91edo: Difference between revisions

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'''91edo''', the '''91 equal division''' divides the octave into 91 parts of 13.187 cents each.

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.

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. From an aesthetic standpoint, the factoring of 91 represents a kind of "yin-yang" since historically, the number 7 symbolizes luck and 13 misfortune.

== Theory ==

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Likewise, it can also recreate Orwells from tridecatonic scale. However, there is not a "trivial" way to do it due to larger amount of notes. The "correct" way to recreate a mode in this fashion would be using the differences of [[Irvic scale|Irvian mode]] and principal mode - that is by applying the generator or construction at the original tonic. For example, [[22edo]]'s Irvian mode for Orwell[13] is 2212212221221, while for 7/6 generator from the tonic is 1221221221222, and applying the differences results in 5795795777779 scale. This scale is quite bulky for musical performance since it contains an even row of 5x7 steps. A more vibrant possible variant is 5795797597579, which is derived from differences of 2212212212221 and 1221222122122 22edo Orwells.

Since 7 and 13 are the only factors of 91, these numbers are the only ones which can produce naive scales~~. From an aesthetic standpoint, this represents a kind of "yin-yang" for 91edo since 7 symbolizes luck and 13 misfortune~~.

Since 7 and 13 are the only factors of 91, these numbers are the only ones which can produce naive scales.

== Scales ==

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 '''91edo''', the '''91 equal division''' divides the octave into 91 parts of 13.187 cents each.
-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.
+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. From an aesthetic standpoint, the factoring of 91 represents a kind of "yin-yang" since historically, the number 7 symbolizes luck and 13 misfortune.
 == Theory ==
@@ Line 15: / Line 15: @@
 Likewise, it can also recreate Orwells from tridecatonic scale. However, there is not a "trivial" way to do it due to larger amount of notes. The "correct" way to recreate a mode in this fashion would be using the differences of [[Irvic scale|Irvian mode]] and principal mode - that is by applying the generator or construction at the original tonic. For example, [[22edo]]'s Irvian mode for Orwell[13] is 2212212221221, while for 7/6 generator from the tonic is 1221221221222, and applying the differences results in 5795795777779 scale. This scale is quite bulky for musical performance since it contains an even row of 5x7 steps. A more vibrant possible variant is 5795797597579, which is derived from differences of 2212212212221 and 1221222122122 22edo Orwells.
-Since 7 and 13 are the only factors of 91, these numbers are the only ones which can produce naive scales. From an aesthetic standpoint, this represents a kind of "yin-yang" for 91edo since 7 symbolizes luck and 13 misfortune.
+Since 7 and 13 are the only factors of 91, these numbers are the only ones which can produce naive scales.
 == Scales ==