Consonance and dissonance - Knowledge (XXG)

580: 2051: 1925: 523: 1837: 625:. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship. In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of amplitude fluctuations. 1790: 2089: 2141:, as produced by vibrating strings and columns of air, on which the West's dominant musical instruments are based. By generalizing Helmholtz's notion of consonance (described above as the "coincidence of partials") to embrace non-harmonic timbres and their related tunings, consonance has recently been "emancipated" from harmonic timbres and their related tunings. Using electronically controlled pseudo-harmonic timbres, rather than strictly harmonic acoustic timbres, provides tonality with new structural resources such as 2114: 1890: 1709: 2158: 891: 1863: 556: 823:(relative to the range of human hearing). If harmonic tones with larger intervals are played, the perceived dissonance is due, at least in part, to the presence of intervals between the harmonics of the two notes that fall within the critical band. The sensory consonance or dissonance of any given interval, in any given tuning, can be adjusted by adjusting the partials in the timbre to be maximally aligned or mis-aligned, respectively, with the notes of the related tuning. 740: 1743: 818:),( Terhardt calls this "sensory dissonance". By this definition, dissonance is dependent not only on the width of the interval between two notes' fundamental frequencies, but also on the widths of the intervals between the two notes' non-fundamental partials. Sensory dissonance (i.e., presence of beating or roughness in a sound) is associated with the inner ear's inability to fully resolve spectral components with excitation patterns whose 4691: 2006: 1960: 1531:("rule of thirds and sixths") required that imperfect consonances should resolve to a perfect one by a half-step progression in one voice and a whole-step progression in another. The viewpoint concerning successions of imperfect consonances—perhaps more concerned by a desire to avoid monotony than by their dissonant or consonant character—has been variable. Anonymous XIII (13th century) allowed two or three, Johannes de Garlandia's 795:

mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone. By these definitions, inharmonic partials of otherwise harmonic spectra are usually processed separately, unless frequency or amplitude modulated coherently with the harmonic partials. For some of these definitions, neural firing supplies the data for pattern matching; see directly below.

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less in a musical context properly speaking: dissonances often play a decisive role in making music pleasant, even in a generally consonant context—which is one of the reasons why the musical definition of consonance/dissonance cannot match the psychophysiologic definition. In addition, the oppositions pleasant/unpleasant or agreeable/disagreeable evidence a confusion between the concepts of "dissonance" and of "

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expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations remain important, through their interaction with the signal's spectral components. This interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones.

1655: 470: 849:). The sonance of the interval between two notes can be maximized (producing consonance) by maximizing the alignment of the two notes' partials, whereas it can be minimized (producing dissonance) by mis-aligning each otherwise nearly aligned pair of partials by an amount equal to the width of the critical band at the average of the two partials' frequencies.( 2428:... "the natural spacing of so-called dissonances is as seconds, as in the overtone series, rather than sevenths and ninths ... Groups spaced in seconds may be made to sound euphonious, particularly if played in conjunction with fundamental chord notes taken from lower in the same overtone series. Blends them together and explains them to the ear." — 1054:

tone played slightly variant to the overall schema will generate a psychological need for resolve. When the consonant is followed thereafter, the listener will encounter a sense of resolution. Within Western music, these particular instances and psychological effects within a composition have come to possess an ornate connotation.

831:) indicating an oddball event. This causes slight stress in the listener, which is causing the sensation of dissonance. In the same paper, Pankovski and Pankovska show by a software simulated neural network that the brain is capable of such remembering and ranking of the sound patterns, thus perfectly reproducing the well known 100:. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural 2380:

offers a new perspective on consonance and dissonance by enabling a pseudo-just tuning and a pseudo-harmonic timbre to remain related despite real-time systematic changes to tuning, to timbre, or to both. This enables any musical interval in said tuning to be made more or less consonant in real time

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Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal. The degree of amplitude fluctuation depends on

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Period length or neural-firing coincidence: with the length of periodic neural firing created by two or more waveforms, higher simple numbers creating longer periods or lesser coincidence of neural firing and thus dissonance. Purely harmonic tones cause neural firing exactly with the period or some

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For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant

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enables any musical interval to be made more or less consonant or dissonant in real time (i.e., during composition and/or performance) by controlling the degree to which the partials of the pseudo-harmonic timbre align with the interval's notes in the related pseudo-just tuning. For example, listen

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standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one just a little less consonant than the perfect fourth and

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points out, this is "the only chord in the whole song that Schumann marks with an accent". Cook goes on to stress that what makes this chord so effective is Schumann's placing of it in its musical context: "in what leads up to it and what comes of it". Cook explains further how the interweaving of

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Various psychological principles constructed through the audience's general conception of tonal fluidity determine how a listener will distinguish an instance of dissonance within a musical composition. Based on one's developed conception of the general tonal fusion within the piece, an unexpected

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theory. Dips in this graph show consonant intervals such as 4:5 and 2:3. Other components not modeled by this theory include critical band roughness, and tonal context (e.g., an augmented second is more dissonant than a minor third although in equal temperament the interval, 300 cents, is the

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In music, even if the opposition often is founded on the preceding, objective distinction, it more often is subjective, conventional, cultural, and style- or period-dependent. Dissonance can then be defined as a combination of sounds that does not belong to the style under consideration; in recent

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in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer

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There are several passing dissonances in this adagio passage, for example on the first beat of bar 3. However the most striking effect here is implied, rather than sounded explicitly. The A flat in the first bar is contradicted by the high A natural in the second bar, but these notes do not sound

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music, and the present article is concerned mainly with this case. Most historical definitions of consonance and dissonance since about the 16th century have stressed their pleasant/unpleasant, or agreeable/disagreeable character. This may be justifiable in a psychophysiological context, but much

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In both cases, the distinction mainly concerns simultaneous sounds; if successive sounds are considered, their consonance or dissonance depends on the memorial retention of the first sound while the second sound (or pitch) is heard. For this reason, consonance and dissonance have been considered

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overlap. If two pure sine waves, without harmonics, are played together, people tend to perceive maximum dissonance when the frequencies are within the critical band for those frequencies, which is as wide as a minor third for low frequencies and as narrow as a minor second for high frequencies

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Sensory dissonance and its two perceptual manifestations (beating and roughness) are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of

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Fusion or pattern matching: fundamentals may be perceived through pattern matching of the separately analyzed partials to a best-fit exact-harmonic template, or the best-fit subharmonic, or harmonics may be perceptually fused into one entity, with dissonances being those intervals less likely

786:(or a sufficiently close approximation thereof), ratios of higher simple numbers are more dissonant than lower ones. However, the farther the timbre departs from the harmonic series, and/or the farther than the tuning departs from a Just Intonation, the less the "frequency ratio" rule applies. 1509:

final cadential consonances of fourth, fifths, and octaves need not be the target of "resolution" on a beat-to-beat (or similar) time basis: minor sevenths and major ninths may move to octaves forthwith, or sixths to fifths (or minor sevenths), but the fourths and fifths within might become

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In Antiquity, these mainly concerned string-length ratios. From the early 17th century onwards, frequency ratios were more often considered. Consonance often is associated with the simplicity of the ratio, i.e. with ratios of lower simple numbers. Many of these definitions do not require

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ordered by consonance/dissonance, for the first time in the history of studying these phenomena. As a consequence, Pankovski and Pankovska suggest that the consonance and dissonance are biologically dependent for the more consonant sounds, and culturally dependent for the more dissonant

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quavers of the initial four bars support four consonances only, all the rest are dissonances, twelve of them being chords containing five different notes. It is a remarkable picture of desperate and unflinching resistance to the Christian to the fell powers of evil."

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Dissonance sensation is a result of brain's response to unusual or rare sound perceptions. The brain is remembering and ranking the sound patterns that usually enters the ears, and if an unusual (rare occurring) sound is listened to, a well known EEG pattern emerges

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Philip Radcliffe speaks of this as "a remarkably poignant passage with surprisingly sharp dissonances". Radcliffe says that the dissonances here "have a vivid foretaste of Schumann and the way they gently melt into the major key is equally prophetic of Schubert."

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Generally, the sonance (i.e., a continuum with pure consonance at one end and pure dissonance at the other) of any given interval can be controlled by adjusting the timbre in which it is played, thereby aligning its partials with the current tuning's notes (or

1852: 1237:"Consonances are said median, when two voices are joined at the same time, which neither can be said perfect, nor imperfect, but which partly agree with the perfect, and partly with the imperfect. And they are of two species, namely the fifth and the fourth.") 4488:, second revised and enlarged edition, translated by Margaret Hamerik with linguistic alterations and additions by Annie I. Fausboll. Copenhagen: E. Munksgaard; Oxford: Oxford University Press. Reprinted, with corrections, New York: Dover Publications, 1970. 485: 1081:

denoted the production of a unified complex, particularly one expressible in numerical ratios. Applied to music, the concept concerned how sounds in a scale or a melody fit together (in this sense, it could also concern the tuning of a scale). The term

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hears that "a final reminder of this comes in the unexpected and almost excruciating dissonance Bach inserts over the very last chord: the melody instruments insist on B natural—the jarring leading tone—before eventually melting in a C minor cadence."

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The terms dissonance and consonance are often considered equivalent to tension and relaxation. A cadence is (among other things) a place where tension is resolved; hence the long tradition of thinking of a musical phrase as consisting of a

673:, the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters, For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies 561:

Dissonance may be the difficulty in determining the relationship between two frequencies, determined by their relative wavelengths. Consonant intervals (low whole number ratios) take less, while dissonant intervals take more time to be

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Imperfect consonance: minor and major thirds. (Imperfect consonances are not formally mentioned in the treatise, but the quotation above concerning median consonances does refer to imperfect consonances, and the section on consonances

1995: 1949: 1853: 484: 1914: 1416:]) to understand these terms, such that imperfect is "unfinished" or "incomplete" and thus an imperfect dissonance is "not quite manifestly dissonant" and perfect consonance is "done almost to the point of excess". Also, 729:"The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called 2078: 1779: 1693: 1645: 1344: 1231:

Medie autem dicuntur, quando duo voces junguntur in eodem tempore; que neque dicuntur perfecte, neque imperfecte, sed partim conveniunt cum perfectis, et partim cum imperfectis. Et sunt due species, scilicet diapente et

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An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are "active"; traditionally they have been considered harsh and have expressed pain, grief, and

1214:" is said perfect, when two voices are joined at the same time, so that the one, by audition, cannot be distinguished from the other because of the concordance, and it is called equisonance, as in unison and octave.") 1094:, where fourths, fifths and octaves (ratios 4:3, 3:2 and 2:1) were directly tunable, while the other scale degrees (other 3 prime ratios) could only be tuned by combinations of the preceding. Until the advent of 1041:

Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods. Relaxation and tension have been used as analogy since the time of Aristotle till the present.

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the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree.

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are said imperfect, when two voices are joined so that by audition although they can to some extent match, nevertheless they do not concord. And there are two species, namely tone plus fifth and minor third plus

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says that this aria "begins with an alarming chord of the seventh... It is meant to depict the horror of the curse upon sin that is threatened in the text". Gillies Whittaker points out that "The thirty-two

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Imperfecte dicuntur, quando due voces junguntur ita, quod secundum auditum vel possunt aliquo modo compati, tamen non concordant. Et sunt due species, scilicet tonus cum diapente et semiditonus cum diapente.

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stop in organs. Other musical styles such as Bosnian ganga singing, pieces exploring the buzzing sound of the Indian tambura drone, stylized improvisations on the Middle Eastern mijwiz, or Indonesian

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If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness.

567: 312: 1345: 1259:"So it appears that there are six species of consonances, that is: unison, octave, fifth, fourth, minor third, major third." The last two are implied to be "imperfect consonances" by deduction.) 910: 1209:

Perfecta dicitur, quando due voces junguntur in eodem tempore, ita quod una, secundum auditum, non percipitur ab alia propter concordantiam, et dicitur equisonantiam, ut in unisono et diapason.

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lines in both piano and voice parts in the bars leading up to this chord (bars 9–14) "are set on a kind of collision course; hence the feeling of tension rising steadily to a breaking point".

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When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.

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chord (G, which consists of the pitches G, B, D and F), it is deemed to be "dissonant" and it normally resolves to E during a cadence, with the G chord changing to a C Major chord.

1880: 2145:. These new resources provide musicians with an alternative to pursuing the musical uses of ever-higher partials of harmonic timbres and, in some people's minds, may resolve what 2041:

Wagner made increasing use of dissonance for dramatic effect as his style developed, particularly in his later operas. In the scene known as "Hagen's Watch" from the first act of

2047:, according to Scruton the music conveys a sense of "matchless brooding evil", and the excruciating dissonance in bars 9–10 below it constitute "a semitonal wail of desolation". 1732: 1303:

Medie dicuntur, quando due voces junguntur ita, quod partim conveniunt cum perfectis, partim cum imperfectis. Et iste sunt due species, scilicet tonus et simitonium cum diapente.

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Iste species dissonantie sunt septem, scilicet: semitonium, tritonus, ditonus cum diapente; tonus cum diapente, semiditonus cum diapente; tonus et semitonium cum diapente.

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are said median when two voices are joined so that they partly match the perfect, partly the imperfect. And they are of two species, namely tone and semitone plus fifth.")

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music, what is considered stylistically dissonant may even correspond to what is said to be consonant in the context of acoustics (e.g. a major triad in 20th century

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Perfect dissonance: semitone, tritone, major seventh (major third + fifth). (Here again, the perfect dissonances can only be deduced by elimination from this phrase:

1187:) ... There are six of these consonances, three simple and three composite, ... octave, fifth, fourth, and octave-plus-fifth, octave-plus-fourth and double octave". 898: 647:

As the rate of fluctuation is increased, the loudness appears constant, and the fluctuations are perceived as "fluttering" or roughness (fluctuations between about

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evoked by an interval or chord, or the difficulty of fitting its pitches to a harmonic series (discussed by Goldstein and Terhardt, see main text) – is modelled by

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parsed this chord (in bars 206 and 208) as a "diminished nineteenth ... a searingly dissonant dominant harmony containing nine different pitches. Who knows what

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were considered consonant. As time progressed, intervals ever higher on the overtone series were considered as such. The final result of this was the so-called "

868:), the sonance of intervals is affected both by tuning progressions and timbre progressions, introducing tension and release into the playing of a single chord. 758: 534: 1978:—horror fanfare." When this passage returns later in the same movement (just before the voices enter) the sound is further complicated with the addition of a 1493:

parallel fourths and fifths were acceptable and necessary, open fourths and fifths inside octaves were the characteristic stable sonority in 3 or more voices,

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These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.")

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If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.

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wrote "Although the ancients formerly would forbid all sequences of more than three or four imperfect consonances, we more modern do not prohibit them."

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says that this movement must have "made Mozart's hearers sit up by its daring modernities... There is a suppressed feeling of discomfort about it."

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As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears

5576: 5058: 4586: 4208:; Milne, Andrew; Tiedje, Stefan; Prechtl, Anthony & Plamondon, James (Summer 2009). "Spectral tools for dynamic tonality and audio morphing". 1646: 2077: 1909:

Piano Concerto 21, K467, where the subtle, but quite explicit dissonances on the first beats of each bar are enhanced by exquisite orchestration:

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was used by Aristoxenus and others to describe the intervals of the fourth, the fifth, the octave and their doublings; other intervals were said

899: 1778: 1153:)". It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand ( 544: 283:). Thus, a note and the note one octave higher are highly consonant because the partials of the higher note are also partials of the lower note. 3684: 1913: 1343: 1192: 757: 2369:

had effectively promoted the major ninth and minor seventh to a legitimacy of harmonic consonance as well, in their fabrics of 4-note chords.

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Scientific definitions have been variously based on experience, frequency, and both physical and psychological considerations. These include:

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partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds (i.e. sounds with

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Nonspecific hebbian neural network model predicts musical scales discreteness and just intonation without using octave-equivalency mapping

579: 469: 1916: 5586: 2190:. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord. 1878: 2080: 6103: 5955: 4579: 1847:

music contains a number of quite radical experiments in dissonance. The following comes from his Adagio and Fugue in C minor, K. 546:

1781: 959:, are played such that their relatively stiff mass is excited to vibration by means of a striking the instrument. This contrasts with 1346: 1181:) of two sounds, which will come about only when two simultaneous sounds from different sources combine into a single musical whole ( 613:

consider this sound an attractive part of the musical timbre and go to great lengths to create instruments that produce this slight "

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Gerson, A., and J. L. Goldstein (1978). "Evidence for a General Template in Central Optimal Processing for Pitch of Complex Tones".

3554: 3528: 3502: 3485: 480:(1940), of a triad's overall consonance or dissonance through the consonance or dissonance of the three intervals contained within. 4548: 908: 112:

stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term

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which softened a bad effect. They were also often filled in by pairs of perfect fourths and perfect fifths respectively, forming

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Another example of a cumulative build-up of dissonance from the early 20th century (1910) can be found in the Adagio that opens

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from Michael Haydn's Missa Quadragesimalis, MH 552 performed by Purcell Choir and Orfeo Orchestra conducted by György Vashegyi

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Cultural Familiarity and Musical Expertise Impact the Pleasantness of Consonance / Dissonance but Not Its Perceived Tension."

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Consonant: minor third, tritone, minor sixth, perfect fourth, perfect fifth, and possibly minor seventh or even major second

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Sic apparet quod sex sunt species concordantie, scilicet: unisonus, diapason, diapente, diatessaron, semiditonus, ditonus.

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One example of modernist dissonance comes from a work that received its first performance in 1913, three years after the

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often considers that, in a dissonant chord, one of the tones alone is in itself deemed to be the dissonance: it is this

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Scriptores ecclesiastici de musica sacra potissimum: ex variis Italiae, Galliae & Germaniae codicibus manuscriptis

926: 28: 4913: 3979:. Translated by Black, Leo. New York, NY / London, UK: St. Martins Press / Faber & Faber. pp. 258–264. 628:"Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation: 532: 933: 5516: 5182: 5152: 4860: 3642:] (in German). Translated by Ellis, A.J. (2nd English / 4th German ed.). New York, NY: Dover Publications. 1941: 1828: 160:). A major second (e.g. the notes C and D played simultaneously) would be considered dissonant if it occurred in a 2134:

The West's progressive embrace of increasingly dissonant intervals occurred almost entirely within the context of

1801:'s Missa Quadragesimalis contains a passage of contrapuntal treatment consisting of various dissonances such as a 6108: 4880: 4808: 4538: 3848:

Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity

3621: 2177: 2103:, for whom the second and Third Symphonies already contained 'unprecedented cacophonies', might have called it?" 614: 271:. By this definition, consonance is dependent not only on the width of the interval between two notes (i.e., the 52: 1789: 1734: 5785: 5197: 5111: 5078: 4923: 4434: 2070: 1979: 764:

Illustrating the roughness and beat oscillations that gradually reduce as the interval moves towards the unison

76: 5921: 4325:. Supported by a Northwest Academic Computing Consortium grant to J. Middleton, Eastern Washington University. 1123:. Boethius (6th century) characterizes consonance by its sweetness, dissonance by its harshness: "Consonance ( 1061:

that is independent of what precedes or follows them. In most Western music, however, dissonances are held to

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Controlling the sonance of pseudo-harmonic timbres played in pseudo-just tunings in real time is an aspect of

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considers consonance to arise from the alignment of partials with notes (as per the video at right; see also

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Kliewer, Vernon L. (1975). "Melody: Linear aspects of twentieth-century music". In Wittlich, Gary E. (ed.).

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While consonance and dissonance exist only between sounds and therefore necessarily describe intervals (or

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Perfect authentic cadence (V–I with roots in the bass and tonic in the highest voice of the final chord):

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An even more famous example from Mozart comes in a magical passage from the slow movement of his popular

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Animation of dynamic tonality's mapping of partials to notes in accordance with the syntonic temperament.

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Consonance may be explained as caused by a larger number of aligning harmonics (blue) between two notes.

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tritones—as a deponent sort of fourth or fifth—were sometimes stacked with perfect fourths and fifths,

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Zwicker, Eberhard; Flottorp, G.; Stevens, S. S. (1957). "Critical band-width in loudness summation".

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Patterson, Roy D. (1986). "Spiral detection of periodicity and the spiral form of musical scales".

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In human hearing, the varying effect of simple ratios may be perceived by one of these mechanisms:

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A stable tone combination is a consonance; consonances are points of arrival, rest, and resolution.

171: 20: 5250: 1527:, the perfect fourth above the bass was considered a dissonance needing immediate resolution. The 879:, the authentic cadence, dominant to tonic (D-T, V-I or V-I), is in part created by the dissonant 6027: 5810: 5596: 5591: 5280: 4953: 4933: 4673: 3464: 2198: 1700: 1678: 1556: 1479: 1475: 1463: 1091: 1066: 5815: 4001:. Translated by Carter, Roy E. Berkeley, CA / Los Angeles, CA: University of California Press. 2357:. In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the 1454:

were "harmonic consonances", meaning that they correctly reproduced the interval ratios of the

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For example, C–E–G consists of three consonances (C–E, E–G, C–G) and is ranked 1 while C–D

5941: 5789: 5750: 5625: 5564: 5167: 5043: 5023: 4993: 4893: 4524: 4504: 4489: 4464: 4446: 4424: 4285: 4228: 4191: 4143: 4021: 4002: 3994: 3980: 3972: 3958: 3939: 3725: 3706: 3631: 3617: 3605: 3550: 3524: 3498: 3481: 3432: 2273: 2146: 1750: 1524: 1447: 1432: 1057:

The application of consonance and dissonance "is sometimes regarded as a property of isolated

968: 948: 144:, the distinction may be objective. In modern times, it usually is based on the perception of 3874:

Consonance and Dissonance in Music Theory and Psychology: Disentangling dissonant dichotomies

6072: 5995: 5980: 5769: 5633: 5601: 5521: 5486: 5367: 5310: 5295: 5245: 5230: 4903: 4898: 4831: 4638: 4623: 4613: 4566: 4514: 4392: 4361: 4339: 4205: 4183: 4155: 3813: 3790: 2377: 2261: 2242: 2161: 2142: 2096: 1874:

opens with an adagio introduction that gave the work its nickname, the "Dissonance Quartet":

1605: 1601: 1467: 1058: 865: 857: 853: 602: 590: 333: 328: 298: 294: 288: 228: 204: 149: 141: 4322: 1982:, creating, in Scruton's words "the most atrocious dissonance that Beethoven ever wrote, a 1742: 6022: 6012: 6000: 5891: 5531: 5240: 5202: 5157: 5142: 5068: 5033: 5018: 4983: 4943: 4870: 4478:, from the Dutch by M. M. Kessler-Button. Symphonia Books. Stockholm: Continental Book Co. 4300:

Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance

3689: 2319: 2258: 2202: 2013: 2005: 1983: 1959: 1806: 1771: 1483: 1443: 1047: 883:

created by the seventh, also dissonant, in the dominant seventh chord, which precedes the

876: 783: 324: 164: 2381:

by aligning, more or less, the partials of said timbre with the notes of said tuning (or

1266:

Imperfect dissonance: major sixth (tone + fifth) and minor seventh (minor third + fifth).

606: 4388: 4357: 4267:

Terhardt, Ernst (1974). "On the Perception of Periodic Sound Fluctuations (Roughness)".

4020:. Eastman Studies in Music. Vol. 60. Rochester, NY: University of Rochester Press. 3408: 2030: 1386:

Strongly discordant: minor seconds, tritonus, and major sevenths, and often minor sixths

1098:

and even later, this remained the basis of the concept of consonance versus dissonance (

5990: 5569: 5544: 5491: 5452: 5290: 5265: 5106: 5038: 5028: 4968: 4888: 4720: 4658: 3666:. Vol. I. Translated by Mendel, Arthur. New York, NY: Associated Music Publishers. 3659: 3647: 2409: 2394: 2346: 2331: 2327: 2323: 2307: 2218: 1971: 1899: 1755: 1639:

Composers in the Baroque era were well aware of the expressive potential of dissonance:

1609: 1536: 972: 921: 819: 389: 327:

to embrace pseudo-harmonic timbres played in related pseudo-just tunings. As a result,

272: 208: 189: 168: 109: 45: 4461:

Introduction to the Theory of Heinrich Schenker: The Nature of the Musical Work of Art

4167: 3463:, vol. I, Ms Cambridge, Trinity College, R.15.22 (944), f. 13v. Electronic edition on 1944:

opens with a startling discord, consisting of a B flat inserted into a D minor chord:

6097: 6082: 5864: 5833: 5606: 5559: 5466: 5350: 5330: 5320: 5305: 5260: 5255: 5212: 5177: 5162: 5116: 5096: 4988: 4845: 4776: 4771: 4725: 4648: 4633: 4481: 4131: 4119: 3760:

Levelt, Willem, and Reiner Plomp (1964). "The Appreciation of Musical Intervals". In

3740: 2404: 2285: 2269: 2186:, presents a slightly different view from classical practice, one widely taken up in 2066: 2023: 1967: 1798: 1596: 1587: 1503: 1462:(blending) units characteristic of the musics of the time, where "resonance" forms a 1425: 1033: 884: 730: 586: 454: 440: 393: 280: 224: 200: 4036: 3626:. Translated by Ellis, Alexander J. (from 4th German ed.). New York, NY: Dover. 2272:. Russell extends by approximation the virtual merits of harmonic consonance to the 669:

Assuming the ear performs a frequency analysis on incoming signals, as indicated by

275:), but also on the combined spectral distribution and thus sound quality (i.e., the 259:

Perception of unity or tonal fusion between different tones and / or their partials.

132:

The opposition between consonance and dissonance can be made in different contexts:

6077: 6052: 6047: 6007: 5828: 5668: 5471: 5381: 5335: 5315: 5285: 5137: 5063: 5048: 4761: 4756: 4643: 4456: 4323:

SRA: A web-based research tool for spectral and roughness analysis of sound signals

4099: 4078: 4057: 3698: 2366: 2254: 2232: 2225: 2210: 1767: 1633: 1629: 1592: 1583: 1439:

in some sense equivalent to minor second) were yet unknown during the Middle Ages.

1421: 836: 473: 450: 436: 351: 220: 216: 167:

from the 1700s; however, the same interval may sound consonant in the context of a

157: 106: 69: 39: 4567:

index of Dissonance for any musical scales in LucyTuning and meantone-type tunings

1654: 687:, the fluctuation rate is equal to the frequency difference between the two sines 601:

Two notes played simultaneously but with slightly different frequencies produce a

3929:. Heidelberg Science Library. Vol. 16. London, UK: English University Press. 2167: 2124: 932: 756: 565: 541: 531: 483: 75: 51: 6067: 6032: 6017: 5916: 5911: 5901: 5496: 5476: 5340: 5270: 4735: 4730: 4715: 4710: 4663: 3404: 2311: 2300: 2296: 2100: 1987: 1802: 1451: 1436: 419: 415: 410: 406: 193: 63: 4309: 2209:

are truly non-dissonant. Thus the harmonic minor seventh, natural major ninth,

1727:("upon sin oppose resistance"), nearly every strong beat carries a dissonance: 1478:, and in practice usually treated as dissonances in the sense that they had to 1413: 227:

procedure. For example, in the key of C Major, if F is produced as part of the

5906: 5875: 5325: 5275: 5235: 5172: 4618: 4543: 4298: 3382: 2228: 2059: 2035: 1822: 1576: 773: 4282:

A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice

3860: 3847: 1466:

with the categories of consonance and dissonance. Conversely, the thirds and

991:

produced by such instruments may differ greatly from that of the rest of the

5896: 5850: 4571: 4463:, translated by John Rothgeb. New York: Longman; London: Collier-Macmillan. 4438: 3705:(sixth brief / student ed.). Boston, MA: McGraw-Hill Higher Education. 3523:, translated by Robert O. Gjerdigan. Princeton: Princeton University Press. 3444: 2235: 1934: 1511: 1459: 1095: 992: 976: 956: 952: 872: 538:

Dissonance is caused by the beating between close but non-aligned harmonics.

180: 161: 137: 101: 4561: 2197:

consideration of "harmonic consonance": that intervals when not subject to

1405: 4517:(1993). "Local Consonance and the Relationship between Timbre and Scale". 3816:; Plamondon, James (Spring 2008). "Tuning continua and keyboard layouts". 3640:

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

1335:

One example of imperfect consonances previously considered dissonances in

6037: 5964: 4653: 3916:

Renard Vallet, Emilio (2016). "Sonancia: una clarificación conceptual ".

3456: 2621: 2619: 2292: 2288: 2246: 2214: 1673: 1621: 1564: 1290: 999: 984: 980: 811: 807: 145: 4342:(May 1961). "Subdivision of the Audible Frequency into Critical Bands". 1506:) were not the sort of intervals upon which stable harmonies were based, 1141:) arriving to the ears. Dissonance is the harsh and unhappy percussion ( 5975: 5870: 5820: 5147: 4918: 4766: 4628: 3776:(1926). "Balladen, rondeaux und virelais". In Ludwig, Friedrich (ed.). 3602:

The Jazz Language: A Theory Text for Jazz Composition and Improvisation

3575:, 3 vols. : Typis San-Blasianis. Reprinted, Hildesheim: G. Olms, 1963. 2315: 2221: 1628:" by some 20th-century composers. Early-20th-century American composer 1613: 1568: 1560: 880: 610: 445: 4396: 4365: 3062:, p. 13, Ballade 14, "Je ne cuit pas qu'onques a creature", mm. 27–31. 2022:, Op. 39, climaxes on a striking dissonance in the fourteenth bar. As 995:, and the consonance or dissonance of the harmonic intervals as well. 802:

Dissonance is more generally defined by the amount of beating between

5838: 5554: 5481: 5086: 4740: 4705: 4227:. London: Rockliff. Reprinted Westport, Conn.: Hyperion Press, 1979. 2342: 2138: 2107: 1720: 1682:, where the agony of Christ's betrayal and crucifixion is portrayed, 1429: 960: 815: 384: 380: 319:

Dynamic Tonality explicitly generalizes the relationship between the

276: 212: 3431:, Vol. I., seventh edition. New York: McGraw-Hill Higher Education. 750:

Two pitches moving from the interval of a Minor 2nd to a unison

4800: 2967: 2965: 2963: 585:

One component of dissonance—the uncertainty or confusion as to the

5855: 5843: 5421: 4998: 4244:, vol. II. Leipzig: S. Hirzel. Reprinted Hilversum: F. Knuf, 1965. 3564:

Music in the Castle of Heaven: A portrait of Johann Sebastian Bach

2281: 2156: 2112: 2087: 2075: 2049: 2029: 2004: 1992: 1958: 1946: 1923: 1911: 1888: 1876: 1861: 1849: 1835: 1788: 1776: 1741: 1729: 1707: 1689: 1672:

Bach uses dissonance to communicate religious ideas in his sacred

1653: 1641: 1397: 1353: 1341: 1050:

and a passage of gradually accumulating tension leading up to it.

964: 920: 906: 895: 889: 468: 302: 185: 116:

has been proposed to encompass or refer indistinctly to the terms

97: 3957:. Vol. 1 (4th ed.). Brookline, MA: Concept Publishing. 2365:

For context: unstated in these theories is that musicians of the

1383:

Relatively tense: major seconds, minor sevenths, and major sixths

782:

Frequency ratios: When harmonic timbres are played in one of the

5860: 2277: 2187: 5937: 5425: 4804: 4575: 4423:

second edition. Deutsch, Diana, ed. San Diego: Academic Press.

4303:. Doctoral dissertation. University of California, Los Angeles. 4018:

Analyzing Atonal Music: Pitch-class set theory and its contexts

3955:

George Russell's Lydian Chromatic Concept of Tonal Organization

2295:), that accidental being the sole pitch difference between the 4136:

The Ring of Truth: The wisdom of Wagner's Ring of the Nibelung

1069:

is tacitly considered integral to consonance and dissonance".

828: 710:

and the following statements represent the general consensus:

4419:

Burns, Edward M. (1999). "Intervals, Scales, and Tuning", in

3766:

Proceedings of the Fifth International Congress of Aesthetics

3472:

Butler, David, and Burdette Green (2002). "From Acoustics to

2201:(at least not by contraction) and correctly reproducing the 738: 5933: 1920:

Mozart, from Piano Concerto No. 21, 2nd movement bars 12–17

605:"wah-wah-wah" sound. This phenomenon is used to create the 3308: 2887: 2625: 2341:, extends the same idea of harmonic consonance and intact 1866:

Dissonance in Mozart's Adagio and Fugue in C minor, K. 546

1858:

Dissonance in Mozart's Adagio and Fugue in C minor, K. 546

4474:

Kempers, Karel Philippus Bernet, and M. G. Bakker. 1949.

3975:(1975) . "Opinion or insight?". In Stein, Leonard (ed.). 3724:. Englewood Cliffs, NJ: Prentice-Hall. pp. 270–321. 3654:(in German). Vol. 1–3. Mainz, DE: B. Schott's Söhne. 1135:) of a high sound with a low one, sweetly and uniformly ( 223:

in particular that needs "resolution" through a specific

4551:

by David Huron at Ohio State University School of Music

2898: 2896: 3936:

The Physics and Psychophysics of Music: An introduction

3784:] (in German). Vol. I. Leipzig, DE: Breitkopf. 3549:, third edition. New York: Holt, Rinehart and Winston, 2925: 2923: 2636: 2634: 4445:. Cambridge and New York: Cambridge University Press. 3977:

Style and Idea: Selected writings of Arnold Schoenberg

3927:

Introduction to the Physics and Psychophysics of Music

3413:. Oxford, UK: Clarendon Press – via archive.org. 3293: 3278: 2712: 2610: 2598: 1559:

to a consonance. There was also a distinction between

1496:

minor sevenths and major ninths were fully structural,

640:

are perceived as loudness fluctuations referred to as

3762:

Actes du cinquième Congrès international d'esthétique

1840:

Benedictus from Michael Haydn's Missa Quadragesimalis

1567:

dissonance. Dissonant melodic intervals included the

665:

depending on the frequency of the interfering tones).

174:

from the early 1900s or an atonal contemporary piece.

4321:

Vassilakis, Panteleimon Nestor, and K. Fitz (2007).

3846:

Pankovski, Toso, and Eva Pankovska (October 2017). "

3422:. New Haven, CT / London, UK: Yale University Press. 2839: 1974:'s description of this chord as introducing "a huge 16:

Categorizations of simultaneous or successive sounds

5884: 5801: 5764: 5717: 5624: 5615: 5530: 5459: 5359: 5221: 5125: 5077: 4879: 4838: 4749: 4698: 4310:"Auditory Roughness as Means of Musical Expression" 2791: 2451: 1650:

Bach Preludio XXI from Well-tempered Clavier, Vol 1

1390:"Perfect" and "imperfect" and the notion of being ( 4443:Chopin: Pianist and Teacher: As Seen by His Pupils 3739:Lahdelma, Imre, and Tuomas Eerola (26 May 2020). " 2241:Most of these pitches exist only in a universe of 1928:Mozart Piano Concerto 21, 2nd movement bars 12–17. 1579:intervals. Dissonant harmonic intervals included: 1012:Variable upon individual instrument: major seventh 943:Instruments producing non-harmonic overtone series 96:are categorizations of simultaneous or successive 3768:, edited by Jan Aler, 901–904. The Hague: Mouton. 3047: 2971: 2914: 1065:onto following consonances, and the principle of 207:, which are often viewed as consonant (e.g., the 4503:. Oxford and New York: Oxford University Press. 4284:. Oxford and New York: Oxford University Press. 3859:Pankovski, Toso, and Ana Pankovska (May 2022). " 3795:"Invariant fingerings across a tuning continuum" 2700: 2535: 2092:Mahler Symphony 10, opening Adagio, bars 201–213 1986:D-minor triad containing all the notes of the D 1489:The salient differences from modern conception: 971:, where the vibrating medium is a light, supple 4334:. London and New York: Oxford University Press. 4262:. New York: Excelsior Music Publishing Company. 3911:. London, UK: British Broadcasting Corporation. 2009:Beethoven, Symphony No. 9, finale, bars 208-210 1820: 1026: 357: 344: 267:With consonance being a greater coincidence of 2183:Lydian Chromatic Concept of Tonal Organization 1963:Beethoven Symphony No. 9, finale, opening bars 5949: 5437: 4816: 4587: 4544:Octave Frequency Sweep, Consonance/Dissonance 3852:Biologically Assisted Cognitive Architectures 3755:. London, UK: Universal Edition and Rockliff. 3495:The Cambridge History of Western Music Theory 3478:The Cambridge History of Western Music Theory 1955:Beethoven Symphony No. 9, finale opening bars 8: 5512:List of intervals in 5-limit just intonation 4520:Journal of the Acoustical Society of America 4376:Journal of the Acoustical Society of America 4345:Journal of the Acoustical Society of America 3872:Parncutt, Richard, and Graham Hair (2011). " 3583:Journal of the Acoustical Society of America 3493:Christensen, Thomas (2002). "Introduction". 3356: 1620:Early in history, only intervals low in the 1090:. This terminology probably referred to the 3938:(3rd ed.). New York: Springer-Verlag. 2995: 2511: 2001:Beethoven Symphony No. 9, finale bars 208ff 1712:Closing bars of the final chorus of Bach's 1636:as the use of higher and higher overtones. 1391: 1380:Relatively blending: minor and major thirds 1322: 1301: 1274: 1252: 1229: 1207: 1182: 1176: 1175:) is the measured and concordant blending ( 1170: 1148: 1142: 1136: 1130: 1124: 1110: 866:Dynamic tonality § Example: C2ShiningC 5956: 5942: 5934: 5621: 5444: 5430: 5422: 4823: 4809: 4801: 4594: 4580: 4572: 4486:The Style of Palestrina and the Dissonance 4260:A History of "Consonance" and "Dissonance" 3878:Journal of Interdisciplinary Music Studies 3521:Studies in the Origin of Harmonic Tonality 3427:Benward, Bruce, and Marilyn Saker (2003). 3167: 3143: 2803: 2779: 2767: 2755: 2688: 2676: 2664: 2550: 2463: 2084:Mahler Symphony No. 10 Adagio bars 201–213 4562:The Keyboard Tuning of Domenico Scarlatti 4555:Bibliography of Consonance and Dissonance 4100:"Pythagorean tuning and Gothic polyphony" 3497:. Cambridge: Cambridge University Press. 3203: 3179: 3107: 3095: 3083: 3071: 2475: 2310:scale representing the provenance of the 2164:constructed from notes of the Lydian mode 1793:Haydn Symphony 82 1st movement bars 51–64 1785:Haydn Symphony 82 1st movement bars 51–63 1396:) must be taken in their contemporaneous 1289:Median dissonance: tone and minor sixth ( 1109:In the early Middle Ages, the Latin term 4549:Consonance and Dissonance—Index to Notes 3368: 3263: 3155: 3119: 3019: 2902: 2875: 2863: 2851: 2827: 2743: 2652: 2586: 2574: 2562: 2149:described as the "crisis of tonality".( 2016:'s song "Auf einer Burg" from his cycle 1676:and Passion settings. At the end of the 1199:Perfect consonance: unisons and octaves. 5059:Temporal dynamics of music and language 4308:Vassilakis, Panteleimon Nestor (2005). 4297:Vassilakis, Panteleimon Nestor (2001). 3902:. Toronto: University of Toronto Press. 3829:"Theories of Consonance and Dissonance" 3332: 3251: 3227: 3131: 3059: 3031: 2954: 2929: 2724: 2444: 2421: 1893:Mozart Dissonance Quartet opening bars. 894:Tritone resolution inwards and outwards 496:–B consists of one mild dissonance (B–D 4190:(2nd ed.). London, UK: Springer. 3693:, text on CHTML at Indiana University. 3344: 3191: 3007: 2983: 2815: 2640: 2523: 2487: 2429: 2153:Neo-classic harmonic consonance theory 1885:Mozart Dissonance Quartet opening bars 1372:Optimally blending: fourths and fifths 1221:Median consonance: fourths and fifths. 771: 293:Like "coincidence of partials" above, 4332:The Cantatas of Johann Sebastian Bach 3547:Tonal Harmony in Concept and Practice 3320: 2942: 2499: 2330:) as the source from which to derive 1184:in unam simul modulationem conveniant 7: 4104:Medieval Music & Arts Foundation 4083:Medieval Music & Arts Foundation 4062:Medieval Music & Arts Foundation 4041:Medieval Music & Arts Foundation 3294:Milne, Sethares & Plamondon 2008 3279:Milne, Sethares & Plamondon 2007 3239: 3215: 3035: 2713:Zwicker, Flottorp & Stevens 1957 2611:Milne, Sethares & Plamondon 2008 2599:Milne, Sethares & Plamondon 2007 2238:note must necessarily be consonant. 2194: 2054:Wagner, Hagen's Watch from act 1 of 1369:Purely blending: unisons and octaves 251:integer tunings, only approximation. 179:particularly in the case of Western 4314:Selected Reports in Ethnomusicology 4251:The Oxford History of Western Music 3900:Pythagoras and Early Pythagoreanism 3841:: 315–316 – via Google books. 3514:. New York: Something Else Press. . 1555:for all dissonances, followed by a 1009:Dissonant: major third, major sixth 4414:The Harmonicon: A Journal of Music 3827:Myers, Charles S. (25 June 1904). 3793:; Plamondon, James (Winter 2007). 3722:Aspects of Twentieth-Century Music 3595:. Culver IN: Culver Academy Press. 3407:(1902). Macran, H. Stewart (ed.). 1350:Machaut "Je ne cuit pas qu'onques" 1002:'s harmony profile is summarized: 14: 5004:Music in psychological operations 3834:The British Journal of Psychology 3636:Die Lehre von den Tonempfindungen 2291:note (approximating the harmonic 1898:together as a discord. (See also 5587:Ptolemy's intense diatonic scale 4949:Generative theory of tonal music 4689: 4164:Experimental Musical Instruments 3819:Journal of Mathematics and Music 3664:The Craft of Musical Composition 3420:Hucbald, Guido and John on Music 3387:Experimental Musical Instruments 2355:The Craft of Musical Composition 2165: 2122: 1147:) of two sounds mixed together ( 1144:aspera atque iniocunda percussio 930: 772:Problems playing this file? See 754: 578: 563: 554: 539: 529: 521: 502:) and two sharp dissonances (C–D 481: 73: 62: 49: 38: 4959:Hedonic music consumption model 4856:Cognitive neuroscience of music 4188:Tuning, Timbre, Spectrum, Scale 3671:Hucbald of Saint-Amand (n.d.). 2888:Pankovski and Pankovska E. 2017 1719:In the opening aria of Cantata 1339:'s "Je ne cuit pas qu'onques": 1178:rata et concordabilis permixtio 998:According to John Gouwens, the 663:75–150 fluctuations per second, 25:North/South Consonance Ensemble 4037:"Thirteenth-century polyphony" 3753:The Symphonies of Joseph Haydn 2318:) replaces or supplements the 2280:and the 12-note octave of the 1626:emancipation of the dissonance 1: 5396:Psychology of Music (journal) 4939:Eye movement in music reading 3751:Landon, H.C. Robbins (1955). 3690:De musica mensurabili positio 3562:Gardiner, John Eliot (2013). 3429:Music: In Theory and Practice 3034:, p. 107; translated in 2284:, granting consonance to the 2257:(minor) seventh note for the 2121:, "Sacrificial Dance" excerpt 1811:half-diminished seventh chord 1510:"dissonant" 5:3, 6:3, or 6:4 1362:According to Margo Schulter: 1154: 1073:Antiquity and the middle ages 235:Acoustics and psychoacoustics 5550:Harry Partch's 43-tone scale 4964:Illusory continuity of tones 4160:"Relating tuning and timbre" 4138:. Allen Lane: Penguin Books. 3383:"Relating Tuning and Timbre" 1502:thirds and sixths (and tall 1424:in some sense equivalent to 632:Slow amplitude fluctuations 508:, C–B) and is ranked 6. 460:Perspectives in Music Theory 5410:This Is Your Brain on Music 5389:Music, Thought, and Feeling 5375:Musicae Scientiae (journal) 3865:Nature - Scientific Reports 3538:A Guide to Musical Analysis 2193:In effect, he returns to a 1106:) in Western music theory. 1023:In history of Western music 814:when occurring in harmonic 29:Dissonance (disambiguation) 6127: 5517:List of meantone intervals 5183:Neuronal encoding of sound 5153:Melodic intonation therapy 4861:Culture in music cognition 4441:, and Naomi Shohet. 1988. 4280:Tymoczko, Dimitri (2011). 4249:Taruskin, Richard (2005). 4079:"Multi-voice combinations" 4016:Schuijer, Michiel (2008). 3934:Roederer, Juan G. (1995). 3925:Roederer, Juan G. (1973). 3907:Radcliffe, Philip (1978). 3593:Composing for the Carillon 1942:Beethoven's Symphony No. 9 1766:, the opening movement of 1529:regola delle terze e seste 799:multiple of the pure tone. 18: 6104:Consonance and dissonance 5986:Consonance and dissonance 5971: 5507:List of musical intervals 5502:Consonance and dissonance 4909:Consonance and dissonance 4790:List of musical intervals 4785: 4687: 4609: 4603:Consonance and dissonance 4435:Eigeldinger, Jean-Jacques 4098:Schulter, Margo (1997d). 4077:Schulter, Margo (1997c). 4056:Schulter, Margo (1997b). 4035:Schulter, Margo (1997a). 3898:Philip, James A. (1966). 3623:On the Sensations of Tone 3566:. London, UK: Allen Lane. 2840:Gerson and Goldstein 1978 2034:Schumann Auf einer Burg. 1746:Bach BWV 54, opening bars 1725:Widerstehe doch der Sünde 1551:, musical style required 1358:Xs mark thirds and sixths 947:Musical instruments like 427:Dissonances may include: 370:Consonances may include: 5198:Psychoanalysis and music 5178:Neurologic music therapy 5112:Music-specific disorders 4924:Embodied music cognition 4914:Deutsch's scale illusion 4330:Whittaker, W.G. (1959). 4126:. London, UK: Continuum. 3953:Russell, George (2008). 3880:5, no. 2 (Fall): 119–66. 3571:Gerbert, Martin (1784). 2792:Vassilakis and Fitz 2007 2452:Lahdelma and Eerola 2020 2337:Dan Haerle, in his 1980 2332:extended tertian harmony 2326:(with minor seventh and 2314:(with major seventh and 2306:(In another sense, that 1980:diminished seventh chord 1872:Quartet in C major, K465 1738:Bach BWV 54 opening bars 1450:, the minor seventh and 476:'s classification, from 6043:Otonality and utonality 5054:Speech-to-song illusion 4866:Evolutionary musicology 4525:A non-technical version 4421:The Psychology of Music 3652:Unterweisung im Tonsatz 3536:Cook, Nicholas (1987). 3519:Dahlhaus, Carl (1990). 3381:Sethares, W.A. (1993). 1668:, vol. I (Preludio XXI) 1660:sharply dissonant chord 1486:and stable sonorities. 1138:suauiter uniformiterque 478:Studies in Counterpoint 264:Coincidence of partials 5403:The World in Six Songs 5346:William Forde Thompson 5102:Musical hallucinations 4499:Rice, Timothy (2004). 4258:Tenney, James (1988). 4211:Computer Music Journal 3909:Mozart Piano Concertos 3800:Computer Music Journal 3703:Music: An appreciation 3591:Gouwens, John (2009). 3545:Forte, Allen. (1979). 3510:Cowell, Henry (1969). 3461:De institutione musica 2972:Parncutt and Hair 2011 2915:Benward and Saker 2003 2400:Dissonant counterpoint 2345:displacement to alter 2251:we already freely take 2174: 2131: 2093: 2085: 2062: 2038: 2010: 2002: 1964: 1956: 1929: 1921: 1894: 1886: 1867: 1859: 1841: 1833: 1805:without its fifth, an 1794: 1786: 1747: 1739: 1716: 1705: 1669: 1651: 1549:common practice period 1543:Common practice period 1418:inversion of intervals 1392: 1359: 1351: 1323: 1302: 1275: 1253: 1230: 1208: 1183: 1177: 1171: 1149: 1143: 1137: 1131: 1125: 1111: 1039: 939: 918: 916: 904: 743: 509: 368: 356: 317: 48:, a consonant interval 5774:Temperament ordinaire 5208:Systematic musicology 4240:Stumpf, Carl (1890). 4225:Orpheus in New Guises 3774:Machaut, Guillaume de 3685:Johannes de Garlandia 3512:New Musical Resources 3418:Babb, Warren (1978). 3048:Johannes de Garlandia 2701:Levelt and Plomp 1964 2536:Butler and Green 2002 2353:gradation table from 2160: 2116: 2091: 2083: 2053: 2033: 2008: 2000: 1962: 1954: 1927: 1919: 1892: 1884: 1865: 1857: 1839: 1792: 1784: 1745: 1737: 1711: 1697: 1665:Well-Tempered Clavier 1657: 1649: 1442:Due to the different 1357: 1349: 1193:Johannes de Garlandia 924: 914: 902: 893: 742: 472: 458:Cooper, Paul (1973). 401:Imperfect consonances 315: 6063:Schenkerian analysis 6058:Progressive tonality 5577:List of compositions 5014:Music-related memory 4851:Cognitive musicology 4515:Sethares, William A. 4223:Stein, Erwin. 1953. 4150:. London, UK: Black. 4058:"Pythagorean tuning" 3814:Sethares, William A. 3791:Sethares, William A. 3600:Haerle, Dan (1980). 3309:Sethares et al. 2009 2626:Sethares et al. 2009 1988:minor harmonic scale 1797:The Benedictus from 1764:H. C. Robbins Landon 1337:Guillaume de Machaut 279:) of the notes (see 19:For other uses, see 5301:Max Friedrich Meyer 5193:Philosophy of music 5188:Performance science 5133:Aesthetics of music 5107:Musician's dystonia 5092:Auditory arrhythmia 4979:Melodic expectation 4539:Atlas of Consonance 4389:1957ASAJ...29..548Z 4358:1961ASAJ...33..248Z 4124:Understanding Music 3887:Psychology of Music 3540:. London, UK: Dent. 3451:. London, UK: Dent. 3146:, pp. 258–264. 2998:, pp. 188–206. 2986:, pp. 123–124. 2854:, pp. 145–149. 2806:, pp. 121–123. 2526:, pp. 127–219. 2249:; notice also that 2203:mathematical ratios 1815:minor seventh chord 1684:John Eliot Gardiner 1464:complementary trine 1150:sibimet permixtorum 1129:) is the blending ( 1077:In Ancient Greece, 653:75–150 per second). 513:Physiological basis 375:Perfect consonances 21:Literary consonance 6001:Secondary function 5811:Chinese musicology 5597:Scale of harmonics 5592:Pythagorean tuning 5540:Euler–Fokker genus 5360:Books and journals 5281:Carol L. Krumhansl 4999:Music and movement 4954:Glissando illusion 4934:Exercise and music 4158:(September 1992). 3995:Schoenberg, Arnold 3973:Schoenberg, Arnold 3778:Musikalische Werke 3744:Scientific Reports 2432:, pp. 111–139 2199:octave equivalence 2175: 2132: 2119:The Rite of Spring 2117:Igor Stravinsky's 2094: 2086: 2063: 2039: 2011: 2003: 1965: 1957: 1930: 1922: 1895: 1887: 1868: 1860: 1842: 1795: 1787: 1748: 1740: 1717: 1714:St Matthew Passion 1706: 1701:St Matthew Passion 1679:St Matthew Passion 1670: 1652: 1533:Optima introductio 1360: 1352: 1115:translated either 1092:Pythagorean tuning 1016:Interval inversion 940: 927:ii–V–I progression 919: 917: 905: 856:. For example, in 837:two-tone intervals 744: 671:Ohm's acoustic law 510: 318: 6091: 6090: 5996:Diatonic function 5931: 5930: 5797: 5796: 5419: 5418: 5168:Musical acoustics 5044:Sharawadji effect 5024:Musical semantics 4994:Music and emotion 4894:Auditory illusion 4798: 4797: 4501:Music in Bulgaria 4397:10.1121/1.1908963 4366:10.1121/1.1908630 4340:Zwicker, Eberhard 4290:978-0-19-533667-2 4233:978-0-88355-765-5 4027:978-1-58046-270-9 4008:978-0-520-04945-1 3999:Theory of Harmony 3712:978-0-07-340134-8 3632:Helmholtz, H.L.F. 3618:Helmholtz, H.L.F. 3457:Boethius, Anicius 3437:978-0-07-294262-0 3357:Hindemith 1937–70 3010:, pp. 11–12. 2339:The Jazz Language 2276:tuning system of 2171: 2147:Arnold Schoenberg 2128: 2081: 1998: 1976:Schreckensfanfare 1952: 1917: 1882: 1855: 1782: 1751:Albert Schweitzer 1735: 1695: 1647: 1525:Renaissance music 1482:to form complete 1347: 989:inharmonic series 936: 912: 900: 759: 623:wave interference 569: 545: 535: 487: 313: 205:perfect intervals 150:harmonic partials 79: 55: 6116: 6109:Music psychology 6073:Tonality diamond 5981:Circle of fifths 5958: 5951: 5944: 5935: 5770:Well temperament 5756:Regular diatonic 5622: 5602:Tonality diamond 5446: 5439: 5432: 5423: 5368:Music Perception 5311:Richard Parncutt 5296:Leonard B. Meyer 5246:Jane W. Davidson 5231:Jamshed Bharucha 5009:Music preference 4904:Background music 4899:Auditory imagery 4832:Music psychology 4825: 4818: 4811: 4802: 4693: 4692: 4596: 4589: 4582: 4573: 4523:, 94(1): 1218. ( 4412:Anon. (1826). . 4400: 4369: 4335: 4326: 4317: 4304: 4293: 4276: 4263: 4254: 4245: 4236: 4219: 4201: 4179: 4177: 4175: 4166:. Archived from 4151: 4139: 4127: 4115: 4113: 4111: 4106:. Todd M. McComb 4094: 4092: 4090: 4085:. Todd M. McComb 4073: 4071: 4069: 4064:. Todd M. McComb 4052: 4050: 4048: 4043:. Todd M. McComb 4031: 4012: 3990: 3968: 3949: 3930: 3921: 3912: 3903: 3894: 3881: 3868: 3855: 3854:22 : 82–94. 3842: 3823: 3808: 3785: 3769: 3756: 3747: 3735: 3716: 3694: 3687:(13th century). 3680: 3667: 3655: 3643: 3627: 3613: 3604:. : Studio 224. 3596: 3587: 3576: 3567: 3558: 3541: 3532: 3515: 3506: 3489: 3468: 3452: 3440: 3423: 3414: 3391: 3390: 3378: 3372: 3366: 3360: 3354: 3348: 3342: 3336: 3330: 3324: 3318: 3312: 3306: 3297: 3291: 3282: 3276: 3267: 3261: 3255: 3249: 3243: 3237: 3231: 3225: 3219: 3213: 3207: 3201: 3195: 3189: 3183: 3177: 3171: 3165: 3159: 3153: 3147: 3141: 3135: 3129: 3123: 3117: 3111: 3105: 3099: 3093: 3087: 3081: 3075: 3069: 3063: 3057: 3051: 3045: 3039: 3029: 3023: 3017: 3011: 3005: 2999: 2996:Aristoxenus 1902 2993: 2987: 2981: 2975: 2969: 2958: 2952: 2946: 2939: 2933: 2927: 2918: 2912: 2906: 2900: 2891: 2885: 2879: 2873: 2867: 2861: 2855: 2849: 2843: 2837: 2831: 2825: 2819: 2813: 2807: 2801: 2795: 2789: 2783: 2777: 2771: 2765: 2759: 2753: 2747: 2741: 2728: 2722: 2716: 2710: 2704: 2698: 2692: 2686: 2680: 2674: 2668: 2662: 2656: 2650: 2644: 2638: 2629: 2623: 2614: 2608: 2602: 2596: 2590: 2584: 2578: 2572: 2566: 2560: 2554: 2548: 2539: 2533: 2527: 2521: 2515: 2512:Christensen 2002 2509: 2503: 2497: 2491: 2485: 2479: 2473: 2467: 2461: 2455: 2449: 2433: 2426: 2378:Dynamic tonality 2320:Mixolydian scale 2173: 2172: 2162:Thirteenth chord 2143:dynamic tonality 2130: 2129: 2097:Richard Taruskin 2082: 1999: 1953: 1918: 1907:"Elvira Madigan" 1883: 1856: 1825: 1783: 1736: 1696: 1648: 1606:diminished fifth 1602:Augmented fourth 1484:perfect cadences 1395: 1348: 1326: 1305: 1278: 1256: 1234: 1211: 1186: 1180: 1174: 1164: 1163: 1162: 1156: 1152: 1146: 1140: 1134: 1128: 1114: 1037: 938: 937: 913: 901: 858:William Sethares 854:dynamic tonality 784:just intonations 761: 760: 741: 709: 707: 701: 694: 691: 683: 676: 664: 662: 654: 650: 639: 637: 591:harmonic entropy 582: 571: 570: 558: 547: 546: 537: 536: 525: 507: 506: 501: 500: 495: 494: 489: 488: 463: 366: 354: 329:dynamic tonality 314: 295:dynamic tonality 289:Dynamic tonality 243:Numerical ratios 229:dominant seventh 142:psychophysiology 81: 80: 66: 57: 56: 42: 6126: 6125: 6119: 6118: 6117: 6115: 6114: 6113: 6094: 6093: 6092: 6087: 6023:Major and minor 6013:Just intonation 5967: 5962: 5932: 5927: 5924:(Bohlen–Pierce) 5892:833 cents scale 5880: 5803: 5793: 5760: 5713: 5611: 5532:Just intonation 5526: 5455: 5453:Musical tunings 5450: 5420: 5415: 5355: 5241:Robert Cutietta 5217: 5203:Sociomusicology 5158:Music education 5143:Ethnomusicology 5121: 5073: 5069:Tritone paradox 5034:Octave illusion 5019:Musical gesture 4984:Melodic fission 4974:Lipps–Meyer law 4944:Franssen effect 4875: 4871:Psychoacoustics 4834: 4829: 4799: 4794: 4781: 4745: 4694: 4690: 4685: 4605: 4600: 4535: 4530: 4527:of the article) 4408: 4406:Further reading 4403: 4372: 4338: 4329: 4320: 4307: 4296: 4279: 4266: 4257: 4248: 4239: 4222: 4204: 4198: 4182: 4173: 4171: 4170:on 10 June 2010 4154: 4142: 4130: 4118: 4109: 4107: 4097: 4088: 4086: 4076: 4067: 4065: 4055: 4046: 4044: 4034: 4028: 4015: 4009: 3993: 3987: 3971: 3965: 3952: 3946: 3933: 3924: 3915: 3906: 3897: 3884: 3871: 3858: 3845: 3826: 3812:Milne, Andrew; 3811: 3789:Milne, Andrew; 3788: 3772: 3759: 3750: 3738: 3732: 3719: 3713: 3697: 3683: 3679:I, pp. 103–122. 3670: 3660:Hindemith, Paul 3658: 3648:Hindemith, Paul 3646: 3630: 3616: 3599: 3590: 3579: 3570: 3561: 3544: 3535: 3518: 3509: 3492: 3471: 3455: 3443: 3426: 3417: 3403: 3399: 3394: 3380: 3379: 3375: 3367: 3363: 3355: 3351: 3343: 3339: 3331: 3327: 3319: 3315: 3307: 3300: 3292: 3285: 3277: 3270: 3262: 3258: 3250: 3246: 3238: 3234: 3226: 3222: 3214: 3210: 3202: 3198: 3190: 3186: 3178: 3174: 3168:Schweitzer 1905 3166: 3162: 3154: 3150: 3144:Schoenberg 1975 3142: 3138: 3130: 3126: 3118: 3114: 3106: 3102: 3094: 3090: 3082: 3078: 3070: 3066: 3058: 3054: 3046: 3042: 3030: 3026: 3018: 3014: 3006: 3002: 2994: 2990: 2982: 2978: 2970: 2961: 2953: 2949: 2940: 2936: 2928: 2921: 2913: 2909: 2901: 2894: 2886: 2882: 2874: 2870: 2862: 2858: 2850: 2846: 2838: 2834: 2826: 2822: 2814: 2810: 2804:Vassilakis 2005 2802: 2798: 2790: 2786: 2780:Vassilakis 2005 2778: 2774: 2768:Vassilakis 2001 2766: 2762: 2756:Vassilakis 2001 2754: 2750: 2742: 2731: 2723: 2719: 2711: 2707: 2699: 2695: 2689:Helmholtz 1954b 2687: 2683: 2677:Vassilakis 2005 2675: 2671: 2665:Vassilakis 2005 2663: 2659: 2651: 2647: 2639: 2632: 2624: 2617: 2609: 2605: 2597: 2593: 2585: 2581: 2573: 2569: 2561: 2557: 2551:Helmholtz 1954a 2549: 2542: 2534: 2530: 2522: 2518: 2514:, pp. 7–8. 2510: 2506: 2498: 2494: 2486: 2482: 2474: 2470: 2464:Schoenberg 1978 2462: 2458: 2450: 2446: 2442: 2437: 2436: 2427: 2423: 2418: 2391: 2375: 2362:perfect fifth. 2266:harmonic series 2245:smaller than a 2213:(quarter tone) 2207:harmonic series 2166: 2155: 2123: 2076: 2056:Götterdämmerung 2044:Götterdämmerung 2014:Robert Schumann 1993: 1984:first inversion 1947: 1912: 1877: 1850: 1834: 1823: 1807:augmented triad 1777: 1772:Symphony No. 82 1730: 1690: 1642: 1622:overtone series 1545: 1521: 1456:harmonic series 1342: 1165:), who writes: 1160: 1159: 1157: 1075: 1038: 1032: 1025: 1018:does not apply. 945: 931: 907: 896: 779: 778: 770: 768: 767: 766: 765: 762: 755: 752: 745: 739: 705: 704: 699: 697: 692: 689: 688: 686: 681: 679: 674: 660: 658: 652: 648: 635: 633: 599: 598: 597: 596: 595: 594:same for both). 583: 574: 573: 572: 564: 559: 550: 549: 548: 540: 530: 526: 515: 504: 503: 498: 497: 492: 491: 482: 457: 390:perfect fourths 367: 364: 355: 350: 343: 325:just intonation 321:harmonic series 303: 299:dynamic timbres 237: 203:), such as the 130: 86: 85: 84: 83: 82: 74: 67: 59: 58: 50: 43: 32: 17: 12: 11: 5: 6124: 6123: 6120: 6112: 6111: 6106: 6096: 6095: 6089: 6088: 6086: 6085: 6080: 6075: 6070: 6065: 6060: 6055: 6050: 6045: 6040: 6035: 6030: 6025: 6020: 6015: 6010: 6005: 6004: 6003: 5993: 5991:Diatonic scale 5988: 5983: 5978: 5972: 5969: 5968: 5963: 5961: 5960: 5953: 5946: 5938: 5929: 5928: 5926: 5925: 5919: 5914: 5909: 5904: 5899: 5894: 5888: 5886: 5882: 5881: 5879: 5878: 5873: 5868: 5858: 5853: 5848: 5847: 5846: 5841: 5836: 5831: 5823: 5818: 5813: 5807: 5805: 5799: 5798: 5795: 5794: 5768: 5766: 5762: 5761: 5759: 5758: 5753: 5748: 5743: 5738: 5723: 5721: 5715: 5714: 5712: 5711: 5706: 5701: 5696: 5691: 5686: 5681: 5676: 5666: 5661: 5656: 5651: 5646: 5641: 5636: 5630: 5628: 5619: 5613: 5612: 5610: 5609: 5604: 5599: 5594: 5589: 5584: 5579: 5574: 5573: 5572: 5567: 5557: 5552: 5547: 5545:Harmonic scale 5542: 5536: 5534: 5528: 5527: 5525: 5524: 5519: 5514: 5509: 5504: 5499: 5494: 5492:Interval ratio 5489: 5484: 5479: 5474: 5469: 5463: 5461: 5457: 5456: 5451: 5449: 5448: 5441: 5434: 5426: 5417: 5416: 5414: 5413: 5406: 5399: 5392: 5385: 5378: 5371: 5363: 5361: 5357: 5356: 5354: 5353: 5348: 5343: 5338: 5333: 5328: 5323: 5318: 5313: 5308: 5303: 5298: 5293: 5291:Daniel Levitin 5288: 5283: 5278: 5273: 5268: 5266:Henkjan Honing 5263: 5258: 5253: 5248: 5243: 5238: 5233: 5227: 5225: 5219: 5218: 5216: 5215: 5210: 5205: 5200: 5195: 5190: 5185: 5180: 5175: 5170: 5165: 5160: 5155: 5150: 5145: 5140: 5135: 5129: 5127: 5126:Related fields 5123: 5122: 5120: 5119: 5114: 5109: 5104: 5099: 5094: 5089: 5083: 5081: 5075: 5074: 5072: 5071: 5066: 5061: 5056: 5051: 5046: 5041: 5039:Relative pitch 5036: 5031: 5029:Musical syntax 5026: 5021: 5016: 5011: 5006: 5001: 4996: 4991: 4986: 4981: 4976: 4971: 4969:Levitin effect 4966: 4961: 4956: 4951: 4946: 4941: 4936: 4931: 4926: 4921: 4916: 4911: 4906: 4901: 4896: 4891: 4889:Absolute pitch 4885: 4883: 4877: 4876: 4874: 4873: 4868: 4863: 4858: 4853: 4848: 4842: 4840: 4836: 4835: 4830: 4828: 4827: 4820: 4813: 4805: 4796: 4795: 4793: 4792: 4786: 4783: 4782: 4780: 4779: 4774: 4769: 4764: 4759: 4753: 4751: 4747: 4746: 4744: 4743: 4738: 4733: 4728: 4723: 4721:Perfect fourth 4718: 4713: 4708: 4702: 4700: 4696: 4695: 4688: 4686: 4684: 4683: 4678: 4677: 4676: 4671: 4666: 4661: 4659:Changing tones 4656: 4646: 4641: 4636: 4631: 4626: 4621: 4616: 4610: 4607: 4606: 4601: 4599: 4598: 4591: 4584: 4576: 4570: 4569: 4564: 4559: 4558: 4557: 4546: 4541: 4534: 4533:External links 4531: 4529: 4528: 4512: 4497: 4482:Jeppesen, Knud 4479: 4472: 4454: 4432: 4417: 4409: 4407: 4404: 4402: 4401: 4383:(5): 548–557. 4370: 4352:(2): 248–249. 4336: 4327: 4318: 4316:, 12: 119–144. 4305: 4294: 4277: 4264: 4255: 4246: 4242:Tonpsychologie 4237: 4220: 4206:Sethares, W.A. 4202: 4196: 4184:Sethares, W.A. 4180: 4156:Sethares, W.A. 4152: 4140: 4132:Scruton, Roger 4128: 4120:Scruton, Roger 4116: 4095: 4074: 4053: 4032: 4026: 4013: 4007: 3991: 3985: 3969: 3963: 3950: 3944: 3931: 3922: 3913: 3904: 3895: 3882: 3869: 3856: 3843: 3824: 3809: 3786: 3770: 3757: 3748: 3736: 3730: 3717: 3711: 3695: 3681: 3668: 3656: 3644: 3628: 3614: 3597: 3588: 3577: 3568: 3559: 3542: 3533: 3516: 3507: 3490: 3474:Tonpsychologie 3469: 3453: 3441: 3424: 3415: 3400: 3398: 3395: 3393: 3392: 3373: 3371:, p. 106. 3361: 3349: 3337: 3325: 3313: 3298: 3283: 3268: 3256: 3254:, p. 127. 3244: 3242:, p. 242. 3232: 3220: 3218:, p. 226. 3208: 3204:Radcliffe 1978 3196: 3194:, p. 415. 3184: 3180:Whittaker 1959 3172: 3160: 3148: 3136: 3124: 3122:, p. 179. 3112: 3108:Schulter 1997d 3100: 3096:Schulter 1997c 3088: 3084:Schulter 1997b 3076: 3072:Schulter 1997a 3064: 3052: 3040: 3024: 3012: 3000: 2988: 2976: 2959: 2957:, p. 290. 2947: 2934: 2919: 2907: 2892: 2880: 2878:, p. 106. 2868: 2856: 2844: 2832: 2820: 2808: 2796: 2784: 2772: 2760: 2748: 2729: 2717: 2705: 2693: 2681: 2679:, p. 121. 2669: 2667:, p. 123. 2657: 2655:, p. 138. 2645: 2630: 2615: 2603: 2591: 2579: 2567: 2565:, p. 165. 2555: 2540: 2538:, p. 264. 2528: 2516: 2504: 2502:, p. 315. 2492: 2480: 2476:Hindemith 1942 2468: 2456: 2443: 2441: 2438: 2435: 2434: 2420: 2419: 2417: 2414: 2413: 2412: 2410:Phonaesthetics 2407: 2402: 2397: 2390: 2387: 2374: 2371: 2347:Paul Hindemith 2328:natural fourth 2324:dominant chord 2180:, in his 1953 2178:George Russell 2154: 2151: 2069:'s unfinished 1940:The finale of 1900:False relation 1819: 1618: 1617: 1610:enharmonically 1599: 1590: 1544: 1541: 1537:Adam von Fulda 1520: 1517: 1516: 1515: 1507: 1504:stacks thereof 1500: 1497: 1494: 1474:severely from 1444:tuning systems 1388: 1387: 1384: 1381: 1374: 1373: 1370: 1333: 1332: 1331: 1330: 1327: 1317: 1316: 1312: 1311: 1310: 1309: 1306: 1295: 1294: 1286: 1285: 1284: 1283: 1279: 1268: 1267: 1263: 1262: 1261: 1260: 1257: 1247: 1246: 1241: 1240: 1239: 1238: 1235: 1223: 1222: 1218: 1217: 1216: 1215: 1212: 1201: 1200: 1189: 1188: 1074: 1071: 1030: 1024: 1021: 1020: 1019: 1013: 1010: 1007: 944: 941: 871:The strongest 864:(discussed at 862:C to Shining C 842: 841: 824: 820:critical bands 800: 796: 788: 787: 769: 763: 753: 748: 747: 746: 737: 736: 735: 719: 718: 715: 702: 695: 684: 677: 667: 666: 655: 645: 638:20 per second) 584: 577: 576: 575: 560: 553: 552: 551: 527: 520: 519: 518: 517: 516: 514: 511: 467: 466: 465: 464: 455:major sevenths 448: 443: 425: 424: 423: 422: 413: 398: 397: 396: 394:perfect fifths 387: 362: 348: 342: 339: 338: 337: 291: 285: 284: 273:musical tuning 265: 261: 260: 257: 253: 252: 244: 236: 233: 215:), Occidental 190:Noise in music 176: 175: 169:Claude Debussy 153: 129: 126: 110:Paul Hindemith 107:music theorist 72:, a dissonance 68: 61: 60: 46:Perfect octave 44: 37: 36: 35: 34: 33: 15: 13: 10: 9: 6: 4: 3: 2: 6122: 6121: 6110: 6107: 6105: 6102: 6101: 6099: 6084: 6083:Voice leading 6081: 6079: 6076: 6074: 6071: 6069: 6066: 6064: 6061: 6059: 6056: 6054: 6051: 6049: 6046: 6044: 6041: 6039: 6036: 6034: 6031: 6029: 6026: 6024: 6021: 6019: 6016: 6014: 6011: 6009: 6006: 6002: 5999: 5998: 5997: 5994: 5992: 5989: 5987: 5984: 5982: 5979: 5977: 5974: 5973: 5970: 5966: 5959: 5954: 5952: 5947: 5945: 5940: 5939: 5936: 5923: 5920: 5918: 5915: 5913: 5910: 5908: 5905: 5903: 5900: 5898: 5895: 5893: 5890: 5889: 5887: 5883: 5877: 5874: 5872: 5869: 5866: 5865:Carnatic raga 5862: 5859: 5857: 5854: 5852: 5849: 5845: 5842: 5840: 5837: 5835: 5834:Turkish makam 5832: 5830: 5827: 5826: 5824: 5822: 5819: 5817: 5814: 5812: 5809: 5808: 5806: 5800: 5791: 5787: 5783: 5779: 5775: 5771: 5767: 5763: 5757: 5754: 5752: 5749: 5747: 5744: 5742: 5739: 5736: 5732: 5731:quarter-comma 5728: 5725: 5724: 5722: 5720: 5716: 5710: 5707: 5705: 5702: 5700: 5697: 5695: 5692: 5690: 5687: 5685: 5682: 5680: 5677: 5674: 5670: 5667: 5665: 5662: 5660: 5657: 5655: 5652: 5650: 5647: 5645: 5642: 5640: 5637: 5635: 5632: 5631: 5629: 5627: 5623: 5620: 5618: 5614: 5608: 5607:Tonality flux 5605: 5603: 5600: 5598: 5595: 5593: 5590: 5588: 5585: 5583: 5580: 5578: 5575: 5571: 5568: 5566: 5563: 5562: 5561: 5558: 5556: 5553: 5551: 5548: 5546: 5543: 5541: 5538: 5537: 5535: 5533: 5529: 5523: 5520: 5518: 5515: 5513: 5510: 5508: 5505: 5503: 5500: 5498: 5495: 5493: 5490: 5488: 5485: 5483: 5480: 5478: 5475: 5473: 5470: 5468: 5465: 5464: 5462: 5458: 5454: 5447: 5442: 5440: 5435: 5433: 5428: 5427: 5424: 5412: 5411: 5407: 5405: 5404: 5400: 5398: 5397: 5393: 5391: 5390: 5386: 5384: 5383: 5379: 5377: 5376: 5372: 5370: 5369: 5365: 5364: 5362: 5358: 5352: 5351:Sandra Trehub 5349: 5347: 5344: 5342: 5339: 5337: 5334: 5332: 5331:Roger Shepard 5329: 5327: 5324: 5322: 5321:Carl Seashore 5319: 5317: 5314: 5312: 5309: 5307: 5306:James Mursell 5304: 5302: 5299: 5297: 5294: 5292: 5289: 5287: 5284: 5282: 5279: 5277: 5274: 5272: 5269: 5267: 5264: 5262: 5261:Tuomas Eerola 5259: 5257: 5256:Diana Deutsch 5254: 5252: 5251:Irène Deliège 5249: 5247: 5244: 5242: 5239: 5237: 5234: 5232: 5229: 5228: 5226: 5224: 5220: 5214: 5213:Zoomusicology 5211: 5209: 5206: 5204: 5201: 5199: 5196: 5194: 5191: 5189: 5186: 5184: 5181: 5179: 5176: 5174: 5171: 5169: 5166: 5164: 5163:Music therapy 5161: 5159: 5156: 5154: 5151: 5149: 5146: 5144: 5141: 5139: 5136: 5134: 5131: 5130: 5128: 5124: 5118: 5117:Tone deafness 5115: 5113: 5110: 5108: 5105: 5103: 5100: 5098: 5097:Beat deafness 5095: 5093: 5090: 5088: 5085: 5084: 5082: 5080: 5076: 5070: 5067: 5065: 5062: 5060: 5057: 5055: 5052: 5050: 5047: 5045: 5042: 5040: 5037: 5035: 5032: 5030: 5027: 5025: 5022: 5020: 5017: 5015: 5012: 5010: 5007: 5005: 5002: 5000: 4997: 4995: 4992: 4990: 4989:Mozart effect 4987: 4985: 4982: 4980: 4977: 4975: 4972: 4970: 4967: 4965: 4962: 4960: 4957: 4955: 4952: 4950: 4947: 4945: 4942: 4940: 4937: 4935: 4932: 4930: 4927: 4925: 4922: 4920: 4917: 4915: 4912: 4910: 4907: 4905: 4902: 4900: 4897: 4895: 4892: 4890: 4887: 4886: 4884: 4882: 4878: 4872: 4869: 4867: 4864: 4862: 4859: 4857: 4854: 4852: 4849: 4847: 4846:Biomusicology 4844: 4843: 4841: 4837: 4833: 4826: 4821: 4819: 4814: 4812: 4807: 4806: 4803: 4791: 4788: 4787: 4784: 4778: 4777:Major seventh 4775: 4773: 4772:Minor seventh 4770: 4768: 4765: 4763: 4760: 4758: 4755: 4754: 4752: 4748: 4742: 4739: 4737: 4734: 4732: 4729: 4727: 4726:Perfect fifth 4724: 4722: 4719: 4717: 4714: 4712: 4709: 4707: 4704: 4703: 4701: 4697: 4682: 4679: 4675: 4672: 4670: 4667: 4665: 4662: 4660: 4657: 4655: 4652: 4651: 4650: 4649:Nonchord tone 4647: 4645: 4642: 4640: 4637: 4635: 4632: 4630: 4627: 4625: 4622: 4620: 4617: 4615: 4612: 4611: 4608: 4604: 4597: 4592: 4590: 4585: 4583: 4578: 4577: 4574: 4568: 4565: 4563: 4560: 4556: 4553: 4552: 4550: 4547: 4545: 4542: 4540: 4537: 4536: 4532: 4526: 4522: 4521: 4516: 4513: 4510: 4509:0-19-514148-2 4506: 4502: 4498: 4495: 4494:9780486223865 4491: 4487: 4483: 4480: 4477: 4476:Italian Opera 4473: 4470: 4469:0-582-28227-6 4466: 4462: 4458: 4457:Jonas, Oswald 4455: 4452: 4451:0-521-36709-3 4448: 4444: 4440: 4436: 4433: 4430: 4429:0-12-213564-4 4426: 4422: 4418: 4415: 4411: 4410: 4405: 4398: 4394: 4390: 4386: 4382: 4378: 4377: 4371: 4367: 4363: 4359: 4355: 4351: 4347: 4346: 4341: 4337: 4333: 4328: 4324: 4319: 4315: 4311: 4306: 4302: 4301: 4295: 4291: 4287: 4283: 4278: 4274: 4270: 4265: 4261: 4256: 4252: 4247: 4243: 4238: 4234: 4230: 4226: 4221: 4217: 4213: 4212: 4207: 4203: 4199: 4197:1-85233-797-4 4193: 4189: 4185: 4181: 4169: 4165: 4161: 4157: 4153: 4149: 4145: 4144:Schweitzer, A 4141: 4137: 4133: 4129: 4125: 4121: 4117: 4105: 4101: 4096: 4084: 4080: 4075: 4063: 4059: 4054: 4042: 4038: 4033: 4029: 4023: 4019: 4014: 4010: 4004: 4000: 3996: 3992: 3988: 3986:0-520-05294-3 3982: 3978: 3974: 3970: 3966: 3964:9780846426004 3960: 3956: 3951: 3947: 3945:0-387-94366-8 3941: 3937: 3932: 3928: 3923: 3919: 3914: 3910: 3905: 3901: 3896: 3892: 3888: 3883: 3879: 3875: 3870: 3866: 3862: 3857: 3853: 3849: 3844: 3840: 3836: 3835: 3830: 3825: 3821: 3820: 3815: 3810: 3806: 3802: 3801: 3796: 3792: 3787: 3783: 3782:Musical Works 3779: 3775: 3771: 3767: 3763: 3758: 3754: 3749: 3745: 3742: 3737: 3733: 3731:0-13-049346-5 3727: 3723: 3718: 3714: 3708: 3704: 3700: 3699:Kamien, Roger 3696: 3692: 3691: 3686: 3682: 3678: 3674: 3669: 3665: 3661: 3657: 3653: 3649: 3645: 3641: 3637: 3633: 3629: 3625: 3624: 3619: 3615: 3611: 3610:0-7604-0014-8 3607: 3603: 3598: 3594: 3589: 3585: 3584: 3578: 3574: 3569: 3565: 3560: 3556: 3555:0-03-020756-8 3552: 3548: 3543: 3539: 3534: 3530: 3529:0-691-09135-8 3526: 3522: 3517: 3513: 3508: 3504: 3503:9780521623711 3500: 3496: 3491: 3487: 3486:9780521623711 3483: 3479: 3475: 3470: 3466: 3462: 3458: 3454: 3450: 3446: 3442: 3438: 3434: 3430: 3425: 3421: 3416: 3412: 3411: 3406: 3402: 3401: 3396: 3388: 3384: 3377: 3374: 3370: 3369:Tymoczko 2011 3365: 3362: 3358: 3353: 3350: 3346: 3341: 3338: 3334: 3329: 3326: 3322: 3317: 3314: 3310: 3305: 3303: 3299: 3295: 3290: 3288: 3284: 3280: 3275: 3273: 3269: 3265: 3264:Taruskin 2005 3260: 3257: 3253: 3248: 3245: 3241: 3236: 3233: 3229: 3224: 3221: 3217: 3212: 3209: 3205: 3200: 3197: 3193: 3188: 3185: 3181: 3176: 3173: 3169: 3164: 3161: 3157: 3156:Gardiner 2013 3152: 3149: 3145: 3140: 3137: 3133: 3128: 3125: 3121: 3120:Dahlhaus 1990 3116: 3113: 3109: 3104: 3101: 3097: 3092: 3089: 3085: 3080: 3077: 3073: 3068: 3065: 3061: 3056: 3053: 3049: 3044: 3041: 3037: 3033: 3028: 3025: 3021: 3020:Boethius n.d. 3016: 3013: 3009: 3004: 3001: 2997: 2992: 2989: 2985: 2980: 2977: 2973: 2968: 2966: 2964: 2960: 2956: 2951: 2948: 2945:, p. 136 2944: 2938: 2935: 2931: 2926: 2924: 2920: 2917:, p. 54. 2916: 2911: 2908: 2904: 2903:Sethares 2005 2899: 2897: 2893: 2889: 2884: 2881: 2877: 2876:Roederer 1995 2872: 2869: 2866:, p. 43. 2865: 2864:Sethares 2005 2860: 2857: 2853: 2852:Roederer 1973 2848: 2845: 2841: 2836: 2833: 2829: 2828:Sethares 2005 2824: 2821: 2817: 2812: 2809: 2805: 2800: 2797: 2793: 2788: 2785: 2781: 2776: 2773: 2769: 2764: 2761: 2757: 2752: 2749: 2745: 2744:Terhardt 1974 2740: 2738: 2736: 2734: 2730: 2726: 2721: 2718: 2714: 2709: 2706: 2702: 2697: 2694: 2690: 2685: 2682: 2678: 2673: 2670: 2666: 2661: 2658: 2654: 2653:Schuijer 2008 2649: 2646: 2643:, p. 41. 2642: 2637: 2635: 2631: 2627: 2622: 2620: 2616: 2612: 2607: 2604: 2600: 2595: 2592: 2588: 2587:Sethares 2005 2583: 2580: 2576: 2575:Sethares 1992 2571: 2568: 2564: 2563:Roederer 1995 2559: 2556: 2552: 2547: 2545: 2541: 2537: 2532: 2529: 2525: 2520: 2517: 2513: 2508: 2505: 2501: 2496: 2493: 2489: 2484: 2481: 2478:, p. 85. 2477: 2472: 2469: 2466:, p. 21. 2465: 2460: 2457: 2453: 2448: 2445: 2439: 2431: 2430:Cowell (1969) 2425: 2422: 2415: 2411: 2408: 2406: 2405:Limit (music) 2403: 2401: 2398: 2396: 2393: 2392: 2388: 2386: 2384: 2379: 2372: 2370: 2368: 2363: 2360: 2356: 2352: 2348: 2344: 2340: 2335: 2333: 2329: 2325: 2321: 2317: 2313: 2309: 2304: 2302: 2298: 2294: 2290: 2287: 2283: 2279: 2275: 2271: 2267: 2263: 2260: 2256: 2252: 2248: 2244: 2239: 2237: 2234: 2230: 2227: 2223: 2220: 2216: 2212: 2208: 2204: 2200: 2196: 2191: 2189: 2185: 2184: 2179: 2163: 2159: 2152: 2150: 2148: 2144: 2140: 2137: 2120: 2115: 2111: 2109: 2104: 2102: 2098: 2090: 2074: 2072: 2071:10th Symphony 2068: 2067:Gustav Mahler 2061: 2057: 2052: 2048: 2046: 2045: 2037: 2032: 2028: 2025: 2024:Nicholas Cook 2021: 2020: 2015: 2007: 1991: 1989: 1985: 1981: 1977: 1973: 1969: 1968:Roger Scruton 1961: 1945: 1943: 1938: 1936: 1926: 1910: 1908: 1903: 1901: 1891: 1875: 1873: 1864: 1848: 1846: 1838: 1832: 1830: 1826: 1818: 1816: 1812: 1808: 1804: 1800: 1799:Michael Haydn 1791: 1775: 1773: 1769: 1765: 1762:According to 1760: 1757: 1752: 1744: 1728: 1726: 1722: 1715: 1710: 1703: 1702: 1688: 1685: 1681: 1680: 1675: 1667: 1666: 1661: 1656: 1640: 1637: 1635: 1634:tone clusters 1631: 1627: 1623: 1615: 1611: 1607: 1603: 1600: 1598: 1597:major seventh 1594: 1591: 1589: 1588:minor seventh 1585: 1582: 1581: 1580: 1578: 1574: 1570: 1566: 1562: 1558: 1554: 1550: 1542: 1540: 1538: 1534: 1530: 1526: 1518: 1513: 1508: 1505: 1501: 1498: 1495: 1492: 1491: 1490: 1487: 1485: 1481: 1477: 1473: 1469: 1465: 1461: 1457: 1453: 1449: 1445: 1440: 1438: 1434: 1431: 1427: 1426:minor seventh 1423: 1419: 1415: 1411: 1407: 1403: 1399: 1394: 1385: 1382: 1379: 1378: 1377: 1371: 1368: 1367: 1366: 1363: 1356: 1340: 1338: 1328: 1325: 1321: 1320: 1319: 1318: 1314: 1313: 1307: 1304: 1299: 1298: 1297: 1296: 1292: 1288: 1287: 1280: 1277: 1272: 1271: 1270: 1269: 1265: 1264: 1258: 1255: 1251: 1250: 1249: 1248: 1243: 1242: 1236: 1233: 1227: 1226: 1225: 1224: 1220: 1219: 1213: 1210: 1205: 1204: 1203: 1202: 1198: 1197: 1196: 1194: 1191:According to 1185: 1179: 1173: 1169:"Consonance ( 1168: 1167: 1166: 1151: 1145: 1139: 1133: 1127: 1122: 1118: 1113: 1107: 1105: 1101: 1097: 1093: 1089: 1085: 1080: 1072: 1070: 1068: 1064: 1060: 1055: 1051: 1049: 1043: 1035: 1034:Lorenz Mizler 1029: 1022: 1017: 1014: 1011: 1008: 1005: 1004: 1003: 1001: 996: 994: 990: 986: 982: 978: 977:column of air 974: 970: 966: 962: 958: 954: 950: 942: 928: 923: 892: 888: 886: 882: 878: 874: 869: 867: 863: 859: 855: 850: 848: 838: 834: 830: 825: 821: 817: 813: 809: 805: 801: 797: 793: 792: 791: 785: 781: 780: 777: 775: 751: 734: 732: 731:critical band 727: 723: 716: 713: 712: 711: 672: 656: 649:20 per second 646: 643: 631: 630: 629: 626: 624: 618: 616: 612: 608: 604: 592: 588: 587:virtual pitch 581: 557: 524: 512: 479: 475: 471: 462:. p. 14. 461: 456: 452: 451:minor seconds 449: 447: 444: 442: 441:minor seventh 438: 437:major seconds 435: 434: 433: 430: 429: 428: 421: 417: 414: 412: 408: 405: 404: 402: 399: 395: 391: 388: 386: 382: 379: 378: 376: 373: 372: 371: 361: 353: 347: 340: 335: 330: 326: 322: 300: 296: 292: 290: 287: 286: 282: 281:Critical band 278: 274: 270: 266: 263: 262: 258: 255: 254: 250: 245: 242: 241: 240: 234: 232: 230: 226: 225:voice leading 222: 218: 214: 210: 206: 202: 197: 195: 191: 188:". (See also 187: 182: 173: 170: 166: 163: 159: 154: 151: 147: 143: 139: 135: 134: 133: 127: 125: 123: 119: 115: 111: 108: 103: 99: 95: 91: 71: 65: 47: 41: 30: 26: 22: 6078:Tonicization 6053:Polytonality 6048:Parallel key 6008:Figured bass 5985: 5922:Lambda scale 5829:Arabic maqam 5786:Werckmeister 5617:Temperaments 5501: 5408: 5401: 5394: 5387: 5382:Musicophilia 5380: 5373: 5366: 5336:John Sloboda 5316:Oliver Sacks 5286:Fred Lerdahl 5138:Bioacoustics 5064:Tonal memory 5049:Shepard tone 4908: 4762:Major second 4757:Minor second 4644:Musical note 4602: 4518: 4500: 4485: 4475: 4460: 4442: 4420: 4413: 4380: 4374: 4349: 4343: 4331: 4313: 4299: 4281: 4275:(4): 201–13. 4272: 4268: 4259: 4250: 4241: 4224: 4215: 4209: 4187: 4172:. Retrieved 4168:the original 4163: 4147: 4135: 4123: 4108:. Retrieved 4103: 4087:. Retrieved 4082: 4066:. Retrieved 4061: 4045:. Retrieved 4040: 4017: 3998: 3976: 3954: 3935: 3926: 3920:, 61: 58–64. 3917: 3908: 3899: 3890: 3886: 3877: 3864: 3851: 3838: 3832: 3817: 3804: 3798: 3781: 3777: 3765: 3761: 3752: 3746:10, no. 8693 3743: 3721: 3702: 3688: 3676: 3672: 3663: 3651: 3639: 3635: 3622: 3601: 3592: 3581: 3572: 3563: 3546: 3537: 3520: 3511: 3494: 3477: 3473: 3460: 3448: 3428: 3419: 3409: 3386: 3376: 3364: 3352: 3347:, p. 4. 3340: 3335:, p. 1. 3333:Russell 2008 3328: 3316: 3259: 3252:Scruton 2016 3247: 3235: 3228:Scruton 2009 3223: 3211: 3199: 3187: 3175: 3163: 3151: 3139: 3132:Gerbert 1784 3127: 3115: 3103: 3091: 3079: 3067: 3060:Machaut 1926 3055: 3043: 3038:, p. 19 3032:Hucbald n.d. 3027: 3015: 3003: 2991: 2979: 2955:Kliewer 1975 2950: 2937: 2932:, p. 3. 2930:Gouwens 2009 2910: 2905:, p. 1. 2883: 2871: 2859: 2847: 2835: 2823: 2811: 2799: 2787: 2775: 2763: 2751: 2725:Zwicker 1961 2720: 2708: 2696: 2684: 2672: 2660: 2648: 2606: 2594: 2582: 2570: 2558: 2531: 2519: 2507: 2495: 2483: 2471: 2459: 2447: 2424: 2395:Chord factor 2382: 2376: 2373:21st century 2367:Romantic Era 2364: 2358: 2354: 2350: 2338: 2336: 2316:sharp fourth 2305: 2240: 2192: 2181: 2176: 2133: 2118: 2105: 2095: 2064: 2055: 2042: 2040: 2017: 2012: 1975: 1966: 1939: 1931: 1904: 1896: 1869: 1843: 1821: 1796: 1761: 1749: 1724: 1718: 1713: 1704:closing bars 1699: 1677: 1671: 1663: 1638: 1630:Henry Cowell 1619: 1612:equivalent, 1593:Minor second 1584:Major second 1546: 1532: 1528: 1522: 1488: 1448:modern times 1446:compared to 1441: 1422:major second 1409: 1401: 1389: 1375: 1364: 1361: 1334: 1232:diatessaron. 1190: 1120: 1116: 1108: 1103: 1099: 1087: 1083: 1078: 1076: 1062: 1056: 1052: 1044: 1040: 1027: 997: 946: 870: 861: 851: 846: 843: 789: 728: 724: 720: 668: 641: 627: 619: 607:Voix céleste 600: 477: 474:Ernst Krenek 459: 431: 426: 420:major sixths 416:minor thirds 411:minor sixths 407:major thirds 400: 374: 369: 365:Roger Kamien 358: 352:Roger Kamien 345: 341:Music theory 248: 238: 217:music theory 198: 177: 158:atonal music 131: 121: 117: 113: 93: 89: 87: 70:Minor second 6068:Sonata form 6033:Neotonality 5917:Delta scale 5912:Gamma scale 5902:Alpha scale 5804:non-Western 5802:Traditional 5497:Pitch class 5477:Millioctave 5460:Measurement 5341:Carl Stumpf 5271:David Huron 5223:Researchers 4929:Entrainment 4750:Dissonances 4736:Major sixth 4731:Minor sixth 4716:Major third 4711:Minor third 4699:Consonances 4669:Preparation 4664:Pedal point 4218:(2): 71–84. 3893:(1): 44–61. 3807:(4): 15–32. 3650:(1937–70). 3586:63:498–510. 3405:Aristoxenus 3345:Haerle 1980 3323:, p. . 3311:, p. . 3296:, p. . 3281:, p. . 3192:Landon 1955 3008:Tenney 1988 2984:Philip 1966 2842:, p. . 2818:, p. . 2816:Philip 1966 2758:, p. . 2746:, p. . 2727:, p. . 2715:, p. . 2703:, p. . 2641:Kamien 2008 2589:, p. . 2553:, p. . 2524:Stumpf 1890 2488:Renard 2016 2312:tonic chord 2301:Lydian mode 2297:major scale 2101:Guido Adler 2019:Liederkreis 1970:alludes to 1803:ninth chord 1553:preparation 1519:Renaissance 1476:pure ratios 1452:major ninth 1437:minor ninth 1410:imperfectum 1172:consonantia 1158: 900 1126:consonantia 1112:consonantia 875:(harmonic) 835:'s list of 562:determined. 194:Noise music 128:Definitions 6098:Categories 6028:Modulation 5907:Beta scale 5885:Non-octave 5876:Tetrachord 5778:Kirnberger 5741:Schismatic 5326:Max Schoen 5276:Nina Kraus 5236:Lola Cuddy 5173:Musicology 4674:Resolution 4619:Avoid note 3634:(1954b) . 3620:(1954a) . 3445:Blom, Eric 3321:Stein 1953 3022:, f. 13v.. 2943:Forte 1979 2941:Quoted in 2500:Myers 1904 2440:References 2383:vice versa 2243:microtones 2231:note, and 2229:thirteenth 2219:untempered 2211:half-sharp 1824:Benedictus 1662:in Bach's 1577:diminished 1557:resolution 1512:chordioids 1400:meanings ( 1376:Unstable: 1245:concludes: 1067:resolution 1059:sonorities 957:Idiophones 953:xylophones 873:homophonic 847:vice versa 774:media help 432:Dissonance 334:C2ShiningC 181:polyphonic 122:dissonance 118:consonance 94:dissonance 90:consonance 88:In music, 5897:A12 scale 5851:Octoechos 5816:Shí-èr-lǜ 5765:Irregular 5582:Otonality 5522:Microtone 5079:Disorders 4439:Roy Howat 4148:J.S. Bach 3918:Quodlibet 3867:12, 8795. 3410:Harmonics 3240:Cook 1987 3216:Blom 1935 3036:Babb 1978 2416:Footnotes 2236:fifteenth 2233:half-flat 2226:half-flat 1935:Eric Blom 1870:Mozart's 1573:augmented 1433:reduction 1402:perfectum 1293:+ fifth). 1121:symphonia 1104:diaphonia 1100:symphonia 1096:polyphony 1088:diaphonos 1084:symphonos 993:orchestra 985:overtones 955:, called 833:Helmholtz 812:overtones 808:harmonics 615:roughness 360:conflict. 162:J.S. 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