thumb|Quarter tone on C
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
thumb|upright=1.5|[[Trumpet with 3 normal valves and a quartering on the extension valve (right)]]
Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikhail Mishaqa about 1840. Composers who have written music using this scale include: Igor Markevitch, Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Thomas Heberer Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Wyschnegradsky, Iannis Xenakis, and Seppe Gebruers (See List of quarter tone pieces.)
Types
Equal-tempered tuning systems
thumb|upright=1.3|Composer Charles Ives chose the four-note chord above (C–D–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.[[File:Ives fundamental chord (quarter tones).oggFile:Ives quarter tone fundamental chord arp.mid]]
thumb|The "subminor seventh": =, 19 quarter tones. It approximates the [[harmonic seventh, . Maneri-Sims notation: ]]
The term quarter 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). or a ratio of 36:35. Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents.
- Valved brass instruments with extra, quarter-tone valves, and natural brass instruments that play through the 11th and 13th partials of the harmonic series
- Voice
- Kazoo
- Pitched percussion instruments, when tuning permits (e.g., timpani), or using special techniques
Other instruments can be used to play quarter tones when using audio signal processing effects such as pitch 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.
Music of the Middle East
Many Persian dastgah and Arabic maqamat contain intervals of three-quarter tone size; a short list of these follows.
- Bayati (): D E F G A B C D
- :<score override_ogg="Arabic-scale bayati.ogg">
\relative c' {
\time 8/4 \omit Staff.TimeSignature
d4 eeh f g a bes c d \bar "|"
}
</score>
- Rast ():
- :C D E F G A B C (ascending)
- :C B A G F E D C (descending)
- :<score override_ogg="Arabic-scale rast.ogg">
\relative c' {
\time 8/4 \omit Staff.TimeSignature
c4 d eeh f g a beh c \bar "|"
}
</score>
- Saba (): D E F G A B C D
- :<score override_ogg="Arabic-scale saba.ogg">
\relative c' {
\time 8/4 \omit Staff.TimeSignature
d4 eeh f ges a bes c d \bar "|"
}
</score>
- Segah (): E F G A B C D E
- :<score sound="1">
\relative c' {
\time 8/4 \omit Staff.TimeSignature
eeh f g a beh c d eeh \bar "|"
}
</score>
- ‘Ajam ()
- Hoseyni
The Islamic philosopher and scientist Al-Farabi described a number of intervals in his work in music, including a number of quarter tones.
Assyrian/Syriac Church Music Scale:
- Qadmoyo (Bayati)
- Trayono (Hussayni)
- Tlithoyo (Segah)
- Rbiʿoyo (Rast)
- Hmishoyo
- Shtithoyo (ʿAjam)
- Shbiʿoyo
- Tminoyo
=== Quarter-tone scale ===<!-- Quarter tone scale redirects directly here. -->
Known as gadwal in Arabic,
The invention of the scale is attributed to Mishaqa who wrote a book devoted to the topic but made clear that his teacher, Sheikh Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.
<score sound="1">
\relative c' {
\cadenzaOn \omit Staff.TimeSignature
\tempo 1 = 90 \set Score.tempoHideNote = ##t
c1 cih cis cisih d dih dis disih e eih f fih fis fisih g gih gis gisih a aih ais aisih b bih \bar "|" c \bar "|." \break
c1 ceh b beh bes beseh a aeh aes aeseh g geh ges geseh f feh e eeh ees eeseh d deh des deseh \bar "|" c \bar "|."
}
</score>
The quarter tone scale may be primarily a theoretical 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.
Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, US.
Another quartertone metal album was issued by the Swedish band Massive Audio Nerve.
Australian psychedelic rock band King Gizzard & the Lizard Wizard's albums Flying Microtonal Banana, K.G., and L.W. heavily emphasize quarter-tones and used a custom-built guitar in 24 tuning.
Jazz violinist / violist Mat Maneri, in conjunction with his father Joe Maneri, made a crossover fusion album, Pentagon (2005), that featured experiments in hip hop with quarter tone pianos, as well as electric organ and mellotron textures, along with distorted trombone, in a post-Bitches Brew type of mixed jazz / rock.
Later, Seppe Gebruers started playing and improvising with two pianos tuned a quarter-tone apart. In 2019 he started a research project at the Royal Conservatory of Ghent, titled 'Unexplored possibilities of contemporary improvisation and the influence of microtonality in the creation process'.
With two pianos tuned a quarter tone apart Gebruers recorded 'The Room: Time & Space' (2018) in a trio formation with drummer Paul Lovens and bassist Hugo Anthunes. In his solo project 'Playing with standards' (album release January 2023), Gebruers plays with famous songs including jazz standards. With Paul Lytton and Nils Vermeulen he forms a 'Playing with standards' trio. In 2026, Quebec rock duet Angine de Poitrine went viral with their performances using 24TET guitar and bass combined in a doubleneck instrument and drumset.
Ancient Greek tetrachords
The enharmonic genus of the Greek tetrachord consisted of a ditone or an approximate major third, and a semitone, which was divided into two microtones. 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).
thumb|left|upright=1.3|Greek Dorian enharmonic genus: two disjunct tetrachords each of a quarter tone, quarter tone, and major third.[[File:Greek Dorian mode on E, enharmonic genus.mid ]]
Interval size in equal temperament
Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by Alois Hába (neutral third, etc.) and Ivan Wyschnegradsky (major fourth, etc.):
:{| class="wikitable"
! Interval name
! Size<BR />(steps)
! Size<BR />(cents)
! MIDI
! Just ratio
! Just<BR />(cents)
! MIDI
! Error<BR />(cents)
|-
| octave
|align=center| 24
|align=center| 1200
| 120px
|align=center| 2:1
|align=center| 1200.00
| 120px
|align=center| 0.00
|-
| semidiminished octave
|align=center| 23
|align=center| 1150
| 120px
|align=center| 35:18
|align=center| 1151.23
| 120px
|align=center| −1.23
|-
| supermajor seventh
|align=center| 23
|align=center| 1150
| 120px
|align=center| 27:14
|align=center| 1137.04
| 120px
|align=center| +12.96
|-
| major seventh
|align=center| 22
|align=center| 1100
| 120px
|align=center| 15:8
|align=center| 1088.27
| 120px
|align=center| +11.73
|-
| neutral seventh, major tone
|align=center| 21
|align=center| 1050
| 120px
|align=center| 11:6
|align=center| 1049.36
| 120px
|align=center| +0.64
|-
| neutral seventh, minor tone
|align=center| 21
|align=center| 1050
| 120px
|align=center| 20:11
|align=center| 1035.00
| 120px
|align=center| +15.00
|-
| large just minor seventh
|align=center| 20
|align=center| 1000
| 120px
|align=center| 9:5
|align=center| 1017.60
| 120px
|align=center| −17.60
|-
| small just minor seventh
|align=center| 20
|align=center| 1000
| 120px
|align=center| 16:9
|align=center| 996.09
| 120px
|align=center| +3.91
|-
| supermajor sixth/subminor seventh
|align=center| 19
|align=center| 950
| 120px
|align=center| 7:4
|align=center| 968.83
| 120px
|align=center| −18.83
|-
| major sixth
|align=center| 18
|align=center| 900
| 120px
|align=center| 5:3
|align=center| 884.36
| 120px
|align=center| +15.64
|-
| neutral sixth
|align=center| 17
|align=center| 850
| 120px
|align=center| 18:11
|align=center| 852.59
| 120px
|align=center| −2.59
|-
| minor sixth
|align=center| 16
|align=center| 800
| 120px
|align=center| 8:5
|align=center| 813.69
| 120px
|align=center| −13.69
|-
| subminor sixth
|align=center| 15
|align=center| 750
| 120px
|align=center| 14:9
|align=center| 764.92
| 120px
|align=center| −14.92
|-
| perfect fifth
|align=center| 14
|align=center| 700
| 120px
|align=center| 3:2
|align=center| 701.96
| 120px
|align=center| −1.96
|-
| minor fifth
|align=center| 13
|align=center| 650
| 120px
|align=center| 16:11
|align=center| 648.68
| 120px
|align=center| +1.32
|-
| lesser septimal tritone
|align=center| 12
|align=center| 600
| 120px
|align=center| 7:5
|align=center| 582.51
| 120px
|align=center| +17.49
|-
| major fourth
|align=center| 11
|align=center| 550
| 120px
|align=center| 11:8
|align=center| 551.32
| 120px
|align=center| −1.32
|-
| perfect fourth
|align=center| 10
|align=center| 500
| 120px
|align=center| 4:3
|align=center| 498.04
| 120px
|align=center| +1.96
|-
| tridecimal major third
|align=center| 9
|align=center| 450
| 120px
|align=center| 13:10
|align=center| 454.21
| 120px
|align=center| −4.21
|-
| septimal major third
|align=center| 9
|align=center| 450
| 120px
|align=center| 9:7
|align=center| 435.08
| 120px
|align=center| +14.92
|-
| major third
|align=center| 8
|align=center| 400
| 120px
|align=center| 5:4
|align=center| 386.31
| 120px
|align=center| +13.69
|-
| undecimal neutral third
|align=center| 7
|align=center| 350
| 120px
|align=center| 11:9
|align=center| 347.41
| 120px
|align=center| +2.59
|-
| minor third
|align=center| 6
|align=center| 300
| 120px
|align=center| 6:5
|align=center| 315.64
| 120px
|align=center| −15.64
|-
| septimal minor third
|align=center| 5
|align=center| 250
| 120px
|align=center| 7:6
|align=center| 266.87
| 120px
|align=center| −16.87
|-
| tridecimal five-quarter tone
|align=center| 5
|align=center| 250
| 120px
|align=center| 15:13
|align=center| 247.74
| 120px
|align=center| +2.26
|-
| septimal whole tone
|align=center| 5
|align=center| 250
| 120px
|align=center| 8:7
|align=center| 231.17
| 120px
|align=center| +18.83
|-
| major second, major tone
|align=center| 4
|align=center| 200
| 120px
|align=center| 9:8
|align=center| 203.91
| 120px
|align=center| −3.91
|-
| major second, minor tone
|align=center| 4
|align=center| 200
| 120px
|align=center| 10:9
|align=center| 182.40
| 120px
|align=center| +17.60
|-
| neutral second, greater undecimal
|align=center| 3
|align=center| 150
| 120px
|align=center| 11:10
|align=center| 165.00
| 120px
|align=center| −15.00
|-
| neutral second, lesser undecimal
|align=center| 3
|align=center| 150
| 120px
|align=center| 12:11
|align=center| 150.64
| 120px
|align=center| −0.64
|-
| 15:14 semitone
|align=center| 2
|align=center| 100
| 120px
|align=center| 15:14
|align=center| 119.44
| 120px
|align=center| −19.44
|-
| diatonic semitone, just
|align=center| 2
|align=center| 100
| 120px
|align=center| 16:15
|align=center| 111.73
| 120px
|align=center| −11.73
|-
| 21:20 semitone
|align=center| 2
|align=center| 100
| 120px
|align=center| 21:20
|align=center| 84.47
| 120px
|align=center| +15.53
|-
| 28:27 semitone
|align=center| 1
|align=center| 50
| 120px
|align=center| 28:27
|align=center| 62.96
| 120px
|align=center| −12.96
|-
| 33:32 semitone
|align=center| 1
|align=center| 50
| 120px
|align=center| 33:32
|align=center| 53.27
| 120px
|align=center| −3.27
|-
| unison
|align=center| 0
|align=center| 0
| 120px
|align=center| 1:1
|align=center| 0.00
| 120px
|align=center| 0.00
|}
Moving from 12-TET to 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include the neutral second, neutral third, and (11:8) ratio, or the 11th harmonic. The septimal minor third and septimal 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.
See also
- Musical temperament
- List of quarter tone pieces
- List of meantone intervals
- Holdrian Comma
- Koron, Sori
References
Further reading
External links
- "quarter-tone / 24-edo", TonalSoft.com