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tritone, a property somewhat contributing to its popularity. The octatonic collection contains two distinct French sixth chords a minor third apart, and since they share no notes, the scale can be thought of as the union of those two chords. For example, two French sixths based on G and E contain all the notes of an octatonic scale between them.
1987:
1309:. "In each piece, changes of motive and phrase correspond to changes from one of the three octatonic scales to another, and one can easily select a single central and referential form of 8–28 in the context of each complete piece." However, even his larger pieces also feature "sections that are intelligible as 'octatonic music
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The octatonic scale is used very frequently for melodic material above a French sixth chord throughout the 19th and 20th centuries, particularly in Russia, in the music of Rimsky-Korsakov, Mussorgsky, Scriabin and
Stravinsky, but also outside Russia in the works of Debussy and Ravel. Examples include
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Both the half-whole diminished and its partner mode, the whole-half diminished (with a tone rather than a semitone beginning the pattern) are commonly used in jazz improvisation, frequently under different names. The whole-half diminished scale is commonly used in conjunction with diminished harmony
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By adding a major sixth above the root, from within the scale, and a major second, from outside the scale, the new chord is the Mystic chord found in some of
Scriabin's late works. While no longer transpositionally invariant, Scriabin teases the tritone symmetry of the French sixth in his music by
1512:. He said "It's a slightly more grownup version of the pentatonic scales that we're all taught to do with xylophones and glockenspiels when you're a kid. It's not a major scale or a minor scale; it's something else. But all the notes work together and make a certain color that is its own thing."
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as a pre-dominant chord in the classical period, late romantic composers saw the French sixth used as a dissonant and unstable chord. The chord can be built from the first, fourth, sixth and eighth degrees of the half-step/whole-step octatonic scale, and is transpositionally invariant about a
955:, in the lower notes between the alternating hands, and in the First Mephisto Waltz, in which a short cadenza (m. 525) makes use of it by harmonizing it with a B-flat Diminished Seventh chord. Later in the 19th century, the notes in the chords of the coronation bells from the opening scene of
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Each of the three distinct scales can form differently named scales with the same sequence of tones by starting at a different point in the scale. With alternative starting points listed below in square brackets, and return to tonic in parentheses, the three are, ascending by semitones:
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Art of Music. General
Questions of Music Theory and Aesthetics: 16–31; Orig. title: Модальная гармония: Модальность как тип гармонической структуры // Музыкальное искусство. Общие вопросы теории и эстетики музыки. Ташкент: Издательство литературы и искусства им. Г.
493:. Thus, the set of transpositions acts on the set of diminished collections as the integers modulo 3. If the transposition is congruent to 0 mod 3 the pitch collection is unchanged and the transpositions by 1 semitone or by 2 semitones are inverse to one another.
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as octatonic. Mark DeVoto describes "Nuages" as "arguably boldest single leap into the musical unknown. 'Nuages' defines a kind of tonality never heard before, based on the centricity of a diminished tonic triad (B-D-F natural)." According to
Stephen Walsh, the
2081:), or from a diminished triad by adding the root's major 7th (called a diminished major 7th, or C#. The diminished octave is inverted creates a minor ninth, creating a C chord, a sound commonly heard in the V chord during an authentic cadence in a minor key.
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Among the collection's remarkable features is that it is the only collection that can be disassembled into four transpositionally related pitch pairs in six different ways, each of which features a different interval class. For example:
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The second movement of
Stravinsky's Octet for wind instruments opens with what Stephen Walsh calls "a broad melody completely in the octatonic scale". Jonathan Cross describes a highly rhythmic passage in the first movement of the
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1582:. The dissonances associated with the scale when used in conjunction with conventional tonality form an integral part of his signature sound which has influenced hundreds of keyboardists of the 21st century.
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From this, one can see that Bartók has partitioned the octatonic collection into two (symmetrical) four-note segments of the natural minor scales a tritone apart. Paul Wilson argues against viewing this as
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theme "hangs in the texture like some motionless object, always the same and always at the same pitch". There is a particularly striking and effective use of the octatonic scale in the opening bars of
286:. The notes from two such seventh-chords combination form an octatonic collection. Because there are three ways to select two from three, there are three octatonic scales in the twelve-tone system.
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in the 7th century AD, where it was called "Zar ef Kend", meaning "string of pearls", the idea being that the two different sizes of intervals were like two different sizes of pearls.
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octatonic collection by the transposition operations, T, T4, T7, T10. In mm. 26–29, all eight pitch classes from the D octatonic collection appear. This collection is related to the E
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was also influenced by the harmonic and coloristic potential of octatonicism. As Mark DeVoto points out, the cascading arpeggios played on the celesta in the "Sugar Plum Fairy" from
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are in the left hand. The collection in the right hand outlines the first four notes of an A minor scale, and the collection in the left hand outlines the first four notes of an E
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Other relevant features of the piece include the groups of three notes taken from the whole-half diminished scale in mm. 12–18. In these measures, the right hand features D
1832:, the tetrachord without the 3rd (F). The left hand has the same tetrachord transposed down a tritone (G, A, C). In mm. 16, both hands transpose down three semitones to B
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for piano that
Messiaen completed in 1929, at the age of 20. Hill speaks of a characteristic "merging of tonality (E major) with the octatonic mode" in this short piece.
900:'s 1797 harmony treatise contains a sequential progression with a descending octatonic bass, supporting harmonies that use all and only the notes of an octatonic scale.
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The
Hungarian major scale and Romanian major scale are both heptatonic subsets of the octatonic scale with one scale degree removed. The Hungarian major scale has the
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as "gloriously octatonic, not an unfamiliar situation in jazz, where this mode is known as the 'diminished scale', but
Stravinsky of course knew it from Rimsky. The '
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describes the harmony of this passage as "really extraordinary". The chord progressions at the beginning of the second and third bars of this passage are octatonic:
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1250:(1958). In fact, "few if any composers have been known to employ relations available to the collection as extensively or in as varied a manner as Stravinsky".
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features chromatic harmonies using eleven of the twelve chromatic notes, within which the eight notes of the octatonic scale may be found in bars 9–10 below:
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951:, "Un Sospiro," for example, where (mm. 66–70) the bass contains a complete falling octatonic scale from D-flat to D-flat, in the opening piano cadenzas of
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without the use of accidentals. Across all conventional key signatures, at least two of the octatonic notes must share similar horizontal alignment on the
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1266:. In celebrating America, the émigré looked back once again to Russia." Van den Toorn catalogues many other octatonic moments in Stravinsky's music.
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965:, which consist of "two dominant seventh chords with roots a tritone apart" according to Taruskin, are entirely derived from an octatonic scale.
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is also closely associated with the octatonic scale, which can be found in most of his works, both solo and as part of a band. Examples include
1856:−. After repeating the structure of mm. 12–19 in mm. 29–34 the piece ends with the treble part returning to A− and the bass part returning to E
1527:, both of which strive for a dissonant and tonally ambiguous sound in their music. Examples include the instrumental break in Dream Theater's
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Bartók also utilizes the two other octatonic collections so that all three possible octatonic collections are found throughout this piece (D
1297:, the octatonic is used with the diatonic, whole tone, and other "abstract pitch formations" all "entwined... in a very complex mixture".
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collection once again). This unfortunately means that the inversions do not act as a simple cyclic group on the set of diminished scales.
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920:. The slow movement of this work contains a passage of what was, for its time, highly dissonant harmony. In a lecture (2005), pianist
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Octatonic scales can be found in Chopin's
Mazurka, Op. 50, No. 3 and in several Liszt piano works: the closing measures of the third
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They are each closed under transpositions by 3, 6, or 9 semitones. A transposition by 1, 4, 7, or 10 semitones will transform the E
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The beta chord (β chord) is a five-note chord, formed from the first five notes of the alpha chord (integers: 0,3,6,9,11; notes: C
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130:'s unpublished treatise "Étude sur les successions alternantes de tons et demi-tons (Et sur la gamme dite majeure-mineure)" (
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1262:' passage... alternates chords of E-flat7 and C7, over and over, distantly recalling the coronation scene from Mussorgsky's
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166:(уменьшённый лад), because of the stable way the diminished fifth functions in it. In more recent Russian theory, the term
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In Saint
Petersburg at the turn of the 20th century, this scale had become so familiar in the circle of composers around
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by adding a diminished octave. It may be created from a major chord by adding the sharpened root (solfege: in C, di is C
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diminished scale appear. In mm. 1–4, the pitch classes A, B, C, and D appear in the right hand, and the pitch classes E
1448:, which he greatly admired, and composed at least one piece—his Piano Sonatina No. 2—entirely in the octatonic system.
1140:. Melodic phrases that move by alternating tones and semitones frequently appear in the works of both these composers.
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Sanguinetti, Giorgio (1993). "Il primo studio teorico sulle scale octatoniche: Le 'scale alternate' di Vito Frazzi."
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minor scale. In mm. 5–11, the left and right hand switch—the A minor tetrachord appears in the left hand, and the E
1706:. All works are full of non-functional French sixths, and the octatonic scale is almost always the mode of choice.
1165:
998:
1323:, the octatonic scale is Mode 2. Peter Hill writes in detail about "La Colombe" (The Dove), the first of a set of
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Wollner, Fritz (1924) "7 mysteries of Stravinsky in Progression" 1924 German international school of music study.
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The gamma chord (γ chord) is 0,3,6,8,11 (Forte number 5-32A) It is the beta chord with one interval diminished: C
1665:
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123:), although there are a total of 43 enharmonically inequivalent, transpositionally inequivalent eight-note sets.
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Octatonic scales first occurred in Western music as byproducts of a series of minor-third transpositions. While
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Another remarkable feature of the diminished scale is that it contains the first four notes of four different
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is not used. Instead, this scale is placed among other symmetrical modes (total 11) under its historical name
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1904:
Two diminished seventh chords in the octatonic scale (one red, one blue) may be rearranged as the alpha chord
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claimed he was conscious of the octatonic collection "as a cohesive frame of reference" in his autobiography
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1728:, octatonic collections form the basis of the pitch content. In mm. 1–11, all eight pitch classes from the E
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Taruskin continues: "Thanks to the reinforcement the lesson has received in some equally famous pieces like
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alternating transpositions of the Mystic chord a tritone apart, implying the notes of an octatonic scale.
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The alpha chord (α chord) collection is, "a vertically organized statement of the octatonic scale as two
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Study of the Succession of Alternating Whole Tones and Semitones (and of the so-called Major-Minor Scale)
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Tymoczko, D. (2017, bars 18-21, right hand part) Transcription of Piano solo from “Freedom Jazz dance”
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made frequent use of the octatonic scale throughout his career as a composer, and indeed in his seven
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2032:). The beta chord can also occur in its reduced form, that is, limited to the characteristic tones (C
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in Schubert's Symphony No. 8 in B minor (1822), 1st mvt., bars 13–20; flat fifth marked with asterisk
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1468:(e.g., the E chord) while the half-whole scale is used in dominant harmony (e.g., with an F chord).
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or major/minor in first inversion (in this case, C major/minor). The number of semitones in the
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octatonic collection from mm. 1–11 by the following transposition operations: T2, T5, T8, T11.
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Baur, Steven (1999). "Ravel's 'Russian' Period: Octatonicism in His Early Works, 1893–1908."
406:, it is not possible to perfectly notate music of the octatonic scale using any conventional
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3116:. Berkeley and Los Angeles: University of California Press. Cited in Wilson directly above.
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1459:, for the oblique relation between the diatonic scale and the harmonic and melodic surface.
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scale. Conversely, transpositions by 2, 5, 8, or 11 semitones acts in the reverse way; the E
31:
1850:, A respectively. Later on, in mm. 20, the right hand moves on to A− and the left back to E
1471:
Examples of octatonic jazz include Jaco Pastorius' composition "Opus Pocus" from the album
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1958:
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The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-Century Music
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since "the larger octatonic collection embraces and supports both supposed tonalities".
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to be juxtaposed unusually but within a rational framework" though the relation of the
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It may also be represented as semitones, either starting with a whole tone (as above):
3519:, Vol. 1: Books I–VII, edited by Lyle Dowling and Arnold Shaw. New York: Carl Fischer.
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4721:
4621:
4553:
4534:
4497:
4399:
4280:
4260:
4091:
4001:
3943:
3576:
Taruskin, Richard (1987). "Chez Pétrouchka- Harmony and Tonality "chez" Stravinsky".
3340:
2126:
1680:
1668:
1520:
1441:
1433:
1365:
1333:
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843:, "its descending whole-step/half-step bass progression is complete and continuous".
411:
407:
213:
198:
91:
835:, instances can be found in music of previous centuries. Eytan Agmon locates one in
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3806:
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2130:
1941:
1637:
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1483:
1349:
1337:
1208:
794:
442:—that is, they are related by a variety of transposition and inversion operations:
294:
290:
102:
88:
3352:
Kholopov, Yuri (1982). "Modal harmony. Modality as a type of harmonic structure".
562:, or B. All other transformations do not change the classes (e.g. reflecting the E
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The scale "allows familiar harmonic and linear configurations such as triads and
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apart – clash, "horribly with each other", when sounded together and create a
1619:
1425:
992:
867:
797:
3148:
New Music in China and the C.C. Liu Collection at the University of Hong Kong
3856:
3776:
3732:
Tymoczko, Dmitri (2002). "Stravinsky and the Octatonic: A Reconsideration".
3380:
3086:
Agmon, Eytan (1990). "Equal Divisions of the Octave in a Scarlatti Sonata."
1962:
1940:
One of the most important subsets of the alpha collection, the alpha chord (
1499:
1393:
1235:
1148:
melody heard near the start of Debussy's "Nuages" from his orchestral suite
952:
396:
212:
Because it was associated in the early 20th century with the Dutch composer
38:
3172:
Cohn, Richard (1991). "Bartók's Octatonic Strategies: A Motivic Approach."
17:
3398:
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3561:(1985). "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle
1332:
Other twentieth-century composers who used octatonic collections include
418:
415:
298:
106:
3970:
3192:
DeVoto, Mark (2003). "The Debussy Sound: Colouyr, Texture, Gesture". In
4236:
3694:
Berger, Arthur (1963). "Problems of Pitch Organization in Stravinsky".
2648:
1661:
1095:
943:
Adagio (2nd movement) from Beethoven's Piano Sonata No. 11, bars 31–33.
935:
Adagio (2nd movement) from Beethoven's Piano Sonata No. 11, bars 31–33.
3716:
The Concise Musical Guide to King Crimson and Robert Fripp (1969–1984)
3323:
In Search of New Scales: Prince Edmond de Polignac, Octatonic Explorer
3131:
Triad Pairs for Jazz: Practice and Application for the Jazz Improvisor
1041:
Cascading arpeggios on celesta from the Dance of the Sugar Plum Fairy.
282:
The twelve tones of the chromatic scale are covered by three disjoint
2924:
Ears Wide Open Online | Deconstructing Rimsky-Korsakov's Scheherazade
1455:
criticized the use of the octatonic scale, specifically Stravinsky's
3305:
Principles of pitch organization in Bartók's Duke Bluebeard's Castle
3221:
DeVoto, Mark (2007) "Boris's Bells, by Way of Schubert and Others".
1010:, the progression is often thought of as being peculiarly Russian."
2113:. It may be considered a major-minor minor seventh chord on A: A, C
1194:(1920). Passages using this scale are unmistakable as early as the
1022:
ballet are made up of dominant seventh chords a minor third apart.
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1524:
1259:
1212:(1910). It also appears in later works by Stravinsky, such as the
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Women of Influence in Contemporary Music: Nine American Composers
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because it can be conceived as a combination of two interlocking
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Nos. 99, 101, and 109 are octatonic pieces, as is No. 33 of the
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can be conceived as a combination of two interlocking augmented
126:
The earliest systematic treatment of the octatonic scale was in
4342:
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3749:
3526:
Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts
1045:"Hagens Watch", one of the darkest and most sinister scenes in
804:
to the melodic and harmonic surface is thus generally oblique.
3663:(1911). "Neskol'ko myslei v sviazi s iubileem Frantsa Lista".
3278:
Mel Bay Jazz and the Classical Guitar Theory and Applications
1671:. The six-note chord is contained within an octatonic scale.
526:
and D collections can be swapped by inversions around E, G, B
158:(Корсаковская гамма). As early as 1911, the Russian theorist
3271:
con diteggiature di Ernesto Consolo. Florence: A. Forlivesi.
1172:
The scale was extensively used by Rimsky-Korsakov's student
1094:
The cor anglais melody from "Nuages", the first movement of
520:, A or C (the tones common to both scales). Similarly, the C
1502:
uses the octatonic scale extensively, such as in the song "
893:
Sarabande from J. S. Bach's English Suite No. 3, bars 17–19
3582:
10, no. 3 (Spring, Special Issue: Resolutions I): 265–286.
3347:. Orig. title: Гармония. Теоретический курс. Moscow: Lan'.
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2818:
https://dmitri.mycpanel.princeton.edu/transcriptions.html
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2 degree removed, while the Romanian major scale has the
1992:
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1444:, who may have inferred the collection from Stravinsky's
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Audio playback is not supported in your browser. You can
839:'s Sonata K. 319. In the following passage, according to
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109:, as shown at right. In classical theory (in contrast to
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octatonic collection from mm. 1–11 is related to this D
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With one more scale tone than described by the western
297:, while the second begins its ascent with a half step (
3463:. Cambridge and New York: Cambridge University Press.
3200:. Cambridge and New York: Cambridge University Press.
2838:"How Jonny Greenwood wrote the year's best film score"
1961:'s terminology, the C alpha chord may be considered a
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1481:'s piano solo on "Freedom Jazz Dance" from the album
885:
Octatonic bars from Sarabande from English Suite No 3
3600:. New Haven and London: Yale University Press. ISBN.
1033:
Cascading arpeggios on celesta from Sugar Plum Fairy
4708:
4676:
4658:
4630:
4572:
4506:
4455:
4418:
4385:
4376:
4335:
4299:
4165:
4049:
4013:
3952:
3870:
3825:
3787:
1787:). In mm. 12–18, all eight pitch classes from the D
1176:, particularly in his Russian-period works such as
820:suggests that the scale was formulated already by
463:scale into the D scale, and the D scale into the E
37:"8-28" redirects here. For the calendar date, see
3480:, translated by Judah A. Joffee. New York: Tudor.
508:collections can be swapped by inversions around E
201:. The two modes are sometimes referred to as the
113:), this symmetrical scale is commonly called the
3705:Herbie Hancock: Freedom Jazz Dance Transcription
3612:. Oxford and New York: Oxford University Press.
3325:. Rochester, NY: University of Rochester Press.
3165:A Study of the Instrumental Music of Frank Zappa
1650:and in later music. In the Petrushka chord, two
1224:(1945), most of the neoclassical works from the
301:). These modes are sometimes referred to as the
3591:. Oxford and New York: Oxford University Press.
2644:"Igor Stravinsky - Symphony in Three Movements"
2416:
2139:9 chord; the notes in this case creating an A.
754:separated by minor thirds. For example: C, D, E
2968:"Gaspard de la nuit: III. Scarbo, piano score"
4354:
3986:
3761:
3688:Journal of the American Musicological Society
3568:Journal of the American Musicological Society
3517:The Schillinger System of Musical Composition
3175:Journal of the American Musicological Society
3167:(PhD dissertation). University of Cincinnati.
2769:
2662:
2586:
2538:
2428:
94:. However, the term most often refers to the
8:
2828:
2826:
2210:List of pieces which use the octatonic scale
1764:minor tetrachord appears in the right hand.
866:Taruskin also cites the following bars from
162:described this collection of pitches as the
3097:The Twelve-Tone Music of Luigi Dallapiccola
2404:
2251:
4382:
4361:
4347:
4339:
3993:
3979:
3971:
3768:
3754:
3746:
3507:TV (16 November; accessed 1 October 2015).
2674:
1618:in the piano during the second tableau of
3437:". Spotify.com (accessed 1 October 2015).
2792:
1539:. Earlier examples of the scale's use in
30:For the sound production technology, see
3718:. Cambridge: Spaceward. pp. 53–58.
3670:
2897:
2503:
2464:
2452:
2365:
2353:
2326:
2314:
2302:
2290:
2279:
2275:
2263:
1722:'s piano piece, "Diminished Fifth" from
1269:The scale also may be found in music of
1132:The scale is also found in the music of
556:collections by inversions around D, F, A
3031:
3007:
2745:
2733:
2721:
2220:
2133:chord, or in jazz music as a Dominant 7
1793:octatonic collection are present. The E
1457:Concerto for Piano and Wind Instruments
3404:
3363:Langlé, Honoré François Marie (1797).
3019:
2995:
2983:
2686:
2562:
2515:
2488:
2476:
2341:
2239:
1972:of the alpha chord corresponds to the
1234:(1957), and even in some of the later
1144:identifies a five-note segment in the
216:, in the Netherlands it is called the
3589:Stravinsky and the Russian Traditions
3377:Béla Bartók: An Analysis of his Music
3253:(1991). "Debussy and the Octatonic".
3058:
3046:
2946:Scriabin's Use Of The Octotonic Scale
2909:
2621:
2609:
2574:
2550:
2440:
2392:
2227:
2129:. This is also commonly known as the
2059:The beta chord may be created from a
862:Scarlatti's Sonata K. 319, bars 62–80
307:half-step/whole step diminished scale
303:whole step/half-step diminished scale
293:: the first begins its ascent with a
289:Each octatonic scale has exactly two
207:whole step/half-step diminished scale
203:half-step/whole step diminished scale
7:
3196:, edited by Simon Tresize, 179–196.
2757:
2698:
2377:
434:The three octatonic collections are
3259:10, nos. 1–2 (March–July): 125–169.
3476:Rimsky-Korsakov, Nicholas (1935).
3365:Traité d'harmonie et de modulation
3194:The Cambridge Companion to Debussy
2143:Hungarian major and Romanian major
1506:" and his soundtrack for the film
25:
3081:, 6–9, p. 12. University College.
1515:The scale is used in progressive
854:Scarlatti Sonata K319, bars 62–80
475:scale goes to the D scale, D to C
181:In jazz theory, it is called the
1120:
908:In 1800, Beethoven composed his
3661:Yavorsky, Boleslav Leopoldovich
568:collection around E gives the E
391:, or starting with a semitone:
154:that it was referred to as the
134:) from c. 1879, which preceded
3900:Emancipation of the dissonance
3700:2, no. 1 (Fall–Winter): 11–42.
3596:Van den Toorn, Pieter (1983).
3383:. London: Kahn & Averill.
3269:Scale alternate per pianoforte
1321:modes of limited transposition
1191:Symphonies of Wind Instruments
140:Scale alternate per pianoforte
1:
3802:Mode of limited transposition
3707:". (Accessed 1 October 2015).
3198:Cambridge Companions to Music
1675:French sixth and Mystic chord
1062:Wagner, "Hagen's Watch" from
78:The two octatonic scales on C
3598:The Music of Igor Stravinsky
3541:Slayton, Michael K. (2010).
3178:44, no. 2 (Summer): 262–300.
3112:Antokoletz, Elliott (1984).
1989:
1890:
1875:
1600:
1080:
263:
248:
233:
64:
49:
3960:List of atonal compositions
3929:Quartal and quintal harmony
3738:24, no. 1 (Spring): 68–102.
3703:Gillespie, Robert (2015). "
3636:Debussy, a Painter in Sound
3571:38, no. 1 (Spring): 72–142.
3444:Classical Music for Dummies
3345:Harmony. Theoretical Course
2009:, with two reduced versions
1554:Emerson Lake & Palmer's
1256:Symphony in Three Movements
1221:Symphony in Three Movements
4823:
4132:Ptolemy's intense diatonic
3638:. London: Faber and Faber.
3524:Schuijer, Michiel (2008).
3308:. University of Helsinki.
3297:. London: Faber and Faber.
2146:
1498:of the English rock group
1440:. Other composers include
1071:Late 19th and 20th century
760:, F and (enharmonically) F
277:The three octatonic scales
187:symmetric diminished scale
36:
29:
3697:Perspectives of New Music
3587:Taruskin, Richard (1996)
3433:Pastorius, Jaco (1976). "
3187:. London: Reaction Books.
1911:diminished seventh chords
1238:compositions such as the
822:Persian traditional music
284:diminished seventh chords
191:diminished seventh chords
4611:descending melodic major
4558:descending melodic minor
3667:no. 45 (8 October): 961.
3645:The Music of Béla Bartók
3235:. Taylor & Francis.
3183:Cross, Jonathan (2015).
2061:diminished seventh chord
2056:). Forte number: 5-31B.
1951:(0347)), such as E–G–C–E
1564:Progressive keyboardist
910:Piano Sonata No. 11 in B
101:composed of alternating
4802:Post-tonal music theory
4586:ascending melodic minor
4524:ascending melodic major
3634:Walsh, Stephen (2018).
3627:The Music of Stravinsky
3625:Walsh, Stephen (1988).
3459:Pople, Anthony (1991).
3163:Clement, Brett (2009).
3146:Chan, Hing-yan (2005).
3129:Campbell, Gary (2001).
3095:Alegant, Brian (2010).
2966:Ravel, Maurice (1908).
2807:on "Freedom Jazz Dance"
2711:"La Colombe" (The Dove)
2181:has a ten-note analogue
1994:download the audio file
1895:download the audio file
1880:download the audio file
1605:download the audio file
1430:Robert Xavier Rodriguez
1306:44 Duos for Two Violins
1166:Bagatelle sans tonalité
1085:download the audio file
829:Nikolai Rimsky-Korsakov
668:major third: (C, E), (F
440:inversionally symmetric
268:download the audio file
253:download the audio file
238:download the audio file
152:Nikolai Rimsky-Korsakov
69:download the audio file
54:download the audio file
4597:Lydian augmented (III)
4370:Modes in Western music
3912:Polymodal chromaticism
3890:Dissonant counterpoint
3852:Second Viennese School
3610:Roots of the Classical
3321:Kahan, Sylvia (2009).
3295:The Messiaen Companion
3276:Hatfield, Ken (2005).
2098:
1519:music such as that by
1206:(both from 1908), and
1129:
1067:
1042:
1034:
1001:
987:Coronation scene from
980:
976:Coronation scene from
944:
936:
894:
886:
863:
855:
4678:Double harmonic scale
4650:Phrygian dominant (V)
4645:Ukrainian Dorian (IV)
3835:Twelve-tone technique
3735:Music Theory Spectrum
3643:Wilson, Paul (1992).
3461:Berg: Violin Concerto
3442:Pogue, David (1997).
2149:Hungarian major scale
2147:Further information:
2096:
1957:; using the theorist
1694:Five Preludes, Op. 74
1586:Harmonic implications
1398:Jean Papineau-Couture
1115:
1061:
1040:
1032:
986:
975:
942:
934:
892:
884:
861:
853:
393:0 1 3 4 6 7 9 10 (12)
389:0 2 3 5 6 8 9 11 (12)
172:Rimsky-Korsakov scale
142:of 1930 by 50 years.
4691:Hungarian minor (IV)
4617:Half diminished (VI)
4607:Aeolian dominant (V)
4203:17 equal temperament
3629:. London: Routledge.
3606:Van der Merwe, Peter
3417:The Jazz Theory Book
3302:Honti, Rita (2007).
3293:Hill, Peter (1995).
3233:Music in Action Film
3231:Durrand, M. (2020).
3225:, no. 83 (Spring): .
2820:accessed 24/11/2021.
2417:Rimsky-Korsakov 1935
2179:15 equal temperament
2153:Romanian major scale
1509:The Power of the Dog
1402:Krzysztof Penderecki
176:Rimsky-Korsakov mode
120:octatonic collection
4686:Double harmonic (I)
3513:Schillinger, Joseph
2880:on 14 February 2008
2866:(August 12, 2001).
1418:Dmitri Shostakovich
1197:Scherzo fantastique
872:English Suite No. 3
4668:Harmonic major (I)
4640:Harmonic minor (I)
4137:Scale of harmonics
3906:Klangfarbenmelodie
3579:19th-Century Music
3223:Current Musicology
2770:Van den Toorn 1983
2663:Van den Toorn 1983
2599:Stravinsky's Octet
2587:Van den Toorn 1983
2539:van der Merwe 2005
2429:Van den Toorn 1983
2278:, 111–113, citing
2169:3 degree removed.
2125:, E, G. See also:
2099:
1974:Fibonacci sequence
1446:The Rite of Spring
1414:Alexander Scriabin
1378:Witold Lutosławski
1271:Alexander Scriabin
1215:Symphony of Psalms
1188:(1913), up to the
1185:The Rite of Spring
1130:
1068:
1043:
1035:
1002:
981:
945:
937:
895:
887:
864:
856:
837:Domenico Scarlatti
818:Joseph Schillinger
790:, and A, B, C, D.
695:perfect fourth: (C
641:minor third: (C, E
128:Edmond de Polignac
4779:
4778:
4704:
4703:
4451:
4450:
4240:
4231:
4217:
4215:Escala nordestina
4205:
4198:
4191:
4184:
4127:Phrygian dominant
3968:
3967:
3797:Equal temperament
3725:978-0-9570489-3-5
3618:978-0-19-816647-4
3559:Taruskin, Richard
3551:978-0-8108-7748-1
3534:978-1-58046-270-9
3332:978-1-58046-305-8
3314:978-952-10-3837-2
3156:978-962-209-772-8
3105:978-1-58046-325-6
2094:
2003:A beta chord on C
1998:
1899:
1884:
1681:used functionally
1609:
1453:Heinrich Schenker
1374:Aram Khachaturian
1362:Alberto Ginastera
1126:
1089:
1030:
973:
957:Modest Mussorgsky
932:
882:
851:
719:), (G, C), (E, A)
436:transpositionally
272:
257:
242:
160:Boleslav Yavorsky
156:Korsakovian scale
73:
58:
16:(Redirected from
4814:
4797:Musical symmetry
4792:Octatonic scales
4383:
4363:
4356:
4349:
4340:
4291:Ukrainian Dorian
4234:
4225:
4213:
4201:
4194:
4187:
4180:
4067:Diminished scale
3995:
3988:
3981:
3972:
3895:Dynamic tonality
3817:Whole tone scale
3770:
3763:
3756:
3747:
3729:
3668:
3656:
3639:
3630:
3621:
3601:
3592:
3583:
3572:
3564:
3554:
3537:
3520:
3508:
3499:Untitled lecture
3490:
3481:
3472:
3455:
3438:
3429:
3402:
3368:
3357:
3348:
3336:
3317:
3298:
3289:
3272:
3260:
3246:
3226:
3217:
3188:
3179:
3168:
3159:
3142:
3125:
3108:
3091:
3082:
3075:Anon. (1977). .
3062:
3056:
3050:
3044:
3035:
3029:
3023:
3017:
3011:
3005:
2999:
2993:
2987:
2981:
2975:
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2972:
2963:
2957:
2956:
2955:
2954:
2941:
2935:
2934:
2933:
2932:
2919:
2913:
2907:
2901:
2895:
2889:
2888:
2886:
2885:
2876:. Archived from
2860:
2854:
2853:
2851:
2850:
2830:
2821:
2814:
2808:
2802:
2796:
2790:
2784:
2779:
2773:
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2719:
2713:
2708:
2702:
2696:
2690:
2684:
2678:
2672:
2666:
2660:
2654:
2653:
2652:. 15 March 2014.
2631:
2625:
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2613:
2607:
2601:
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2590:
2584:
2578:
2572:
2566:
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2519:
2513:
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2474:
2468:
2462:
2456:
2450:
2444:
2438:
2432:
2426:
2420:
2414:
2408:
2405:Schillinger 1946
2402:
2396:
2390:
2381:
2375:
2369:
2363:
2357:
2351:
2345:
2339:
2330:
2324:
2318:
2312:
2306:
2300:
2294:
2288:
2282:
2273:
2267:
2261:
2255:
2252:Sanguinetti 1993
2249:
2243:
2237:
2231:
2225:
2168:
2167:
2162:
2161:
2138:
2137:
2124:
2123:
2118:
2117:
2112:
2111:
2106:
2105:
2095:
2080:
2079:
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2068:
2067:
2055:
2054:
2049:
2048:
2043:
2042:
2037:
2036:
2031:
2030:
2025:
2024:
2019:
2018:
2008:
2007:
1956:
1955:
1936:
1935:
1930:
1929:
1924:
1923:
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1917:
1861:
1860:
1855:
1854:
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1786:
1785:
1780:
1779:
1763:
1762:
1757:
1756:
1751:
1750:
1745:
1744:
1739:
1738:
1733:
1732:
1659:
1658:
1580:King of Delusion
1577:Sons of Apollo's
1541:progressive rock
1410:Sergei Prokofiev
1342:Benjamin Britten
1317:Olivier Messiaen
1312:
1128:
1127:
1031:
995:
974:
949:Étude de Concert
933:
916:
915:
883:
852:
841:Richard Taruskin
789:
788:
783:
782:
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672:
664:
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636:
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619:
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531:
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525:
524:
519:
518:
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512:
507:
506:
501:
500:
492:
491:
486:
485:
480:
479:
474:
473:
468:
467:
462:
461:
456:
455:
451:scale into the D
450:
449:
395:, or labeled as
394:
390:
382:
381:
376:
375:
370:
369:
361:
360:
355:
354:
346:
345:
340:
339:
334:
333:
328:
327:
322:
321:
309:, respectively.
183:diminished scale
32:Octophonic sound
21:
4822:
4821:
4817:
4816:
4815:
4813:
4812:
4811:
4782:
4781:
4780:
4775:
4709:Number of tones
4700:
4672:
4654:
4626:
4568:
4502:
4447:
4414:
4372:
4367:
4331:
4295:
4256:Hungarian minor
4251:Hungarian major
4182:Double harmonic
4161:
4152:Synthetic scale
4077:Double harmonic
4045:
4009:
3999:
3969:
3964:
3948:
3872:
3866:
3827:
3821:
3812:Octatonic scale
3789:
3783:
3774:
3744:
3726:
3714:(2013). "Red".
3712:Keeling, Andrew
3710:
3681:
3679:Further reading
3676:
3659:
3642:
3633:
3624:
3604:
3595:
3586:
3575:
3562:
3557:
3540:
3523:
3511:
3493:
3484:
3478:My Musical Life
3475:
3458:
3441:
3432:
3410:
3391:
3371:
3367:. Paris: Boyer.
3362:
3351:
3339:
3333:
3320:
3301:
3292:
3275:
3263:
3249:
3243:
3230:
3220:
3191:
3185:Igor Stravinsky
3182:
3171:
3162:
3145:
3128:
3111:
3094:
3085:
3074:
3065:
3057:
3053:
3045:
3038:
3030:
3026:
3018:
3014:
3006:
3002:
2994:
2990:
2982:
2978:
2970:
2965:
2964:
2960:
2952:
2950:
2949:, 20 March 2022
2943:
2942:
2938:
2930:
2928:
2921:
2920:
2916:
2908:
2904:
2896:
2892:
2883:
2881:
2868:"The Searchers"
2862:
2861:
2857:
2848:
2846:
2832:
2831:
2824:
2815:
2811:
2803:
2799:
2791:
2787:
2780:
2776:
2768:
2764:
2756:
2752:
2744:
2740:
2732:
2728:
2720:
2716:
2709:
2705:
2697:
2693:
2685:
2681:
2675:Antokoletz 1984
2673:
2669:
2661:
2657:
2642:
2639:Wayback Machine
2632:
2628:
2620:
2616:
2608:
2604:
2597:
2593:
2585:
2581:
2573:
2569:
2561:
2557:
2549:
2545:
2537:
2533:
2528:"Hagen's Watch"
2526:
2522:
2514:
2510:
2502:
2495:
2487:
2483:
2479:, 72, ex. 25.2.
2475:
2471:
2463:
2459:
2451:
2447:
2439:
2435:
2427:
2423:
2415:
2411:
2403:
2399:
2391:
2384:
2376:
2372:
2364:
2360:
2352:
2348:
2340:
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2313:
2309:
2301:
2297:
2289:
2285:
2274:
2270:
2262:
2258:
2250:
2246:
2238:
2234:
2226:
2222:
2218:
2185:Complexe sonore
2175:
2165:
2164:
2159:
2158:
2155:
2145:
2135:
2134:
2121:
2120:
2115:
2114:
2109:
2108:
2103:
2102:
2089:
2087:
2077:
2076:
2071:
2070:
2065:
2064:
2052:
2051:
2046:
2045:
2040:
2039:
2034:
2033:
2028:
2027:
2022:
2021:
2016:
2015:
2012:
2011:
2010:
2005:
2004:
2001:
2000:
1999:
1997:
1982:
1953:
1952:
1933:
1932:
1927:
1926:
1921:
1920:
1915:
1914:
1907:
1906:
1905:
1902:
1901:
1900:
1898:
1886:
1885:
1883:
1868:
1858:
1857:
1852:
1851:
1846:
1845:
1840:
1839:
1834:
1833:
1828:
1827:
1822:
1821:
1816:
1815:
1807:
1806:
1801:
1800:
1795:
1794:
1789:
1788:
1783:
1782:
1777:
1776:
1760:
1759:
1754:
1753:
1748:
1747:
1742:
1741:
1736:
1735:
1730:
1729:
1716:
1677:
1656:
1655:
1654:, C major and F
1642:Igor Stravinsky
1640:device used in
1636:is a recurring
1634:Petrushka chord
1630:
1629:
1628:
1616:Petrushka chord
1612:
1611:
1610:
1608:
1593:
1591:Petrushka chord
1588:
1566:Derek Sherinian
1496:Jonny Greenwood
1493:
1465:
1406:Francis Poulenc
1386:Henri Dutilleux
1358:Ross Lee Finney
1310:
1288:Cantata Profana
1241:Canticum Sacrum
1174:Igor Stravinsky
1121:
1110:
1109:
1108:
1106:Link to passage
1092:
1091:
1090:
1088:
1073:
1064:Götterdämmerung
1052:Götterdämmerung
1025:
994:Link to passage
993:
968:
927:
913:
912:
906:
877:
846:
833:My Musical Life
815:
810:
786:
785:
780:
779:
774:
773:
768:
767:
762:
761:
756:
755:
742:
741:
736:
735:
730:
729:
724:
723:
715:
714:
709:
708:
703:
702:
697:
696:
688:
687:
682:
681:
676:
675:
670:
669:
661:
660:
655:
654:
649:
648:
643:
642:
634:
633:
628:
627:
622:
621:
616:
615:
607:
606:
601:
600:
595:
594:
589:
588:
587:semitone: (C, C
580:
570:
569:
564:
563:
558:
557:
552:
551:
550:and the D and E
546:
545:
540:
539:
534:
533:
528:
527:
522:
521:
516:
515:
510:
509:
504:
503:
498:
497:
489:
488:
483:
482:
477:
476:
471:
470:
465:
464:
459:
458:
453:
452:
447:
446:
432:
427:
392:
388:
379:
378:
373:
372:
367:
366:
358:
357:
352:
351:
343:
342:
337:
336:
331:
330:
325:
324:
319:
318:
280:
279:
278:
275:
274:
273:
271:
259:
258:
256:
244:
243:
241:
226:
195:augmented scale
164:diminished mode
148:
115:octatonic scale
99:symmetric scale
85:octatonic scale
81:
80:
79:
76:
75:
74:
72:
60:
59:
57:
42:
35:
28:
23:
22:
15:
12:
11:
5:
4820:
4818:
4810:
4809:
4804:
4799:
4794:
4784:
4783:
4777:
4776:
4774:
4773:
4767:
4761:
4755:
4749:
4743:
4737:
4731:
4725:
4719:
4712:
4710:
4706:
4705:
4702:
4701:
4699:
4698:
4693:
4688:
4682:
4680:
4674:
4673:
4671:
4670:
4664:
4662:
4660:Harmonic major
4656:
4655:
4653:
4652:
4647:
4642:
4636:
4634:
4632:Harmonic minor
4628:
4627:
4625:
4624:
4619:
4614:
4604:
4599:
4594:
4592:Dorian ♭2 (II)
4589:
4582:Jazz minor (I)
4578:
4576:
4570:
4569:
4567:
4566:
4561:
4547:
4545:Mixolydian (V)
4542:
4537:
4535:Phrygian (III)
4532:
4527:
4512:
4510:
4504:
4503:
4501:
4500:
4495:
4490:
4485:
4480:
4475:
4470:
4465:
4459:
4457:
4453:
4452:
4449:
4448:
4446:
4445:
4443:Hypomixolydian
4440:
4435:
4430:
4424:
4422:
4416:
4415:
4413:
4412:
4407:
4402:
4397:
4391:
4389:
4380:
4374:
4373:
4368:
4366:
4365:
4358:
4351:
4343:
4337:
4333:
4332:
4330:
4329:
4324:
4319:
4314:
4309:
4303:
4301:
4297:
4296:
4294:
4293:
4288:
4286:Romanian major
4283:
4278:
4273:
4268:
4263:
4258:
4253:
4248:
4243:
4242:
4241:
4232:
4220:
4219:
4218:
4208:
4207:
4206:
4199:
4192:
4185:
4175:
4169:
4167:
4163:
4162:
4160:
4159:
4154:
4149:
4147:Synthetic mode
4144:
4139:
4134:
4129:
4124:
4119:
4114:
4109:
4107:Harmonic minor
4104:
4102:Harmonic major
4099:
4094:
4089:
4084:
4079:
4074:
4072:Distance model
4069:
4064:
4059:
4053:
4051:
4047:
4046:
4044:
4043:
4038:
4033:
4028:
4023:
4017:
4015:
4011:
4010:
4002:Musical scales
4000:
3998:
3997:
3990:
3983:
3975:
3966:
3965:
3963:
3962:
3956:
3954:
3950:
3949:
3947:
3946:
3941:
3936:
3931:
3926:
3925:
3924:
3922:Distance model
3914:
3909:
3902:
3897:
3892:
3887:
3882:
3876:
3874:
3868:
3867:
3865:
3864:
3862:Spectral music
3859:
3854:
3849:
3848:
3847:
3842:
3831:
3829:
3823:
3822:
3820:
3819:
3814:
3809:
3804:
3799:
3793:
3791:
3785:
3784:
3775:
3773:
3772:
3765:
3758:
3750:
3743:
3742:
3739:
3730:
3724:
3708:
3701:
3692:
3682:
3680:
3677:
3675:
3674:
3671:Taruskin (1985
3657:
3640:
3631:
3622:
3602:
3593:
3584:
3573:
3555:
3538:
3521:
3509:
3495:Schiff, András
3491:
3487:Studi Musicali
3482:
3473:
3456:
3439:
3430:
3420:. Sher Music.
3408:
3389:
3369:
3360:
3349:
3341:Kholopov, Yuri
3337:
3331:
3318:
3299:
3290:
3273:
3261:
3256:Music Analysis
3247:
3241:
3228:
3218:
3189:
3180:
3169:
3160:
3143:
3126:
3109:
3092:
3090:11, no. 5:1–8.
3088:In Theory Only
3083:
3071:
3064:
3063:
3051:
3036:
3024:
3012:
3000:
2988:
2976:
2958:
2936:
2927:, 15 June 2020
2914:
2902:
2890:
2873:The New Yorker
2855:
2843:The New Yorker
2836:(2021-12-19).
2822:
2809:
2797:
2793:Pastorius 1976
2785:
2774:
2762:
2750:
2738:
2726:
2714:
2703:
2691:
2679:
2667:
2655:
2626:
2614:
2602:
2591:
2579:
2567:
2555:
2543:
2531:
2520:
2508:
2493:
2481:
2469:
2457:
2445:
2433:
2421:
2409:
2397:
2382:
2370:
2358:
2346:
2331:
2319:
2307:
2295:
2283:
2268:
2256:
2244:
2232:
2219:
2217:
2214:
2213:
2212:
2207:
2202:
2197:
2192:
2187:
2182:
2174:
2171:
2144:
2141:
2086:
2083:
2002:
1991:
1988:
1986:
1985:
1984:
1983:
1981:
1978:
1970:interval array
1903:
1892:
1889:
1887:
1877:
1874:
1872:
1871:
1870:
1869:
1867:
1864:
1715:
1712:
1676:
1673:
1613:
1602:
1599:
1597:
1596:
1595:
1594:
1592:
1589:
1587:
1584:
1545:King Crimson's
1492:
1489:
1479:Herbie Hancock
1464:
1461:
1451:In the 1920s,
1422:Toru Takemitsu
1382:Darius Milhaud
1346:Julian Cochran
1294:Improvisations
1283:Fourth Quartet
1277:. In Bartók's
1163:'s late piece
1134:Claude Debussy
1093:
1082:
1079:
1077:
1076:
1075:
1074:
1072:
1069:
1047:Richard Wagner
1019:The Nutcracker
905:
902:
874:as octatonic:
814:
813:Early examples
811:
809:
806:
802:diatonic scale
772:, A, B. Also E
748:
747:
722:tritone: (C, F
720:
693:
666:
639:
614:whole step: (C
612:
579:
576:
431:
428:
426:
423:
404:diatonic scale
385:
384:
363:
348:
276:
265:
262:
260:
250:
247:
245:
235:
232:
230:
229:
228:
227:
225:
222:
193:, just as the
147:
144:
77:
66:
63:
61:
51:
48:
46:
45:
44:
43:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4819:
4808:
4807:Persian music
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4789:
4787:
4771:
4768:
4765:
4762:
4759:
4756:
4753:
4750:
4747:
4744:
4741:
4738:
4735:
4732:
4729:
4726:
4723:
4720:
4717:
4714:
4713:
4711:
4707:
4697:
4694:
4692:
4689:
4687:
4684:
4683:
4681:
4679:
4675:
4669:
4666:
4665:
4663:
4661:
4657:
4651:
4648:
4646:
4643:
4641:
4638:
4637:
4635:
4633:
4629:
4623:
4622:Altered (VII)
4620:
4618:
4615:
4612:
4608:
4605:
4603:
4602:Acoustic (IV)
4600:
4598:
4595:
4593:
4590:
4587:
4583:
4580:
4579:
4577:
4575:
4571:
4565:
4564:Locrian (VII)
4562:
4559:
4555:
4554:natural minor
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4531:
4528:
4525:
4521:
4520:natural major
4517:
4514:
4513:
4511:
4509:
4505:
4499:
4498:Reciting tone
4496:
4494:
4491:
4489:
4486:
4484:
4481:
4479:
4476:
4474:
4471:
4469:
4466:
4464:
4461:
4460:
4458:
4454:
4444:
4441:
4439:
4436:
4434:
4431:
4429:
4426:
4425:
4423:
4421:
4417:
4411:
4408:
4406:
4403:
4401:
4398:
4396:
4393:
4392:
4390:
4388:
4384:
4381:
4379:
4375:
4371:
4364:
4359:
4357:
4352:
4350:
4345:
4344:
4341:
4338:
4334:
4328:
4327:Bohlen–Pierce
4325:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4304:
4302:
4298:
4292:
4289:
4287:
4284:
4282:
4279:
4277:
4274:
4272:
4271:Jewish nusach
4269:
4267:
4264:
4262:
4259:
4257:
4254:
4252:
4249:
4247:
4244:
4239:
4238:
4233:
4230:
4229:
4224:
4223:
4221:
4216:
4212:
4211:
4209:
4204:
4200:
4197:
4193:
4190:
4189:Major Locrian
4186:
4183:
4179:
4178:
4176:
4174:
4171:
4170:
4168:
4166:Ethnic origin
4164:
4158:
4155:
4153:
4150:
4148:
4145:
4143:
4140:
4138:
4135:
4133:
4130:
4128:
4125:
4123:
4122:Major Locrian
4120:
4118:
4115:
4113:
4110:
4108:
4105:
4103:
4100:
4098:
4095:
4093:
4092:Flamenco mode
4090:
4088:
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4054:
4052:
4048:
4042:
4039:
4037:
4034:
4032:
4029:
4027:
4024:
4022:
4019:
4018:
4016:
4012:
4007:
4003:
3996:
3991:
3989:
3984:
3982:
3977:
3976:
3973:
3961:
3958:
3957:
3955:
3951:
3945:
3944:Unified field
3942:
3940:
3937:
3935:
3932:
3930:
3927:
3923:
3920:
3919:
3918:
3915:
3913:
3910:
3908:
3907:
3903:
3901:
3898:
3896:
3893:
3891:
3888:
3886:
3883:
3881:
3878:
3877:
3875:
3869:
3863:
3860:
3858:
3855:
3853:
3850:
3846:
3843:
3841:
3838:
3837:
3836:
3833:
3832:
3830:
3824:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3794:
3792:
3786:
3782:
3781:post-tonality
3778:
3771:
3766:
3764:
3759:
3757:
3752:
3751:
3748:
3740:
3737:
3736:
3731:
3727:
3721:
3717:
3713:
3709:
3706:
3702:
3699:
3698:
3693:
3690:
3689:
3684:
3683:
3678:
3672:
3666:
3662:
3658:
3654:
3653:0-300-05111-5
3650:
3646:
3641:
3637:
3632:
3628:
3623:
3619:
3615:
3611:
3607:
3603:
3599:
3594:
3590:
3585:
3581:
3580:
3574:
3570:
3569:
3560:
3556:
3552:
3548:
3544:
3539:
3535:
3531:
3527:
3522:
3518:
3514:
3510:
3506:
3505:
3500:
3496:
3492:
3488:
3483:
3479:
3474:
3470:
3469:0-521-39976-9
3466:
3462:
3457:
3453:
3452:0-7645-5009-8
3449:
3445:
3440:
3436:
3431:
3427:
3426:1-883217-04-0
3423:
3419:
3418:
3413:
3409:
3406:
3405:Wilson (1992)
3400:
3396:
3392:
3390:0-900707-04-6
3386:
3382:
3379:. introd. by
3378:
3374:
3373:Lendvai, Ernő
3370:
3366:
3361:
3359:
3356:
3350:
3346:
3342:
3338:
3334:
3328:
3324:
3319:
3315:
3311:
3307:
3306:
3300:
3296:
3291:
3287:
3286:0-7866-7236-6
3283:
3279:
3274:
3270:
3266:
3262:
3258:
3257:
3252:
3248:
3244:
3242:9781351204255
3238:
3234:
3229:
3224:
3219:
3215:
3214:0-521-65478-5
3211:
3207:
3206:0-521-65243-X
3203:
3199:
3195:
3190:
3186:
3181:
3177:
3176:
3170:
3166:
3161:
3157:
3153:
3149:
3144:
3140:
3139:0-7579-0357-6
3136:
3132:
3127:
3123:
3122:0-520-06747-9
3119:
3115:
3110:
3106:
3102:
3098:
3093:
3089:
3084:
3080:
3079:
3073:
3072:
3070:
3069:
3060:
3055:
3052:
3048:
3043:
3041:
3037:
3033:
3028:
3025:
3021:
3016:
3013:
3009:
3004:
3001:
2997:
2992:
2989:
2985:
2980:
2977:
2969:
2962:
2959:
2948:
2947:
2940:
2937:
2926:
2925:
2918:
2915:
2911:
2906:
2903:
2899:
2898:Taruskin 1987
2894:
2891:
2879:
2875:
2874:
2869:
2865:
2859:
2856:
2845:
2844:
2839:
2835:
2829:
2827:
2823:
2819:
2813:
2810:
2806:
2801:
2798:
2794:
2789:
2786:
2783:
2778:
2775:
2771:
2766:
2763:
2759:
2754:
2751:
2747:
2742:
2739:
2735:
2730:
2727:
2723:
2718:
2715:
2712:
2707:
2704:
2700:
2695:
2692:
2688:
2683:
2680:
2676:
2671:
2668:
2664:
2659:
2656:
2651:
2650:
2645:
2640:
2636:
2630:
2627:
2623:
2618:
2615:
2611:
2606:
2603:
2600:
2595:
2592:
2588:
2583:
2580:
2576:
2571:
2568:
2564:
2559:
2556:
2552:
2547:
2544:
2540:
2535:
2532:
2529:
2524:
2521:
2517:
2512:
2509:
2505:
2504:Taruskin 1996
2500:
2498:
2494:
2490:
2485:
2482:
2478:
2473:
2470:
2466:
2465:Taruskin 1996
2461:
2458:
2454:
2453:Taruskin 1996
2449:
2446:
2442:
2437:
2434:
2431:, 329, 493n5.
2430:
2425:
2422:
2418:
2413:
2410:
2406:
2401:
2398:
2394:
2389:
2387:
2383:
2379:
2374:
2371:
2367:
2366:Schuijer 2008
2362:
2359:
2355:
2354:Taruskin 1985
2350:
2347:
2343:
2338:
2336:
2332:
2328:
2327:Hatfield 2005
2323:
2320:
2316:
2315:Campbell 2001
2311:
2308:
2304:
2303:Kholopov 2003
2299:
2296:
2292:
2291:Kholopov 1982
2287:
2284:
2281:
2280:Yavorsky 1911
2277:
2276:Taruskin 1985
2272:
2269:
2265:
2264:Taruskin 1985
2260:
2257:
2253:
2248:
2245:
2241:
2236:
2233:
2229:
2224:
2221:
2215:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2180:
2177:
2176:
2172:
2170:
2154:
2150:
2142:
2140:
2132:
2128:
2127:Elektra chord
2084:
2082:
2062:
2057:
1995:
1979:
1977:
1975:
1971:
1967:
1964:
1960:
1950:
1947:
1943:
1938:
1913:", such as: C
1912:
1896:
1881:
1865:
1863:
1812:
1773:
1771:
1765:
1727:
1726:
1721:
1713:
1711:
1707:
1705:
1704:
1699:
1695:
1692:, Scriabin's
1691:
1685:
1682:
1674:
1672:
1670:
1667:
1663:
1653:
1649:
1648:
1643:
1639:
1635:
1627:
1626:
1621:
1617:
1606:
1590:
1585:
1583:
1581:
1578:
1574:
1571:
1567:
1562:
1560:
1559:
1558:The Barbarian
1555:
1551:
1550:
1546:
1542:
1538:
1537:
1532:
1531:
1526:
1522:
1521:Dream Theater
1518:
1513:
1511:
1510:
1505:
1501:
1497:
1490:
1488:
1486:
1485:
1480:
1476:
1475:
1469:
1462:
1460:
1458:
1454:
1449:
1447:
1443:
1442:Willem Pijper
1439:
1435:
1434:John Williams
1431:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1399:
1395:
1391:
1390:Robert Morris
1387:
1383:
1379:
1375:
1371:
1367:
1366:John Harbison
1363:
1359:
1355:
1351:
1347:
1343:
1339:
1335:
1334:Samuel Barber
1330:
1328:
1327:
1322:
1318:
1314:
1308:
1307:
1302:
1301:
1296:
1295:
1290:
1289:
1284:
1280:
1276:
1272:
1267:
1265:
1264:Boris Godunov
1261:
1257:
1251:
1249:
1248:
1243:
1242:
1237:
1233:
1232:
1227:
1223:
1222:
1217:
1216:
1211:
1210:
1205:
1204:
1199:
1198:
1193:
1192:
1187:
1186:
1181:
1180:
1175:
1170:
1168:
1167:
1162:
1158:
1153:
1152:
1147:
1143:
1139:
1138:Maurice Ravel
1135:
1118:
1117:Istrian scale
1114:
1107:
1103:
1102:
1097:
1086:
1070:
1065:
1060:
1056:
1054:
1053:
1048:
1039:
1023:
1021:
1020:
1015:
1011:
1009:
1008:
1000:
996:
990:
989:Boris Godunov
985:
979:
978:Boris Godunov
966:
964:
963:
962:Boris Godunov
958:
954:
950:
941:
925:
923:
922:András Schiff
919:
911:
903:
901:
899:
898:Honoré Langlé
891:
875:
873:
869:
860:
844:
842:
838:
834:
830:
825:
823:
819:
812:
807:
805:
803:
799:
796:
791:
753:
721:
694:
667:
640:
632:), (G, A), (B
613:
586:
585:
584:
577:
575:
494:
443:
441:
437:
429:
424:
422:
420:
417:
413:
409:
408:key signature
405:
400:
398:
364:
349:
316:
315:
314:
310:
308:
304:
300:
296:
292:
287:
285:
269:
254:
239:
223:
221:
219:
215:
214:Willem Pijper
210:
208:
204:
200:
196:
192:
188:
184:
179:
177:
173:
169:
165:
161:
157:
153:
145:
143:
141:
137:
133:
129:
124:
122:
121:
116:
112:
108:
104:
100:
97:
96:ancohemitonic
93:
92:musical scale
90:
87:is any eight-
86:
70:
55:
40:
33:
27:Musical scale
19:
4757:
4696:Oriental (V)
4550:Aeolian (VI)
4433:Hypophrygian
4235:
4226:
4196:Quarter tone
4066:
4014:Main Western
3953:Compositions
3939:Tone cluster
3917:Polytonality
3904:
3880:Chromaticism
3873:and concepts
3811:
3807:Mystic chord
3733:
3715:
3695:
3686:
3664:
3644:
3635:
3626:
3609:
3597:
3588:
3577:
3566:
3542:
3525:
3516:
3504:The Guardian
3502:
3486:
3477:
3460:
3443:
3415:
3412:Levine, Mark
3376:
3364:
3358:
3353:
3344:
3322:
3303:
3294:
3277:
3268:
3265:Frazzi, Vito
3254:
3251:Forte, Allen
3232:
3222:
3193:
3184:
3173:
3164:
3147:
3130:
3113:
3096:
3087:
3076:
3067:
3066:
3054:
3032:Slayton 2010
3027:
3015:
3008:Lendvai 1971
3003:
2991:
2979:
2961:
2951:, retrieved
2945:
2939:
2929:, retrieved
2923:
2917:
2905:
2893:
2882:. Retrieved
2878:the original
2871:
2858:
2847:. Retrieved
2841:
2812:
2800:
2788:
2782:"Opus Pocus"
2777:
2765:
2753:
2746:Clement 2009
2741:
2734:Durrand 2020
2729:
2722:Alegant 2010
2717:
2706:
2694:
2682:
2670:
2658:
2647:
2635:Ghostarchive
2633:Archived at
2629:
2617:
2605:
2594:
2582:
2570:
2558:
2546:
2534:
2523:
2511:
2484:
2472:
2460:
2448:
2436:
2424:
2412:
2400:
2373:
2361:
2349:
2322:
2310:
2298:
2286:
2271:
2259:
2247:
2235:
2223:
2156:
2107:, E, G, A, C
2100:
2058:
2013:
1959:Ernő Lendvai
1942:Forte number
1939:
1908:
1813:
1774:
1766:
1723:
1717:
1708:
1701:
1700:and Ravel's
1697:
1696:, Debussy's
1693:
1690:Scheherezade
1689:
1686:
1678:
1652:major triads
1645:
1631:
1623:
1579:
1572:
1563:
1556:
1547:
1534:
1533:and Opeth's
1528:
1514:
1507:
1494:
1491:Rock and pop
1484:Miles Smiles
1482:
1472:
1470:
1466:
1450:
1445:
1370:Jacques Hétu
1350:George Crumb
1338:Ernest Bloch
1331:
1324:
1315:
1304:
1298:
1292:
1286:
1278:
1268:
1263:
1255:
1252:
1245:
1239:
1229:
1219:
1218:(1930), the
1213:
1209:The Firebird
1207:
1201:
1195:
1189:
1183:
1177:
1171:
1164:
1149:
1131:
1104:, bars 5–8.
1099:
1063:
1050:
1044:
1017:
1012:
1007:Scheherazade
1005:
1003:
988:
977:
960:
948:
946:
907:
904:19th century
896:
865:
832:
826:
816:
792:
752:minor scales
749:
581:
495:
457:scale, the C
444:
433:
401:
399: 8‑28.
386:
311:
306:
302:
288:
281:
224:Construction
218:Pijper scale
217:
211:
206:
202:
186:
182:
180:
175:
171:
167:
163:
155:
149:
146:Nomenclature
139:
131:
125:
119:
118:
114:
84:
82:
4540:Lydian (IV)
4530:Dorian (II)
4488:Hypolocrian
4478:Hypoaeolian
4050:Other types
3691:52, no. 1:.
3020:Wilson 1992
2996:Wilson 1992
2984:Wilson 1992
2736:, p. .
2687:Wilson 1992
2563:DeVoto 2003
2516:DeVoto 2007
2489:Schiff 2005
2477:Langlé 1797
2342:Levine 1995
2240:Frazzi 1930
2205:Gamma scale
2200:Delta scale
2190:Alpha scale
2097:Gamma chord
2085:Gamma chord
1966:major chord
1946:pitch class
1866:Alpha chord
1725:Mikrokosmos
1720:Béla Bartók
1573:Desert Girl
1536:Deliverance
1517:heavy metal
1438:Frank Zappa
1354:Irving Fine
1300:Mikrokosmos
1275:Béla Bartók
1244:(1955) and
1169:from 1885.
1157:cor anglais
1146:cor anglais
1142:Allen Forte
1014:Tchaikovsky
798:tetrachords
740:, G), (E, B
686:, G), (A, C
659:, E), (G, B
605:, G), (A, B
136:Vito Frazzi
111:jazz theory
18:Gamma chord
4786:Categories
4752:Heptatonic
4740:Pentatonic
4734:Tetratonic
4574:Jazz minor
4516:Ionian (I)
4493:Pentatonic
4468:Hypoionian
4438:Hypolydian
4428:Hypodorian
4410:Mixolydian
4300:Non-octave
4276:Neapolitan
4157:Whole tone
4117:Jazz minor
4082:Enharmonic
4031:Pentatonic
3934:Tone Clock
3885:Cyclic set
3871:Techniques
3826:Genres and
3788:Scales and
3489:22, no. 2:
3435:Opus Pocus
3059:Anon. 1977
3047:Honti 2007
2953:2023-08-19
2931:2023-08-19
2910:Pogue 1997
2884:2021-07-11
2864:Ross, Alex
2849:2021-12-19
2834:Ross, Alex
2805:Piano solo
2622:Cross 2015
2610:Walsh 1988
2575:Walsh 2018
2553:, 144–145.
2551:Forte 1991
2441:Agmon 1990
2393:Pople 1991
2228:Kahan 2009
2216:References
2195:Beta scale
1980:Beta chord
1949:prime form
1781:, D, and E
1770:bitonality
1714:Bitonality
1660:major – a
1644:'s ballet
1622:'s ballet
1620:Stravinsky
1570:Planet X's
1530:Octavarium
1426:Joan Tower
1279:Bagatelles
1228:(1923) to
868:J. S. Bach
425:Properties
295:whole step
107:half steps
4770:Chromatic
4764:Decatonic
4758:Octatonic
4746:Hexatonic
4716:Monotonic
4387:Authentic
4378:Gregorian
4142:Symmetric
4087:Enigmatic
4041:Chromatic
3857:Serialism
3777:Atonality
3669:Cited in
3497:(2005). "
3403:Cited in
3381:Alan Bush
3208:(cloth);
3078:Soundings
2772:, 464n11.
2758:Chan 2005
2699:Hill 1995
2378:Cohn 1991
2075:, E, G, C
2038:, E, G, C
2020:, E, G, B
1688:Rimsky's
1666:dissonant
1647:Petrushka
1638:polytonal
1625:Petrushka
1500:Radiohead
1474:Pastorius
1394:Carl Orff
1203:Fireworks
1179:Petrushka
1151:Nocturnes
1101:Nocturnes
1049:'s opera
959:'s opera
953:Totentanz
397:set class
350:D E G A
168:octatonic
39:August 28
4728:Tritonic
4508:Diatonic
4400:Phrygian
4266:Japanese
4222:Gamelan
4173:Algerian
4097:Harmonic
4036:Diatonic
3608:(2005).
3515:(1946).
3414:(1995).
3375:(1971).
3343:(2003).
3267:(1930).
2689:, 26–27.
2637:and the
2173:See also
2166:♭
2160:♭
2136:♯
2122:♯
2116:♮
2110:♮
2104:♯
2078:♮
2072:♯
2066:♯
2053:♮
2047:♯
2041:♮
2035:♯
2029:♮
2023:♭
2017:♯
2006:♯
1963:mistuned
1954:♭
1944:: 4-17,
1934:♯
1928:♭
1922:♭
1916:♯
1859:♭
1853:♭
1847:♭
1844:and E, G
1841:♭
1835:♭
1829:♭
1823:♭
1817:♭
1808:♭
1802:♭
1796:♭
1790:♭
1784:♭
1778:♭
1761:♭
1755:♭
1749:♭
1743:♭
1737:♭
1731:♭
1657:♯
1543:include
1487:(1967).
1326:Preludes
1182:(1911),
918:, Op. 22
914:♭
787:♭
781:♭
775:♭
769:♯
763:♯
757:♭
743:♭
737:♯
734:, A), (C
731:♭
725:♯
716:♭
710:♭
704:♯
698:♯
689:♯
683:♭
677:♭
671:♯
662:♭
656:♯
653:, A), (C
650:♯
644:♭
635:♭
629:♯
626:), (E, F
623:♯
617:♯
608:♭
602:♯
596:♯
590:♯
571:♭
565:♭
559:♭
553:♭
547:♯
541:♭
535:♯
529:♭
523:♯
517:♯
511:♭
505:♯
499:♭
490:♭
484:♯
478:♯
472:♭
466:♭
460:♯
454:♭
448:♭
430:Symmetry
419:tonality
416:diatonic
380:♭
374:♭
368:♭
359:♯
353:♯
344:♯
338:♯
332:♯
326:♯
320:♯
305:and the
299:semitone
205:and the
117:(or the
4722:Ditonic
4483:Locrian
4473:Aeolian
4281:Persian
4261:Istrian
4237:Slendro
4210:Brazil
4177:Arabic
3828:schools
3673:, 113).
3068:Sources
2649:YouTube
2131:Hendrix
1826:, and G
1746:, and A
1662:tritone
1096:Debussy
1066:, act 1
999:YouTube
808:History
599:, E) (F
578:Subsets
377:B D (E
4463:Ionian
4420:Plagal
4405:Lydian
4395:Dorian
3790:tuning
3722:
3665:Muzyka
3651:
3616:
3549:
3532:
3467:
3450:
3424:
3399:240301
3397:
3387:
3355:Гуляма
3329:
3312:
3284:
3239:
3216:(pbk).
3212:
3204:
3154:
3137:
3120:
3103:
3049:, 305.
2900:, 269.
2748:, 214.
2724:, 109.
2624:, 144.
2612:, 127.
2577:, 137.
2565:, 183.
2541:, 228.
2518:, 144.
2506:, 283.
2467:, 269.
2455:, 266.
2443:, 1–8.
2380:, 271.
2368:, 109.
2329:, 125.
2317:, 126.
2305:, 227.
2266:, 132.
2050:, G, C
1919:–E–G–B
1838:, C, E
1740:, F, G
1703:Scarbo
1698:Nuages
1679:While
1291:, and
1247:Threni
1236:serial
778:, F, G
412:staves
199:triads
4456:Other
4336:Modes
4322:Delta
4317:Gamma
4307:Alpha
4246:Gypsy
4228:Pelog
4062:Blues
4057:Bebop
4026:Minor
4021:Major
3061:, 12.
3034:, 15.
2986:, 27.
2971:(PDF)
2912:, 80.
2760:, 52.
2701:, 73.
2589:, 42.
2356:, 73.
2344:, 78.
2293:, 30.
2044:and C
1669:chord
1525:Opeth
1260:rumba
1226:Octet
1161:Liszt
795:modal
728:), (E
707:), (B
680:), (E
647:), (F
593:), (D
502:and C
496:The E
481:and C
291:modes
174:, or
103:whole
4772:(12)
4766:(10)
4556:and
4522:and
4312:Beta
4112:Jazz
4006:list
3845:List
3779:and
3720:ISBN
3649:ISBN
3614:ISBN
3547:ISBN
3530:ISBN
3465:ISBN
3448:ISBN
3422:ISBN
3395:OCLC
3385:ISBN
3327:ISBN
3310:ISBN
3282:ISBN
3237:ISBN
3210:ISBN
3202:ISBN
3152:ISBN
3135:ISBN
3118:ISBN
3101:ISBN
3022:, 9.
2998:, 7.
2395:, 2.
2151:and
1937:–A.
1925:–C–E
1632:The
1614:The
1575:and
1552:and
1523:and
1504:Just
1477:and
1463:Jazz
1436:and
1273:and
1231:Agon
1136:and
638:, C)
487:to E
438:and
371:F A
335:A B
105:and
89:note
4760:(8)
4754:(7)
4748:(6)
4742:(5)
4736:(4)
4730:(3)
4724:(2)
4718:(1)
3840:Row
3647:.
3565:".
3528:.
3501:".
3446:.
3150:.
3133:.
3099:.
2677:, .
2407:, .
2254:, .
2230:, .
2119:, C
2069:: C
2026:, C
1820:, E
1718:In
1549:Red
1313:".
1098:'s
997:on
870:'s
784:, A
766:, G
713:, E
701:, F
674:, B
620:, D
538:, D
514:, F
362:(D)
185:or
178:.)
138:'s
83:An
4788::
3545:.
3393:.
3280:.
3039:^
2870:.
2840:.
2825:^
2646:.
2641::
2496:^
2385:^
2334:^
1976:.
1931:–F
1862:.
1561:.
1432:,
1428:,
1424:,
1420:,
1416:,
1412:,
1408:,
1404:,
1400:,
1396:,
1392:,
1388:,
1384:,
1380:,
1376:,
1372:,
1368:,
1364:,
1360:,
1356:,
1352:,
1348:,
1344:,
1340:,
1336:,
1285:,
1281:,
1200:,
991:.
544:/C
532:/A
421:.
341:(C
220:.
209:.
4613:)
4609:(
4588:)
4584:(
4560:)
4552:(
4526:)
4518:(
4362:e
4355:t
4348:v
4008:)
4004:(
3994:e
3987:t
3980:v
3769:e
3762:t
3755:v
3728:.
3655:.
3620:.
3563:'
3553:.
3536:.
3471:.
3454:.
3428:.
3407:.
3401:.
3335:.
3316:.
3288:.
3245:.
3227:.
3158:.
3141:.
3124:.
3107:.
3010:.
2973:.
2887:.
2852:.
2795:.
2665:.
2491:.
2419:.
2242:.
1996:.
1897:.
1882:.
1607:.
1311:'
1087:.
746:)
692:)
665:)
611:)
383:)
365:E
356:C
347:)
329:F
323:D
317:C
270:.
255:.
240:.
71:.
56:.
41:.
34:.
20:)
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