User:Zhenlige/12neji: Difference between revisions
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== 1 == | == 1 == | ||
<pre> | <pre> | ||
(* 12neji-1 *) | |||
(* 192:204:216:228:243:256:272:288:305:324:342:363:384 *) | |||
17/16 "G♯" | |||
9/8 "A" | |||
17/16 | 19/16 "A♯" | ||
9/8 | 81/64 "B" | ||
19/16 | 4/3 "C" | ||
81/64 | 17/12 "C♯" | ||
4/3 | 3/2 "D" | ||
17/12 | 305/192 "D♯" | ||
3/2 | 27/16 "E" | ||
305/192 | 57/32 "F" | ||
27/16 | 121/64 "F♯" | ||
57/32 | 2/1 "G" | ||
121/64 | |||
2/1 | |||
</pre> | </pre> | ||
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== 2 == | == 2 == | ||
<pre> | <pre> | ||
(* 12neji-2 *) | |||
(* 192:204:216:228:242:256:272:288:305:323:342:363:384 *) | |||
17/16 "G♯" | |||
9/8 "A" | |||
17/16 | 19/16 "A♯" | ||
9/8 | 121/96 "B" | ||
19/16 | 4/3 "C" | ||
121/96 | 17/12 "C♯" | ||
4/3 | 3/2 "D" | ||
17/12 | 305/192 "D♯" | ||
3/2 | 323/192 "E" | ||
305/192 | 57/32 "F" | ||
323/192 | 121/64 "F♯" | ||
57/32 | 2/1 "G" | ||
121/64 | |||
2/1 | |||
</pre> | </pre> | ||
=== Fifths === | === Fifths === | ||
Assuming G centered: | Assuming G centered: | ||
*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 [[324/323]] (~5. | **One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯ | ||
*One fifth flatten by [[513/512]] (~3. | **One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯ | ||
*One fifth flatten by [[969/968]] (~1. | *One fifth flatten by [[324/323]] (~5.352 cents) at A-E | ||
*One fifth flatten by [[1089/1088]] (~1. | *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 | *Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F | ||
[[Category: | [[Category:Scales]] | ||
[[Category:12-tone scales]] | [[Category:12-tone scales]] | ||
[[Category:Just intonation scales]] | |||
[[Category:Tempered scales]] | [[Category:Tempered scales]] | ||
Latest revision as of 04:40, 12 March 2026
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 *) (* 192:204:216:228:243:256:272:288:305:324:342:363:384 *) 17/16 "G♯" 9/8 "A" 19/16 "A♯" 81/64 "B" 4/3 "C" 17/12 "C♯" 3/2 "D" 305/192 "D♯" 27/16 "E" 57/32 "F" 121/64 "F♯" 2/1 "G"
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 *) (* 192:204:216:228:242:256:272:288:305:323:342:363:384 *) 17/16 "G♯" 9/8 "A" 19/16 "A♯" 121/96 "B" 4/3 "C" 17/12 "C♯" 3/2 "D" 305/192 "D♯" 323/192 "E" 57/32 "F" 121/64 "F♯" 2/1 "G"
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