User:Zhenlige/12neji

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