293edo: Difference between revisions

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Nonetheless, a number of mappings can be considered.

Using the [[patent val]], {{val|293 464 680 823}}, 293edo [[tempering out|tempers out]] the [[parakleisma]] and {{monzo| -40 15 7 }} in the 5-limit and the [[marvel comma]] in the 7-limit.

Using the [[patent val]], {{val|293 464 680 823}}, 293edo [[tempering out|tempers out]] the [[parakleisma]] and {{monzo| -40 15 7 }} in the 5-limit and the [[marvel comma]] in the 7-limit. The 293bb val, with {{val|293 '''463''' 680 823}}, is a tuning close to the [[POTE]] tuning for the [[meantone]] temperament. 293bcd, {{val|293 '''465 681 822'''}} is a tuning for [[quartonic]].

~~The 293bb~~ val, ~~with~~ {{val|293 '''~~463~~''' ~~680 823~~}}~~, is~~ a tuning close to the [[POTE]] tuning for the [[~~meantone~~]] ~~temperament~~.

In the 11-limit, 293de val, {{val|293 464 680 '''822 1013'''}} provides a tuning close to the [[POTE]] tuning for [[hemiseven]], and and in the 13-limit, 293ef val {{val|293 464 680 823 '''1013 1085'''}} tunes [[merman]].

293edo nonetheless has good approximations to [[6/5]], [[11/7]], [[17/11]], [[19/17]], [[24/23]], [[25/17]], [[25/19]], and respectively their octave inversions. [[21/16]], which is a composite octave-reduced harmonic, is also well represented.

In the 17-limit, although inconsistent, 293edo in the patent val is a tuning for the [[Symmetry454]] temperament which is constructed from a calendar ~~layout by~~ the same name. See the dedicated page.

=== Symmetry454 temperament ===

In the 17-limit, although inconsistent, 293edo in the patent val is a tuning for the [[Symmetry454]] temperament which is described as the 52 & 293 temperament, and constructed from a 52-tone maximal evenness scale which is exactly the distribution of leap years in the 293-year cycle of {{W|Symmetry454}}, the calendar with the same name. 62\293, mapped to [[52/45]], is the generator. See the dedicated page.

=== Odd harmonics ===

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== Regular temperament properties ==

=== Commas ===

~~293edo tempers out the 2.43 {{monzo| 1590 293 }} comma in the [[patent val]], equating a stack of 293 43rd harmonics with 1590 octaves.~~

Using the patent val, it tempers out 225/224, 2500000/2470629, and 344373768/341796875 in the 7-limit; 6250/6237, 8019/8000, 14700/14641, and 16896/16807 in the 11-limit; 351/350, 625/624, 1625/1617, and 13122/13013 in the 13-limit; 715/714, 850/847, 1089/1088, 1377/1375, 2058/2057, and 2880/2873 in the 17-limit.

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== Scales ==

The 33L 19s [[Maximal evenness|maximally even]] scale of 293edo is a leap year pattern of a proposed calendar. It employs 62\293 as a generator, described as "accumulator" by the creator of the calendar himself. Likewise, a 71-note cycle with 260\293 generator can be constructed by analogy.

~~The corresponding rank two temperament is therefore called~~ [[Symmetry454]].

* Symmetry454[5]: 45 79 45 79 45

* Symmetry454[19]: 17 11 17 17 17 11 17 17 17 11 17 17 17 11 17 17 17 11 17

* Symmetry454[52]: 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5

== Music ==

@@ Line 7: / Line 7: @@
 Nonetheless, a number of mappings can be considered.
-Using the [[patent val]], {{val|293 464 680 823}}, 293edo [[tempering out|tempers out]] the [[parakleisma]] and {{monzo| -40 15 7 }} in the 5-limit and the [[marvel comma]] in the 7-limit.
+Using the [[patent val]], {{val|293 464 680 823}}, 293edo [[tempering out|tempers out]] the [[parakleisma]] and {{monzo| -40 15 7 }} in the 5-limit and the [[marvel comma]] in the 7-limit. The 293bb val, with {{val|293 '''463''' 680 823}}, is a tuning close to the [[POTE]] tuning for the [[meantone]] temperament. 293bcd, {{val|293 '''465 681 822'''}} is a tuning for [[quartonic]].
-The 293bb val, with {{val|293 '''463''' 680 823}}, is a tuning close to the [[POTE]] tuning for the [[meantone]] temperament.
+In the 11-limit, 293de val, {{val|293 464 680 '''822 1013'''}} provides a tuning close to the [[POTE]] tuning for [[hemiseven]], and and in the 13-limit, 293ef val {{val|293 464 680 823 '''1013 1085'''}} tunes [[merman]].
 edo nonetheless has good approximations to [[6/5]], [[11/7]], [[17/11]], [[19/17]], [[24/23]], [[25/17]], [[25/19]], and respectively their octave inversions. [[21/16]], which is a composite octave-reduced harmonic, is also well represented.
-In the 17-limit, although inconsistent, 293edo in the patent val is a tuning for the [[Symmetry454]] temperament which is constructed from a calendar layout by the same name. See the dedicated page.
+=== Symmetry454 temperament ===
+{{Main|Symmetry454}}
+In the 17-limit, although inconsistent, 293edo in the patent val is a tuning for the [[Symmetry454]] temperament which is described as the 52 & 293 temperament, and constructed from a 52-tone maximal evenness scale which is exactly the distribution of leap years in the 293-year cycle of {{W|Symmetry454}}, the calendar with the same name. 62\293, mapped to [[52/45]], is the generator. See the dedicated page.
 === Odd harmonics ===
@@ Line 23: / Line 26: @@
 == Regular temperament properties ==
 === Commas ===
-edo tempers out the 2.43 {{monzo| 1590 293 }} comma in the [[patent val]], equating a stack of 293 43rd harmonics with 1590 octaves.
 Using the patent val, it tempers out 225/224, 2500000/2470629, and 344373768/341796875 in the 7-limit; 6250/6237, 8019/8000, 14700/14641, and 16896/16807 in the 11-limit; 351/350, 625/624, 1625/1617, and 13122/13013 in the 13-limit; 715/714, 850/847, 1089/1088, 1377/1375, 2058/2057, and 2880/2873 in the 17-limit.
@@ Line 77: / Line 78: @@
 == Scales ==
-The 33L 19s [[Maximal evenness|maximally even]] scale of 293edo is a leap year pattern of a proposed calendar. It employs 62\293 as a generator, described as "accumulator" by the creator of the calendar himself. Likewise, a 71-note cycle with 260\293 generator can be constructed by analogy.
-The corresponding rank two temperament is therefore called [[Symmetry454]].
+* Symmetry454[5]: 45 79 45 79 45
+* Symmetry454[19]: 17 11 17 17 17 11 17 17 17 11 17 17 17 11 17 17 17 11 17
+* Symmetry454[52]: 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 5 6 5 6 6 5
 == Music ==