135edo: Difference between revisions

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{{Infobox ET

| Prime factorization = 3<sup>3</sup> × 5

| Step size = 8.88889¢

| Fifth = 79\135 (702.22¢)

| Semitones = 13:10 (115.56¢ : 88.89¢)

| Consistency = 7

}}

The '''135 equal divisions of the octave''' ('''135edo'''), or the '''135(-tone) equal temperament''' ('''135tet''', '''135et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 135 parts of about 8.89 [[cent]]s each.

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Using the 135f [[val]] {{val| 135 214 313 379 467 '''499''' }}, which tends flat, 135et tempers out 32805/32768 ([[schisma]]) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], [[3125/3087]], and 28824005/28697814 in the 7-limit, [[385/384]], [[540/539]], 2200/2187, 12005/11979 and the [[quartisma]] in the 11-limit; [[169/168]] and [[364/363]] in the 13-limit.

Using the 135c val {{val| 135 214 '''314''' 379 467 500 }}, which tends sharp, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and 16384/16335 in the 11-limit; [[196/195]], [[351/350]], [[352/351]], [[676/675]], and 6656/6655 in the 13-limit.

Using the 135c val {{val| 135 214 '''314''' 379 467 500 }}, which tends sharp, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and [[16384/16335]] in the 11-limit; [[196/195]], [[351/350]], [[352/351]], [[676/675]], and [[6656/6655]] in the 13-limit.

As every other step of the full 13-limit monster – [[270edo|270et]], 135et probably makes more sense as a 2.3.7.11 [[subgroup]] temperament, where it tempers out the [[garischisma]] and the [[symbiotic comma]].

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+{{Infobox ET
+| Prime factorization = 3<sup>3</sup> × 5
+| Step size = 8.88889¢
+| Fifth = 79\135 (702.22¢)
+| Semitones = 13:10 (115.56¢ : 88.89¢)
+| Consistency = 7
+}}
 The '''135 equal divisions of the octave''' ('''135edo'''), or the '''135(-tone) equal temperament''' ('''135tet''', '''135et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 135 parts of about 8.89 [[cent]]s each.
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 Using the 135f [[val]] {{val| 135 214 313 379 467 '''499''' }}, which tends flat, 135et tempers out 32805/32768 ([[schisma]]) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], [[3125/3087]], and 28824005/28697814 in the 7-limit, [[385/384]], [[540/539]], 2200/2187, 12005/11979 and the [[quartisma]] in the 11-limit; [[169/168]] and [[364/363]] in the 13-limit.
-Using the 135c val {{val| 135 214 '''314''' 379 467 500 }}, which tends sharp, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and 16384/16335 in the 11-limit; [[196/195]], [[351/350]], [[352/351]], [[676/675]], and 6656/6655 in the 13-limit.
+Using the 135c val {{val| 135 214 '''314''' 379 467 500 }}, which tends sharp, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and [[16384/16335]] in the 11-limit; [[196/195]], [[351/350]], [[352/351]], [[676/675]], and [[6656/6655]] in the 13-limit.
 As every other step of the full 13-limit monster – [[270edo|270et]], 135et probably makes more sense as a 2.3.7.11 [[subgroup]] temperament, where it tempers out the [[garischisma]] and the [[symbiotic comma]].