198edo: Difference between revisions
→Theory: +octave stretch |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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Like 99, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[10976/10935]] in the 7-limit. In the 11-limit, [[3025/3024]], [[3388/3375]], [[9801/9800]], [[14641/14580]], and [[16384/16335]]; in the 13-limit, [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[2200/2197]] and [[6656/6655]]. | Like 99, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[10976/10935]] in the 7-limit. In the 11-limit, [[3025/3024]], [[3388/3375]], [[9801/9800]], [[14641/14580]], and [[16384/16335]]; in the 13-limit, [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[2200/2197]] and [[6656/6655]]. | ||
It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[major minthmic chords]], it enables [[essentially tempered | It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[major minthmic chords]], it enables [[essentially tempered chord]]s including [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the [[13-odd-limit]], in addition to [[island chords]] in the [[15-odd-limit]]. | ||
Notably, it is the last edo to map [[64/63]] and [[81/80]] to the same step consistently. | Notably, it is the last edo to map [[64/63]] and [[81/80]] to the same step consistently. | ||
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== Intervals == | == Intervals == | ||
{{Main| Table of 198edo intervals }} | {{Main| Table of 198edo intervals }} | ||
== Notation == | |||
=== Ups and downs notation === | |||
198edo can be notated using [[Kite's ups and downs notation|ups and downs]] with quarter-tone accidentals: | |||
{{Ups and downs sharpness|198|true}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| 13/12 | | 13/12 | ||
| [[Quasijerome]] | | [[Quasijerome]] | ||
|- | |||
| 1 | |||
| 29\198 | |||
| 175.76 | |||
| 72/65 | |||
| [[Quadrafifths]] | |||
|- | |- | ||
| 1 | | 1 | ||
| 65\198 | | 65\198 | ||
| 393. | | 393.94 | ||
| 49/39 | | 49/39 | ||
| [[Hitch]] | | [[Hitch]] | ||
| Line 121: | Line 132: | ||
| 2 | | 2 | ||
| 31\198 | | 31\198 | ||
| 187. | | 187.88 | ||
| 39/35 | | 39/35 | ||
| [[Semiwitch]] | | [[Semiwitch]] | ||
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| 2 | | 2 | ||
| 74\198<br>(25\198) | | 74\198<br>(25\198) | ||
| 448.48<br>(151. | | 448.48<br>(151.52) | ||
| 35/27<br>(12/11) | | 35/27<br>(12/11) | ||
| [[Neusec]] | | [[Neusec]] | ||
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| 3 | | 3 | ||
| 41\198<br>(25\198) | | 41\198<br>(25\198) | ||
| 248.48<br>(151. | | 248.48<br>(151.52) | ||
| 15/13<br>(12/11) | | 15/13<br>(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
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| [[Icosidillic]] | | [[Icosidillic]] | ||
|} | |} | ||
<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 | ||
[[Category:99edo]] | [[Category:99edo]] | ||
[[Category:Major minthmic]] | [[Category:Major minthmic]] | ||
[[Category:Namaka]] | [[Category:Namaka]] | ||