User:Zhenlige/12neji: Difference between revisions
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This is a list of 12-tone [[NEJI]]s designed by me. The goal is to make a scale | This is a list of 12-tone [[NEJI]]s designed by me. The goal is to make a scale that satisfy the restrictions below: | ||
*The [[octave]] is just, and all [[3/2|fifths]] are acceptable (≤8 [[cent]]s off from just). | |||
*The least common denominator is small enough (≤256). | |||
*Most notes are in a manageable [[prime limit]]. | |||
*It contains some simple just intervals. | |||
== 1 == | == 1 == | ||
| Line 25: | Line 29: | ||
Assuming G centered: | Assuming G centered: | ||
*One fifth flatten by [[243/242]] (~7.139 cents) at B-F♯ | *One fifth flatten by [[243/242]] (~7.139 cents) at B-F♯ | ||
*Two fifths flatten by approximately half of [[153/152]] (~5. | *Two fifths flatten by approximately half of [[153/152]] at G♯-D♯-A♯ | ||
*One fifth flatten by [[513/512]] (~3. | **One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯ | ||
*One fifth flatten by [[1089/1088]] (~1. | **One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯ | ||
*Seven | *One fifth flatten by [[513/512]] (~3.378 cents) at F-C | ||
*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯ | |||
*Seven just fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F | |||
== 2 == | == 2 == | ||
| Line 50: | Line 56: | ||
2/1 | 2/1 | ||
</pre> | </pre> | ||
=== Fifths === | |||
Assuming G centered: | |||
*Two fifths flatten by approximately half of [[153/152]] at G♯-D♯-A♯ | |||
**One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯ | |||
**One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯ | |||
*One fifth flatten by [[324/323]] (~5.352 cents) at A-E | |||
*One fifth flatten by [[513/512]] (~3.378 cents) at F-C | |||
*One fifth flatten by [[969/968]] (~1.788 cents) at E-B | |||
*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯ | |||
*Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F | |||
[[Category:Pages with Scala files]] | [[Category:Pages with Scala files]] | ||
[[Category:12-tone scales]] | [[Category:12-tone scales]] | ||
[[Category:Tempered scales]] | [[Category:Tempered scales]] | ||
Latest revision as of 04:41, 2 April 2025
This is a list of 12-tone NEJIs designed by me. The goal is to make a scale that satisfy the restrictions below:
- The octave is just, and all fifths are acceptable (≤8 cents off from just).
- The least common denominator is small enough (≤256).
- Most notes are in a manageable prime limit.
- It contains some simple just intervals.
1
! 12neji-1.scl ! A 12-tone NEJI 192:204:216:228:243:256:272:288:305:324:342:363:384 12 ! 17/16 9/8 19/16 81/64 4/3 17/12 3/2 305/192 27/16 57/32 121/64 2/1
Fifths
Assuming G centered:
- One fifth flatten by 243/242 (~7.139 cents) at B-F♯
- Two fifths flatten by approximately half of 153/152 at G♯-D♯-A♯
- One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯
- One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯
- One fifth flatten by 513/512 (~3.378 cents) at F-C
- One fifth flatten by 1089/1088 (~1.590 cents) at F♯-C♯
- Seven just fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F
2
! 12neji-2.scl ! A 12-tone NEJI 192:204:216:228:242:256:272:288:305:323:342:363:384 12 ! 17/16 9/8 19/16 121/96 4/3 17/12 3/2 305/192 323/192 57/32 121/64 2/1
Fifths
Assuming G centered:
- Two fifths flatten by approximately half of 153/152 at G♯-D♯-A♯
- One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯
- One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯
- One fifth flatten by 324/323 (~5.352 cents) at A-E
- One fifth flatten by 513/512 (~3.378 cents) at F-C
- One fifth flatten by 969/968 (~1.788 cents) at E-B
- One fifth flatten by 1089/1088 (~1.590 cents) at F♯-C♯
- Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F