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.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 (~5.7 cents each) at G♯-D♯-A♯
• One fifth flatten by 513/512 (~3.3 cents) at F-C
• One fifth flatten by 1089/1088 (~1.6 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 (~5.7 cents each) at G♯-D♯-A♯
• One fifth flatten by 324/323 (~5.4 cents) at A-E
• One fifth flatten by 513/512 (~3.3 cents) at F-C
• One fifth flatten by 969/968 (~1.8 cents) at E-B
• One fifth flatten by 1089/1088 (~1.6 cents) at F♯-C♯
• Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F