Diasem: Difference between revisions

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'''Diasem''' is a [[Maximum variety|max-variety-3]] scale with step pattern 5L 2M 2s (with two rotationally non-equivalent ~~patterns~~ LMLSLMLSL or LSLMLSLML; these are mirror images) that is equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. It can be tuned as a 7-limit (specifically [[Just intonation subgroup|2.3.7 subgroup]]) JI scale or a tempered version thereof. This results in better melodic properties than the diatonic scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semiquartal" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], a defining step size in the scale.

'''Diasem''' is a [[Maximum variety|max-variety-3]] scale with step pattern 5L 2M 2s (with two rotationally non-equivalent variants LMLSLMLSL or LSLMLSLML; these are mirror images) that is equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. It can be tuned as a 7-limit (specifically [[Just intonation subgroup|2.3.7 subgroup]]) JI scale or a tempered version thereof. This results in better melodic properties than the diatonic scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semiquartal" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], a defining step size in the scale.

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Like [[superpyth]], diasem is great for diatonic melodies in the 2.3.7 subgroup; however, it does not temper 64/63, adding two diesis-sized steps to what would normally be a diatonic scale. Not tempering 64/63 is actually quite useful, because it's the difference between only two 4/3 and a 7/4, so the error is spread over just two perfect fourths, unlike the syntonic comma where the error is spread out over four perfect fifths. As a result, the results of tempering out [[81/80]] are not as bad, because each fifth only needs to be bent by about half as much to achieve the same optimization for the 5-limit. So in the case of 2.3.7, it may actually be worth it to accept the addition of small step sizes in order to improve tuning accuracy. Another advantage of detempering the septimal comma is that it allows one to use both 9/8 and 8/7, as well as 21/16 and 4/3, in the same scale. Semaphore in a sense does the opposite of what superpyth does, exaggerating 64/63 to the point that 21/16 is no longer recognizable, and the small steps of diasem become equal to the medium steps.

== Tunings ==

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-'''Diasem''' is a [[Maximum variety|max-variety-3]] scale with step pattern 5L 2M 2s (with two rotationally non-equivalent patterns LMLSLMLSL or LSLMLSLML; these are mirror images) that is equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. It can be tuned as a 7-limit (specifically [[Just intonation subgroup|2.3.7 subgroup]]) JI scale or a tempered version thereof. This results in better melodic properties than the diatonic scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semiquartal" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], a defining step size in the scale.
+'''Diasem''' is a [[Maximum variety|max-variety-3]] scale with step pattern 5L 2M 2s (with two rotationally non-equivalent variants LMLSLMLSL or LSLMLSLML; these are mirror images) that is equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. It can be tuned as a 7-limit (specifically [[Just intonation subgroup|2.3.7 subgroup]]) JI scale or a tempered version thereof. This results in better melodic properties than the diatonic scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semiquartal" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], a defining step size in the scale.
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 Like [[superpyth]], diasem is great for diatonic melodies in the 2.3.7 subgroup; however, it does not temper 64/63, adding two diesis-sized steps to what would normally be a diatonic scale. Not tempering 64/63 is actually quite useful, because it's the difference between only two 4/3 and a 7/4, so the error is spread over just two perfect fourths, unlike the syntonic comma where the error is spread out over four perfect fifths. As a result, the results of tempering out [[81/80]] are not as bad, because each fifth only needs to be bent by about half as much to achieve the same optimization for the 5-limit. So in the case of 2.3.7, it may actually be worth it to accept the addition of small step sizes in order to improve tuning accuracy. Another advantage of detempering the septimal comma is that it allows one to use both 9/8 and 8/7, as well as 21/16 and 4/3, in the same scale. Semaphore in a sense does the opposite of what superpyth does, exaggerating 64/63 to the point that 21/16 is no longer recognizable, and the small steps of diasem become equal to the medium steps.
 == Tunings ==
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