24edo: Difference between revisions
→Instruments: replace dead links for guitar sales with currently active ones, add another method of partial 24edo that I suspect will soon be copied and spread more widely. |
→Instruments: Add quarter-tone vibraphone |
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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. | ||
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| 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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'''Pros:''' easy to read. | '''Pros:''' easy to read. | ||
'''Cons:''' | '''Cons:''' does not fit with standard notation well. | ||
=== Sagittal notation === | === Sagittal notation === | ||
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== Counterpoint == | == Counterpoint == | ||
24edo is the first edo to have both a [[sqrt(25/24)]] distinct from [[25/24]] and a correct [[5-odd-limit]]. It is thus the first edo which allows to lead the two voices of a major third to a minor third by | 24edo is the first edo to have both a [[sqrt(25/24)]] distinct from [[25/24]] and a correct [[5-odd-limit]]. It is thus the first edo which allows to lead the two voices of a major third to a minor third by strict {{W|Contrapuntal_motion#Contrary_motion|contrary motion}}. And vice versa. | ||
Furthermore, in the same fashion, every sequence of intervals available in 12edo are reachable by equal contrary motion in 24edo. | Furthermore, in the same fashion, every sequence of intervals available in 12edo are reachable by equal contrary motion in 24edo. | ||
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== Instruments == | == Instruments == | ||
The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This [[Microtonal_Keyboards#twelvenoteoctavescales|"12 note octave scales"]] approach is used in a wide part of the existing literature—see below. | The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This [[Microtonal_Keyboards#twelvenoteoctavescales|"12 note octave scales"]] approach is used in a wide part of the existing literature—see below. It is usually done with pianos, since tuning one of them to displace it from the other by a quarter-tone is simple (although laborious); nevertheless, it can be done with fixed-pitch 12EDO instruments by manufacturing a custom set of bars (etc.) for one fo them, as shown in djmoderne's [https://www.youtube.com/watch?v=hs5vQyMbq8I ''Quarter tone Vibraphone tests''] (2014). | ||
=== Guitar === | === Guitar === | ||
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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]]. | 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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==== Quarter-tone instruments ==== | ==== Quarter-tone instruments ==== | ||
a very small number of quarter-tone pianos have been built which combine two keyboards (with the bottom one repeated at the top) in a single instrument. This arrangement works well enough for other keyboard instruments such as harpsichords and organs having multiple manuals to get different tonal quality and volume, but yields rather poor ergonomics for playing chords that span the keyboards. That said, some quarter-tone styles of composition mainly alternate between the two circles of fifths and only rarely play notes from both at the same time, and for such styles the ergonomic problem would be greatly mitigated. It also makes instruments that either sacrifice power or are very large and heavy. Here are a couple of videos of these instruments being tested/played experimentally (to demonstrate their capabilities rather than to play specific compositions that would qualify for the 24edo Music section): | |||
; Quarter-tone grand piano, Czech Museum of Music (this piano is essentially two stacked grand pianos, and as such is massive, in order to avoid sacrificing strings per note) | ; Quarter-tone grand piano, Czech Museum of Music (this piano is essentially two stacked grand pianos, and as such is massive, in order to avoid sacrificing strings per note) | ||
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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 == | ||