87edo: Difference between revisions
→Theory: "purely consistent" meant exactly the same thing as what immediately followed |
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The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]), {{monzo| 26 -12 -3 }} ([[misty comma]]), and {{monzo| 46 -29 }} ([[29-comma]]) in the 5-limit, in addition to [[245/243]], [[1029/1024]], [[3136/3125]], and [[5120/5103]] in the 7-limit. In the 13-limit, notably [[196/195]], [[325/324]], [[352/351]], [[364/363]], [[385/384]], [[441/440]], [[625/624]], [[676/675]], and [[1001/1000]]. | The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]), {{monzo| 26 -12 -3 }} ([[misty comma]]), and {{monzo| 46 -29 }} ([[29-comma]]) in the 5-limit, in addition to [[245/243]], [[1029/1024]], [[3136/3125]], and [[5120/5103]] in the 7-limit. In the 13-limit, notably [[196/195]], [[325/324]], [[352/351]], [[364/363]], [[385/384]], [[441/440]], [[625/624]], [[676/675]], and [[1001/1000]]. | ||
87edo is a particularly good tuning for [[rodan]], the 41 & 46 temperament. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE generator]] and is close to the [[11-limit]] POTE generator also. Also, the 32\87 generator for [[Kleismic family #Clyde|clyde temperament]] is 0.04455 cents sharp of the 7-limit POTE generator. | 87edo is a particularly good tuning for [[rodan]], the {{nowrap|41 & 46}} temperament. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE generator]] and is close to the [[11-limit]] POTE generator also. Also, the 32\87 generator for [[Kleismic family #Clyde|clyde temperament]] is 0.04455 cents sharp of the 7-limit POTE generator. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 363: | Line 363: | ||
| 15625/15552, 67108864/66430125 | | 15625/15552, 67108864/66430125 | ||
| {{mapping| 87 138 202 }} | | {{mapping| 87 138 202 }} | ||
| | | −0.299 | ||
| 0.455 | | 0.455 | ||
| 3.30 | | 3.30 | ||
| Line 384: | Line 384: | ||
| 196/195, 245/243, 352/351, 364/363, 625/624 | | 196/195, 245/243, 352/351, 364/363, 625/624 | ||
| {{mapping| 87 138 202 244 301 322 }} | | {{mapping| 87 138 202 244 301 322 }} | ||
| | | −0.011 | ||
| 0.625 | | 0.625 | ||
| 4.53 | | 4.53 | ||
| Line 391: | Line 391: | ||
| 154/153, 196/195, 245/243, 273/272, 364/363, 375/374 | | 154/153, 196/195, 245/243, 273/272, 364/363, 375/374 | ||
| {{mapping| 87 138 202 244 301 322 356 }} | | {{mapping| 87 138 202 244 301 322 356 }} | ||
| | | −0.198 | ||
| 0.738 | | 0.738 | ||
| 5.35 | | 5.35 | ||
| Line 398: | Line 398: | ||
| 154/153, 196/195, 210/209, 245/243, 273/272, 286/285, 364/363 | | 154/153, 196/195, 210/209, 245/243, 273/272, 286/285, 364/363 | ||
| {{mapping| 87 138 202 244 301 322 356 370 }} | | {{mapping| 87 138 202 244 301 322 356 370 }} | ||
| | | −0.348 | ||
| 0.796 | | 0.796 | ||
| 5.77 | | 5.77 | ||
| Line 506: | Line 506: | ||
| [[Mystery]] | | [[Mystery]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
87 can serve as a MOS in these: | 87 can serve as a MOS in these: | ||
* [[Avicenna (temperament)|Avicenna]] ([[Breed|87&270]]) {{multival| 24 -9 -66 12 27 … }} | * [[Avicenna (temperament)|Avicenna]] ([[Breed|87 & 270]]) {{multival| 24 -9 -66 12 27 … }} | ||
* [[Breed|87&494]] {{multival| 51 -1 -133 11 32 … }} | * [[Breed|87 & 494]] {{multival| 51 -1 -133 11 32 … }} | ||
== Scales == | == Scales == | ||
| Line 669: | Line 669: | ||
== Music == | == Music == | ||
; [[Gene Ward Smith]] | ; [[Gene Ward Smith]] | ||
* ''Pianodactyl'' (archived 2010) | * ''Pianodactyl'' (archived 2010) – [https://soundcloud.com/genewardsmith/pianodactyl SoundCloud] | [http://www.archive.org/details/Pianodactyl detail] | [http://www.archive.org/download/Pianodactyl/pianodactyl.mp3 play] – rodan[26] in 87edo tuning | ||
[[Category:Zeta|##]] <!-- 2-digit number --> | [[Category:Zeta|##]] <!-- 2-digit number --> | ||