Vulture family: Difference between revisions

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=== 2.3.5.19 ===

It can be observed that the generator of vulture is very close to [[25/19]]; this corresponds to tempering out [[1216/1215]] = ([[19/15]])/([[9/8|18/16]])<sup>2</sup> = S16/S18. It results in a surprising decrease in Dirichlet badness, and (up to [[octave equivalence]]) finds [[19/16]] at 41 generators so that [[19/10]] is found at 20 generators, [[38/27]] is found at 18, [[19/15]] is found at 16 (as 3 is found at 4) and 76/45 is found at 12 so that it's equated with [[27/16]], which is tuned slightly sharp, as 76/45 is 1216/1215 above it. Note that unless you are fine with the low accuracy* tuning offered by [[53edo]], you cannot temper out the [[schisma]], nor can you equate 32/27 with 19/16, meaning both the schisma and [[~~361~~/~~360~~]][[~]][[~~513~~/~~512~~]] are observed. * Compared to what the ~~microtemp~~ is ~~capable~~ of. Also note that 164 - 53 = 53 + 58 = [[111edo]] is a possible tuning ~~not appearing~~ in the optimal ET sequence ~~which doesn't appear~~ because it's less accurate than 53edo on the 2.3.5.19 subgroup.

It can be observed that the generator of vulture is very close to [[25/19]]; this corresponds to tempering out [[1216/1215]] = ([[19/15]])/([[9/8|18/16]])<sup>2</sup> = S16/S18. It results in a surprising decrease in Dirichlet badness, and (up to [[octave equivalence]]) finds [[19/16]] at 41 generators so that [[19/10]] is found at 20 generators, [[38/27]] is found at 18, [[19/15]] is found at 16 (as 3 is found at 4) and 76/45 is found at 12 so that it's equated with [[27/16]], which is tuned slightly sharp, as 76/45 is 1216/1215 above it. Note that unless you are fine with the low accuracy* tuning offered by [[53edo]], you cannot temper out the [[schisma]], nor can you equate 32/27 with 19/16 or 24/19 with 19/15, meaning both the schisma and [[513/512]][[~]][[361/360]] (resp.) are observed. * Compared to what this microtemperament is capable of. This means that the step size of [[270edo]] is especially ideal, being between 361/360 and 513/512, with [[217edo]] exaggerating the comma to be slightly sharp of 361/360. Also note that 164 - 53 = 53 + 58 = [[111edo]] is a possible tuning which doesn't appear in the optimal ET sequence because it's less accurate than 53edo on the 2.3.5.19 subgroup.

Subgroup: 2.3.5.19

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 === 2.3.5.19 ===
-It can be observed that the generator of vulture is very close to [[25/19]]; this corresponds to tempering out [[1216/1215]] = ([[19/15]])/([[9/8|18/16]])<sup>2</sup> = S16/S18. It results in a surprising decrease in Dirichlet badness, and (up to [[octave equivalence]]) finds [[19/16]] at 41 generators so that [[19/10]] is found at 20 generators, [[38/27]] is found at 18, [[19/15]] is found at 16 (as 3 is found at 4) and 76/45 is found at 12 so that it's equated with [[27/16]], which is tuned slightly sharp, as 76/45 is 1216/1215 above it. Note that unless you are fine with the low accuracy* tuning offered by [[53edo]], you cannot temper out the [[schisma]], nor can you equate 32/27 with 19/16, meaning both the schisma and [[361/360]][[~]][[513/512]] are observed. * Compared to what the microtemp is capable of. Also note that 164 - 53 = 53 + 58 = [[111edo]] is a possible tuning not appearing in the optimal ET sequence which doesn't appear because it's less accurate than 53edo on the 2.3.5.19 subgroup.
+It can be observed that the generator of vulture is very close to [[25/19]]; this corresponds to tempering out [[1216/1215]] = ([[19/15]])/([[9/8|18/16]])<sup>2</sup> = S16/S18. It results in a surprising decrease in Dirichlet badness, and (up to [[octave equivalence]]) finds [[19/16]] at 41 generators so that [[19/10]] is found at 20 generators, [[38/27]] is found at 18, [[19/15]] is found at 16 (as 3 is found at 4) and 76/45 is found at 12 so that it's equated with [[27/16]], which is tuned slightly sharp, as 76/45 is 1216/1215 above it. Note that unless you are fine with the low accuracy* tuning offered by [[53edo]], you cannot temper out the [[schisma]], nor can you equate 32/27 with 19/16 or 24/19 with 19/15, meaning both the schisma and [[513/512]][[~]][[361/360]] (resp.) are observed. * Compared to what this microtemperament is capable of. This means that the step size of [[270edo]] is especially ideal, being between 361/360 and 513/512, with [[217edo]] exaggerating the comma to be slightly sharp of 361/360. Also note that 164 - 53 = 53 + 58 = [[111edo]] is a possible tuning which doesn't appear in the optimal ET sequence because it's less accurate than 53edo on the 2.3.5.19 subgroup.
 Subgroup: 2.3.5.19