Xenharmonic Wiki:Cross-platform dialogue: Difference between revisions

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As for primes > 13, I highly recommend looking at the [[25-odd-limit]] in all its glory if you are unfamiliar with using primes > 13, but as a quick summary, 17 is notable as introducing subminor ([[17/14]]) and supramajor ([[21/17]]) and neogothic minor ([[20/17]]) and neogothic major ([[51/40]]) and a good approximation of the half-octave of [[17/12]]~[[24/17]] but also for its naturalness as the general-purpose semitone in [[srutal archagall]], 19 introduces the harmonic minor third [[19/16]] between [[6/5]] and [[13/11]], and is close to [[32/27]] (and equated with it in [[nestoria]]), 23 introduces [[23/16]] which is what can be thought of as a harmonic augmented fourth in sharp-fifth systems and a harmonic diminished fifth in flat-fifth systems; it also introduces [[23/20]] which is between supermajor ([[8/7]]) and a semifourth ([[15/13]]), plus two new shades of supraminor third at [[23/19]] and [[28/23]], although the latter is more like a subneutral third, [[29/16]] is notable for being basically free in multiples of [[7edo]] (although is also notable as [[29/23]] approximates 400c reasonably well so [[21edo]] (and therefore [[63edo]] and [[84edo]]) has a good 23:29:32:39 chord for example), [[32/31]] is the subharmonic quarter-tone, [[37/32]] is the harmonic semifourth (implying a fourth around that of [[19edo]], so for higher-accuracy systems it works especially well with dual-semifourths; remarkably [[15/13]] and [[37/32]] are made fourth-complements in the miraculous harmonic series autotuner [[311edo]]), [[41/32]] is the harmonic supermajor third and [[43/32]] is the harmonic perfect fourth (as it approximates [[4/3]] significantly better than [[21/16]] and much better than [[11/8]]).

Ranking poll is here: https://strawpoll.com/~~6QnMOMP7aZe~~

Ranking poll is here: https://strawpoll.com/wAg3A53dMy8

Revision as of 12:41, 16 May 2024 view source Godtone (talk \| contribs) autopatrolled 2,289 edits m →Ranking poll for "good" EDOs from 27 to 140: typo ← Older edit		Revision as of 12:51, 16 May 2024 view source Godtone (talk \| contribs) autopatrolled 2,289 edits m →Ranking poll for "good" EDOs from 27 to 140: two erroneous votes including my own and the only legitimate vote was my own so restarted the poll for cleanliness Newer edit →
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	As for primes > 13, I highly recommend looking at the [[25-odd-limit]] in all its glory if you are unfamiliar with using primes > 13, but as a quick summary, 17 is notable as introducing subminor ([[17/14]]) and supramajor ([[21/17]]) and neogothic minor ([[20/17]]) and neogothic major ([[51/40]]) and a good approximation of the half-octave of [[17/12]]~[[24/17]] but also for its naturalness as the general-purpose semitone in [[srutal archagall]], 19 introduces the harmonic minor third [[19/16]] between [[6/5]] and [[13/11]], and is close to [[32/27]] (and equated with it in [[nestoria]]), 23 introduces [[23/16]] which is what can be thought of as a harmonic augmented fourth in sharp-fifth systems and a harmonic diminished fifth in flat-fifth systems; it also introduces [[23/20]] which is between supermajor ([[8/7]]) and a semifourth ([[15/13]]), plus two new shades of supraminor third at [[23/19]] and [[28/23]], although the latter is more like a subneutral third, [[29/16]] is notable for being basically free in multiples of [[7edo]] (although is also notable as [[29/23]] approximates 400c reasonably well so [[21edo]] (and therefore [[63edo]] and [[84edo]]) has a good 23:29:32:39 chord for example), [[32/31]] is the subharmonic quarter-tone, [[37/32]] is the harmonic semifourth (implying a fourth around that of [[19edo]], so for higher-accuracy systems it works especially well with dual-semifourths; remarkably [[15/13]] and [[37/32]] are made fourth-complements in the miraculous harmonic series autotuner [[311edo]]), [[41/32]] is the harmonic supermajor third and [[43/32]] is the harmonic perfect fourth (as it approximates [[4/3]] significantly better than [[21/16]] and much better than [[11/8]]).		As for primes > 13, I highly recommend looking at the [[25-odd-limit]] in all its glory if you are unfamiliar with using primes > 13, but as a quick summary, 17 is notable as introducing subminor ([[17/14]]) and supramajor ([[21/17]]) and neogothic minor ([[20/17]]) and neogothic major ([[51/40]]) and a good approximation of the half-octave of [[17/12]]~[[24/17]] but also for its naturalness as the general-purpose semitone in [[srutal archagall]], 19 introduces the harmonic minor third [[19/16]] between [[6/5]] and [[13/11]], and is close to [[32/27]] (and equated with it in [[nestoria]]), 23 introduces [[23/16]] which is what can be thought of as a harmonic augmented fourth in sharp-fifth systems and a harmonic diminished fifth in flat-fifth systems; it also introduces [[23/20]] which is between supermajor ([[8/7]]) and a semifourth ([[15/13]]), plus two new shades of supraminor third at [[23/19]] and [[28/23]], although the latter is more like a subneutral third, [[29/16]] is notable for being basically free in multiples of [[7edo]] (although is also notable as [[29/23]] approximates 400c reasonably well so [[21edo]] (and therefore [[63edo]] and [[84edo]]) has a good 23:29:32:39 chord for example), [[32/31]] is the subharmonic quarter-tone, [[37/32]] is the harmonic semifourth (implying a fourth around that of [[19edo]], so for higher-accuracy systems it works especially well with dual-semifourths; remarkably [[15/13]] and [[37/32]] are made fourth-complements in the miraculous harmonic series autotuner [[311edo]]), [[41/32]] is the harmonic supermajor third and [[43/32]] is the harmonic perfect fourth (as it approximates [[4/3]] significantly better than [[21/16]] and much better than [[11/8]]).

	Ranking poll is here: https://strawpoll.com/~~6QnMOMP7aZe~~		Ranking poll is here: https://strawpoll.com/wAg3A53dMy8