24edo: Difference between revisions
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== Notation == | == Notation == | ||
There are multiple ways of notating 24edo. While an arguably common form can be seen on [[Wikipedia: Quarter tone #Interval size in equal temperament|Wikipedia's page on quartertones]], there are other forms, and it is these other forms that will be considered here. | There are multiple ways of notating 24edo. While an arguably common form can be seen on [[Wikipedia: Quarter tone #Interval size in equal temperament|Wikipedia's page on quartertones]], there are other forms, and it is these other forms that will be considered here. | ||
=== Ups and downs notation === | === Ups and downs notation === | ||
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! Degree | ! Degree | ||
! Cents | ! Cents | ||
! Approximate ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.19 | ! Approximate ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.19 [[subgroup]]}}</ref> | ||
! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and d2) | ! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and d2) | ||
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U or S {{=}} 1)}} | ! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U or S {{=}} 1)}} | ||
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| 1 | | 1 | ||
| 50 | | 50 | ||
| 33/32, 34/33 | | 33/32, 34/33 | ||
| ^P1, vm2 | | ^P1, vm2 | ||
| up-unison, downminor 2nd | | up-unison, downminor 2nd | ||
| Line 108: | Line 76: | ||
| 3 | | 3 | ||
| 150 | | 150 | ||
| | | 13/12, 12/11, 11/10 | ||
| ~2 | | ~2 | ||
| mid 2nd | | mid 2nd | ||
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=== Sagittal notation === | === Sagittal notation === | ||
This notation uses the same sagittal sequence as EDOs [[17edo#Sagittal notation|17]], [[31edo#Sagittal notation|31]], and [[38edo#Sagittal notation|38]], is a subset of the notations for EDOs [[48edo#Sagittal notation|48]] and [[72edo#Sagittal notation|72]], and is a superset of the notations for EDOs [[12edo#Sagittal notation|12]], [[8edo#Sagittal notation|8]], and [[6edo#Sagittal notation|6]]. | This notation uses the same sagittal sequence as EDOs [[17edo#Sagittal notation|17]], [[31edo#Sagittal notation|31]], and [[38edo#Sagittal notation|38]], is a subset of the notations for EDOs [[48edo#Sagittal notation|48]] and [[72edo#Sagittal notation|72]], and is a superset of the notations for EDOs [[12edo#Sagittal notation|12]], [[8edo#Sagittal notation|8]], and [[6edo#Sagittal notation|6]]. | ||
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* Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top | * Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top | ||
* Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | * Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | ||
=== Quartertone notations === | |||
Besides ups and downs, there are various systems for notating quarter tones. Here are some of them, along with their pros and cons. | |||
==== Mainstream quartertone accidentals ==== | |||
[[Category:IMPORTDEBUG - Change External Images]] | |||
{{Sharpness-sharp2|24}} | |||
{| class="wikitable center-1" | |||
|- | |||
| style="width: 40px;" | [[File:HeQu1.svg|21px|center]] | |||
| A "semisharp" or "half-sharp" accidental comprising one half of a regular musical sharp symbol. | |||
|- | |||
| style="width: 40px;" | [[File:HeQu3.svg|32px|center]] | |||
| A "sharp and a half" or "sesquisharp" accidental, comprising the above half-sharp symbol connected to the right side of a normal sharp. | |||
|- | |||
| style="width: 40px;" | [[File:HeQd1.svg|22px|center]] | |||
| 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|36px|center]] | |||
| A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back. | |||
|} | |||
'''Pros:''' Familiar, fairly easy to learn | |||
[[Category:IMPORTDEBUG - Change External Images]] | |||
'''Cons:''' Clutters a score easily, can get confusing when sight read at faster paces | |||
==== Persian accidentals ==== | |||
{| class="wikitable" | |||
|- | |||
| width="40px" |[[File:Koron_sign.svg|39px|center]] | |||
| '''Koron''' ([[Wikipedia: Koron (music)|Wikipedia]]) = Quarter-tone flat | |||
|- | |||
| width="40px" |[[File:Sori_sign.svg|39px|center]] | |||
| '''Sori''' ([[Wikipedia: Sori (music)|Wikipedia]]) = Quarter-tone sharp | |||
|} | |||
'''Pros:''' Easy to read | |||
'''Cons:''' Hard to write on a computer, doesn't fit with standard notation well | |||
==== Sagittal accidentals==== | |||
[[Sagittal notation]] works extremely well for 24edo notation as well as other systems. | |||
It is easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat. | |||
A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them with Sagittal signs for sharp and flat. | |||
[[File:sagittal_24.PNG|alt=sagittal 24.PNG|sagittal 24.PNG]] | |||
'''Pros:''' Easy to read, and less likely to clutter the score | |||
'''Cons:''' Not as familiar as traditional notation, and thus not immediately accessible to many traditional musicians who are just starting out with microtonality | |||
We also have, from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 24edo in the Revo flavor of Sagittal: | |||
[[File:24edo Sagittal.png|800px]] | |||
=== Further discussion of 24edo notation === | === Further discussion of 24edo notation === | ||