User:FilterNashi/Temperaments and tuning methods
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Semitonismic & Rastmic
| rank | 2 | |
|---|---|---|
| subgroup | 2.3.11.17 | |
| comma basis | [ -1 5 -2 0] 243/242
[ -5 -2 0 2] 289/288 | |
| edos | 24, 10, 14, 34, 58, 38, 82, 62, 106, 6[+11], 130, 86[-11, -17], 44[+11], 154 | |
| edo join | 24 & 10 | |
| mapping | [⟨2 0 -1 5], ⟨0 2 5 2]] | |
| preimage | 17/12 | 153/88 |
| WE tuning | 600.224 | 950.678 |
| CWE tuning | 600.000 | 950.476 |
| WE errors | 0.447, -0.600, 1.847, -2.482 | |
| CWE errors | 0.000, -1.003, 1.061, -4.004 | |
| badness | 0.204 | |
all the patent val: 10 14 24 34 38 48 58 62 72 82 96 106 120 130 154
ed16.67074¢
This segment is about the equal temperament of EPD16.67074cents.
This is about 71.9824EDO, so it's simply an alternative tuning of 72edo. The comma basis, mappings, etc. show up as same as 72edo.
I use this for 2.3.5.7.11.17.19 subgroup.
72edo didn't work well with 2.3.7.11.13 subgroup because it can't deal with the Harmonisma, and map it to 1 step.
see[1]
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.29 | -1.49 | -2.30 | -1.34 | -0.30 | -6.11 | -3.76 | +3.73 | +6.39 | +5.18 | +6.42 |
| Relative (%) | +1.8 | -8.9 | -13.8 | -8.0 | -1.8 | -36.7 | -22.5 | +22.4 | +38.3 | +31.1 | +38.5 | |
| Steps (reduced) |
72 (0.017600000000002) |
114 (42.0176) |
167 (23.0352) |
202 (58.0352) |
249 (33.0528) |
266 (50.0528) |
294 (6.0704) |
306 (18.0704) |
326 (38.0704) |
350 (62.0704) |
357 (69.0704) | |
ed38.80714¢
This segment is about the equal temperament of EPD38.80714cents.
This is about 30.922EDO, so it's simply an alternative tuning of 31edo. The comma basis, mappings, etc. show up as same as 31edo.
I use this for 2.3.5.7.11 subgroup.
see[2]
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.0 | -0.4 | +7.8 | +7.4 | +1.1 | -16.5 | -15.2 | -13.8 | +4.8 | -8.5 | -7.5 |
| Relative (%) | +7.8 | -1.0 | +20.1 | +19.1 | +2.7 | -42.5 | -39.3 | -35.4 | +12.2 | -21.8 | -19.4 | |
| Steps (reduced) |
31 (0.077999999999999) |
49 (18.078) |
72 (10.156) |
87 (25.156) |
107 (14.234) |
114 (21.234) |
126 (2.312) |
131 (7.312) |
140 (16.312) |
150 (26.312) |
153 (29.312) | |
ed20.71628¢
This segment is about the equal temperament of EPD20.71628cents.
This is about 57.925EDO, so it's simply an alternative tuning of 58edo. The comma basis, mappings, etc. show up as same as 58edo.
I use this for 2.3.5.7.11.13 subgroup.
This is a parahemif.
see[3]
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.96 | -10.31 | +7.95 | +7.92 | -8.03 | -7.21 | -6.35 | +4.84 | -1.27 | -8.80 | -0.57 |
| Relative (%) | +19.1 | -49.8 | +38.4 | +38.2 | -38.8 | -34.8 | -30.7 | +23.4 | -6.1 | -42.5 | -2.7 | |
| Steps (reduced) |
92 (34.075) |
134 (18.15) |
163 (47.15) |
184 (10.225) |
200 (26.225) |
214 (40.225) |
226 (52.225) |
237 (5.3) |
246 (14.3) |
254 (22.3) |
262 (30.3) | |
ed63.77698¢
This segment is about the equal temperament of EPD63.77698cents.
This is about 18.8EDO, so it's simply an alternative tuning of 19edo. The comma basis, mappings, etc. show up as same as 19edo.
I use this for 2.3.5.7 subgroup.
see[4]
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.9 | +22.2 | +14.2 | +25.9 | -2.4 | +27.6 | -28.7 | +9.9 | +8.9 | +27.1 | -2.7 |
| Relative (%) | +20.3 | +34.8 | +22.2 | +40.5 | -3.7 | +43.2 | -45.0 | +15.6 | +13.9 | +42.4 | -4.3 | |
| Steps (reduced) |
30 (11.2) |
44 (6.4) |
53 (15.4) |
60 (3.6) |
65 (8.6) |
70 (13.6) |
73 (16.6) |
77 (1.8) |
80 (4.8) |
83 (7.8) |
85 (9.8) | |
ed44.21793¢
This segment is about the equal temperament of EPD44.21793cents.
This is about 27.1383EDO, so it's simply an alternative tuning of 27edo. The comma basis, mappings, etc. show up as same as 27edo.
I use this for 2.3.5.7 subgroup.
see[5]
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.2 | -0.7 | -0.8 | -8.5 | +4.9 | -19.0 | +2.9 | -12.8 | +10.2 | +6.8 | -20.2 |
| Relative (%) | -14.0 | -1.6 | -1.7 | -19.2 | +11.1 | -43.0 | +6.6 | -28.9 | +23.1 | +15.4 | -45.7 | |
| Steps (reduced) |
27 (27) |
43 (15.86) |
63 (8.72) |
76 (21.72) |
94 (12.58) |
100 (18.58) |
111 (2.44) |
115 (6.44) |
123 (14.44) |
132 (23.44) |
134 (25.44) | |
56edo
I use this for 2.3.5.7.17.19 subgroup.
This is a meantone and it map 513/512 to -1 step.
Equal temperaments for 19-horizon
ed24.04706c~49.9021edo 50edo see[7] this one can't deal with harmonisma but i'm okay with it
ed14.93521c~80.347edo 80edo see[8] this is a gentle.
Equal temperaments for 5-horizon
ed63.16848c~18.9968edo 19edo see[10]
ed22.64371c~52.9948edo 53edo see[12]
Tuning methods
For 2.3.5.19 subgroup, i need a meantone while also separate the 19/16 and 6/5 in the right position. This requires a 96/95 on positive size, so 513/512 is on negative size.
50edo and 56edo can handle this.
For 13-horizon, i need a gentle or parahemif while also mapping 91/90, 78/77, 66/65, 55/54, 65/64, 56/55, 99/98 on positive sizes.
41edo, 58edo are parahemifs would handle this. 80edo, 87edo are gentles would handle this.