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{{Infobox ET}} | {{Infobox ET}} | ||
'''[[EDF|Division of the just perfect fifth]] into 35 equal parts''' (35EDF) is related to [[60edo | '''[[EDF|Division of the just perfect fifth]] into 35 equal parts''' (35EDF) is related to [[60edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave stretch|stretched]] by about 3.3514 [[cents]] and the step size is about 20.0559 cents (corresponding to 59.8329 [[edo]], practically identical to every sixth step of [[359edo]]). | ||
The [[patent val]] has a generally sharp tendency for [[harmonic]]s up to 18, with the exception for 13. Unlike 60edo, it is only consistent up to the 7-[[integer-limit]], with discrepancy for the 8th harmonic (three octaves). | |||
Lookalikes: [[60edo]], [[95edt]] | Lookalikes: [[60edo]], [[95edt]] | ||
== Harmonics == | |||
{{Harmonics in equal|35|3|2|intervals=prime}} | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals in 35edf | |||
|- | |- | ||
! Degrees of 60edo | ! Degrees of 60edo | ||
| Line 367: | Line 373: | ||
|} | |} | ||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 07:38, 18 December 2024
| ← 34edf | 35edf | 36edf → |
Division of the just perfect fifth into 35 equal parts (35EDF) is related to 60edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 3.3514 cents and the step size is about 20.0559 cents (corresponding to 59.8329 edo, practically identical to every sixth step of 359edo).
The patent val has a generally sharp tendency for harmonics up to 18, with the exception for 13. Unlike 60edo, it is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.35 | +3.35 | +1.45 | +0.56 | +0.24 | -8.18 | +8.73 | -3.33 | +6.86 | +6.68 | -8.50 |
| Relative (%) | +16.7 | +16.7 | +7.2 | +2.8 | +1.2 | -40.8 | +43.5 | -16.6 | +34.2 | +33.3 | -42.4 | |
| Steps (reduced) |
60 (25) |
95 (25) |
139 (34) |
168 (28) |
207 (32) |
221 (11) |
245 (0) |
254 (9) |
271 (26) |
291 (11) |
296 (16) | |
Intervals
| Degrees of 60edo | Cents value | Approximate ratios in the 2.3.5.13 subgroup | Additional ratios of 7 and 11 (assuming flat values for primes) |
|---|---|---|---|
| 0 | |||
| 1 | 20.0559 | 81/80 | |
| 2 | 40.1117 | ||
| 3 | 60.1676 | 28/27, 27/26 | |
| 4 | 80.2234 | 21/20 | |
| 5 | 100.2793 | ||
| 6 | 120.3351 | 16/15 | |
| 7 | 140.391 | ||
| 8 | 160.4469 | 12/11, 11/10 | |
| 9 | 180.5027 | 10/9 | |
| 10 | 200.5586 | 9/8 | |
| 11 | 220.6144 | ||
| 12 | 240.6703 | 15/13 | 8/7 |
| 13 | 260.7621 | 7/6 | |
| 14 | 280.782 | ||
| 15 | 300.8379 | ||
| 16 | 320.8937 | 6/5 | |
| 17 | 340.9496 | 11/9 | |
| 18 | 361.0054 | 16/13 | |
| 19 | 381.0613 | 5/4 | |
| 20 | 401.1171 | ||
| 21 | 421.173 | 14/11 | |
| 22 | 441.2289 | 9/7 | |
| 23 | 461.2847 | 13/10 | |
| 24 | 481.3406 | ||
| 25 | 501.3964 | 4/3 | |
| 26 | 521.4523 | ||
| 27 | 541.5081 | 11/8, 15/11 | |
| 28 | 561.564 | 18/13 | |
| 29 | 581.6199 | 7/5 | |
| 30 | 601.6757 | ||
| 31 | 621.7315 | 10/7 | |
| 32 | 641.7874 | 13/9 | |
| 33 | 661.8433 | 16/11, 22/15 | |
| 34 | 681.8891 | ||
| 35 | 701.955 | 3/2 | |
| 36 | 722.0109 | ||
| 37 | 742.0667 | 20/13 | |
| 38 | 762.1226 | 14/9 | |
| 39 | 782.1784 | 11/7 | |
| 40 | 802.2343 | ||
| 41 | 822.2901 | 8/5 | |
| 42 | 842.346 | 13/8 | |
| 43 | 862.4019 | 18/11 | |
| 44 | 882.4577 | 5/3 | |
| 45 | 902.5136 | ||
| 46 | 922.5694 | ||
| 47 | 942.6253 | 12/7 | |
| 48 | 962.6811 | 26/15 | 7/4 |
| 49 | 982.737 | ||
| 50 | 1002.7929 | 16/9 | |
| 51 | 1022.8487 | 9/5 | |
| 52 | 1042.9046 | 11/6, 20/11 | |
| 53 | 1062.9604 | ||
| 54 | 1083.0163 | 15/8 | |
| 55 | 1103.0721 | ||
| 56 | 1123.128 | ||
| 57 | 1143.1839 | ||
| 58 | 1163.2397 | ||
| 59 | 1183.2956 | ||
| 60 | 1203.3514 | ||
| 61 | 1223.4073 | 81/40 | |
| 62 | 1243.4631 | ||
| 63 | 1263.519 | 56/27, 27/13 | |
| 64 | 1283.5749 | 21/10 | |
| 65 | 1303.6307 | ||
| 66 | 1323.6866 | 32/15 | |
| 67 | 1343.7424 | ||
| 68 | 1363.7983 | 24/11, 11/5 | |
| 69 | 1383.85415 | 20/9 | |
| 70 | 1403.91 | 9/4 | |