61edo: Difference between revisions
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== Theory == | |||
61edo provides the [[optimal patent val]] for the [[freivald]] (24&37) temperament in the 7-, 11- and 13-limit. | 61edo provides the [[optimal patent val]] for the [[freivald]] (24&37) temperament in the 7-, 11- and 13-limit. | ||
61edo is the 18th [[prime edo]], after of [[59edo]] and before of [[67edo]]. | 61edo is the 18th [[prime edo]], after of [[59edo]] and before of [[67edo]]. | ||
== Table of intervals == | |||
== | |||
== Intervals == | == Intervals == | ||
| Line 222: | Line 201: | ||
| 1200.000 | | 1200.000 | ||
|} | |} | ||
== Miscellany == | |||
=== Mnemonic descriptive poem == | |||
These 61 equal divisions of the octave, | |||
though rare are assuredly a ROCK-tave (har har), | |||
while the 3rd and 5th harmonics are about six cents sharp, | |||
(and the flattish 15th poised differently on the harp), | |||
the 7th and 11th err by less, around three, | |||
and thus mayhap, a good orgone tuning found to be; | |||
slightly sharp as well, is the 13th harmonic's place, | |||
but the 9th and 17th lack near so much grace, | |||
interestingly the 19th is good but a couple cents flat, | |||
and the 21st and 23rd are but a cent or two sharp! | |||
{{Harmonics in equal|61|columns=11}} | |||
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 19:41, 10 January 2023
| ← 60edo | 61edo | 62edo → |
Theory
61edo provides the optimal patent val for the freivald (24&37) temperament in the 7-, 11- and 13-limit.
61edo is the 18th prime edo, after of 59edo and before of 67edo.
Table of intervals
Intervals
| # | Cents |
|---|---|
| 0 | 0.000 |
| 1 | 19.672 |
| 2 | 39.344 |
| 3 | 59.016 |
| 4 | 78.689 |
| 5 | 98.361 |
| 6 | 118.033 |
| 7 | 137.705 |
| 8 | 157.377 |
| 9 | 177.049 |
| 10 | 196.721 |
| 11 | 216.393 |
| 12 | 236.066 |
| 13 | 255.738 |
| 14 | 275.410 |
| 15 | 295.082 |
| 16 | 314.754 |
| 17 | 334.426 |
| 18 | 354.098 |
| 19 | 373.770 |
| 20 | 393.443 |
| 21 | 413.115 |
| 22 | 432.787 |
| 23 | 452.459 |
| 24 | 472.131 |
| 25 | 491.803 |
| 26 | 511.475 |
| 27 | 531.148 |
| 28 | 550.820 |
| 29 | 570.492 |
| 30 | 590.164 |
| 31 | 609.836 |
| 32 | 629.508 |
| 33 | 649.180 |
| 34 | 668.852 |
| 35 | 688.525 |
| 36 | 708.197 |
| 37 | 727.869 |
| 38 | 747.541 |
| 39 | 767.213 |
| 40 | 786.885 |
| 41 | 806.557 |
| 42 | 826.230 |
| 43 | 845.902 |
| 44 | 865.574 |
| 45 | 885.246 |
| 46 | 904.918 |
| 47 | 924.590 |
| 48 | 944.262 |
| 49 | 963.934 |
| 50 | 983.607 |
| 51 | 1003.279 |
| 52 | 1022.951 |
| 53 | 1042.623 |
| 54 | 1062.295 |
| 55 | 1081.967 |
| 56 | 1101.639 |
| 57 | 1121.311 |
| 58 | 1140.984 |
| 59 | 1160.656 |
| 60 | 1180.328 |
| 61 | 1200.000 |
Miscellany
= Mnemonic descriptive poem
These 61 equal divisions of the octave,
though rare are assuredly a ROCK-tave (har har),
while the 3rd and 5th harmonics are about six cents sharp,
(and the flattish 15th poised differently on the harp),
the 7th and 11th err by less, around three,
and thus mayhap, a good orgone tuning found to be;
slightly sharp as well, is the 13th harmonic's place,
but the 9th and 17th lack near so much grace,
interestingly the 19th is good but a couple cents flat,
and the 21st and 23rd are but a cent or two sharp!
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.24 | +7.13 | -4.89 | -7.19 | -0.50 | +5.37 | -6.30 | -6.59 | -2.43 | +1.35 | +1.23 |
| Relative (%) | +31.7 | +36.2 | -24.9 | -36.5 | -2.5 | +27.3 | -32.0 | -33.5 | -12.4 | +6.9 | +6.3 | |
| Steps (reduced) |
97 (36) |
142 (20) |
171 (49) |
193 (10) |
211 (28) |
226 (43) |
238 (55) |
249 (5) |
259 (15) |
268 (24) |
276 (32) | |