Fractional sharp notation: Difference between revisions
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VERY WIP (I'll move it to the main namespace if it's finished.) | VERY WIP (I'll move it to the main namespace if it's finished.) | ||
The '''letter notation''' is a notation scheme developed by [[User:CompactStar|CompactStar]] for [[just intonation]] up to the [[ | The '''letter notation''' is a notation scheme developed by [[User:CompactStar|CompactStar]] for [[just intonation]] up to the [[31-limit]] and some [[regular temperaments]]. It is [[Pythagorean tuning|Pythagorean]] notation with the letters H-Y used as accidentals for higher prime limits (starting from H to avoid conflict with note names). These are fairly easy to memorize as they go in alphabetical order as the [[prime limit]] increases. | ||
== Accidentals == | == Accidentals == | ||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
! | !Prime limit | ||
!Letter | !Letter | ||
!Ratio | !Ratio | ||
| Line 16: | Line 17: | ||
|I | |I | ||
|80/81 | |80/81 | ||
|- | |||
|7 | |||
|J | |||
|[[64/63]] | |||
|K | |||
|63/64 | |||
|- | |||
|11 | |||
|L | |||
|[[33/32]] | |||
|M | |||
|32/33 | |||
|- | |||
|13 | |||
|N | |||
|[[1053/1024]] | |||
|O | |||
|1024/1053 | |||
|- | |||
|17 | |||
|P | |||
|[[4131/4096]] | |||
|Q | |||
|4096/4131 | |||
|- | |||
|19 | |||
|R | |||
|[[513/512]] | |||
|S | |||
|512/513 | |||
|- | |||
|23 | |||
|T | |||
|[[736/729]] | |||
|U | |||
|729/736 | |||
|- | |||
|29 | |||
|V | |||
|[[261/256]] | |||
|W | |||
|256/261 | |||
|- | |||
|31 | |||
|X | |||
|[[32/31]] | |||
|Y | |||
|31/32 | |||
|} | |} | ||
For example, [[5/4]] is IM3 (I-major third) | For example, [[5/4]] is IM3 and [[7/4]] is Km7 (spoken names, if mechanical-sounding, can also be made out of these like "I-major third"). | ||
This system can also be used to notate [[regular temperament]]s (including both equal temperaments and rank-2 or higher). For example, [[24edo]] could be notated by using [[12edo]] notation together with L/M to denote the tempered [[33/32]] quartertone of 50 cents: | |||
{|class="wikitable" | |||
|- | |||
!Notation | |||
! | |||
Revision as of 07:12, 5 February 2024
VERY WIP (I'll move it to the main namespace if it's finished.)
The letter notation is a notation scheme developed by CompactStar for just intonation up to the 31-limit and some regular temperaments. It is Pythagorean notation with the letters H-Y used as accidentals for higher prime limits (starting from H to avoid conflict with note names). These are fairly easy to memorize as they go in alphabetical order as the prime limit increases.
Accidentals
| Prime limit | Letter | Ratio | Letter | Ratio |
|---|---|---|---|---|
| 5 | H | 81/80 | I | 80/81 |
| 7 | J | 64/63 | K | 63/64 |
| 11 | L | 33/32 | M | 32/33 |
| 13 | N | 1053/1024 | O | 1024/1053 |
| 17 | P | 4131/4096 | Q | 4096/4131 |
| 19 | R | 513/512 | S | 512/513 |
| 23 | T | 736/729 | U | 729/736 |
| 29 | V | 261/256 | W | 256/261 |
| 31 | X | 32/31 | Y | 31/32 |
For example, 5/4 is IM3 and 7/4 is Km7 (spoken names, if mechanical-sounding, can also be made out of these like "I-major third").
This system can also be used to notate regular temperaments (including both equal temperaments and rank-2 or higher). For example, 24edo could be notated by using 12edo notation together with L/M to denote the tempered 33/32 quartertone of 50 cents:
| Notation |
|---|