91edo: Difference between revisions

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The equal temperament also tempers out the {{monzo| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching|stretched 23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size.

The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val. There are more than one way to interpret this in regular temperament theory. First, in the 13-limit, is to assume that 27\91 is directly equivalent to 16/13 and set a temperament in the 2.3.5.7.13 subgroup, which produces a 27 & 91b temperament with the comma basis 91/90, 6272/6075, {{monzo| 84 13 11 -10 }}. Second is to directly take the 27 & 91b val in the 13-limit, which can also be taken using the 27e & 91b.

=== Odd harmonics ===

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91 is the smallest composite number whose composite character is not immediately evident in the decimal system; it is, in fact, the product of 7 and 13.

~~Since the number 7 has historically represented luck, and the number 13 has always stood~~ for ~~bad luck~~, ~~from an aesthetic standpoint, the factoring~~ of 91 ~~represents a kind of "yin-yang"~~, ~~a combination of opposites~~.

The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val.

== Regular temperament properties ==

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 The equal temperament also tempers out the {{monzo| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching|stretched 23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size.
-The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val. There are more than one way to interpret this in regular temperament theory. First, in the 13-limit, is to assume that 27\91 is directly equivalent to 16/13 and set a temperament in the 2.3.5.7.13 subgroup, which produces a 27 & 91b temperament with the comma basis 91/90, 6272/6075, {{monzo| 84 13 11 -10 }}. Second is to directly take the 27 & 91b val in the 13-limit, which can also be taken using the 27e & 91b.
 === Odd harmonics ===
@@ Line 17: / Line 15: @@
 is the smallest composite number whose composite character is not immediately evident in the decimal system; it is, in fact, the product of 7 and 13.
-Since the number 7 has historically represented luck, and the number 13 has always stood for bad luck, from an aesthetic standpoint, the factoring of 91 represents a kind of "yin-yang", a combination of opposites.
+The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val.
 == Regular temperament properties ==