User:Contribution/Basic analysis of selected EDOs: Difference between revisions
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= EDOs with a strong local zeta peak = | = 9-cents-minimum-limit = | ||
== EDOs with a strong local zeta peak == | |||
== 12edo == | === 12edo === | ||
sharpness = 1 | sharpness = 1 | ||
L = 2 ; s = 1 | L = 2 ; s = 1 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Degree | |||
!Degree | ! Notation | ||
!Notation | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Notation | ||
!Notation | ! Degree | ||
!Degree | |||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|12 | | 12 | ||
|- | |- | ||
|1 | | 1 | ||
|m2 | | m2 | ||
| | | | ||
| | | | ||
|M7 | | M7 | ||
|11 | | 11 | ||
|- | |- | ||
|2 | | 2 | ||
|M2 | | M2 | ||
|10/9, 9/8 | | 10/9, 9/8 | ||
|16/9, 9/5 | | 16/9, 9/5 | ||
|m7 | | m7 | ||
|10 | | 10 | ||
|- | |- | ||
|3 | | 3 | ||
|m3 | | m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|M6 | | M6 | ||
|9 | | 9 | ||
|- | |- | ||
|4 | | 4 | ||
|M3 | | M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|m6 | | m6 | ||
|8 | | 8 | ||
|- | |- | ||
|5 | | 5 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|7 | | 7 | ||
|- | |- | ||
|6 | | 6 | ||
|A4 | | A4 | ||
| colspan="2" |7/5, 10/7 | | colspan="2" | 7/5, 10/7 | ||
|d5 | | d5 | ||
|6 | | 6 | ||
|} | |} | ||
== 19edo == | === 19edo === | ||
sharpness = 1 | sharpness = 1 | ||
L = 3 ; s = 2 | L = 3 ; s = 2 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Degree | |||
!Degree | ! Notation | ||
!Notation | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Notation | ||
!Notation | ! Degree | ||
!Degree | |||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|19 | | 19 | ||
|- | |- | ||
|1 | | 1 | ||
|A1, d2 | | A1, d2 | ||
| | | | ||
| | | | ||
|A7, d8 | | A7, d8 | ||
|18 | | 18 | ||
|- | |- | ||
|2 | | 2 | ||
|m2 | | m2 | ||
|14/13 | | 14/13 | ||
|13/7 | | 13/7 | ||
|M7 | | M7 | ||
|17 | | 17 | ||
|- | |- | ||
|3 | | 3 | ||
|M2 | | M2 | ||
|10/9, 9/8 | | 10/9, 9/8 | ||
|16/9, 9/5 | | 16/9, 9/5 | ||
|m7 | | m7 | ||
|16 | | 16 | ||
|- | |- | ||
|4 | | 4 | ||
|A2, d3 | | A2, d3 | ||
|15/13 | | 15/13 | ||
|26/15 | | 26/15 | ||
|A6, d7 | | A6, d7 | ||
|15 | | 15 | ||
|- | |- | ||
|5 | | 5 | ||
|m3 | | m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|M6 | | M6 | ||
|14 | | 14 | ||
|- | |- | ||
|6 | | 6 | ||
|M3 | | M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|m6 | | m6 | ||
|13 | | 13 | ||
|- | |- | ||
|7 | | 7 | ||
|A3, d4 | | A3, d4 | ||
|9/7, 13/10 | | 9/7, 13/10 | ||
|20/13, 14/9 | | 20/13, 14/9 | ||
|A5, d6 | | A5, d6 | ||
|12 | | 12 | ||
|- | |- | ||
|8 | | 8 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|11 | | 11 | ||
|- | |- | ||
|9 | | 9 | ||
|A4 | | A4 | ||
|18/13 | | 18/13 | ||
|13/9 | | 13/9 | ||
|d5 | | d5 | ||
|10 | | 10 | ||
|} | |} | ||
== 22edo == | === 22edo === | ||
sharpness = 3 | sharpness = 3 | ||
L = 4 ; s = 1 | L = 4 ; s = 1 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Degree | |||
!Degree | ! Notation | ||
!Notation | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Notation | ||
!Notation | ! Degree | ||
!Degree | |||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|22 | | 22 | ||
|- | |- | ||
|1 | | 1 | ||
|m2 | | m2 | ||
| | | | ||
| | | | ||
|M7 | | M7 | ||
|21 | | 21 | ||
|- | |- | ||
|2 | | 2 | ||
|↑m2 | | ↑m2 | ||
|16/15 | | 16/15 | ||
|15/8 | | 15/8 | ||
|↓M7 | | ↓M7 | ||
|20 | | 20 | ||
|- | |- | ||
|3 | | 3 | ||
|↓M2 | | ↓M2 | ||
|11/10 | | 11/10 | ||
|20/11 | | 20/11 | ||
|↑m7 | | ↑m7 | ||
|19 | | 19 | ||
|- | |- | ||
|4 | | 4 | ||
|M2 | | M2 | ||
|9/8, 8/7 | | 9/8, 8/7 | ||
|7/4, 16/9 | | 7/4, 16/9 | ||
|m7 | | m7 | ||
|18 | | 18 | ||
|- | |- | ||
|5 | | 5 | ||
|m3 | | m3 | ||
|7/6 | | 7/6 | ||
|12/7 | | 12/7 | ||
|M6 | | M6 | ||
|17 | | 17 | ||
|- | |- | ||
|6 | | 6 | ||
|↑m3 | | ↑m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|↓M6 | | ↓M6 | ||
|16 | | 16 | ||
|- | |- | ||
|7 | | 7 | ||
|↓M3 | | ↓M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|↑m6 | | ↑m6 | ||
|15 | | 15 | ||
|- | |- | ||
|8 | | 8 | ||
|M3 | | M3 | ||
|9/7 | | 9/7 | ||
|14/9 | | 14/9 | ||
|m6 | | m6 | ||
|14 | | 14 | ||
|- | |- | ||
|9 | | 9 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|13 | | 13 | ||
|- | |- | ||
|10 | | 10 | ||
|↑P4 | | ↑P4 | ||
|11/8 | | 11/8 | ||
|16/11 | | 16/11 | ||
|↓P5 | | ↓P5 | ||
|12 | | 12 | ||
|- | |- | ||
|11 | | 11 | ||
|↓A4 | | ↓A4 | ||
| colspan="2" |7/5, 10/7 | | colspan="2" | 7/5, 10/7 | ||
|↑d5 | | ↑d5 | ||
|11 | | 11 | ||
|} | |} | ||
== 24edo == | === 24edo === | ||
sharpness = 2 | sharpness = 2 | ||
L = 4 ; s = 2 | L = 4 ; s = 2 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
24d | 24d | ||
!Degree | ! Degree | ||
!Notation | ! Notation | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Notation | ! Notation | ||
!Degree | ! Degree | ||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|24 | | 24 | ||
|- | |- | ||
|1 | | 1 | ||
|↑P1, ↓m2 | | ↑P1, ↓m2 | ||
| | | | ||
| | | | ||
|↑M7, ↓P8 | | ↑M7, ↓P8 | ||
|23 | | 23 | ||
|- | |- | ||
|2 | | 2 | ||
|m2 | | m2 | ||
| | | | ||
| | | | ||
|M7 | | M7 | ||
|22 | | 22 | ||
|- | |- | ||
|3 | | 3 | ||
|~2 | | ~2 | ||
|12/11 | | 12/11 | ||
|11/6 | | 11/6 | ||
|~7 | | ~7 | ||
|21 | | 21 | ||
|- | |- | ||
|4 | | 4 | ||
|M2 | | M2 | ||
|10/9, 9/8 | | 10/9, 9/8 | ||
|16/9, 9/5 | | 16/9, 9/5 | ||
|m7 | | m7 | ||
|20 | | 20 | ||
|- | |- | ||
|5 | | 5 | ||
|↑M2, ↓m3 | | ↑M2, ↓m3 | ||
|15/13 | | 15/13 | ||
|26/15 | | 26/15 | ||
|↑M6, ↓m7 | | ↑M6, ↓m7 | ||
|19 | | 19 | ||
|- | |- | ||
|6 | | 6 | ||
|m3 | | m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|M6 | | M6 | ||
|18 | | 18 | ||
|- | |- | ||
|7 | | 7 | ||
|~3 | | ~3 | ||
|11/9 | | 11/9 | ||
|18/11 | | 18/11 | ||
|~6 | | ~6 | ||
|17 | | 17 | ||
|- | |- | ||
|8 | | 8 | ||
|M3 | | M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|m6 | | m6 | ||
|16 | | 16 | ||
|- | |- | ||
|9 | | 9 | ||
|↑M3, ↓P4 | | ↑M3, ↓P4 | ||
|13/10 | | 13/10 | ||
|20/13 | | 20/13 | ||
|↑P5, ↓m6 | | ↑P5, ↓m6 | ||
|15 | | 15 | ||
|- | |- | ||
|10 | | 10 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|14 | | 14 | ||
|- | |- | ||
|11 | | 11 | ||
|~4 | | ~4 | ||
|11/8 | | 11/8 | ||
|16/11 | | 16/11 | ||
|~5 | | ~5 | ||
|13 | | 13 | ||
|- | |- | ||
|12 | | 12 | ||
|A4 | | A4 | ||
| colspan="2" |7/5, 10/7 | | colspan="2" | 7/5, 10/7 | ||
|d5 | | d5 | ||
|12 | | 12 | ||
|} | |} | ||
== 27edo == | === 27edo === | ||
sharpness = 4 | sharpness = 4 | ||
L = 5 ; s = 1 | L = 5 ; s = 1 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
27e | 27e | ||
!Degree | ! Degree | ||
!Notation | ! Notation | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Notation | ! Notation | ||
!Degree | ! Degree | ||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|27 | | 27 | ||
|- | |- | ||
|1 | | 1 | ||
|m2 | | m2 | ||
| | | | ||
| | | | ||
|M7 | | M7 | ||
|26 | | 26 | ||
|- | |- | ||
|2 | | 2 | ||
|↑m2 | | ↑m2 | ||
| | | | ||
| | | | ||
|↓M7 | | ↓M7 | ||
|25 | | 25 | ||
|- | |- | ||
|3 | | 3 | ||
|~2 | | ~2 | ||
|14/13, 13/12 | | 14/13, 13/12 | ||
|24/13, 13/7 | | 24/13, 13/7 | ||
|~7 | | ~7 | ||
|24 | | 24 | ||
|- | |- | ||
|4 | | 4 | ||
|↓M2 | | ↓M2 | ||
|10/9 | | 10/9 | ||
|9/5 | | 9/5 | ||
|↑m7 | | ↑m7 | ||
|23 | | 23 | ||
|- | |- | ||
|5 | | 5 | ||
|M2 | | M2 | ||
|9/8, 8/7 | | 9/8, 8/7 | ||
|7/4, 16/9 | | 7/4, 16/9 | ||
|m7 | | m7 | ||
|22 | | 22 | ||
|- | |- | ||
|6 | | 6 | ||
|m3 | | m3 | ||
|7/6 | | 7/6 | ||
|12/7 | | 12/7 | ||
|M6 | | M6 | ||
|21 | | 21 | ||
|- | |- | ||
|7 | | 7 | ||
|↑m3 | | ↑m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|↓M6 | | ↓M6 | ||
|20 | | 20 | ||
|- | |- | ||
|8 | | 8 | ||
|~3 | | ~3 | ||
|16/13 | | 16/13 | ||
|13/8 | | 13/8 | ||
|~6 | | ~6 | ||
|19 | | 19 | ||
|- | |- | ||
|9 | | 9 | ||
|↓M3 | | ↓M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|↑m6 | | ↑m6 | ||
|18 | | 18 | ||
|- | |- | ||
|10 | | 10 | ||
|M3 | | M3 | ||
|9/7, 13/10 | | 9/7, 13/10 | ||
|20/13, 14/9 | | 20/13, 14/9 | ||
|m6 | | m6 | ||
|17 | | 17 | ||
|- | |- | ||
|11 | | 11 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|16 | | 16 | ||
|- | |- | ||
|12 | | 12 | ||
|↑P4 | | ↑P4 | ||
|15/11 | | 15/11 | ||
|22/15 | | 22/15 | ||
|↓P5 | | ↓P5 | ||
|15 | | 15 | ||
|- | |- | ||
|13 | | 13 | ||
|~4 | | ~4 | ||
|7/5 | | 7/5 | ||
|10/7 | | 10/7 | ||
|~5 | | ~5 | ||
|14 | | 14 | ||
|} | |} | ||
== 31edo == | === 31edo === | ||
sharpness = 2 | sharpness = 2 | ||
L = 5 ; s = 3 | L = 5 ; s = 3 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Degree | |||
!Degree | ! Notation | ||
!Notation | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Notation | ||
!Notation | ! Degree | ||
!Degree | |||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|31 | | 31 | ||
|- | |- | ||
|1 | | 1 | ||
|↑P1 | | ↑P1 | ||
| | | | ||
| | | | ||
|↓P8 | | ↓P8 | ||
|30 | | 30 | ||
|- | |- | ||
|2 | | 2 | ||
|↓m2 | | ↓m2 | ||
| | | | ||
| | | | ||
|↑M7 | | ↑M7 | ||
|29 | | 29 | ||
|- | |- | ||
|3 | | 3 | ||
|m2 | | m2 | ||
|16/15, 15/14 | | 16/15, 15/14 | ||
|28/15, 15/8 | | 28/15, 15/8 | ||
|M7 | | M7 | ||
|28 | | 28 | ||
|- | |- | ||
|4 | | 4 | ||
|~2 | | ~2 | ||
|12/11, 11/10 | | 12/11, 11/10 | ||
|20/11, 11/6 | | 20/11, 11/6 | ||
|~7 | | ~7 | ||
|27 | | 27 | ||
|- | |- | ||
|5 | | 5 | ||
|M2 | | M2 | ||
|10/9, 9/8 | | 10/9, 9/8 | ||
|16/9, 9/5 | | 16/9, 9/5 | ||
|m7 | | m7 | ||
|26 | | 26 | ||
|- | |- | ||
|6 | | 6 | ||
|↑M2 | | ↑M2 | ||
|8/7 | | 8/7 | ||
|7/4 | | 7/4 | ||
|↓m7 | | ↓m7 | ||
|25 | | 25 | ||
|- | |- | ||
|7 | | 7 | ||
|↓m3 | | ↓m3 | ||
|7/6 | | 7/6 | ||
|12/7 | | 12/7 | ||
|↑M6 | | ↑M6 | ||
|24 | | 24 | ||
|- | |- | ||
|8 | | 8 | ||
|m3 | | m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|M6 | | M6 | ||
|23 | | 23 | ||
|- | |- | ||
|9 | | 9 | ||
|~3 | | ~3 | ||
|11/9 | | 11/9 | ||
|18/11 | | 18/11 | ||
|~6 | | ~6 | ||
|22 | | 22 | ||
|- | |- | ||
|10 | | 10 | ||
|M3 | | M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|m6 | | m6 | ||
|21 | | 21 | ||
|- | |- | ||
|11 | | 11 | ||
|↑M3 | | ↑M3 | ||
|14/11, 9/7 | | 14/11, 9/7 | ||
|14/9, 11/7 | | 14/9, 11/7 | ||
|↓m6 | | ↓m6 | ||
|20 | | 20 | ||
|- | |- | ||
|12 | | 12 | ||
|↓P4 | | ↓P4 | ||
|17/13 | | 17/13 | ||
|26/17 | | 26/17 | ||
|↑P5 | | ↑P5 | ||
|19 | | 19 | ||
|- | |- | ||
|13 | | 13 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|18 | | 18 | ||
|- | |- | ||
|14 | | 14 | ||
|~4 | | ~4 | ||
|15/11, 11/8 | | 15/11, 11/8 | ||
|16/11, 22/15 | | 16/11, 22/15 | ||
|~5 | | ~5 | ||
|17 | | 17 | ||
|- | |- | ||
|15 | | 15 | ||
|A4 | | A4 | ||
|7/5 | | 7/5 | ||
|10/7 | | 10/7 | ||
|d5 | | d5 | ||
|16 | | 16 | ||
|} | |} | ||
== 34edo == | === 34edo === | ||
=== 41edo === | |||
== 36edo == | === 46edo === | ||
=== 50edo === | |||
=== 53edo === | |||
=== 58edo === | |||
=== 60edo === | |||
=== 65edo === | |||
=== 68edo === | |||
=== 72edo === | |||
=== 77edo === | |||
=== 80edo === | |||
=== 84edo === | |||
=== 87edo === | |||
=== 94edo === | |||
=== 99edo === | |||
=== 111edo === | |||
=== 118edo === | |||
=== 130edo === | |||
== EDOs from 9 to 17 == | |||
=== 9edo === | |||
=== 10edo === | |||
=== 11edo === | |||
=== 13edo === | |||
=== 14edo === | |||
=== 15edo === | |||
=== 16edo === | |||
=== 17edo === | |||
== Other noteworthy EDOs == | |||
=== 23edo === | |||
=== 26edo === | |||
=== 29edo === | |||
=== 36edo === | |||
sharpness = 3 | sharpness = 3 | ||
L = 6 ; s = 3 | L = 6 ; s = 3 | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Degree | |||
!Degree | ! Notation | ||
!Notation | ! Approximate Ratios | ||
!Approximate Ratios | ! Approximate Ratios | ||
!Approximate Ratios | ! Notation | ||
!Notation | ! Degree | ||
!Degree | |||
|- | |- | ||
|0 | | 0 | ||
|P1 | | P1 | ||
|1/1 | | 1/1 | ||
|2/1 | | 2/1 | ||
|P8 | | P8 | ||
|36 | | 36 | ||
|- | |- | ||
|1 | | 1 | ||
|↑P1 | | ↑P1 | ||
| | | | ||
| | | | ||
|↓P8 | | ↓P8 | ||
|35 | | 35 | ||
|- | |- | ||
|2 | | 2 | ||
|↓m2 | | ↓m2 | ||
| | | | ||
| | | | ||
|↑M7 | | ↑M7 | ||
|34 | | 34 | ||
|- | |- | ||
|3 | | 3 | ||
|m2 | | m2 | ||
|ϕ<sup>3</sup>/4 | | ϕ<sup>3</sup>/4 | ||
|8/ϕ<sup>3</sup> | | 8/ϕ<sup>3</sup> | ||
|M7 | | M7 | ||
|33 | | 33 | ||
|- | |- | ||
|4 | | 4 | ||
|↑m2 | | ↑m2 | ||
|14/13, 13/12 | | 14/13, 13/12 | ||
|24/13, 13/7 | | 24/13, 13/7 | ||
|↓M7 | | ↓M7 | ||
|32 | | 32 | ||
|- | |- | ||
|5 | | 5 | ||
|↓M2 | | ↓M2 | ||
|11/10 | | 11/10 | ||
|20/11 | | 20/11 | ||
|↑m7 | | ↑m7 | ||
|31 | | 31 | ||
|- | |- | ||
|6 | | 6 | ||
|M2 | | M2 | ||
|9/8 | | 9/8 | ||
|16/9 | | 16/9 | ||
|m7 | | m7 | ||
|30 | | 30 | ||
|- | |- | ||
|7 | | 7 | ||
|↑M2 | | ↑M2 | ||
|8/7 | | 8/7 | ||
|7/4 | | 7/4 | ||
|↓m7 | | ↓m7 | ||
|29 | | 29 | ||
|- | |- | ||
|8 | | 8 | ||
|↓m3 | | ↓m3 | ||
|7/6 | | 7/6 | ||
|12/7 | | 12/7 | ||
|↑M6 | | ↑M6 | ||
|28 | | 28 | ||
|- | |- | ||
|9 | | 9 | ||
|m3 | | m3 | ||
|6/5 | | 6/5 | ||
|5/3 | | 5/3 | ||
|M6 | | M6 | ||
|27 | | 27 | ||
|- | |- | ||
|10 | | 10 | ||
|↑m3 | | ↑m3 | ||
|17/14 | | 17/14 | ||
|28/17 | | 28/17 | ||
|↓M6 | | ↓M6 | ||
|26 | | 26 | ||
|- | |- | ||
|11 | | 11 | ||
|↓M3 | | ↓M3 | ||
|2/ϕ | | 2/ϕ | ||
|ϕ | | ϕ | ||
|↑m6 | | ↑m6 | ||
|25 | | 25 | ||
|- | |- | ||
|12 | | 12 | ||
|M3 | | M3 | ||
|5/4 | | 5/4 | ||
|8/5 | | 8/5 | ||
|m6 | | m6 | ||
|24 | | 24 | ||
|- | |- | ||
|13 | | 13 | ||
|↑M3 | | ↑M3 | ||
|9/7 | | 9/7 | ||
|14/9 | | 14/9 | ||
|↓m6 | | ↓m6 | ||
|23 | | 23 | ||
|- | |- | ||
|14 | | 14 | ||
|↓P4 | | ↓P4 | ||
|ϕ<sup>2</sup>/2 | | ϕ<sup>2</sup>/2 | ||
|4/ϕ<sup>2</sup> | | 4/ϕ<sup>2</sup> | ||
|↑P5 | | ↑P5 | ||
|22 | | 22 | ||
|- | |- | ||
|15 | | 15 | ||
|P4 | | P4 | ||
|4/3 | | 4/3 | ||
|3/2 | | 3/2 | ||
|P5 | | P5 | ||
|21 | | 21 | ||
|- | |- | ||
|16 | | 16 | ||
|↑P4 | | ↑P4 | ||
|15/11 | | 15/11 | ||
|22/15 | | 22/15 | ||
|↓P5 | | ↓P5 | ||
|20 | | 20 | ||
|- | |- | ||
|17 | | 17 | ||
|↓A4 | | ↓A4 | ||
|18/13 | | 18/13 | ||
|13/9 | | 13/9 | ||
|↑d5 | | ↑d5 | ||
|19 | | 19 | ||
|- | |- | ||
|18 | | 18 | ||
|A4 | | A4 | ||
| colspan="2" |24/17, 17/12 | | colspan="2" | 24/17, 17/12 | ||
|d5 | | d5 | ||
|18 | | 18 | ||
|} | |} | ||
== | === 37edo === | ||
=== 49edo === | |||
== | === 93edo === | ||
= 4 exceptions outside the 9-cents-minimum-limit = | |||
== | == 7-limit == | ||
=== 171edo === | |||
= | == 15-limit == | ||
=== 270edo === | |||
== | == Harmonic series == | ||
=== 311edo === | |||
= | == 31-limit == | ||
=== 16808edo === | |||
== | |||
== | |||
== 171edo == | |||
= | |||
== | |||
== | |||
== | |||
== | |||
== | |||
= | |||
== | |||
Latest revision as of 15:10, 13 August 2024
9-cents-minimum-limit
EDOs with a strong local zeta peak
12edo
sharpness = 1 L = 2 ; s = 1
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 12 |
| 1 | m2 | M7 | 11 | ||
| 2 | M2 | 10/9, 9/8 | 16/9, 9/5 | m7 | 10 |
| 3 | m3 | 6/5 | 5/3 | M6 | 9 |
| 4 | M3 | 5/4 | 8/5 | m6 | 8 |
| 5 | P4 | 4/3 | 3/2 | P5 | 7 |
| 6 | A4 | 7/5, 10/7 | d5 | 6 | |
19edo
sharpness = 1 L = 3 ; s = 2
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 19 |
| 1 | A1, d2 | A7, d8 | 18 | ||
| 2 | m2 | 14/13 | 13/7 | M7 | 17 |
| 3 | M2 | 10/9, 9/8 | 16/9, 9/5 | m7 | 16 |
| 4 | A2, d3 | 15/13 | 26/15 | A6, d7 | 15 |
| 5 | m3 | 6/5 | 5/3 | M6 | 14 |
| 6 | M3 | 5/4 | 8/5 | m6 | 13 |
| 7 | A3, d4 | 9/7, 13/10 | 20/13, 14/9 | A5, d6 | 12 |
| 8 | P4 | 4/3 | 3/2 | P5 | 11 |
| 9 | A4 | 18/13 | 13/9 | d5 | 10 |
22edo
sharpness = 3 L = 4 ; s = 1
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 22 |
| 1 | m2 | M7 | 21 | ||
| 2 | ↑m2 | 16/15 | 15/8 | ↓M7 | 20 |
| 3 | ↓M2 | 11/10 | 20/11 | ↑m7 | 19 |
| 4 | M2 | 9/8, 8/7 | 7/4, 16/9 | m7 | 18 |
| 5 | m3 | 7/6 | 12/7 | M6 | 17 |
| 6 | ↑m3 | 6/5 | 5/3 | ↓M6 | 16 |
| 7 | ↓M3 | 5/4 | 8/5 | ↑m6 | 15 |
| 8 | M3 | 9/7 | 14/9 | m6 | 14 |
| 9 | P4 | 4/3 | 3/2 | P5 | 13 |
| 10 | ↑P4 | 11/8 | 16/11 | ↓P5 | 12 |
| 11 | ↓A4 | 7/5, 10/7 | ↑d5 | 11 | |
24edo
sharpness = 2 L = 4 ; s = 2
24d| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 24 |
| 1 | ↑P1, ↓m2 | ↑M7, ↓P8 | 23 | ||
| 2 | m2 | M7 | 22 | ||
| 3 | ~2 | 12/11 | 11/6 | ~7 | 21 |
| 4 | M2 | 10/9, 9/8 | 16/9, 9/5 | m7 | 20 |
| 5 | ↑M2, ↓m3 | 15/13 | 26/15 | ↑M6, ↓m7 | 19 |
| 6 | m3 | 6/5 | 5/3 | M6 | 18 |
| 7 | ~3 | 11/9 | 18/11 | ~6 | 17 |
| 8 | M3 | 5/4 | 8/5 | m6 | 16 |
| 9 | ↑M3, ↓P4 | 13/10 | 20/13 | ↑P5, ↓m6 | 15 |
| 10 | P4 | 4/3 | 3/2 | P5 | 14 |
| 11 | ~4 | 11/8 | 16/11 | ~5 | 13 |
| 12 | A4 | 7/5, 10/7 | d5 | 12 | |
27edo
sharpness = 4 L = 5 ; s = 1
27e| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 27 |
| 1 | m2 | M7 | 26 | ||
| 2 | ↑m2 | ↓M7 | 25 | ||
| 3 | ~2 | 14/13, 13/12 | 24/13, 13/7 | ~7 | 24 |
| 4 | ↓M2 | 10/9 | 9/5 | ↑m7 | 23 |
| 5 | M2 | 9/8, 8/7 | 7/4, 16/9 | m7 | 22 |
| 6 | m3 | 7/6 | 12/7 | M6 | 21 |
| 7 | ↑m3 | 6/5 | 5/3 | ↓M6 | 20 |
| 8 | ~3 | 16/13 | 13/8 | ~6 | 19 |
| 9 | ↓M3 | 5/4 | 8/5 | ↑m6 | 18 |
| 10 | M3 | 9/7, 13/10 | 20/13, 14/9 | m6 | 17 |
| 11 | P4 | 4/3 | 3/2 | P5 | 16 |
| 12 | ↑P4 | 15/11 | 22/15 | ↓P5 | 15 |
| 13 | ~4 | 7/5 | 10/7 | ~5 | 14 |
31edo
sharpness = 2 L = 5 ; s = 3
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 31 |
| 1 | ↑P1 | ↓P8 | 30 | ||
| 2 | ↓m2 | ↑M7 | 29 | ||
| 3 | m2 | 16/15, 15/14 | 28/15, 15/8 | M7 | 28 |
| 4 | ~2 | 12/11, 11/10 | 20/11, 11/6 | ~7 | 27 |
| 5 | M2 | 10/9, 9/8 | 16/9, 9/5 | m7 | 26 |
| 6 | ↑M2 | 8/7 | 7/4 | ↓m7 | 25 |
| 7 | ↓m3 | 7/6 | 12/7 | ↑M6 | 24 |
| 8 | m3 | 6/5 | 5/3 | M6 | 23 |
| 9 | ~3 | 11/9 | 18/11 | ~6 | 22 |
| 10 | M3 | 5/4 | 8/5 | m6 | 21 |
| 11 | ↑M3 | 14/11, 9/7 | 14/9, 11/7 | ↓m6 | 20 |
| 12 | ↓P4 | 17/13 | 26/17 | ↑P5 | 19 |
| 13 | P4 | 4/3 | 3/2 | P5 | 18 |
| 14 | ~4 | 15/11, 11/8 | 16/11, 22/15 | ~5 | 17 |
| 15 | A4 | 7/5 | 10/7 | d5 | 16 |
34edo
41edo
46edo
50edo
53edo
58edo
60edo
65edo
68edo
72edo
77edo
80edo
84edo
87edo
94edo
99edo
111edo
118edo
130edo
EDOs from 9 to 17
9edo
10edo
11edo
13edo
14edo
15edo
16edo
17edo
Other noteworthy EDOs
23edo
26edo
29edo
36edo
sharpness = 3 L = 6 ; s = 3
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 36 |
| 1 | ↑P1 | ↓P8 | 35 | ||
| 2 | ↓m2 | ↑M7 | 34 | ||
| 3 | m2 | ϕ3/4 | 8/ϕ3 | M7 | 33 |
| 4 | ↑m2 | 14/13, 13/12 | 24/13, 13/7 | ↓M7 | 32 |
| 5 | ↓M2 | 11/10 | 20/11 | ↑m7 | 31 |
| 6 | M2 | 9/8 | 16/9 | m7 | 30 |
| 7 | ↑M2 | 8/7 | 7/4 | ↓m7 | 29 |
| 8 | ↓m3 | 7/6 | 12/7 | ↑M6 | 28 |
| 9 | m3 | 6/5 | 5/3 | M6 | 27 |
| 10 | ↑m3 | 17/14 | 28/17 | ↓M6 | 26 |
| 11 | ↓M3 | 2/ϕ | ϕ | ↑m6 | 25 |
| 12 | M3 | 5/4 | 8/5 | m6 | 24 |
| 13 | ↑M3 | 9/7 | 14/9 | ↓m6 | 23 |
| 14 | ↓P4 | ϕ2/2 | 4/ϕ2 | ↑P5 | 22 |
| 15 | P4 | 4/3 | 3/2 | P5 | 21 |
| 16 | ↑P4 | 15/11 | 22/15 | ↓P5 | 20 |
| 17 | ↓A4 | 18/13 | 13/9 | ↑d5 | 19 |
| 18 | A4 | 24/17, 17/12 | d5 | 18 | |