24edo: Difference between revisions
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Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]]. | Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]]. | ||
While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; | While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; however, they are better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]]. | ||
A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate. | A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate. | ||
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| A "semiflat" or "half-flat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left. | | A "semiflat" or "half-flat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left. | ||
|- | |- | ||
| style="width: 40px;" | [[File:HeQd3.svg| | | style="width: 40px;" | [[File:HeQd3.svg|40px|center]] | ||
| A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back. | | A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back. | ||
|} | |} | ||
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'''Pros:''' familiar, intuitive, and fairly easy to learn. | '''Pros:''' familiar, intuitive, and fairly easy to learn. | ||
'''Cons:''' can clutter a score easily (especially when used in microtonal key signatures), can get confusing when sight read at faster paces. | '''Cons:''' can clutter a score easily (especially when used in microtonal key signatures), can get confusing when sight read at faster paces. | ||
=== Persian quartertone accidentals === | === Persian quartertone accidentals === | ||
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| 0.42 | | 0.42 | ||
| Sathurugu | | Sathurugu | ||
| | | Minisma | ||
|- | |- | ||
| 17 | | 17 | ||
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Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones. | Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones. | ||
Guitars with 24 frets per octave are also an option | Guitars with 24 frets per octave are also an option, although only [https://eastwoodguitars.com/products/hi-flier-edo-24-electric-microtonal-guitar Eastwood] offer this as a standard production model at the time of writing. Other luthiers you can commission custom microtonal instruments from, including 24edo ones, include [https://www.etsy.com/uk/listing/1154683769 JLJ instruments] and [https://meantoneguitar.com Meantone Guitar]. | ||
[[File:24edo_guitar.jpg|500px]] | [[File:24edo_guitar.jpg|500px]] | ||
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While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales. | While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales. | ||
More common is the "Sazocaster" tuning popularised by Australian band King Gizzard | More common is the "Sazocaster" tuning popularised by Australian band [[King Gizzard & the Lizard Wizard]], which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/sg2c-flying-banana-mt Eastwood] and [https://salamuzik.com/collections/guitar/products/professional-microtonal-electric-classical-guitar-with-equalizer-kg-5 Sala Muzik] have produced Sazocaster variations. | ||
[[File:Eastwood-guitars-phase-4-mt-2307179.jpg|500px]] | [[File:Eastwood-guitars-phase-4-mt-2307179.jpg|500px]] | ||
It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]]. Guitars using this layout are available at [https://www.microtonalguitar.org/product-page/angine-de-poitrine-style-fixed-microtonal-electric-guitar-ap24 microtonalguitar.org] and doubleneck guitar/basses are available from [https://eastwoodguitars.com/products/eastwood-microtonal-doubleneck-electric-guitar-bass Eastwood]. | |||
=== Harp, Harpsichord, and Piano === | === Harp, Harpsichord, and Piano === | ||
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=== Brass === | === Brass === | ||
Since the trombone is a free-pitched instrument, playing quartertones, or any other edo simply requires increased precision in moving the slide. If you want a brass instrument with fixed steps, [https://www.a-courtois.com/en/instruments/trompettes-2/t-o-m-a Courtois] and [https://www.vanlaartrumpets.nl/en/trumpets/quartertone Van Laar] both produce trumpets with an additional valve that enable you to easily play quartertones. | Since the trombone is a free-pitched instrument, playing quartertones, or any other edo simply requires increased precision in moving the slide. If you want a brass instrument with fixed steps, [https://www.a-courtois.com/en/instruments/trompettes-2/t-o-m-a Courtois] and [https://www.vanlaartrumpets.nl/en/trumpets/quartertone Van Laar] both produce trumpets with an additional valve that enable you to easily play quartertones. In addition, {{W|Renold Schilke|Schilke Music Products Incorporated}} built quartertone trumpets (model B5), as shown in All Things Brass And Technology's [https://www.youtube.com/watch?v=1ip0lOlQ2Xo&list=WL&index=257 ''Schilke B5 Quartertone Trumpet from 1971''] (2023). | ||
== Music == | == Music == | ||