111edo: Difference between revisions
→Theory: 23-limit notability |
Sensible -> warrior |
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It further tempers out among others [[351/350]], [[352/351]], [[640/637]], [[676/675]], [[847/845]], [[1001/1000]], [[1188/1183]], [[1573/1568]] in the 13-limit; [[256/255]], [[325/324]], [[442/441]] in the 17-limit; [[286/285]], [[400/399]], [[476/475]] in the 19-limit. It excels as a full [[23-limit]] temperament, tempering out [[253/252]] and [[276/275]]. The [[23/1|23]] is tuned a little flat, unlike the lower primes. [[23/19]], [[23/21]] and their [[octave complement]]s are the only inconsistently mapped intervals in the [[23-odd-limit]]. | It further tempers out among others [[351/350]], [[352/351]], [[640/637]], [[676/675]], [[847/845]], [[1001/1000]], [[1188/1183]], [[1573/1568]] in the 13-limit; [[256/255]], [[325/324]], [[442/441]] in the 17-limit; [[286/285]], [[400/399]], [[476/475]] in the 19-limit. It excels as a full [[23-limit]] temperament, tempering out [[253/252]] and [[276/275]]. The [[23/1|23]] is tuned a little flat, unlike the lower primes. [[23/19]], [[23/21]] and their [[octave complement]]s are the only inconsistently mapped intervals in the [[23-odd-limit]]. | ||
It is a particularly good tuning for the 11- or 13-limit versions of [[semisept]], the {{nowrap| 31 & 80 }} temperament, and [[buzzard]], the {{nowrap| 53 & 58 }} temperament. [[Gene Ward Smith]]'s trio in [[#Music]] section is in [[guanyin]] temperament, the [[rank-3 temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val. | It is a particularly good tuning for the 11- or 13-limit versions of [[semisept]], the {{nowrap| 31 & 80 }} temperament, and [[buzzard]], the {{nowrap| 53 & 58 }} temperament, as well as [[warrior]], the {{nowrap| 46 & 65d }} temperament. [[Gene Ward Smith]]'s trio in [[#Music]] section is in [[guanyin]] temperament, the [[rank-3 temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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| 1 | | 1 | ||
| 10.8 | | 10.8 | ||
| [[121/120]], [[126/125]], [[144/143]], [[169/168]], [[196/195]], [[225/224]] | | [[121/120]], [[126/125]], [[144/143]], [[161/160]], [[169/168]], [[196/195]], [[225/224]] | ||
| {{UDnote|step=1}} | | {{UDnote|step=1}} | ||
|- | |- | ||
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| 23 | | 23 | ||
| 248.6 | | 248.6 | ||
| [[15/13]] | | [[15/13]], [[22/19]] | ||
| {{UDnote|step=23}} | | {{UDnote|step=23}} | ||
|- | |- | ||
| 24 | | 24 | ||
| 259.5 | | 259.5 | ||
| | | | ||
| {{UDnote|step=24}} | | {{UDnote|step=24}} | ||
|- | |- | ||
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| 32 | | 32 | ||
| 345.9 | | 345.9 | ||
| [[11/9]], | | [[11/9]], [[28/23]], [[39/32]] | ||
| {{UDnote|step=32}} | | {{UDnote|step=32}} | ||
|- | |- | ||
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| 45 | | 45 | ||
| 486.5 | | 486.5 | ||
| [[65/49]] | | [[45/34]], [[65/49]] | ||
| {{UDnote|step=45}} | | {{UDnote|step=45}} | ||
|- | |- | ||
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| … | | … | ||
|} | |} | ||
<nowiki/>* As a 23-limit temperament | <nowiki/>* As a 23-limit temperament, inconsistently mapped intervals in ''italic'' | ||
== Approximation to JI == | == Approximation to JI == | ||
=== Interval mappings === | === Interval mappings === | ||
{{Q-odd-limit intervals}} | {{Q-odd-limit intervals}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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| 4/3<br>(18/17~19/18) | | 4/3<br>(18/17~19/18) | ||
| [[Misty]] | | [[Misty]] | ||
|- | |||
| 37 | |||
| 46\111<br>(1\111) | |||
| 497.30<br>(10.81) | |||
| 4/3<br>(169/168) | |||
| [[Rubidium]] | |||
|} | |} | ||
<nowiki/>* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* Direct sunlight (subset of [[Sensi]][19]): 5 7 34 19 5 36 5 ((5, 12, 46, 65, 70, 106, 111)\111) | * Direct sunlight (subset of [[Sensi]][19]): 5 7 34 19 5 36 5 ((5, 12, 46, 65, 70, 106, 111)\111) | ||
* Hypersakura (subset of Sensi[19]): 5 41 19 5 41 ((5, 46, 65, 70, 111)\111) | * Hypersakura (subset of Sensi[19]): 5 41 19 5 41 ((5, 46, 65, 70, 111)\111) | ||
== Instruments == | |||
* [[Lumatone mapping for 111edo]] | |||
== Music == | == Music == | ||
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[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Buzzard]] | [[Category:Buzzard]] | ||
[[Category:Warrior]] | |||
[[Category:Semisept]] | [[Category:Semisept]] | ||
[[Category:Orwellismic]] | [[Category:Orwellismic]] | ||
[[Category:Guanyin]] | [[Category:Guanyin]] | ||
[[Category:Valinorsmic]] | [[Category:Valinorsmic]] | ||