User:Hotcrystal0/27edo: Difference between revisions
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27edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup: | 27edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup: | ||
* | * 28/27 | ||
* 36/35 | |||
* 49/48 | |||
* 50/49 | |||
* 81/80 | |||
===Chords=== | ===Chords=== | ||
| Line 27: | Line 31: | ||
=== 81edo === | === 81edo === | ||
81edo is a convergent to golden meantone, and is also the last one to support [[Meantone]] in its patent val. | |||
{{Harmonics in ED|81|31|0}} | {{Harmonics in ED|81|31|0}} | ||
Latest revision as of 20:40, 1 August 2026
27edo, or 27 equal divisions of the octave, is the equal tuning featuring steps of (1200/27) ~= 44.44 cents, 27 of which stack to the perfect octave 2/1.
Theory
JI approximation
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | +13.7 | +9.0 | -18.0 | +3.9 | -16.1 | +13.6 | -6.1 | -7.4 | +10.5 |
| Relative (%) | 0.0 | +20.6 | +30.8 | +20.1 | -40.5 | +8.8 | -36.1 | +30.6 | -13.6 | -16.5 | +23.7 | |
| Steps (reduced) |
27 (0) |
43 (16) |
63 (9) |
76 (22) |
93 (12) |
100 (19) |
110 (2) |
115 (7) |
122 (14) |
131 (23) |
134 (26) | |
Edostep interpretations
27edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup:
- 28/27
- 36/35
- 49/48
- 50/49
- 81/80
Chords
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Scales
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Multiples
54edo
54edo is a good tuning of Pajara and its 11-limit extension Pajarous.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | -8.5 | +9.0 | +4.2 | +3.9 | +6.2 | -8.6 | -6.1 | -7.4 | +10.5 |
| Relative (%) | 0.0 | +41.2 | -38.4 | +40.3 | +19.1 | +17.6 | +27.7 | -38.8 | -27.2 | -33.1 | +47.3 | |
| Steps (reduced) |
54 (0) |
86 (32) |
125 (17) |
152 (44) |
187 (25) |
200 (38) |
221 (5) |
229 (13) |
244 (28) |
262 (46) |
268 (52) | |
81edo
81edo is a convergent to golden meantone, and is also the last one to support Meantone in its patent val.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -5.7 | -1.1 | -5.9 | -3.2 | +3.9 | -1.3 | -1.2 | -6.1 | -7.4 | -4.3 |
| Relative (%) | 0.0 | -38.2 | -7.6 | -39.6 | -21.4 | +26.4 | -8.4 | -8.2 | -40.9 | -49.6 | -29.0 | |
| Steps (reduced) |
81 (0) |
128 (47) |
188 (26) |
227 (65) |
280 (37) |
300 (57) |
331 (7) |
344 (20) |
366 (42) |
393 (69) |
401 (77) | |
270edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +0.3 | +0.4 | +0.1 | -0.2 | -0.5 | +1.7 | +0.3 | -1.6 | +1.5 | +1.6 |
| Relative (%) | 0.0 | +6.0 | +7.9 | +1.4 | -4.7 | -11.9 | +38.5 | +6.0 | -36.2 | +34.5 | +36.7 | |
| Steps (reduced) |
270 (0) |
428 (158) |
627 (87) |
758 (218) |
934 (124) |
999 (189) |
1104 (24) |
1147 (67) |
1221 (141) |
1312 (232) |
1338 (258) | |
