Aquarter tone is a pitch halfway between the usual notes of achromatic scale or aninterval about half as wide (orally, or logarithmically) as asemitone, which itself is half awhole tone. Quarter tones divide the octave by 50cents each, and have 24 different pitches.
Quarter tones have their roots in the music of the Middle East and more specifically inPersian traditional music.[1] However, the first evidenced proposal of theequally-tempered quarter tone scale, or24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823[2] andMikhail Mishaqa about 1840.[3] Composers who have written music using this scale include:Pierre Boulez,Julián Carrillo,Mildred Couper,George Enescu,Alberto Ginastera,Gérard Grisey,Alois Hába,Ljubica Marić,Charles Ives,Tristan Murail,Krzysztof Penderecki,Giacinto Scelsi,Ammar El Sherei,Karlheinz Stockhausen,Tui St. George Tucker,Ivan Wyschnegradsky,Iannis Xenakis, andSeppe Gebruers (SeeList of quarter tone pieces.)
–G–A) as good possibility for a "fundamental" chord in the quarter-tone scale, akin not to the tonic but to the major chord of traditional tonality.[4]
=A
, 19 quarter tones. It approximates theharmonic seventh,B
♭. Maneri-Sims notation:B
♭The termquarter tone can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., D♯–E♭).[2] In the quarter-tone scale, also called24-tone equal temperament (24-TET), the quarter tone is 50cents, or a frequency ratio of24√2 or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). In this scale the quarter tone is the smalleststep. A semitone is thus made of two steps, and three steps make athree-quarter tone orneutral second, half of aminor third. The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone.
Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems.22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas53-TET has an interval of 45.28 cents, slightly smaller.72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in31 equal temperament (the "diesis" of 38.71 cents) is half achromatic semitone, one-third of adiatonic semitone and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-toneor a sixth-tone.
Injust intonation the quarter tone can be represented by theseptimal quarter tone, 36:35 (48.77 cents), or by theundecimal quarter tone (i.e. thethirty-third harmonic), 33:32 (53.27 cents), approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between aminor third (6:5) andseptimal minor third (7:6).
ComposerBen Johnston, to accommodate thejust septimal quarter tone, uses a small "7" () as an accidental to indicate a note is lowered 49 cents, or an upside down "7" (
) to indicate a note is raised 49 cents,[5] or a ratio of 36:35.[6] Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents.[6] TheManeri-Sims notation system designed for72-et uses the accidentals
and for a quarter tone (36:35 or 48.77 cents) up and down.
Any tunable musical instrument can be used to perform quarter tones, if two players and two identical instruments, with one tuned a quarter tone higher, are used. As this requires neither a special instrument nor special techniques, much quarter toned music is written for pairs of pianos, violins, harps, etc. The retuning of the instrument, and then returning it to its former pitch, is easy for violins, harder for harps, and slow and relatively expensive for pianos.
The following deals with the ability of single instruments to produce quarter tones. In Western instruments, this means "in addition to the usual 12-tone system". Because many musical instruments manufactured today (2018) are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used.
Conventional musical instruments thatcannot play quarter tones (except by using special techniques—see below) include:
Conventional musical instruments thatcan play quarter tones include
Other instruments can be used to play quarter tones when usingaudio signal processing effects such aspitch shifting.
Quarter-tone pianos have been built, which consist essentially of two pianos with two keyboards stacked one above the other in a single case, one tuned a quarter tone higher than the other.[citation needed]
Many Persiandastgah and Arabicmaqamat contain intervals of three-quarter tone size; a short list of these follows.[8]
F G A B♭ C D F G A B C (ascending) D C (descending) F G♭ A B♭ C D F G A B C D EThe Islamic philosopher and scientistAl-Farabi described a number of intervals in his work in music, including a number of quarter tones.
Assyrian/Syriac Church Music Scale:[9]
Known asgadwal in Arabic,[8] thequarter-tone scale was developed in the Middle East in the eighteenth century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones.[10]The invention of the scale is attributed toMishaqa who wrote a book devoted to the topic[11] but made clear that his teacher, Sheikh Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.[12]
The quarter tone scale may be primarily atheoretical construct in Arabic music. The quarter tone gives musicians a "conceptual map" they can use to discuss and compare intervals by number of quarter tones, and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory a mainstream requirement since that period.[10]
Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed bySafi al-Din al-Urmawi in the thirteenth century.[12]
ComposerCharles Ives chose the chord C–D–F–G–B♭ as good possibility for a "secondary" chord in the quarter-tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale[4] Here is the secondary "minor" and its "first inversion":
The bass descent ofNancy Sinatra's version of "These Boots Are Made for Walkin'" includes quarter tone descents.[13]Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, USA.[14][15]Another quartertone metal album was issued by the Swedish band Massive Audio Nerve.[16]Australianpsychedelic rock bandKing Gizzard & the Lizard Wizard's albumsFlying Microtonal Banana,K.G., andL.W. heavily emphasize quarter-tones and used a custom-built guitar in 24 TET tuning.[17]Jazz violinist / violistMat Maneri, in conjunction with his fatherJoe Maneri, made a crossover fusion album,Pentagon (2005),[18] that featured experiments in hip hop with quarter tone pianos, as well as electric organ andmellotron textures, along with distorted trombone, in a post-Bitches Brew type of mixedjazz /rock.[19]
Later,Seppe Gebruers started playing and improvising with two pianos tuned a quarter-tone apart. In 2019 he started a research project at theRoyal Conservatory of Ghent, titled 'Unexplored possibilities of contemporary improvisation and the influence of microtonality in the creation process'.[20]With two pianos tuned a quarter tone apart Gebruers recorded 'The Room: Time & Space' (2018) in a trio formation with drummerPaul Lovens and bassistHugo Anthunes. In his solo project 'Playing with standards' (album release January 2023), Gebruers plays with famous songs including jazz standards. WithPaul Lytton andNils Vermeulen he forms a 'Playing with standards' trio.
Theenharmonic genus of theGreektetrachord consisted of aditone or an approximatemajor third, and asemitone, which was divided into twomicrotones.Aristoxenos,Didymos and others presented the semitone as being divided into two approximate quarter tone intervals of about the same size, while other ancient Greek theorists described the microtones resulting from dividing the semitone of the enharmonic genus as unequal in size (i.e., one smaller than a quarter tone and one larger).[21][22]
Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed byAlois Hába (neutral third, etc.) andIvan Wyschnegradsky (major fourth, etc.):
| Interval name | Size (steps) | Size (cents) | MIDI | Just ratio | Just (cents) | MIDI | Error (cents) |
|---|---|---|---|---|---|---|---|
| octave | 24 | 1200 | 2:1 | 1200.00 | 0.00 | ||
| semidiminished octave | 23 | 1150 | 35:18 | 1151.23 | −1.23 | ||
| supermajor seventh | 23 | 1150 | 27:14 | 1137.04 | +12.96 | ||
| major seventh | 22 | 1100 | 15:8 | 1088.27 | +11.73 | ||
| neutral seventh,major tone | 21 | 1050 | 11:6 | 1049.36 | +0.64 | ||
| neutral seventh,minor tone | 21 | 1050 | 20:11 | 1035.00 | +15.00 | ||
| large justminor seventh | 20 | 1000 | 9:5 | 1017.60 | −17.60 | ||
| small justminor seventh | 20 | 1000 | 16:9 | 996.09 | +3.91 | ||
| supermajor sixth/subminor seventh | 19 | 950 | 7:4 | 968.83 | −18.83 | ||
| major sixth | 18 | 900 | 5:3 | 884.36 | +15.64 | ||
| neutral sixth | 17 | 850 | 18:11 | 852.59 | −2.59 | ||
| minor sixth | 16 | 800 | 8:5 | 813.69 | −13.69 | ||
| subminor sixth | 15 | 750 | 14:9 | 764.92 | −14.92 | ||
| perfect fifth | 14 | 700 | 3:2 | 701.96 | −1.96 | ||
| minor fifth | 13 | 650 | 16:11 | 648.68 | +1.32 | ||
| lesserseptimal tritone | 12 | 600 | 7:5 | 582.51 | +17.49 | ||
| major fourth | 11 | 550 | 11:8 | 551.32 | −1.32 | ||
| perfect fourth | 10 | 500 | 4:3 | 498.04 | +1.96 | ||
| tridecimalmajor third | 9 | 450 | 13:10 | 454.21 | −4.21 | ||
| septimal major third | 9 | 450 | 9:7 | 435.08 | +14.92 | ||
| major third | 8 | 400 | 5:4 | 386.31 | +13.69 | ||
| undecimalneutral third | 7 | 350 | 11:9 | 347.41 | +2.59 | ||
| minor third | 6 | 300 | 6:5 | 315.64 | −15.64 | ||
| septimal minor third | 5 | 250 | 7:6 | 266.87 | −16.87 | ||
| tridecimal five-quarter tone | 5 | 250 | 15:13 | 247.74 | +2.26 | ||
| septimal whole tone | 5 | 250 | 8:7 | 231.17 | +18.83 | ||
| major second,major tone | 4 | 200 | 9:8 | 203.91 | −3.91 | ||
| major second,minor tone | 4 | 200 | 10:9 | 182.40 | +17.60 | ||
| neutral second, greater undecimal | 3 | 150 | 11:10 | 165.00 | −15.00 | ||
| neutral second, lesser undecimal | 3 | 150 | 12:11 | 150.64 | −0.64 | ||
| 15:14 semitone | 2 | 100 | 15:14 | 119.44 | −19.44 | ||
| diatonic semitone,just | 2 | 100 | 16:15 | 111.73 | −11.73 | ||
| 21:20 semitone | 2 | 100 | 21:20 | 84.47 | +15.53 | ||
| 28:27 semitone | 1 | 50 | 28:27 | 62.96 | −12.96 | ||
| 33:32 semitone | 1 | 50 | 33:32 | 53.27 | −3.27 | ||
| unison | 0 | 0 | 1:1 | 0.00 | 0.00 |
Moving from12-TET to 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include theneutral second,neutral third, and (11:8) ratio, or the 11th harmonic. Theseptimal minor third andseptimal major third are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th and 13th harmonics more closely than the 7th.
{{cite book}}: CS1 maint: multiple names: authors list (link)| Twelve- semitone (post-Bach Western) |
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