61edo: Difference between revisions
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61edo is the 18th [[prime edo]], after [[59edo]] and before [[67edo]]. [[183edo]], which triples it, corrects its approximation to many of the lower harmonics. | 61edo is the 18th [[prime edo]], after [[59edo]] and before [[67edo]]. [[183edo]], which triples it, corrects its approximation to many of the lower harmonics. | ||
== | == Notation == | ||
===Sagittal notation=== | |||
In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | |||
This notation uses the same sagittal sequence as [[54edo#Sagittal notation|54-EDO]]. | |||
====Evo flavor==== | |||
<imagemap> | |||
File:61-EDO_Evo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 704 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[513/512]] | |||
rect 140 80 240 106 [[81/80]] | |||
rect 240 80 360 106 [[33/32]] | |||
rect 360 80 480 106 [[27/26]] | |||
default [[File:61-EDO_Evo_Sagittal.svg]] | |||
</imagemap> | |||
====Revo flavor==== | |||
<imagemap> | |||
File:61-EDO_Revo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 650 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[513/512]] | |||
rect 140 80 240 106 [[81/80]] | |||
rect 240 80 360 106 [[33/32]] | |||
rect 360 80 480 106 [[27/26]] | |||
default [[File:61-EDO_Revo_Sagittal.svg]] | |||
</imagemap> | |||
====Evo-SZ flavor==== | |||
<imagemap> | |||
File:61-EDO_Evo-SZ_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 696 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[513/512]] | |||
rect 140 80 240 106 [[81/80]] | |||
rect 240 80 360 106 [[33/32]] | |||
rect 360 80 480 106 [[27/26]] | |||
default [[File:61-EDO_Evo-SZ_Sagittal.svg]] | |||
</imagemap> | |||
[[Category:Todo:add rank 2 temperaments table]] | [[Category:Todo:add rank 2 temperaments table]] | ||
Revision as of 05:30, 29 December 2024
| ← 60edo | 61edo | 62edo → |
Theory
As an equal temperament, 61et is characterized by tempering out 20000/19683 (tetracot comma) and 262144/253125 (passion comma) in the 5-limit. In the 7-limit, the patent val ⟨61 97 142 171] supports valentine (15 & 46), and is the optimal patent val for freivald (24 & 37) in the 7-, 11- and 13-limit. The 61d val ⟨61 97 142 172] is a great tuning for modus and quasisuper, and is a simple but out-of-tune edo tuning for parakleismic. Peter Kosmorsky has an interesting poem about its tuning profile, as follows.
Introductory 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!
Odd harmonics
| 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) | |
Subsets and supersets
61edo is the 18th prime edo, after 59edo and before 67edo. 183edo, which triples it, corrects its approximation to many of the lower harmonics.
Notation
Sagittal notation
In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's primary comma (the comma it exactly represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it approximately represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
This notation uses the same sagittal sequence as 54-EDO.
Evo flavor
Revo flavor
Evo-SZ flavor
