Unit 1",

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type of interval (including the semitone) changes depending on the note that starts the interval. This is the art of

3152: 114:. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a 9241: 8467: 7879: 7857: 7707:, for example sections 3.3.1 and 5.4.2. New Haven: Yale University Press. Reprinted Oxford University Press, 2007. 6795: 165:

In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the

4029:) is considered a chord. Chords are classified based on the quality and number of the intervals that define them. 8885: 8250: 7389:, p. 183: "Here I have stopped, because the 7th partial tone is entirely eliminated, or at least much weakened.". 5252:

of the 5-limit tuning scale provides a juster value for the minor seventh (9:5, rather than 16:9). Moreover, the

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In this table, the interval widths used in four different tuning systems are compared. To facilitate comparison,

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The interval number and the number of its inversion always add up to nine (4 + 5 = 9, in the example just given).

1238: 303: 31: 7324:, p. 172: "The roughness from sounding two tones together depends... the number of beats produced in a second.". 2897:

For example, the four intervals listed in the table below are all enharmonically equivalent, because the notes F

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is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.

7830: 7435: 6723: 5192:-comma meantone was designed to produce just major thirds, but only 8 of them are just (5:4, about 386 cents). 4497: 4260:

font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.

4050: 6979:(30th edition, revised and largely rewritten ed.), London: Augener; Boston: Boston Music Co., p. 1, 5244:

The above-mentioned symmetric scale 1, defined in the 5-limit tuning system, is not the only method to obtain

1753: 3219:

is 64:63 (27.3 cents), and is the difference between the Pythagorean or 3-limit "7th" and the "harmonic 7th".

9072: 8963: 8845: 8583: 8522: 7899: 7588: 7443: 7147: 6800: 6353: 6313: 5295: 4470: 2692: 2581: 1596: 484:

is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term

8643: 6915: 6441: 6412: 5804: 5464: 5389: 5373: 5170: 5115: 4592: 4398: 3116: 2869: 2664: 2545: 2471: 8638: 8449: 7816: 7357: 7089: 6883: 6805: 6422: 5770: 2678: 2670: 3197:

is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the

1118: 302:

Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called

2408: 48: 9098: 8825: 8578: 8485: 8479: 8065: 7826: 7676: 7593: 7366: 7017: 6911: 6753: 6325: 5208: 4149:), m is the chord quality and refers to the m3 interval, while M refers to the M7 interval. When the 3100: 2541: 2239: 1403: 5221:-comma meantone, it is tempered to a size smaller than 700. A more detailed analysis is provided at 2696: 8951: 8608: 8473: 8455: 6907: 6903: 6815: 6471: 5606: 4445: 4420: 3333: 2714: 2396:

Intervals can be described, classified, or compared with each other according to various criteria.

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contexts. The combination of number (or generic interval) and quality (or modifier) is called the

8956: 8721: 8158: 7892: 7820: 7795: 7620:

Robert De Handlo: The Rules, and Johannes Hanboys, The Summa: A New Critical Text and Translation

7361: 7094: 6887: 6434: 6180: 5836: 5454: 5404: 5365: 5222: 5196: 4585: 3842: 2769:, is a linear interval between two consecutive notes of a scale. Any larger interval is called a 2660: 2347:

There are two rules to determine the number and quality of the inversion of any simple interval:

2336: 1929: 1744: 1281: 963: 516: 456:

The table shows the most widely used conventional names for the intervals between the notes of a

252: 214: 7511: 4065:

used for chord quality are similar to those used for interval quality (see above). In addition,

7776:(1994). "A principle of correlativity of perception and its application to music recognition". 1723:). Conversely, since neither kind of third is perfect, the larger one is called "major third" ( 8663: 8603: 8164: 8140: 8128: 8109: 7923: 7753: 7728: 7708: 7680: 7623: 7603: 7559: 7519: 7495: 7474: 7447: 7411: 7370: 7283: 7275: 7254: 7183: 7151: 7117: 7071: 7047: 7021: 6980: 6498: 6475: 6461: 6396: 6285: 6250: 6007: 5840: 5579: 5525: 5513: 5420: 5412: 5408: 5407:

the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the

5369: 5322: 5156: 5108: 5104: 4608: 3193: 3089: 3021: 2655: 2537: 2318: 2309: 2304: 1979:) are the only augmented and diminished intervals that appear in diatonic scales (see table). 1588: 1300:(spanning 2 semitones) are thirds, like the corresponding natural interval B—D (3 semitones). 1077: 1039: 765: 603: 520: 512: 345: 337: 333: 307: 6391:. This allows one to name all intervals in 24-TET or 31-TET, the latter of which was used by 1991:

alone. As explained above, the number of staff positions must be taken into account as well.

464:(also known as perfect prime) is an interval formed by two identical notes. Its size is zero 9189: 9174: 9157: 8906: 8896: 8733: 8558: 8503: 8497: 8491: 8395: 8295: 8268: 8152: 8134: 8079: 8073: 7787: 7778: 7773: 7745: 6867: 6785: 6503: 6479: 6465: 6440:

In atonal or musical set theory, there are numerous types of intervals, the first being the

6430: 6346: 6309: 6110: 5972: 5942: 5741: 5720: 5591: 5343: 5275: 5257: 5144: 4373: 4199: 4181: 4133: 3811: 3736: 3303: 3054: 2674: 2128: 2094: 1304:"1"), even though there is no difference between the endpoints. Continuing, the interval E–F 1179: 887: 727: 684: 641: 6886:

thereof. In other words, a scale that can be written using seven consecutive notes without

6421:

theory, originally developed for equal-tempered European classical music written using the

5290: 1355:

This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see

87:

if it refers to successively sounding tones, such as two adjacent pitches in a melody, and

9194: 9169: 9091: 8701: 8425: 8213: 8103: 8097: 8085: 8028: 7991: 7868: 6335: 6215: 6145: 6042: 5381: 5326: 5245: 5127:, by definition 11 perfect fifths have a size of approximately 697 cents (700 − 5100: 5092: 4352: 4129: 4046: 3855: 3776: 2748: 2499: 2223: 2215: 2164: 1395: 1387: 1285: 1260: 1001: 925: 803: 457: 340:, and along that scale the distance between a given frequency and its double (also called 256: 103: 7852: 7643: 7752:. Lecture Notes in Artificial Intelligence. Vol. 746. Berlin-Heidelberg: Springer. 2620:

are not contained in the C major scale. However, it is diatonic to others, such as the A

1556:), with five and seven semitones respectively. One occurrence of a fourth is augmented ( 9147: 9003: 8941: 8681: 8675: 8669: 8441: 7968: 7535: 7246: 6972: 6863: 6757: 6516: 6449: 6408: 6392: 6368: 5800: 5697: 5493: 5459: 5416: 5385: 5348: 5339: 5306: 5261: 5249: 5234: 5229: 5078: 4580: 4568: 4236:

If the number is 5, the chord (technically not a chord in the traditional sense, but a

4222: 4207: 4058: 3215: 3206: 3139: 3127: 3085: 2935: 2826: 2816: 2782: 2552: 2488: 2385: 2067: 1711: 1537: 1473: 1449:

is the quality of the simple interval on which it is based. Some other qualifiers like

1372: 1288:

interval, formed by the same notes without accidentals. For instance, the intervals B–D

1246: 1242: 1211: 1187: 795: 595: 523:), these intervals also have the same width. Namely, all semitones have a width of 100 461: 280: 260: 238: 150: 111: 5169:-comma meantone fifth and the average fifth). A more detailed analysis is provided at 1110: 9235: 9220: 9179: 9162: 9152: 9059: 9054: 9008: 8931: 8916: 8805: 8654: 8573: 8568: 8514: 8375: 8315: 8201: 8189: 8054: 8017: 7974: 7863: 7844: 7662: 7305: 7230: 7003: 6945: 6895: 6891: 6810: 5760: 5707: 5686: 5661: 5636: 5400: 5396: 5238: 5074: 4904: 4896: 4820: 4812: 4777: 4741: 4267: 4254:), and some of the symbols used to denote them. The interval qualities or numbers in 4174: 4166: 4137: 4113: 4008: 3283: 3176: 3162: 2887: 2556: 1183: 1031: 993: 879: 276: 178: 127: 123: 96: 72: 344:) is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone 9215: 9044: 9039: 8926: 8820: 8777: 8772: 8633: 8279: 8036: 7999: 7551: 6871: 6790: 6777: 6732:

The term "interval" can also be generalized to other music elements besides pitch.

6372: 6364: 5621: 5556: 5352: 4280: 4237: 4203: 4192: 4125: 4062: 4026: 4018: 3321: 3312: 3184: 2794: 2786: 2566: 1530: 1128: 676: 633: 524: 477: 465: 329: 323: 155: 107: 64: 7212: 2859: 2242:, followed by the interval number. The indications M and P are often omitted. The 1367: 6722: 5419:(81:80) can neither be regarded as a diminished second, nor as its opposite. See 3340: 3179:, as they describe small discrepancies, observed in some tuning systems, between 3151: 2866: 2721: 2578: 2513: 1994:

For example, as shown in the table below, there are six semitones between C and F

1987:

Neither the number, nor the quality of an interval can be determined by counting

1595:

of the two notes, it hardly affects their level of consonance (matching of their

1117: 9204: 9018: 9013: 8998: 8993: 8946: 8782: 8613: 8048: 8042: 8011: 8005: 7700: 7431: 7179: 7144:

The Complete Musician: An Integrated Approach to Theory, Analysis, and Listening

6950: 6899: 6879: 6875: 6733: 6715: 5674: 5649: 5279: 5199:

is characterized by smaller differences because they are multiples of a smaller

4331: 4297: 4241: 4211: 4202:(e.g., C = C = C) and contains, together with the implied major triad, an extra 4170: 4162: 4121: 4117: 4042: 4038: 4022: 3789: 3768: 3749: 3728: 3267: 2959: 2820: 2809: 2802: 2317:

A simple interval (i.e., an interval smaller than or equal to an octave) may be

1592: 1204: 955: 917: 757: 719: 502: 489: 288: 284: 272: 174: 17: 1591:

of a perfect interval is also perfect. Since the inversion does not change the

1438:(sometimes used only for intervals appearing in the diatonic scale), or simply 519:

is tuned so that the 12 notes of the chromatic scale are equally spaced (as in

146:. Intervals can be arbitrarily small, and even imperceptible to the human ear. 8901: 8815: 8709: 8207: 8120: 7873: 7403: 6767: 6741: 6339: 5630: 5541: 5302: 5269: 5140: 3928: 3902: 3882: 3868: 3238: 3180: 2878: 2854: 2684: 2231: 1411: 692: 488:

is also used to indicate an interval spanning two whole tones (for example, a

473: 131: 7542:. New York: Associated Music Publishers. Cited in Cope (1997), p. 40–41. 7492:

A Player's Guide to Chords and Harmony: Music Theory for Real-World Musicians

5411:

is its opposite (531441:524288, or about 23.5 cents). 5-limit tuning defines

1316:

is only one staff position, or diatonic-scale degree, above E. Similarly, E—G

9210: 8854: 8715: 8219: 6719:

Division of the measure/chromatic scale, followed by pitch/time-point series

6426: 6418: 3987: 3962: 3948: 3198: 3172: 3166: 2562: 1988: 1427: 248: 159: 119: 5399:

is a diminished second, but this is not always true (for more details, see

5301:

Although intervals are usually designated in relation to their lower note,

2365:

above it is a minor third. By the two rules just given, the interval from E

1194: 9126: 8936: 8747: 8195: 7943: 5820: 5564: 5088: 5083: 4256: 3798: 3678: 3317: 3132: 2891: 2650:

These terms are relative to the usage of different compositional styles.

2482: 649: 550: 469: 353: 349: 115: 7822:

On the Sensations of Tone as a Theoretical Basis for the Theory of Music

7799: 7362:

On the Sensations of Tone as a Theoretical Basis for the Theory of Music

442:{\displaystyle n=1200\cdot \log _{2}\left({\frac {f_{2}}{f_{1}}}\right)} 259:

tuning system, the size of the main intervals can be expressed by small-

9142: 9132: 9049: 8911: 8753: 8741: 8727: 8146: 8091: 7002:

Lindley, Mark; Campbell, Murray; Greated, Clive (2001). "Interval". In

6906:

scales, but does not include some other seven-tone scales, such as the

6837: 6330: 5728: 5253: 4177:

by definition (see below). This rule has one exception (see next rule).

3859: 3262: 3247: 2443: 2429: 2251: 2250:

is usually referred to simply as "a unison" but can be labeled P1. The

1564:), both spanning six semitones. For instance, in an E-major scale, the 1222:

and the figure above show intervals with numbers ranging from 1 (e.g.,

866: 843: 835: 481: 311: 6840:

is sometimes used more strictly as a synonym of augmented fourth (A4).

2706:

All of the above analyses refer to vertical (simultaneous) intervals.

9199: 9184: 9114: 9023: 8988: 8810: 8787: 8695: 8689: 7980: 7962: 7875:

Just intervals, from the unison to the octave, played on a drone note

7791: 6745: 5783: 5533: 3279: 3230: 3224: 3095:

The discussion above assumes the use of the prevalent tuning system,

2450: 2433: 2322: 2247: 2243: 1069: 485: 341: 268: 264: 7518:, p. 63. Hammondsworth (England), and New York: Penguin Books. 7369:(1885) reprinted by Dover Publications with new introduction (1954) 4250:

The table shows the intervals contained in some of the main chords (

3119:, all four intervals shown in the example above would be different. 2673:(1821–1894) theorised that dissonance was caused by the presence of 2551:

By a commonly used definition of diatonic scale (which excludes the

1340:), not a sixth. Similarly, a stack of three thirds, such as B—D, D—F 4195:

and a number (e.g., "C seventh", or C) are interpreted as follows:

472:

is any interval between two adjacent notes in a chromatic scale, a

8183: 6714: 6377:

diminished, subminor, minor, neutral, major, supermajor, augmented

5816: 5289: 4244:. Only the root, a perfect fifth and usually an octave are played. 3715: 3332: 3131:

Pythagorean comma on C; the note depicted as lower on the staff (B

3126: 2858: 2731:

A simple interval is an interval spanning at most one octave (see

2713: 2561: 1606: 1472: 1366: 1193: 1178: 1109: 244: 7725:

Repetition in Music: Theoretical and Metatheoretical Perspectives

1259:–D. This is not true for all kinds of scales. For instance, in a 359:

Mathematically, the size in cents of the interval from frequency

243:

The size of an interval between two notes may be measured by the

3534:{\displaystyle DN_{c}=1+(DN_{1}-1)+(DN_{2}-1)+...+(DN_{n}-1),\ } 9087: 8858: 7888: 7068:

How Equal Temperament Ruined Harmony (and Why You Should Care)

5147:); 8 major thirds have size about 386 cents (400 − 4 2808:

For example, C to D (major second) is a step, whereas C to E (

1378:

The name of any interval is further qualified using the terms

95:

if it pertains to simultaneously sounding tones, such as in a

527:, and all intervals spanning 4 semitones are 400 cents wide. 7884: 3092:

of the notes these intervals incorporate is very different.

579: 531: 6138:

hexachordum minus, semitonus maius cum diapente, tetratonus

1956:–C spans seven semitones, falling short of a minor sixth (E 1210:

The number of an interval is the number of letter names or

7558:, p. 21. California: University of California Press. 224:

Example: Minor third on D in equal temperament: 300 cents.

9083: 6898:, or with no signature. This includes, for instance, the 4096:

Deducing component intervals from chord names and symbols

2407:

Audio playback is not supported in your browser. You can

2335:

Audio playback is not supported in your browser. You can

1548:) are perfect. Most fourths and fifths are also perfect ( 328:

The standard system for comparing interval sizes is with

312:§ Size of intervals used in different tuning systems 213:

Audio playback is not supported in your browser. You can

47:

Audio playback is not supported in your browser. You can

6208:

heptachordum minus, semiditonus cum diapente, pentatonus

3654:{\displaystyle DN_{c}=DN_{1}+DN_{2}+...+DN_{n}-(n-1),\ } 1269:–D. This is the reason interval numbers are also called 291:). Intervals with small-integer ratios are often called 7176:

Tonal Harmony, with an Introduction to Post-Tonal Music

6740:

uses interval as a generic measure of distance between

5267:

In the diatonic system, every interval has one or more

1950:—C) by one semitone, while a diminished sixth such as E 106:

music, intervals are most commonly differences between

7410:, pp. 40–41. New York, New York: Schirmer Books. 6487:

1, with respect to the conventional interval numbers.

5392:(or epimoric ratio). The same is true for the octave. 3286:), with a frequency ratio of 15625:15552 (8.1 cents) ( 2258:. The interval qualities may be also abbreviated with 1719:), the 6-semitone fifth is called "diminished fifth" ( 1334:

are thirds, but joined together they form a fifth (B—F

476:

is an interval spanning two semitones (for example, a

7174:

Kostka, Stefan; Payne, Dorothy; Almén, Byron (2018).

6997: 6995: 4198:

If the number is 2, 4, 6, etc., the chord is a major

3553: 3409: 2453:

if they sound successively. Melodic intervals can be

381: 126:, and describe small discrepancies, observed in some 7116:(1st ed.). New York: W. W. Norton. p. 55. 6367:(50 cents, half a chromatic step). For example, the 4145:, rather than chord qualities. For instance, in Cm ( 4124:

always refer to the interval of the third above the

3183:

notes. In the following list, the interval sizes in

2498:

is a non-diatonic interval formed by two notes of a

336:

unit of measurement. If frequency is expressed in a

173:(unison, second, third, etc.). Examples include the 75:

between two sounds. An interval may be described as

9032: 8981: 8796: 8763: 8652: 8622: 8592: 8549: 8540: 8513: 8440: 8423: 8265: 8248: 8237: 8174: 8119: 8064: 8027: 7990: 7955: 7937: 7922: 4104:are summarized below. Further details are given at 2909:

indicate the same pitch, and the same is true for A

2254:, an augmented fourth or diminished fifth is often 169:(perfect, major, minor, augmented, diminished) and 7066:Duffin, Ross W. (2007), "3. Non-keyboard tuning", 6345:The most common of these extended qualities are a 4553:Size of intervals used in different tuning systems 4221:If the number is 7, 9, 11, 13, etc., the chord is 3653: 3533: 2845:melodic motions, characterized by frequent skips. 441: 7705:Generalized Musical Intervals and Transformations 7098:. Oxford University Press. Accessed August 2013. 6738:Generalized Musical Intervals and Transformations 5372:, or meantone temperament tuning systems such as 5151:), 4 have size about 427 cents (400 + 8 492:), or more strictly as a synonym of major third. 7112:Burstein, L. Poundie; Straus, Joseph N. (2016). 7672:The New Grove Dictionary of Music and Musicians 7638: 7636: 7301:The New Grove Dictionary of Music and Musicians 7013:The New Grove Dictionary of Music and Musicians 2753:Linear (melodic) intervals may be described as 1944:spans ten semitones, exceeding a major sixth (E 118:. Intervals smaller than a semitone are called 515:. However, they both span 4 semitones. If the 9099: 8870: 7900: 6352:, in between a minor and major interval; and 3175:, and some of them can be also classified as 2510:Ascending and descending chromatic scale on C 1163:) describes the quality of the interval, and 8: 4187:Names and symbols that contain only a plain 4013:Chord names and symbols (jazz and pop music) 1230:). Intervals with larger numbers are called 7750:Artificial Perception and Music Recognition 7426: 7424: 6870:, which is either a sequence of successive 6832: 6830: 6293: 6276: 6258: 6241: 6223: 6206: 6188: 6171: 6153: 6136: 6118: 6101: 6083: 6068: 6050: 6033: 6015: 5998: 5980: 5963: 5933: 5915: 5900: 5882: 5825: 5223:Pythagorean tuning § Size of intervals 5095:tuning systems, by definition the width of 2921:. All these intervals span four semitones. 1462: 1371:Intervals formed by the notes of a C major 1241:between staff positions and diatonic-scale 542:(compound intervals) are introduced below. 9106: 9092: 9084: 8877: 8863: 8855: 8841: 8546: 8437: 8262: 8245: 7952: 7934: 7907: 7893: 7885: 7661:Roeder, John (2001). "Interval Class". In 6858: 6856: 6854: 6852: 6850: 6848: 6846: 6389:diminished, sub, perfect, super, augmented 7386: 7345: 7333: 7321: 6395:. Various further extensions are used in 3621: 3593: 3577: 3561: 3552: 3510: 3470: 3442: 3417: 3408: 3361:, spans one octave plus one major third. 3103:, the pitches of pairs of notes such as F 2371:to the C above it must be a major sixth. 2359:For example, the interval from C to the E 1757:Augmented and diminished intervals on C: 1263:, there are four notes from B to D: B–C–C 1155:) is an interval name, in which the term 427: 417: 411: 398: 380: 30:For albums or bands named Intervals, see 8175: 7465: 7463: 7201: 7199: 6926: 6924: 6494: 6243:heptachordum maius, ditonus cum diapente 5845: 5425: 5262:5-limit tuning § The justest ratios 5091:to integers. Notice that in each of the 4575:Comparison of interval width (in cents) 4556: 4262: 3672: 2923: 2505: 2487:is an interval formed by two notes of a 2308: 2055: 1752: 1131:, an interval is named according to its 544: 154:reason, intervals are often measured in 7869:Elements of Harmony: Vertical Intervals 7408:Techniques of the Contemporary Composer 7399: 7397: 7395: 6964: 6826: 5360:Alternative interval naming conventions 5235:5-limit tuning § Size of intervals 4216:names and symbols for added tone chords 4106:Rules to decode chord names and symbols 3379:simple intervals with diatonic numbers 2736: 2457:(lower pitch precedes higher pitch) or 2206:Intervals are often abbreviated with a 1446: 1356: 1253:diatonic scale, the three notes are B–C 1231: 539: 348:(12-TET), a tuning system in which all 6748:, or more abstract musical phenomena. 4033:Chord qualities and interval qualities 149:In physical terms, an interval is the 27:Difference in pitch between two sounds 7471:A History of Music in Western Culture 7365:, 2nd English edition, translated by 7169: 7167: 7114:Concise Introduction to Tonal Harmony 7046:(4th ed.), Schirmer, p. 8, 6173:hexachordum maius, tonus cum diapente 5727: 5520: 5450: 3142:) is slightly higher in pitch (than C 2446:if the two notes sound simultaneously 1352:—A, is a seventh (B-A), not a ninth. 832: 535: 7: 7137: 7135: 7133: 5421:Diminished seconds in 5-limit tuning 3084:When played as isolated chords on a 7298:Drabkin, William (2001). "Fourth". 6433:is often used, most prominently in 5815:Up to the end of the 18th century, 5077:as provided by 5-limit tuning (see 4092:alone is not used for diminished). 3375:of a compound interval formed from 3351: 2732: 2596:. For instance, the perfect fifth A 1219: 7644:"Extended-diatonic interval names" 7270:See for example William Lovelock, 7237:, p. 21. First edition, 1984. 6711:Generalizations and non-pitch uses 5087:font, and the values in cents are 3324:. It is equal to exactly 50 cents. 3099:("12-TET"). But in other historic 2700: 2608:is chromatic to C major, because A 2305:Inversion (music) § Intervals 1727:), the smaller one "minor third" ( 25: 6371:, the characteristic interval of 5843:(about a quarter of a semitone). 5180:-comma meantone Size of intervals 3201:ratio 531441:524288 (23.5 cents). 2863:Enharmonic tritones: A4 = d5 on C 2592:. All other intervals are called 8972: 8840: 7540:The Craft of Musical Composition 7251:Harmony: Its Theory and Practice 6977:Harmony, Its Theory and Practice 6866:is herein strictly defined as a 6770: 6720: 5401:Alternative definitions of comma 5376:. All the intervals with prefix 4161:Without contrary information, a 3338: 3149: 2886:, if they both contain the same 2864: 2719: 2576: 2511: 2438:An interval can be described as 1611:Major and minor intervals on C: 1273:, and this convention is called 1115: 4191:(e.g., "seventh chord") or the 4100:The main rules to decode chord 3337:Simple and compound major third 3320:, which is half the width of a 2718:Simple and compound major third 2687:(1997) suggests the concept of 2291:d5 (or dim5): diminished fifth, 2288:A4 (or aug4): augmented fourth, 1560:) and one fifth is diminished ( 7774:Tanguiane (Tangian), Andranick 7746:Tanguiane (Tangian), Andranick 7070:(1st ed.), W. W. Norton, 6456:Generic and specific intervals 5325:by popular terminology), or a 3642: 3630: 3544:which can also be written as: 3522: 3500: 3482: 3460: 3454: 3432: 3266:is the difference between six 2837:melodic motion, as opposed to 2418:Melodic and harmonic intervals 2321:by raising the lower pitch an 1294:(spanning 4 semitones) and B–D 1137:diatonic number, interval size 58:Melodic and harmonic intervals 1: 5803:, are canonically defined in 4527:Half-diminished seventh chord 4037:The main chord qualities are 4021:of the chord. For instance a 2876:Two intervals are considered 2294:P5 (or perf5): perfect fifth. 7304:, second edition, edited by 5854: 5442: 5309:both suggest the concept of 4142: 3694: 3683: 2523: 2404: 2332: 1975:) and the diminished fifth ( 566: 555: 210: 166: 44: 8462:septimal chromatic semitone 6448:pitch-class intervals, see 6387:, yielding the progression 5858: 5446: 5388:, shown in the table, is a 5064: 5059: 5054: 5049: 5033: 5030: 5027: 5020: 5002: 4999: 4994: 4987: 4969: 4966: 4963: 4956: 4938: 4933: 4930: 4925: 4909: 4901: 4891: 4884: 4866: 4861: 4856: 4847: 4825: 4817: 4807: 4800: 4782: 4772: 4767: 4762: 4746: 4738: 4733: 4726: 4708: 4705: 4700: 4693: 4675: 4672: 4669: 4662: 4642: 4637: 4632: 4627: 4188: 4180:When the fifth interval is 4150: 2801:), with all intervals of a 2282:m2 (or min2): minor second, 1106:Interval number and quality 538:(commas or microtones) and 170: 9258: 8468:septimal diatonic semitone 8256:(Numbers in brackets refer 7846:Essentials of Music Theory 7178:(8th ed.). New York: 7146:(4th ed.). New York: 6975:(1903), "I-Introduction", 6878:, C–D–E–F–G–A–B, or the A- 6796:List of meantone intervals 6703: 6689: 6675: 6661: 6647: 6633: 6617: 6601: 6587: 6573: 6559: 6545: 6531: 6459: 6406: 6307: 6070:semidiapente, semitritonus 5337: 5041: 5010: 4977: 4946: 4917: 4874: 4833: 4790: 4754: 4716: 4683: 4652: 4619: 4006: 3160: 2852: 2746: 2633: 2469: 2427: 2302: 2285:M3 (or maj3): major third, 1742: 1198:Fifth from C to G in the A 321: 236: 158:, a unit derived from the 29: 9121: 9073:List of musical intervals 9068: 8970: 8892: 8886:Consonance and dissonance 8838: 8258:to fractional semitones.) 8251:24-tone equal temperament 7843:Gardner, Carl E. (1912): 7469:Bonds, Mark Evan (2006). 7233:; Payne, Dorothy (2008). 7142:Laitz, Steven G. (2016). 7044:Harmony and Voice Leading 6507: 6502: 6497: 6266: 6231: 6196: 6161: 6126: 6091: 6058: 6023: 5988: 5953: 5923: 5890: 5792: 5790: 5769: 5767: 5716: 5706: 5704: 5685: 5681: 5656: 5635: 5628: 5563: 5552: 5531: 5522: 5517: 5512: 5502: 5489: 5463: 5458: 5453: 5441: 5436: 5433: 5428: 4574: 4567: 4564: 4559: 4296: 4271: 4265: 4147:minor major seventh chord 4088:for dominant (the symbol 4084:for half diminished, and 3831: 3829: 3826: 3181:enharmonically equivalent 3097:12-tone equal temperament 2934: 2931: 2926: 2884:enharmonically equivalent 2641:Consonance and dissonance 2636:Consonance and dissonance 2066: 2063: 2058: 1710:As shown in the table, a 1357:§ Compound intervals 1239:one-to-one correspondence 850: 847: 842: 829: 536:smaller than one semitone 304:12-tone equal temperament 132:enharmonically equivalent 32:Interval (disambiguation) 7831:Longmans, Green, and Co. 7829:(3rd English ed.). 7723:Ockelford, Adam (2005). 7675:(2nd ed.). London: 7358:Helmholtz, Hermann L. F. 7090:"Prime (ii). See Unison" 7016:(2nd ed.). London: 6882:, A–B–C–D–E–F–G) or any 5546:greater diesis (648:625) 5318:its strongest interval. 4498:Diminished seventh chord 2647:to consonant intervals. 1739:Augmented and diminished 1477:Perfect intervals on C: 1171:) indicates its number. 695:, whole tone, whole step 505:, while that from D to G 162:of the frequency ratio. 8846:List of pitch intervals 8584:Subminor and supermajor 8523:minor diatonic semitone 8433:refer to pitch ratios.) 7858:Encyclopædia Britannica 7817:Helmholtz, H. L. F. von 7444:Hal Leonard Corporation 7211:Weber, Godfrey (1841). 7148:Oxford University Press 7100:(subscription required) 6801:List of pitch intervals 6314:Subminor and supermajor 5451:Other naming convention 4471:Augmented seventh chord 4073:is used for augmented, 3669:Main compound intervals 3316:is half the width of a 2805:or larger being skips. 2797:(sometimes also called 2789:(sometimes also called 2630:Consonant and dissonant 2449:Horizontal, linear, or 2409:download the audio file 2337:download the audio file 215:download the audio file 49:download the audio file 8644:Undecimal quarter tone 7556:The Listening Composer 7272:The Rudiments of Music 6916:Diatonic and chromatic 6729: 6442:ordered pitch interval 6413:Ordered pitch interval 6304:Non-diatonic intervals 6295:heptachordum superflua 6294: 6277: 6259: 6242: 6224: 6207: 6189: 6172: 6154: 6137: 6119: 6102: 6084: 6069: 6051: 6034: 6016: 5999: 5981: 5964: 5934: 5916: 5901: 5883: 5826: 5805:Indian classical music 5390:superparticular number 5374:quarter-comma meantone 5298: 4399:Dominant seventh chord 3655: 3535: 3347: 3158: 3117:quarter-comma meantone 2873: 2728: 2665:common practice period 2656:15th- and 16th-century 2585: 2542:harmonic C-minor scale 2519: 2472:Diatonic and chromatic 2466:Diatonic and chromatic 2314: 1971:The augmented fourth ( 1925: 1707: 1525: 1463:non-diatonic intervals 1418:). This is called its 1375: 1207: 1191: 1124: 652:, half tone, half step 540:larger than one octave 443: 8639:Septimal quarter tone 8450:septimal quarter tone 7214:General Music Teacher 6806:Music and mathematics 6718: 6423:twelve-tone technique 6403:Pitch-class intervals 6308:Further information: 6225:hexachordum superflua 5423:for further details. 5293: 5209:meantone temperaments 3910:Diminished fourteenth 3656: 3536: 3336: 3130: 3101:meantone temperaments 2862: 2785:, a step is either a 2717: 2671:Hermann von Helmholtz 2565: 2509: 2312: 1756: 1743:Further information: 1610: 1476: 1370: 1197: 1182: 1114:Main intervals from C 1113: 444: 263:ratios, such as 1:1 ( 8826:Incomposite interval 8579:Pythagorean interval 8431:(Numbers in brackets 7939:(Numbers in brackets 7827:Alexander John Ellis 7677:Macmillan Publishers 7579:(Venice, 1558): 162. 7440:Harmony & Theory 7312:. London: Macmillan. 7018:Macmillan Publishers 6894:with a conventional 6513:Number of semitones 6326:septimal minor third 5403:). For instance, in 4272:Component intervals 4158:for further details. 3971:Augmented fourteenth 3551: 3407: 3400:, is determined by: 3368:The diatonic number 3359:compound major third 2849:Enharmonic intervals 2594:chromatic to C major 2424:Melodic and harmonic 379: 8609:Pythagorean apotome 8456:septimal third tone 7490:Aikin, Jim (2004). 7367:Ellis, Alexander J. 6816:Regular temperament 6472:diatonic set theory 5601:chromatic semitone, 5413:four kinds of comma 5109:most often observed 5079:symmetric scale n.1 4446:Major seventh chord 4421:Minor seventh chord 4252:component intervals 4112:For 3-note chords ( 4003:Intervals in chords 2710:Simple and compound 2590:diatonic to C major 2540:, occurring in the 1968:) by one semitone. 1749:Diminished interval 1587:By definition, the 71:is a difference in 8722:Septimal semicomma 7575:Gioseffo Zarlino, 7207:perfect consonance 7182:. pp. 16–18. 7150:. pp. 27–31. 7095:Grove Music Online 6730: 6435:musical set theory 6181:Diminished seventh 6155:diapente superflua 5917:unisonus superflua 5837:Pythagorean tuning 5811:Latin nomenclature 5595:or augmented prime 5574:diatonic semitone, 5455:Pythagorean tuning 5405:Pythagorean tuning 5366:Pythagorean tuning 5323:added sixth chords 5299: 5250:asymmetric version 5197:Pythagorean tuning 5157:diminished fourths 4143:interval qualities 3843:Augmented eleventh 3834:Diminished twelfth 3651: 3531: 3348: 3329:Compound intervals 3159: 2874: 2729: 2661:Johannes Tinctoris 2586: 2520: 2496:chromatic interval 2315: 2202:Shorthand notation 1930:chromatic semitone 1926: 1745:Augmented interval 1708: 1568:is between A and D 1526: 1376: 1310:is a second, but F 1275:diatonic numbering 1232:compound intervals 1208: 1192: 1125: 964:Diminished seventh 532:a separate section 439: 253:musical instrument 9242:Intervals (music) 9229: 9228: 9081: 9080: 8852: 8851: 8834: 8833: 8664:Pythagorean comma 8604:Pythagorean limma 8536: 8535: 8532: 8531: 8498:supermajor fourth 8474:supermajor second 8419: 8418: 8233: 8232: 8229: 8228: 7941:are the number of 7759:978-3-540-57394-4 7713:978-0-19-531713-8 7686:978-1-56159-239-5 7516:Introducing Music 7473:, p.123. 2nd ed. 7123:978-0-393-26476-0 7077:978-0-393-33420-3 7027:978-1-56159-239-5 6914:scales (see also 6726: 6708: 6707: 6620:Diminished fifth 6618:Augmented fourth 6499:Specific interval 6480:generic intervals 6462:Specific interval 6417:In post-tonal or 6397:Xenharmonic music 6301: 6300: 6286:Augmented seventh 6251:Diminished octave 6052:ditonus superflua 6008:Diminished fourth 5841:Pythagorean comma 5797: 5796: 5526:Pythagorean comma 5514:diminished second 5409:Pythagorean comma 5384:tuned, and their 5370:five-limit tuning 5294:Intervals in the 5105:equal temperament 5071: 5070: 4834:Augmented fourth 4550: 4549: 3996: 3995: 3890:Augmented twelfth 3650: 3530: 3344: 3194:Pythagorean comma 3187:are approximate. 3155: 3090:diatonic function 3082: 3081: 3022:diminished fourth 2870: 2725: 2689:interval strength 2582: 2538:diminished fourth 2516: 2413: 2341: 2199: 2198: 1447:compound interval 1445:The quality of a 1436:diatonic interval 1432:specific interval 1322:is a third, but G 1121: 1103: 1102: 1078:Augmented seventh 1040:Diminished octave 766:Diminished fourth 604:Diminished second 580:alternative names 521:equal temperament 513:diminished fourth 433: 346:equal temperament 338:logarithmic scale 255:is tuned using a 219: 53: 16:(Redirected from 9249: 9108: 9101: 9094: 9085: 8976: 8975: 8879: 8872: 8865: 8856: 8844: 8843: 8734:Septimal kleisma 8547: 8504:subminor seventh 8486:supermajor third 8438: 8426:Just intonations 8411: 8410: 8406: 8403: 8391: 8390: 8386: 8383: 8371: 8370: 8366: 8363: 8351: 8350: 8346: 8343: 8331: 8330: 8326: 8323: 8311: 8310: 8306: 8303: 8291: 8290: 8286: 8263: 8246: 7953: 7935: 7909: 7902: 7895: 7886: 7876: 7833: 7825:. Translated by 7804: 7803: 7792:10.2307/40285634 7779:Music Perception 7770: 7764: 7763: 7742: 7736: 7721: 7715: 7698: 7692: 7690: 7658: 7652: 7651: 7648:Xenharmonic wiki 7640: 7631: 7617: 7611: 7597: 7586: 7580: 7573: 7567: 7549: 7543: 7533: 7527: 7509: 7503: 7488: 7482: 7467: 7458: 7457: 7428: 7419: 7401: 7390: 7384: 7378: 7355: 7349: 7343: 7337: 7331: 7325: 7319: 7313: 7296: 7290: 7268: 7262: 7244: 7238: 7228: 7222: 7221: 7203: 7194: 7193: 7171: 7162: 7161: 7139: 7128: 7127: 7109: 7103: 7101: 7087: 7081: 7080: 7063: 7057: 7056: 7039: 7033: 7031: 6999: 6990: 6989: 6969: 6954: 6942: 6936: 6928: 6919: 6860: 6841: 6834: 6786:Circle of fifths 6780: 6775: 6774: 6773: 6754:interval hearing 6728: 6727: 6504:Generic interval 6495: 6466:Generic interval 6431:integer notation 6329:, since it is a 6310:Neutral interval 6297: 6280: 6262: 6245: 6227: 6210: 6192: 6190:semiheptachordum 6175: 6157: 6140: 6122: 6111:Diminished sixth 6105: 6087: 6077:Augmented fourth 6072: 6062:Diminished fifth 6054: 6037: 6019: 6002: 5984: 5973:Augmented second 5967: 5943:Diminished third 5937: 5919: 5909:Augmented unison 5904: 5886: 5846: 5829: 5742:augmented fourth 5721:diminished fifth 5592:augmented unison 5497:or perfect prime 5473: 5472: 5468: 5426: 5344:Identity (music) 5276:augmented second 5258:harmonic seventh 5220: 5219: 5215: 5191: 5190: 5186: 5179: 5178: 5174: 5168: 5167: 5163: 5145:diminished sixth 5124: 5123: 5119: 4836:Diminished fifth 4601: 4600: 4596: 4557: 4505: 4381: 4374:Diminished triad 4263: 4200:added tone chord 4102:names or symbols 4081:for diminished, 3965:or Double octave 3941:Major fourteenth 3921:Minor fourteenth 3812:Perfect eleventh 3757:Diminished tenth 3737:Augmented octave 3673: 3660: 3658: 3657: 3652: 3648: 3626: 3625: 3598: 3597: 3582: 3581: 3566: 3565: 3540: 3538: 3537: 3532: 3528: 3515: 3514: 3475: 3474: 3447: 3446: 3422: 3421: 3346: 3345: 3304:septimal kleisma 3297: 3296: 3295: 3293: 3256: 3255: 3157: 3156: 3147: 3146: 3137: 3136: 3123:Minute intervals 3114: 3113: 3108: 3107: 3075: 3074: 3067: 3066: 3055:augmented second 3045: 3044: 3031: 3030: 3013: 3012: 3002: 3001: 2980: 2979: 2969: 2968: 2924: 2920: 2919: 2914: 2913: 2908: 2907: 2902: 2901: 2872: 2871: 2727: 2726: 2625: 2624: 2619: 2618: 2613: 2612: 2607: 2606: 2601: 2600: 2584: 2583: 2572: 2571: 2535: 2534: 2518: 2517: 2370: 2369: 2364: 2363: 2190: 2189: 2179: 2178: 2155: 2154: 2129:diminished fifth 2118: 2117: 2095:augmented fourth 2056: 2051: 2050: 2045: 2044: 2036: 2035: 2027: 2026: 2017: 2016: 2011: 2010: 2005: 2004: 1999: 1998: 1967: 1966: 1961: 1960: 1955: 1954: 1949: 1948: 1943: 1942: 1937: 1936: 1924: 1923: 1922: 1920: 1912: 1911: 1910: 1908: 1900: 1899: 1898: 1896: 1888: 1887: 1886: 1884: 1876: 1875: 1874: 1872: 1864: 1863: 1862: 1860: 1852: 1851: 1850: 1848: 1840: 1839: 1838: 1836: 1828: 1827: 1826: 1824: 1816: 1815: 1814: 1812: 1804: 1803: 1802: 1800: 1792: 1791: 1790: 1788: 1780: 1779: 1778: 1776: 1768: 1767: 1766: 1764: 1706: 1705: 1704: 1702: 1694: 1693: 1692: 1690: 1682: 1681: 1680: 1678: 1670: 1669: 1668: 1666: 1658: 1657: 1656: 1654: 1646: 1645: 1644: 1642: 1634: 1633: 1632: 1630: 1622: 1621: 1620: 1618: 1583: 1582: 1573: 1572: 1524: 1523: 1522: 1520: 1512: 1511: 1510: 1508: 1500: 1499: 1498: 1496: 1488: 1487: 1486: 1484: 1420:interval quality 1351: 1350: 1345: 1344: 1339: 1338: 1333: 1332: 1327: 1326: 1321: 1320: 1315: 1314: 1309: 1308: 1299: 1298: 1293: 1292: 1280:If one adds any 1271:diatonic numbers 1268: 1267: 1258: 1257: 1203: 1202: 1147:. For instance, 1141:generic interval 1123: 1122: 1099: 1098: 1097: 1095: 1061: 1060: 1059: 1057: 1023: 1022: 1021: 1019: 985: 984: 983: 981: 947: 946: 945: 943: 909: 908: 907: 905: 888:Diminished sixth 867:Augmented fourth 861: 860: 859: 857: 836:Diminished fifth 825: 824: 823: 821: 787: 786: 785: 783: 749: 748: 747: 745: 728:Augmented second 711: 710: 709: 707: 685:Diminished third 668: 667: 666: 664: 642:Augmented unison 625: 624: 623: 621: 545: 510: 509: 500: 499: 448: 446: 445: 440: 438: 434: 432: 431: 422: 421: 412: 403: 402: 332:. The cent is a 233:Frequency ratios 196: 195: 190: 189: 145: 144: 139: 138: 21: 18:Interval quality 9257: 9256: 9252: 9251: 9250: 9248: 9247: 9246: 9232: 9231: 9230: 9225: 9195:Steps and skips 9117: 9112: 9082: 9077: 9064: 9028: 8977: 8973: 8968: 8888: 8883: 8853: 8848: 8830: 8792: 8759: 8702:Septimal diesis 8648: 8618: 8588: 8542: 8528: 8509: 8432: 8429: 8415: 8408: 8404: 8401: 8399: 8388: 8384: 8381: 8379: 8368: 8364: 8361: 8359: 8348: 8344: 8341: 8339: 8328: 8324: 8321: 8319: 8308: 8304: 8301: 8299: 8288: 8284: 8283: 8273: 8272: 8271: 8267: 8257: 8254: 8241: 8239: 8225: 8170: 8115: 8060: 8023: 7986: 7947: 7942: 7940: 7930: 7928: 7925: 7918: 7913: 7874: 7840: 7815: 7812: 7807: 7772: 7771: 7767: 7760: 7744: 7743: 7739: 7722: 7718: 7699: 7695: 7687: 7660: 7659: 7655: 7642: 7641: 7634: 7618: 7614: 7591: 7589:J. F. Niermeyer 7587: 7583: 7574: 7570: 7550: 7546: 7536:Hindemith, Paul 7534: 7530: 7510: 7506: 7489: 7485: 7468: 7461: 7454: 7436:Schroeder, Carl 7430: 7429: 7422: 7402: 7393: 7385: 7381: 7356: 7352: 7344: 7340: 7332: 7328: 7320: 7316: 7297: 7293: 7269: 7265: 7247:Prout, Ebenezer 7245: 7241: 7229: 7225: 7219:perfect concord 7210: 7204: 7197: 7190: 7173: 7172: 7165: 7158: 7141: 7140: 7131: 7124: 7111: 7110: 7106: 7099: 7088: 7084: 7078: 7065: 7064: 7060: 7054: 7041: 7040: 7036: 7028: 7001: 7000: 6993: 6987: 6973:Prout, Ebenezer 6971: 6970: 6966: 6962: 6957: 6944:All triads are 6943: 6939: 6929: 6922: 6874:(such as the C- 6862:The expression 6861: 6844: 6835: 6828: 6824: 6776: 6771: 6769: 6766: 6721: 6713: 6704:Perfect octave 6619: 6614: 6602:Perfect fourth 6532:Perfect unison 6493: 6468: 6460:Main articles: 6458: 6415: 6407:Main articles: 6405: 6336:just intonation 6316: 6306: 6216:Augmented sixth 6146:Augmented fifth 6120:semihexachordum 6043:Augmented third 6017:semidiatessaron 5982:tonus superflua 5867: 5850: 5813: 5602: 5594: 5575: 5570: 5568: 5545: 5529:(524288:531441) 5528: 5524: 5496: 5475: 5470: 5466: 5465: 5437:Specific names 5430: 5386:frequency ratio 5362: 5349:Interval cycles 5346: 5338:Main articles: 5336: 5334:Interval cycles 5327:first inversion 5296:harmonic series 5288: 5246:just intonation 5217: 5213: 5212: 5188: 5184: 5183: 5176: 5172: 5171: 5165: 5161: 5160: 5125:-comma meantone 5121: 5117: 5116: 5101:just intonation 5081:) are shown in 5024: 5017: 4991: 4984: 4960: 4953: 4903: 4895: 4888: 4881: 4863: 4858: 4851: 4842: 4835: 4819: 4811: 4804: 4797: 4776: 4769: 4740: 4735: 4730: 4723: 4697: 4690: 4666: 4659: 4610: 4603: 4598: 4594: 4593: 4587: 4571: 4561: 4555: 4503: 4476: 4379: 4353:Augmented triad 4231:extended chords 4189:interval number 4165:interval and a 4098: 4055:half-diminished 4035: 4015: 4007:Main articles: 4005: 3856:Perfect twelfth 3819:Augmented tenth 3777:Augmented ninth 3696: 3685: 3677: 3671: 3617: 3589: 3573: 3557: 3549: 3548: 3506: 3466: 3438: 3413: 3405: 3404: 3399: 3392: 3385: 3374: 3339: 3331: 3291: 3289: 3288: 3287: 3276:perfect twelfth 3253: 3252: 3169: 3161:Main articles: 3150: 3144: 3143: 3134: 3133: 3125: 3111: 3110: 3105: 3104: 3072: 3071: 3064: 3063: 3042: 3041: 3028: 3027: 3010: 3009: 2999: 2998: 2977: 2976: 2966: 2965: 2936:Staff positions 2928: 2917: 2916: 2911: 2910: 2905: 2904: 2899: 2898: 2865: 2857: 2851: 2779:disjunct motion 2773:(also called a 2767:conjunct motion 2751: 2749:Steps and skips 2745: 2743:Steps and skips 2720: 2712: 2697:Lipps–Meyer law 2693:harmonic series 2638: 2632: 2622: 2621: 2616: 2615: 2610: 2609: 2604: 2603: 2598: 2597: 2577: 2569: 2568: 2532: 2531: 2512: 2500:chromatic scale 2474: 2468: 2436: 2428:Main articles: 2426: 2421: 2420: 2419: 2416: 2415: 2414: 2412: 2394: 2367: 2366: 2361: 2360: 2343: 2342: 2340: 2307: 2301: 2204: 2187: 2186: 2176: 2175: 2165:augmented third 2152: 2151: 2115: 2114: 2068:Staff positions 2060: 2048: 2047: 2042: 2041: 2033: 2032: 2024: 2023: 2014: 2013: 2008: 2007: 2002: 2001: 1996: 1995: 1985: 1964: 1963: 1958: 1957: 1952: 1951: 1946: 1945: 1940: 1939: 1934: 1933: 1918: 1916: 1915: 1914: 1906: 1904: 1903: 1902: 1894: 1892: 1891: 1890: 1882: 1880: 1879: 1878: 1870: 1868: 1867: 1866: 1858: 1856: 1855: 1854: 1846: 1844: 1843: 1842: 1834: 1832: 1831: 1830: 1822: 1820: 1819: 1818: 1810: 1808: 1807: 1806: 1798: 1796: 1795: 1794: 1786: 1784: 1783: 1782: 1774: 1772: 1771: 1770: 1762: 1760: 1759: 1758: 1751: 1741: 1700: 1698: 1697: 1696: 1688: 1686: 1685: 1684: 1676: 1674: 1673: 1672: 1664: 1662: 1661: 1660: 1652: 1650: 1649: 1648: 1640: 1638: 1637: 1636: 1628: 1626: 1625: 1624: 1616: 1614: 1613: 1612: 1605: 1603:Major and minor 1580: 1579: 1570: 1569: 1544:) and octaves ( 1518: 1516: 1515: 1514: 1506: 1504: 1503: 1502: 1494: 1492: 1491: 1490: 1482: 1480: 1479: 1478: 1471: 1365: 1348: 1347: 1342: 1341: 1336: 1335: 1330: 1329: 1324: 1323: 1318: 1317: 1312: 1311: 1306: 1305: 1296: 1295: 1290: 1289: 1265: 1264: 1261:chromatic scale 1255: 1254: 1212:staff positions 1200: 1199: 1188:staff positions 1177: 1116: 1108: 1093: 1091: 1090: 1089: 1055: 1053: 1052: 1051: 1017: 1015: 1014: 1013: 1002:Augmented sixth 979: 977: 976: 975: 941: 939: 938: 937: 926:Augmented fifth 903: 901: 900: 899: 855: 853: 852: 851: 819: 817: 816: 815: 804:Augmented third 781: 779: 778: 777: 743: 741: 740: 739: 705: 703: 702: 701: 662: 660: 659: 658: 619: 617: 616: 615: 578: 568: 557: 549: 507: 506: 497: 496: 458:chromatic scale 454: 423: 413: 407: 394: 377: 376: 372: 365: 326: 320: 257:just intonation 241: 235: 227: 226: 225: 222: 221: 220: 218: 203: 193: 192: 187: 186: 142: 141: 136: 135: 134:notes such as C 61: 60: 59: 56: 55: 54: 52: 35: 28: 23: 22: 15: 12: 11: 5: 9255: 9253: 9245: 9244: 9234: 9233: 9227: 9226: 9224: 9223: 9218: 9213: 9208: 9202: 9197: 9192: 9187: 9182: 9177: 9172: 9167: 9166: 9165: 9155: 9150: 9148:Melodic motion 9145: 9140: 9135: 9130: 9122: 9119: 9118: 9113: 9111: 9110: 9103: 9096: 9088: 9079: 9078: 9076: 9075: 9069: 9066: 9065: 9063: 9062: 9057: 9052: 9047: 9042: 9036: 9034: 9030: 9029: 9027: 9026: 9021: 9016: 9011: 9006: 9004:Perfect fourth 9001: 8996: 8991: 8985: 8983: 8979: 8978: 8971: 8969: 8967: 8966: 8961: 8960: 8959: 8954: 8949: 8944: 8942:Changing tones 8939: 8929: 8924: 8919: 8914: 8909: 8904: 8899: 8893: 8890: 8889: 8884: 8882: 8881: 8874: 8867: 8859: 8850: 8849: 8839: 8836: 8835: 8832: 8831: 8829: 8828: 8823: 8818: 8813: 8808: 8802: 8800: 8794: 8793: 8791: 8790: 8785: 8780: 8775: 8769: 8767: 8761: 8760: 8758: 8757: 8751: 8745: 8738: 8737: 8731: 8725: 8719: 8713: 8706: 8705: 8699: 8696:Greater diesis 8693: 8686: 8685: 8682:Septimal comma 8679: 8676:Holdrian comma 8673: 8670:Syntonic comma 8667: 8660: 8658: 8650: 8649: 8647: 8646: 8641: 8636: 8630: 8628: 8620: 8619: 8617: 8616: 8611: 8606: 8600: 8598: 8590: 8589: 8587: 8586: 8581: 8576: 8571: 8566: 8561: 8555: 8553: 8544: 8538: 8537: 8534: 8533: 8530: 8529: 8527: 8526: 8519: 8517: 8511: 8510: 8508: 8507: 8501: 8495: 8492:subminor fifth 8489: 8483: 8480:subminor third 8477: 8471: 8465: 8459: 8453: 8446: 8444: 8435: 8421: 8420: 8417: 8416: 8414: 8413: 8393: 8373: 8353: 8333: 8313: 8293: 8276: 8274: 8266: 8260: 8243: 8235: 8234: 8231: 8230: 8227: 8226: 8224: 8223: 8217: 8211: 8205: 8199: 8193: 8187: 8180: 8178: 8172: 8171: 8169: 8168: 8162: 8156: 8150: 8144: 8138: 8132: 8125: 8123: 8117: 8116: 8114: 8113: 8107: 8101: 8095: 8089: 8083: 8077: 8070: 8068: 8062: 8061: 8059: 8058: 8052: 8046: 8040: 8033: 8031: 8025: 8024: 8022: 8021: 8015: 8009: 8003: 7996: 7994: 7988: 7987: 7985: 7984: 7978: 7972: 7966: 7959: 7957: 7950: 7932: 7920: 7919: 7914: 7912: 7911: 7904: 7897: 7889: 7883: 7882: 7871: 7866: 7861: 7850: 7839: 7838:External links 7836: 7835: 7834: 7811: 7808: 7806: 7805: 7786:(4): 465–502. 7765: 7758: 7737: 7716: 7693: 7685: 7663:Sadie, Stanley 7653: 7632: 7612: 7581: 7568: 7544: 7528: 7504: 7494:, p. 24. 7483: 7459: 7452: 7446:. p. 77. 7420: 7391: 7387:Helmholtz 1895 7379: 7350: 7348:, p. 182. 7346:Helmholtz 1895 7338: 7334:Helmholtz 1895 7326: 7322:Helmholtz 1895 7314: 7291: 7263: 7239: 7231:Kostka, Stefan 7223: 7205:Definition of 7195: 7188: 7163: 7156: 7129: 7122: 7104: 7082: 7076: 7058: 7053:978-0495189756 7052: 7034: 7026: 7004:Sadie, Stanley 6991: 6986:978-0781207836 6985: 6963: 6961: 6958: 6956: 6955: 6937: 6920: 6912:harmonic minor 6864:diatonic scale 6842: 6825: 6823: 6820: 6819: 6818: 6813: 6808: 6803: 6798: 6793: 6788: 6782: 6781: 6765: 6762: 6758:absolute pitch 6712: 6709: 6706: 6705: 6702: 6699: 6696: 6692: 6691: 6690:Major seventh 6688: 6685: 6682: 6678: 6677: 6676:Minor seventh 6674: 6671: 6668: 6664: 6663: 6660: 6657: 6654: 6650: 6649: 6646: 6643: 6640: 6636: 6635: 6634:Perfect fifth 6632: 6629: 6626: 6622: 6621: 6616: 6611: 6608: 6604: 6603: 6600: 6597: 6594: 6590: 6589: 6586: 6583: 6580: 6576: 6575: 6572: 6569: 6566: 6562: 6561: 6558: 6555: 6552: 6548: 6547: 6544: 6541: 6538: 6534: 6533: 6530: 6527: 6524: 6520: 6519: 6517:Interval class 6514: 6510: 6509: 6508:Diatonic name 6506: 6501: 6492: 6489: 6457: 6454: 6450:interval class 6409:Interval class 6404: 6401: 6393:Adriaan Fokker 6369:neutral second 6321:subminor third 6305: 6302: 6299: 6298: 6291: 6288: 6282: 6281: 6274: 6271: 6270:Perfect octave 6268: 6264: 6263: 6256: 6253: 6247: 6246: 6239: 6236: 6233: 6229: 6228: 6221: 6218: 6212: 6211: 6204: 6201: 6198: 6194: 6193: 6186: 6183: 6177: 6176: 6169: 6166: 6163: 6159: 6158: 6151: 6148: 6142: 6141: 6134: 6131: 6128: 6124: 6123: 6116: 6113: 6107: 6106: 6099: 6096: 6093: 6089: 6088: 6081: 6078: 6074: 6073: 6066: 6063: 6060: 6056: 6055: 6048: 6045: 6039: 6038: 6031: 6028: 6027:Perfect fourth 6025: 6021: 6020: 6013: 6010: 6004: 6003: 5996: 5993: 5990: 5986: 5985: 5978: 5975: 5969: 5968: 5961: 5958: 5955: 5951: 5950: 5948: 5945: 5939: 5938: 5931: 5928: 5925: 5921: 5920: 5913: 5910: 5906: 5905: 5898: 5895: 5892: 5888: 5887: 5880: 5877: 5876:Perfect unison 5874: 5870: 5869: 5864: 5861: 5852: 5823:is from Latin 5812: 5809: 5795: 5794: 5791: 5789: 5786: 5784:perfect octave 5781: 5777: 5776: 5774: 5768: 5766: 5763: 5758: 5754: 5753: 5751: 5749: 5747: 5744: 5738: 5737: 5735: 5733: 5731: 5726: 5723: 5718: 5714: 5713: 5711: 5705: 5703: 5700: 5698:perfect fourth 5695: 5691: 5690: 5684: 5682: 5680: 5677: 5672: 5668: 5667: 5665: 5659: 5657: 5655: 5652: 5647: 5643: 5642: 5640: 5634: 5627: 5624: 5619: 5615: 5614: 5612: 5610: 5604: 5603:minor semitone 5599: 5596: 5588: 5587: 5585: 5583: 5577: 5576:major semitone 5572: 5562: 5559: 5554: 5550: 5549: 5547: 5538: 5537: 5530: 5521: 5519: 5516: 5510: 5509: 5507: 5505: 5503: 5501: 5498: 5494:perfect unison 5491: 5487: 5486: 5483: 5479: 5478: 5462: 5460:5-limit tuning 5457: 5452: 5449: 5439: 5438: 5435: 5432: 5417:syntonic comma 5361: 5358: 5340:Interval cycle 5335: 5332: 5287: 5284: 5239:wolf intervals 5230:5-limit tuning 5075:just intervals 5069: 5068: 5063: 5058: 5053: 5048: 5043: 5042:Perfect octave 5040: 5036: 5035: 5032: 5029: 5026: 5019: 5012: 5009: 5005: 5004: 5001: 4998: 4993: 4986: 4979: 4976: 4972: 4971: 4968: 4965: 4962: 4955: 4948: 4945: 4941: 4940: 4937: 4932: 4929: 4924: 4919: 4916: 4912: 4911: 4908: 4900: 4890: 4883: 4876: 4873: 4869: 4868: 4865: 4860: 4855: 4846: 4837: 4832: 4828: 4827: 4824: 4816: 4806: 4799: 4792: 4791:Perfect fourth 4789: 4785: 4784: 4781: 4771: 4766: 4761: 4756: 4753: 4749: 4748: 4745: 4737: 4732: 4725: 4718: 4715: 4711: 4710: 4707: 4704: 4699: 4692: 4685: 4682: 4678: 4677: 4674: 4671: 4668: 4661: 4654: 4651: 4647: 4646: 4641: 4636: 4631: 4626: 4621: 4620:Perfect unison 4618: 4614: 4613: 4606: 4590: 4583: 4581:5-limit tuning 4577: 4576: 4573: 4572:(pitch ratio) 4569:5-limit tuning 4566: 4563: 4554: 4551: 4548: 4547: 4541: 4535: 4532: 4529: 4523: 4522: 4516: 4510: 4507: 4500: 4494: 4493: 4487: 4481: 4478: 4473: 4467: 4466: 4460: 4457: 4451: 4448: 4442: 4441: 4435: 4432: 4426: 4423: 4417: 4416: 4410: 4407: 4404: 4401: 4395: 4394: 4392: 4386: 4383: 4376: 4370: 4369: 4367: 4361: 4358: 4355: 4349: 4348: 4346: 4343: 4337: 4334: 4328: 4327: 4325: 4322: 4316: 4312: 4311: 4309: 4306: 4303: 4300: 4294: 4293: 4290: 4287: 4284: 4278: 4274: 4273: 4270: 4248: 4247: 4246: 4245: 4234: 4219: 4185: 4178: 4159: 4097: 4094: 4034: 4031: 4004: 4001: 3994: 3993: 3990: 3984: 3982: 3980: 3976: 3975: 3972: 3969: 3966: 3959: 3955: 3954: 3951: 3945: 3942: 3939: 3935: 3934: 3931: 3925: 3922: 3919: 3915: 3914: 3911: 3908: 3905: 3899: 3895: 3894: 3891: 3888: 3885: 3879: 3875: 3874: 3871: 3865: 3862: 3853: 3849: 3848: 3845: 3839: 3838: 3835: 3832: 3830: 3828: 3824: 3823: 3820: 3817: 3814: 3809: 3805: 3804: 3801: 3795: 3792: 3787: 3783: 3782: 3779: 3774: 3771: 3766: 3762: 3761: 3758: 3755: 3752: 3747: 3743: 3742: 3739: 3734: 3731: 3726: 3722: 3721: 3718: 3712: 3710: 3708: 3704: 3703: 3700: 3692: 3689: 3681: 3670: 3667: 3662: 3661: 3647: 3644: 3641: 3638: 3635: 3632: 3629: 3624: 3620: 3616: 3613: 3610: 3607: 3604: 3601: 3596: 3592: 3588: 3585: 3580: 3576: 3572: 3569: 3564: 3560: 3556: 3542: 3541: 3527: 3524: 3521: 3518: 3513: 3509: 3505: 3502: 3499: 3496: 3493: 3490: 3487: 3484: 3481: 3478: 3473: 3469: 3465: 3462: 3459: 3456: 3453: 3450: 3445: 3441: 3437: 3434: 3431: 3428: 3425: 3420: 3416: 3412: 3397: 3390: 3383: 3372: 3352:Main intervals 3330: 3327: 3326: 3325: 3308: 3299: 3258: 3243: 3234: 3220: 3216:septimal comma 3211: 3207:syntonic comma 3202: 3124: 3121: 3086:piano keyboard 3080: 3079: 3076: 3068: 3060: 3057: 3051: 3047: 3046: 3038: 3035: 3032: 3024: 3019: 3015: 3014: 3006: 3003: 2995: 2992: 2989: 2985: 2984: 2981: 2973: 2970: 2962: 2957: 2953: 2952: 2949: 2946: 2943: 2939: 2938: 2933: 2930: 2853:Main article: 2850: 2847: 2827:Melodic motion 2783:diatonic scale 2747:Main article: 2744: 2741: 2739:for details). 2733:Main intervals 2711: 2708: 2704: 2703: 2701:#Interval root 2682: 2668: 2634:Main article: 2631: 2628: 2553:harmonic minor 2504: 2503: 2492: 2489:diatonic scale 2470:Main article: 2467: 2464: 2463: 2462: 2447: 2425: 2422: 2417: 2406: 2403: 2401: 2400: 2399: 2398: 2393: 2392:Classification 2390: 2386:interval class 2357: 2356: 2352: 2345: 2344: 2334: 2331: 2329: 2303:Main article: 2300: 2297: 2296: 2295: 2292: 2289: 2286: 2283: 2203: 2200: 2197: 2196: 2194: 2191: 2183: 2180: 2172: 2161: 2157: 2156: 2148: 2145: 2142: 2139: 2136: 2126: 2122: 2121: 2119: 2111: 2108: 2105: 2102: 2092: 2088: 2087: 2084: 2081: 2078: 2075: 2071: 2070: 2065: 2062: 2054: 2053: 2038: 2029: 1984: 1981: 1740: 1737: 1712:diatonic scale 1604: 1601: 1538:diatonic scale 1470: 1467: 1373:diatonic scale 1364: 1361: 1247:diatonic scale 1245:(the notes of 1226:) to 8 (e.g., 1176: 1173: 1107: 1104: 1101: 1100: 1087: 1085: 1083: 1080: 1075: 1072: 1070:Perfect octave 1067: 1063: 1062: 1049: 1047: 1045: 1042: 1037: 1034: 1029: 1025: 1024: 1011: 1009: 1007: 1004: 999: 996: 991: 987: 986: 973: 971: 969: 966: 961: 958: 953: 949: 948: 935: 933: 931: 928: 923: 920: 915: 911: 910: 897: 895: 893: 890: 885: 882: 877: 873: 872: 869: 863: 862: 849: 846: 841: 838: 833: 831: 827: 826: 813: 811: 809: 806: 801: 798: 796:Perfect fourth 793: 789: 788: 775: 773: 771: 768: 763: 760: 755: 751: 750: 737: 735: 733: 730: 725: 722: 717: 713: 712: 699: 696: 690: 687: 682: 679: 674: 670: 669: 656: 653: 647: 644: 639: 636: 631: 627: 626: 613: 611: 609: 606: 601: 598: 596:Perfect unison 593: 589: 588: 585: 582: 575: 572: 564: 561: 553: 462:perfect unison 453: 452:Main intervals 450: 437: 430: 426: 420: 416: 410: 406: 401: 397: 393: 390: 387: 384: 370: 363: 322:Main article: 319: 316: 308:equal-tempered 297:pure intervals 293:just intervals 281:perfect fourth 239:Interval ratio 237:Main article: 234: 231: 223: 212: 209: 207: 206: 205: 204: 202: 199: 128:tuning systems 112:diatonic scale 57: 46: 43: 41: 40: 39: 38: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 9254: 9243: 9240: 9239: 9237: 9222: 9221:Voice leading 9219: 9217: 9214: 9212: 9209: 9206: 9203: 9201: 9198: 9196: 9193: 9191: 9188: 9186: 9183: 9181: 9178: 9176: 9173: 9171: 9168: 9164: 9161: 9160: 9159: 9156: 9154: 9151: 9149: 9146: 9144: 9141: 9139: 9136: 9134: 9131: 9129: 9128: 9124: 9123: 9120: 9116: 9109: 9104: 9102: 9097: 9095: 9090: 9089: 9086: 9074: 9071: 9070: 9067: 9061: 9060:Major seventh 9058: 9056: 9055:Minor seventh 9053: 9051: 9048: 9046: 9043: 9041: 9038: 9037: 9035: 9031: 9025: 9022: 9020: 9017: 9015: 9012: 9010: 9009:Perfect fifth 9007: 9005: 9002: 9000: 8997: 8995: 8992: 8990: 8987: 8986: 8984: 8980: 8965: 8962: 8958: 8955: 8953: 8950: 8948: 8945: 8943: 8940: 8938: 8935: 8934: 8933: 8932:Nonchord tone 8930: 8928: 8925: 8923: 8920: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8898: 8895: 8894: 8891: 8887: 8880: 8875: 8873: 8868: 8866: 8861: 8860: 8857: 8847: 8837: 8827: 8824: 8822: 8819: 8817: 8814: 8812: 8809: 8807: 8804: 8803: 8801: 8799: 8795: 8789: 8786: 8784: 8781: 8779: 8776: 8774: 8771: 8770: 8768: 8766: 8762: 8755: 8752: 8749: 8746: 8743: 8740: 8739: 8735: 8732: 8729: 8726: 8723: 8720: 8717: 8714: 8711: 8708: 8707: 8703: 8700: 8697: 8694: 8691: 8690:Lesser diesis 8688: 8687: 8683: 8680: 8677: 8674: 8671: 8668: 8665: 8662: 8661: 8659: 8657: 8656: 8651: 8645: 8642: 8640: 8637: 8635: 8632: 8631: 8629: 8627: 8626: 8625:Quarter tones 8621: 8615: 8612: 8610: 8607: 8605: 8602: 8601: 8599: 8597: 8596: 8591: 8585: 8582: 8580: 8577: 8575: 8574:Pseudo-octave 8572: 8570: 8567: 8565: 8562: 8560: 8557: 8556: 8554: 8552: 8548: 8545: 8539: 8524: 8521: 8520: 8518: 8516: 8512: 8505: 8502: 8499: 8496: 8493: 8490: 8487: 8484: 8481: 8478: 8475: 8472: 8469: 8466: 8463: 8460: 8457: 8454: 8451: 8448: 8447: 8445: 8443: 8439: 8436: 8434: 8428: 8427: 8422: 8397: 8394: 8377: 8374: 8357: 8354: 8337: 8334: 8317: 8314: 8297: 8294: 8281: 8278: 8277: 8275: 8270: 8264: 8261: 8259: 8253: 8252: 8247: 8244: 8236: 8221: 8218: 8215: 8212: 8209: 8206: 8203: 8200: 8197: 8194: 8191: 8188: 8185: 8182: 8181: 8179: 8177: 8173: 8166: 8163: 8160: 8157: 8154: 8151: 8148: 8145: 8142: 8139: 8136: 8133: 8130: 8127: 8126: 8124: 8122: 8118: 8111: 8108: 8105: 8102: 8099: 8096: 8093: 8090: 8087: 8084: 8081: 8078: 8075: 8072: 8071: 8069: 8067: 8063: 8056: 8053: 8050: 8047: 8044: 8041: 8038: 8035: 8034: 8032: 8030: 8026: 8019: 8016: 8013: 8010: 8007: 8004: 8001: 7998: 7997: 7995: 7993: 7989: 7982: 7979: 7976: 7973: 7970: 7967: 7964: 7961: 7960: 7958: 7954: 7951: 7949: 7945: 7936: 7933: 7927: 7921: 7917: 7910: 7905: 7903: 7898: 7896: 7891: 7890: 7887: 7881: 7877: 7872: 7870: 7867: 7865: 7862: 7860: 7859: 7854: 7851: 7848: 7847: 7842: 7841: 7837: 7832: 7828: 7824: 7823: 7818: 7814: 7813: 7809: 7801: 7797: 7793: 7789: 7785: 7781: 7780: 7775: 7769: 7766: 7761: 7755: 7751: 7747: 7741: 7738: 7734: 7733:0-7546-3573-2 7730: 7727:, p. 7. 7726: 7720: 7717: 7714: 7710: 7706: 7702: 7697: 7694: 7688: 7682: 7678: 7674: 7673: 7668: 7667:Tyrrell, John 7664: 7657: 7654: 7649: 7645: 7639: 7637: 7633: 7629: 7625: 7621: 7616: 7613: 7609: 7608:90-04-04794-8 7605: 7601: 7595: 7590: 7585: 7582: 7578: 7572: 7569: 7565: 7564:0-520-06991-9 7561: 7557: 7553: 7552:Perle, George 7548: 7545: 7541: 7537: 7532: 7529: 7525: 7524:0-14-020659-0 7521: 7517: 7513: 7512:Károlyi, Ottó 7508: 7505: 7501: 7500:0-87930-798-6 7497: 7493: 7487: 7484: 7480: 7479:0-13-193104-0 7476: 7472: 7466: 7464: 7460: 7455: 7453:9780793579914 7449: 7445: 7441: 7437: 7433: 7427: 7425: 7421: 7417: 7416:0-02-864737-8 7413: 7409: 7405: 7400: 7398: 7396: 7392: 7388: 7383: 7380: 7376: 7375:0-486-60753-4 7372: 7368: 7364: 7363: 7359: 7354: 7351: 7347: 7342: 7339: 7335: 7330: 7327: 7323: 7318: 7315: 7311: 7307: 7306:Stanley Sadie 7303: 7302: 7295: 7292: 7289: 7288:9781873497203 7285: 7281: 7280:9780713507447 7277: 7273: 7267: 7264: 7260: 7259:0-403-00326-1 7256: 7252: 7248: 7243: 7240: 7236: 7235:Tonal Harmony 7232: 7227: 7224: 7220: 7216: 7215: 7208: 7202: 7200: 7196: 7191: 7189:9781259447099 7185: 7181: 7177: 7170: 7168: 7164: 7159: 7157:9780199347094 7153: 7149: 7145: 7138: 7136: 7134: 7130: 7125: 7119: 7115: 7108: 7105: 7097: 7096: 7091: 7086: 7083: 7079: 7073: 7069: 7062: 7059: 7055: 7049: 7045: 7038: 7035: 7029: 7023: 7019: 7015: 7014: 7009: 7008:Tyrrell, John 7005: 6998: 6996: 6992: 6988: 6982: 6978: 6974: 6968: 6965: 6959: 6952: 6947: 6941: 6938: 6935: 6927: 6925: 6921: 6917: 6913: 6909: 6908:melodic minor 6905: 6904:natural minor 6901: 6897: 6896:key signature 6893: 6889: 6885: 6884:transposition 6881: 6877: 6873: 6872:natural notes 6869: 6865: 6859: 6857: 6855: 6853: 6851: 6849: 6847: 6843: 6839: 6833: 6831: 6827: 6821: 6817: 6814: 6812: 6811:Pseudo-octave 6809: 6807: 6804: 6802: 6799: 6797: 6794: 6792: 6789: 6787: 6784: 6783: 6779: 6768: 6763: 6761: 6759: 6755: 6749: 6747: 6743: 6739: 6735: 6717: 6710: 6700: 6697: 6694: 6693: 6686: 6683: 6680: 6679: 6672: 6669: 6666: 6665: 6658: 6655: 6652: 6651: 6644: 6641: 6638: 6637: 6630: 6627: 6624: 6623: 6612: 6609: 6606: 6605: 6598: 6595: 6592: 6591: 6584: 6581: 6578: 6577: 6570: 6567: 6564: 6563: 6560:Major second 6556: 6553: 6550: 6549: 6546:Minor second 6542: 6539: 6536: 6535: 6528: 6525: 6522: 6521: 6518: 6515: 6512: 6511: 6505: 6500: 6496: 6490: 6488: 6484: 6481: 6477: 6473: 6467: 6463: 6455: 6453: 6451: 6445: 6443: 6438: 6436: 6432: 6428: 6424: 6420: 6414: 6410: 6402: 6400: 6398: 6394: 6390: 6386: 6382: 6378: 6374: 6370: 6366: 6362: 6360: 6356: 6351: 6349: 6343: 6341: 6337: 6332: 6328: 6327: 6322: 6315: 6311: 6303: 6296: 6292: 6289: 6287: 6284: 6283: 6279: 6275: 6272: 6269: 6265: 6261: 6257: 6254: 6252: 6249: 6248: 6244: 6240: 6237: 6235:Major seventh 6234: 6230: 6226: 6222: 6219: 6217: 6214: 6213: 6209: 6205: 6202: 6200:Minor seventh 6199: 6195: 6191: 6187: 6184: 6182: 6179: 6178: 6174: 6170: 6167: 6164: 6160: 6156: 6152: 6149: 6147: 6144: 6143: 6139: 6135: 6132: 6129: 6125: 6121: 6117: 6114: 6112: 6109: 6108: 6104: 6100: 6097: 6095:Perfect fifth 6094: 6090: 6086: 6082: 6079: 6076: 6075: 6071: 6067: 6064: 6061: 6057: 6053: 6049: 6046: 6044: 6041: 6040: 6036: 6032: 6029: 6026: 6022: 6018: 6014: 6011: 6009: 6006: 6005: 6001: 5997: 5994: 5991: 5987: 5983: 5979: 5976: 5974: 5971: 5970: 5966: 5962: 5959: 5956: 5952: 5949: 5946: 5944: 5941: 5940: 5936: 5932: 5929: 5926: 5922: 5918: 5914: 5911: 5908: 5907: 5903: 5899: 5896: 5893: 5889: 5885: 5881: 5878: 5875: 5872: 5871: 5868:nomenclature 5865: 5862: 5860: 5856: 5853: 5848: 5847: 5844: 5842: 5838: 5832: 5830: 5828: 5822: 5818: 5810: 5808: 5806: 5802: 5793:duplex (2:1) 5787: 5785: 5782: 5779: 5778: 5775: 5772: 5771:sesquialterum 5764: 5762: 5761:perfect fifth 5759: 5756: 5755: 5752: 5750: 5748: 5745: 5743: 5740: 5739: 5736: 5734: 5732: 5730: 5724: 5722: 5719: 5715: 5712: 5709: 5708:sesquitertium 5701: 5699: 5696: 5693: 5692: 5688: 5687:sesquiquartum 5683: 5678: 5676: 5673: 5670: 5669: 5666: 5663: 5662:sesquiquintum 5660: 5658: 5653: 5651: 5648: 5645: 5644: 5641: 5638: 5637:sesquioctavum 5632: 5625: 5623: 5620: 5617: 5616: 5613: 5611: 5608: 5605: 5600: 5597: 5593: 5590: 5589: 5586: 5584: 5581: 5578: 5573: 5566: 5560: 5558: 5555: 5551: 5548: 5543: 5540: 5539: 5535: 5527: 5515: 5511: 5508: 5506: 5504: 5499: 5495: 5492: 5488: 5484: 5481: 5480: 5477: 5461: 5456: 5448: 5444: 5440: 5434:Generic names 5427: 5424: 5422: 5418: 5414: 5410: 5406: 5402: 5398: 5395:Typically, a 5393: 5391: 5387: 5383: 5379: 5375: 5371: 5367: 5359: 5357: 5354: 5350: 5345: 5341: 5333: 5331: 5328: 5324: 5319: 5316: 5312: 5311:interval root 5308: 5304: 5297: 5292: 5286:Interval root 5285: 5283: 5281: 5277: 5273: 5271: 5265: 5263: 5259: 5255: 5251: 5247: 5242: 5240: 5236: 5231: 5226: 5224: 5210: 5206: 5202: 5198: 5193: 5181: 5158: 5154: 5150: 5146: 5142: 5138: 5134: 5131:cents, where 5130: 5126: 5112: 5110: 5106: 5102: 5098: 5094: 5090: 5086: 5085: 5080: 5076: 5067: 5062: 5057: 5052: 5047: 5044: 5038: 5037: 5023: 5016: 5013: 5011:Major seventh 5007: 5006: 4997: 4990: 4983: 4980: 4978:Minor seventh 4974: 4973: 4959: 4952: 4949: 4943: 4942: 4936: 4928: 4923: 4920: 4914: 4913: 4906: 4898: 4894: 4887: 4880: 4877: 4875:Perfect fifth 4871: 4870: 4854: 4850: 4845: 4841: 4838: 4830: 4829: 4822: 4814: 4810: 4803: 4796: 4793: 4787: 4786: 4779: 4775: 4765: 4760: 4757: 4751: 4750: 4743: 4729: 4722: 4719: 4713: 4712: 4703: 4696: 4689: 4686: 4680: 4679: 4665: 4658: 4655: 4649: 4648: 4645: 4640: 4635: 4630: 4625: 4622: 4616: 4615: 4612: 4607: 4605: 4591: 4589: 4584: 4582: 4579: 4578: 4570: 4558: 4552: 4546: 4542: 4539: 4536: 4533: 4530: 4528: 4525: 4524: 4521: 4517: 4514: 4511: 4508: 4501: 4499: 4496: 4495: 4492: 4488: 4485: 4482: 4479: 4474: 4472: 4469: 4468: 4465: 4461: 4458: 4455: 4452: 4449: 4447: 4444: 4443: 4440: 4436: 4433: 4430: 4427: 4424: 4422: 4419: 4418: 4415: 4411: 4408: 4405: 4402: 4400: 4397: 4396: 4393: 4390: 4387: 4384: 4377: 4375: 4372: 4371: 4368: 4365: 4362: 4359: 4356: 4354: 4351: 4350: 4347: 4344: 4341: 4338: 4335: 4333: 4330: 4329: 4326: 4323: 4320: 4317: 4314: 4313: 4310: 4307: 4304: 4301: 4299: 4295: 4291: 4288: 4285: 4282: 4279: 4276: 4275: 4269: 4264: 4261: 4259: 4258: 4253: 4243: 4239: 4235: 4232: 4228: 4224: 4220: 4217: 4213: 4209: 4205: 4201: 4197: 4196: 4194: 4190: 4186: 4183: 4179: 4176: 4172: 4168: 4167:perfect fifth 4164: 4160: 4157: 4152: 4148: 4144: 4139: 4135: 4131: 4127: 4123: 4119: 4115: 4111: 4110: 4109: 4107: 4103: 4095: 4093: 4091: 4087: 4083: 4080: 4076: 4072: 4068: 4064: 4060: 4056: 4052: 4048: 4044: 4040: 4032: 4030: 4028: 4024: 4020: 4014: 4010: 4009:Chord (music) 4002: 4000: 3991: 3989: 3985: 3983: 3981: 3978: 3977: 3973: 3970: 3967: 3964: 3960: 3957: 3956: 3952: 3950: 3946: 3943: 3940: 3937: 3936: 3932: 3930: 3926: 3923: 3920: 3917: 3916: 3912: 3909: 3906: 3904: 3900: 3897: 3896: 3892: 3889: 3886: 3884: 3880: 3877: 3876: 3872: 3870: 3866: 3863: 3861: 3857: 3854: 3851: 3850: 3846: 3844: 3841: 3840: 3836: 3833: 3825: 3821: 3818: 3815: 3813: 3810: 3807: 3806: 3802: 3800: 3796: 3793: 3791: 3788: 3785: 3784: 3780: 3778: 3775: 3772: 3770: 3767: 3764: 3763: 3759: 3756: 3753: 3751: 3748: 3745: 3744: 3740: 3738: 3735: 3732: 3730: 3727: 3724: 3723: 3719: 3717: 3713: 3711: 3709: 3706: 3705: 3701: 3698: 3693: 3690: 3687: 3684:Minor, major, 3682: 3680: 3675: 3674: 3668: 3666: 3645: 3639: 3636: 3633: 3627: 3622: 3618: 3614: 3611: 3608: 3605: 3602: 3599: 3594: 3590: 3586: 3583: 3578: 3574: 3570: 3567: 3562: 3558: 3554: 3547: 3546: 3545: 3525: 3519: 3516: 3511: 3507: 3503: 3497: 3494: 3491: 3488: 3485: 3479: 3476: 3471: 3467: 3463: 3457: 3451: 3448: 3443: 3439: 3435: 3429: 3426: 3423: 3418: 3414: 3410: 3403: 3402: 3401: 3396: 3389: 3382: 3378: 3371: 3366: 3362: 3360: 3355: 3353: 3335: 3328: 3323: 3319: 3315: 3314: 3309: 3306: 3305: 3300: 3294: 3285: 3284:perfect fifth 3281: 3277: 3273: 3269: 3265: 3264: 3259: 3250: 3249: 3244: 3241: 3240: 3235: 3232: 3227: 3226: 3221: 3218: 3217: 3212: 3209: 3208: 3203: 3200: 3196: 3195: 3190: 3189: 3188: 3186: 3182: 3178: 3174: 3168: 3164: 3163:Comma (music) 3141: 3138: 3129: 3122: 3120: 3118: 3102: 3098: 3093: 3091: 3087: 3077: 3069: 3061: 3058: 3056: 3052: 3049: 3048: 3039: 3036: 3033: 3025: 3023: 3020: 3017: 3016: 3007: 3004: 2996: 2993: 2990: 2987: 2986: 2982: 2974: 2971: 2963: 2961: 2958: 2955: 2954: 2950: 2947: 2944: 2941: 2940: 2937: 2932:Interval name 2925: 2922: 2895: 2893: 2889: 2885: 2881: 2880: 2861: 2856: 2848: 2846: 2844: 2840: 2836: 2832: 2828: 2824: 2822: 2818: 2817:tuning system 2813: 2812:) is a skip. 2811: 2806: 2804: 2800: 2796: 2792: 2788: 2784: 2780: 2776: 2772: 2768: 2764: 2760: 2756: 2750: 2742: 2740: 2738: 2734: 2716: 2709: 2707: 2702: 2698: 2694: 2690: 2686: 2683: 2680: 2676: 2672: 2669: 2666: 2662: 2657: 2653: 2652: 2651: 2648: 2646: 2642: 2637: 2629: 2627: 2626:major scale. 2595: 2591: 2574: 2564: 2560: 2558: 2557:melodic minor 2554: 2549: 2547: 2543: 2539: 2528: 2525: 2508: 2501: 2497: 2493: 2490: 2486: 2484: 2479: 2478: 2477: 2473: 2465: 2460: 2456: 2452: 2448: 2445: 2441: 2440: 2439: 2435: 2431: 2423: 2410: 2397: 2391: 2389: 2387: 2382: 2379: 2375: 2372: 2353: 2350: 2349: 2348: 2338: 2328: 2327: 2326: 2324: 2320: 2311: 2306: 2298: 2293: 2290: 2287: 2284: 2281: 2280: 2279: 2277: 2273: 2269: 2265: 2261: 2257: 2253: 2249: 2246:is P8, and a 2245: 2241: 2237: 2233: 2229: 2225: 2221: 2217: 2213: 2210:for perfect, 2209: 2201: 2195: 2192: 2184: 2181: 2173: 2170: 2166: 2162: 2159: 2158: 2149: 2146: 2143: 2140: 2137: 2134: 2130: 2127: 2124: 2123: 2120: 2112: 2109: 2106: 2103: 2100: 2096: 2093: 2090: 2089: 2085: 2082: 2079: 2076: 2073: 2072: 2069: 2064:Interval name 2057: 2039: 2030: 2021: 2020: 2019: 1992: 1990: 1982: 1980: 1978: 1974: 1969: 1931: 1921: 1909: 1897: 1885: 1873: 1861: 1849: 1837: 1825: 1813: 1801: 1789: 1777: 1765: 1755: 1750: 1746: 1738: 1736: 1732: 1730: 1726: 1722: 1718: 1713: 1703: 1691: 1679: 1667: 1655: 1643: 1631: 1619: 1609: 1602: 1600: 1598: 1594: 1590: 1585: 1577: 1567: 1563: 1559: 1555: 1551: 1547: 1543: 1540:all unisons ( 1539: 1534: 1532: 1521: 1509: 1497: 1485: 1475: 1468: 1466: 1464: 1461:are used for 1460: 1456: 1452: 1448: 1443: 1441: 1437: 1433: 1429: 1425: 1421: 1417: 1413: 1409: 1405: 1401: 1397: 1393: 1389: 1385: 1381: 1374: 1369: 1362: 1360: 1358: 1353: 1301: 1287: 1283: 1278: 1276: 1272: 1262: 1252: 1251:natural minor 1248: 1244: 1240: 1235: 1233: 1229: 1225: 1221: 1217: 1213: 1206: 1196: 1189: 1185: 1181: 1174: 1172: 1170: 1166: 1162: 1158: 1154: 1150: 1146: 1142: 1138: 1135:(also called 1134: 1130: 1112: 1105: 1096: 1088: 1086: 1084: 1081: 1079: 1076: 1073: 1071: 1068: 1065: 1064: 1058: 1050: 1048: 1046: 1043: 1041: 1038: 1035: 1033: 1032:Major seventh 1030: 1027: 1026: 1020: 1012: 1010: 1008: 1005: 1003: 1000: 997: 995: 994:Minor seventh 992: 989: 988: 982: 974: 972: 970: 967: 965: 962: 959: 957: 954: 951: 950: 944: 936: 934: 932: 929: 927: 924: 921: 919: 916: 913: 912: 906: 898: 896: 894: 891: 889: 886: 883: 881: 880:Perfect fifth 878: 875: 874: 870: 868: 865: 864: 858: 845: 839: 837: 834: 828: 822: 814: 812: 810: 807: 805: 802: 799: 797: 794: 791: 790: 784: 776: 774: 772: 769: 767: 764: 761: 759: 756: 753: 752: 746: 738: 736: 734: 731: 729: 726: 723: 721: 718: 715: 714: 708: 700: 697: 694: 691: 688: 686: 683: 680: 678: 675: 672: 671: 665: 657: 654: 651: 648: 645: 643: 640: 637: 635: 632: 629: 628: 622: 614: 612: 610: 607: 605: 602: 599: 597: 594: 591: 590: 586: 583: 581: 576: 573: 570: 565: 562: 559: 556:Minor, major, 554: 552: 547: 546: 543: 541: 537: 533: 528: 526: 522: 518: 514: 504: 493: 491: 487: 483: 479: 475: 471: 467: 463: 459: 451: 449: 435: 428: 424: 418: 414: 408: 404: 399: 395: 391: 388: 385: 382: 374: 369: 366:to frequency 362: 357: 355: 351: 347: 343: 339: 335: 331: 325: 317: 315: 313: 309: 305: 300: 298: 294: 290: 286: 282: 278: 277:perfect fifth 274: 270: 266: 262: 258: 254: 250: 246: 240: 232: 230: 216: 200: 198: 184: 180: 179:perfect fifth 176: 172: 168: 163: 161: 157: 152: 147: 133: 129: 125: 121: 117: 113: 109: 105: 100: 98: 94: 90: 86: 82: 78: 74: 70: 66: 50: 37: 33: 19: 9137: 9125: 9045:Major second 9040:Minor second 8927:Musical note 8921: 8797: 8764: 8750:(0.72 cents) 8744:(1.95 cents) 8724:(13.8 cents) 8718:(10.1 cents) 8712:(19.5 cents) 8704:(35.7 cents) 8698:(62.6 cents) 8692:(41.1 cents) 8684:(27.3 cents) 8678:(22.6 cents) 8672:(21.5 cents) 8666:(23.5 cents) 8653: 8634:Quarter tone 8624: 8623: 8594: 8593: 8550: 8515:Higher-limit 8430: 8424: 8336:major fourth 8280:quarter tone 8255: 8249: 7938: 7915: 7856: 7849:, p. 38 7845: 7821: 7783: 7777: 7768: 7749: 7740: 7724: 7719: 7704: 7701:Lewin, David 7696: 7670: 7656: 7647: 7619: 7615: 7599: 7584: 7576: 7571: 7555: 7547: 7539: 7531: 7515: 7507: 7491: 7486: 7470: 7439: 7432:Wyatt, Keith 7407: 7382: 7360: 7353: 7341: 7329: 7317: 7310:John Tyrrell 7299: 7294: 7271: 7266: 7250: 7242: 7234: 7226: 7218: 7213: 7206: 7175: 7143: 7113: 7107: 7093: 7085: 7067: 7061: 7043: 7037: 7011: 6976: 6967: 6951:minor thirds 6940: 6932: 6868:7-tone scale 6791:Ear training 6778:Music portal 6750: 6737: 6731: 6662:Major sixth 6648:Minor sixth 6588:Major third 6574:Minor third 6485: 6469: 6446: 6439: 6416: 6388: 6384: 6380: 6376: 6373:Arabic music 6365:quarter tone 6358: 6354: 6347: 6344: 6324: 6320: 6317: 6260:semidiapason 5927:Major second 5894:Minor second 5833: 5824: 5814: 5798: 5633:, whole step 5622:major second 5557:minor second 5394: 5377: 5363: 5353:George Perle 5347: 5320: 5314: 5310: 5300: 5268: 5266: 5243: 5227: 5211:, including 5204: 5200: 5194: 5152: 5148: 5136: 5132: 5128: 5113: 5096: 5082: 5072: 5065: 5060: 5055: 5050: 5045: 5021: 5014: 4995: 4988: 4981: 4957: 4950: 4934: 4926: 4921: 4892: 4885: 4878: 4852: 4848: 4843: 4839: 4808: 4801: 4794: 4773: 4763: 4758: 4727: 4720: 4701: 4694: 4687: 4684:Major second 4663: 4656: 4653:Minor second 4643: 4638: 4633: 4628: 4623: 4544: 4537: 4531:C, Cm, or Cm 4519: 4512: 4490: 4483: 4463: 4453: 4438: 4428: 4413: 4388: 4363: 4339: 4318: 4255: 4251: 4249: 4156:main article 4101: 4099: 4089: 4085: 4082: 4078: 4074: 4070: 4066: 4036: 4016: 3997: 3695:Augmented or 3663: 3543: 3394: 3387: 3380: 3376: 3369: 3367: 3363: 3358: 3356: 3349: 3313:quarter tone 3311: 3302: 3275: 3271: 3268:minor thirds 3261: 3246: 3237: 3233:for details. 3223: 3214: 3205: 3192: 3170: 3094: 3083: 2929:of semitones 2896: 2883: 2877: 2875: 2842: 2838: 2834: 2830: 2825: 2814: 2807: 2798: 2795:major second 2790: 2787:minor second 2778: 2774: 2770: 2766: 2762: 2758: 2754: 2752: 2730: 2705: 2695:. See also: 2688: 2679:fundamentals 2649: 2644: 2639: 2593: 2589: 2587: 2550: 2546:main article 2529: 2521: 2495: 2481: 2476:In general, 2475: 2458: 2454: 2442:Vertical or 2437: 2395: 2383: 2380: 2376: 2373: 2358: 2346: 2316: 2278:. Examples: 2275: 2271: 2267: 2263: 2259: 2255: 2235: 2227: 2219: 2211: 2207: 2205: 2168: 2132: 2098: 2061:of semitones 1993: 1986: 1976: 1972: 1970: 1927: 1733: 1728: 1724: 1720: 1716: 1709: 1586: 1578:is between D 1575: 1565: 1561: 1557: 1553: 1549: 1545: 1541: 1535: 1531:contrapuntal 1527: 1458: 1454: 1450: 1444: 1439: 1435: 1431: 1423: 1419: 1415: 1407: 1399: 1391: 1383: 1379: 1377: 1354: 1302: 1279: 1274: 1270: 1236: 1227: 1223: 1215: 1209: 1168: 1164: 1160: 1156: 1152: 1148: 1144: 1140: 1136: 1132: 1129:music theory 1126: 677:Major second 634:Minor second 567:Augmented or 534:. Intervals 529: 494: 478:major second 455: 375: 367: 360: 358: 327: 324:Cent (music) 301: 296: 292: 242: 228: 164: 148: 101: 92: 88: 84: 80: 76: 68: 65:music theory 62: 36: 9033:Dissonances 9019:Major sixth 9014:Minor sixth 8999:Major third 8994:Minor third 8982:Consonances 8952:Preparation 8947:Pedal point 8783:Millioctave 8765:Measurement 8756:(0.4 cents) 8736:(7.7 cents) 8730:(8.1 cents) 8614:Major limma 8356:minor fifth 7592: [ 7404:Cope, David 7180:McGraw Hill 6888:accidentals 6880:minor scale 6876:major scale 6742:time points 6734:David Lewin 6165:Major sixth 6130:Minor sixth 6035:diatessaron 5992:Major third 5965:semiditonus 5957:Minor third 5675:major third 5650:minor third 5609:(2187:2048) 5544:(2048:2025) 5280:minor third 5272:equivalents 5155:, actually 4947:Major sixth 4918:Minor sixth 4755:Major third 4717:Minor third 4611:temperament 4586:Pythagorean 4450:CM, or Cmaj 4425:Cm, or Cmin 4357:C+, or Caug 4336:Cm, or Cmin 4332:Minor triad 4315:CM, or Cmaj 4298:Major triad 4242:power chord 4208:perfect 4th 4171:major triad 4163:major third 4023:major triad 3947:Diminished 3867:Diminished 3797:Diminished 3790:Major tenth 3769:Minor tenth 3750:Major ninth 3729:Minor ninth 3714:Diminished 2991:major third 2960:major third 2821:pitch space 2810:major third 2803:minor third 1593:pitch class 1282:accidentals 1237:There is a 1205:major scale 1149:major third 1127:In Western 956:Major sixth 918:Minor sixth 758:Major third 720:Minor third 577:Widely used 503:major third 490:major third 334:logarithmic 289:minor third 285:major third 273:major sixth 249:frequencies 175:minor third 8957:Resolution 8902:Avoid note 8816:Semiditone 8710:Diaschisma 8525:(17-limit) 8216:(22 or 23) 8214:fourteenth 8210:(20 or 21) 8208:thirteenth 8204:(18 or 19) 8198:(17 or 18) 8192:(15 or 16) 8186:(13 or 14) 8121:Diminished 7948:interval.) 7929:(post-Bach 7853:"Interval" 7628:0803279345 6960:References 6491:Comparison 6359:supermajor 6340:microtonal 5631:whole tone 5569:half tone, 5542:diaschisma 5536:(128:125) 5523:descending 5303:David Cope 5274:, such as 5270:enharmonic 5141:wolf fifth 4562:semitones 4193:chord root 4182:diminished 4169:interval ( 4134:diminished 4051:diminished 3986:Augmented 3929:thirteenth 3927:Augmented 3903:thirteenth 3883:thirteenth 3869:thirteenth 3697:diminished 3686:or perfect 3322:whole tone 3239:diaschisma 3173:microtones 2879:enharmonic 2855:Enharmonic 2799:whole step 2685:David Cope 2522:The table 2459:descending 2232:diminished 1574:, and the 1459:supermajor 1412:diminished 569:diminished 558:or perfect 517:instrument 474:whole tone 130:, between 120:microtones 77:horizontal 9211:Ululation 8778:Centitone 8716:Semicomma 8595:Semitones 8559:Microtone 8543:intervals 8220:fifteenth 8066:Augmented 7944:semitones 7916:Intervals 7819:(1895) . 6836:The term 6760:hearing. 6427:serialism 6361:intervals 5902:semitonus 5851:semitones 5849:Number of 5827:semitonus 5582:(256:243) 5571:half step 5431:semitones 5429:Number of 5307:Hindemith 5093:non-equal 4560:Number of 4506:, or Cdim 4475:C+, Caug, 4382:, or Cdim 4283:examples 4212:major 6th 4204:major 2nd 4175:minor 7th 4130:augmented 4126:root note 4047:augmented 3988:fifteenth 3963:fifteenth 3949:fifteenth 3699:intervals 3688:intervals 3679:semitones 3676:Number of 3637:− 3628:− 3517:− 3477:− 3449:− 3199:frequency 3167:Microtone 2892:semitones 2791:half step 2781:. In the 2455:ascending 2384:Since an 2299:Inversion 2240:augmented 2000:, C and G 1989:semitones 1597:harmonics 1589:inversion 1536:Within a 1428:chromatic 1404:augmented 1190:indicated 571:intervals 560:intervals 551:semitones 548:Number of 480:), and a 405:⁡ 392:⋅ 350:semitones 251:. When a 247:of their 160:logarithm 9236:Category 9207:(figure) 9190:Sequence 9175:Phrasing 9158:Ornament 9138:Interval 9127:Balungan 8937:Cambiata 8922:Interval 8897:Argument 8748:Breedsma 8196:eleventh 8176:Compound 7931:Western) 7926:semitone 7800:40285634 7748:(1993). 7703:(1987). 7669:(eds.). 7554:(1990). 7538:(1934). 7514:(1965), 7438:(1998). 7406:(1997). 7249:(1903). 7010:(eds.). 6910:and the 6902:and the 6764:See also 6476:specific 6355:subminor 6350:interval 6342:scales. 6278:diapason 6103:diapente 6085:tritonus 5884:unisonus 5821:semitone 5565:semitone 5476:meantone 4604:meantone 4292:Seventh 4257:boldface 4223:dominant 4128:, while 4059:dominant 3961:Perfect 3799:eleventh 3354:below). 3318:semitone 3270:and one 3254:♭ 3145:♮ 3135:♯ 3112:♭ 3106:♯ 3073:♯ 3065:♭ 3043:♭ 3029:♯ 3011:♭ 3000:♭ 2978:♯ 2967:♯ 2918:♭ 2912:♯ 2906:♭ 2900:♯ 2843:disjunct 2839:skipwise 2835:conjunct 2831:stepwise 2819:and the 2645:resolved 2623:♭ 2617:♭ 2611:♭ 2605:♭ 2599:♭ 2570:♭ 2533:♭ 2485:interval 2483:diatonic 2444:harmonic 2368:♭ 2362:♭ 2319:inverted 2188:♯ 2177:♭ 2153:♭ 2116:♯ 2049:♯ 2043:♭ 2034:♭ 2025:♯ 2015:♯ 2009:♭ 2003:♭ 1997:♯ 1965:♯ 1959:♯ 1953:♯ 1947:♭ 1941:♯ 1935:♭ 1581:♯ 1571:♯ 1455:subminor 1440:interval 1424:modifier 1363:Quality 1349:♯ 1343:♯ 1337:♯ 1331:♯ 1325:♯ 1319:♯ 1313:♯ 1307:♯ 1297:♭ 1291:♯ 1266:♯ 1256:♯ 1201:♭ 650:Semitone 508:♭ 498:♯ 470:semitone 354:semitone 287:), 6:5 ( 283:), 5:4 ( 279:), 4:3 ( 275:), 3:2 ( 271:), 5:3 ( 267:), 2:1 ( 194:♭ 188:♯ 143:♭ 137:♯ 116:semitone 93:harmonic 89:vertical 69:interval 9170:Pattern 9143:Melisma 9133:Cadence 9050:Tritone 8964:Spectra 8912:Cadence 8907:Beating 8754:Ragisma 8742:Schisma 8728:Kleisma 8564:5-limit 8470:(15:14) 8464:(21:20) 8458:(28:27) 8452:(36:35) 8442:7-limit 8407:⁄ 8396:seventh 8387:⁄ 8367:⁄ 8347:⁄ 8327:⁄ 8307:⁄ 8287:⁄ 8269:Neutral 8242:systems 8202:twelfth 8159:seventh 8110:seventh 8055:seventh 8018:seventh 7956:Perfect 7924:Twelve- 7880:YouTube 7810:Sources 7282:(pbk). 6946:tertian 6838:tritone 6746:timbres 6348:neutral 6331:7-limit 6000:ditonus 5855:Quality 5801:shrutis 5729:tritone 5607:apotome 5532:lesser 5469:⁄ 5443:Quality 5378:sesqui- 5254:tritone 5216:⁄ 5187:⁄ 5175:⁄ 5164:⁄ 5120:⁄ 5089:rounded 4597:⁄ 4477:C, or C 4403:C, or C 4240:) is a 4227:seventh 4063:symbols 3860:Tritave 3393:, ..., 3282:plus a 3272:tritave 3263:kleisma 3248:schisma 3078: 3053:doubly 2983: 2888:pitches 2451:melodic 2430:Harmony 2252:tritone 2163:doubly 2006:, and C 1983:Example 1584:and A. 1469:Perfect 1451:neutral 1410:), and 1380:perfect 1359:below. 1346:, and F 1286:natural 1243:degrees 1186:, with 1145:quality 844:Tritone 482:tritone 261:integer 191:and G–A 183:spelled 167:quality 104:Western 85:melodic 9200:Timbre 9185:Rhythm 9115:Melody 9024:Octave 8989:Unison 8811:Ditone 8798:Others 8788:Savart 8655:Commas 8551:Groups 8500:(10:7) 8296:second 8240:tuning 8165:octave 8141:fourth 8129:second 8092:fourth 8080:second 8074:unison 8037:second 8000:second 7981:octave 7969:fourth 7963:unison 7946:in the 7798: 7756: 7731: 7711: 7683: 7626: 7606: 7562: 7522: 7498: 7477: 7450: 7414: 7373: 7286: 7278: 7257: 7186: 7154: 7120: 7074: 7050: 7024: 6983: 6419:atonal 5859:number 5689:(5:4) 5629:tone, 5534:diesis 5485:Short 5474:-comma 5447:number 5382:justly 5139:, the 5111:one). 4905:(wolf) 4897:(wolf) 4821:(wolf) 4813:(wolf) 4778:(wolf) 4742:(wolf) 4602:-comma 4588:tuning 4504:° 4380:° 4289:Fifth 4286:Third 4281:Symbol 4268:chords 4151:number 4114:triads 4061:. The 4057:, and 3901:Major 3881:Minor 3702:Short 3649: 3529: 3280:octave 3257:in C.) 3231:diesis 3225:diesis 3177:commas 3059: 3037: 3034: 3005: 2994: 2972: 2927:Number 2823:used. 2777:), or 2573:-major 2434:Melody 2355:versa. 2323:octave 2248:unison 2244:octave 2193: 2182: 2147: 2144: 2141: 2110: 2107: 2059:Number 2018:, but 1457:, and 1175:Number 1143:) and 1133:number 587:Audio 486:ditone 342:octave 269:octave 265:unison 171:number 124:commas 81:linear 9216:Voice 9180:Pitch 9163:Trill 9153:Motif 8917:Chord 8821:Secor 8569:Comma 8541:Other 8506:(7:4) 8494:(7:5) 8488:(9:7) 8482:(7:6) 8476:(8:7) 8376:sixth 8316:third 8238:Other 8190:tenth 8184:ninth 8153:sixth 8147:fifth 8135:third 8104:sixth 8098:fifth 8086:third 8049:sixth 8043:third 8029:Minor 8012:sixth 8006:third 7992:Major 7975:fifth 7796:JSTOR 7596:] 7209:from 6900:major 6892:staff 6890:on a 6822:Notes 6756:over 6385:super 5935:tonus 5866:Latin 5863:Short 5817:Latin 5773:(3:2) 5710:(4:3) 5664:(6:5) 5639:(9:8) 5580:limma 5397:comma 5103:. 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Index