198edo: Difference between revisions
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== Theory == | == Theory == | ||
198edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and 6144/6125 in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079. | 198edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and [[6144/6125]] in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]] and [[2080/2079]]. | ||
It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the [[15-odd-limit]], and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99. | It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the [[15-odd-limit]]. It factors into 2 × 3<sup>2</sup> × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99. | ||
=== Primary intervals === | |||
{{Primes in edo|198|prec=2|columns=11}} | |||
== Intervals == | == Intervals == | ||
{{main|Table of 198edo intervals}} | {{main|Table of 198edo intervals}} | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 06:59, 13 January 2021
198 equal temperament divides the octave into 198 parts of 6.061 cents each.
Theory
198edo is contorted in the 7-limit, with the same tuning as 99edo, but makes for a good 11- and 13-limit system. Like 99, it tempers out 2401/2400, 4375/4374, 3136/3125, 5120/5103 and 6144/6125 in the 7-limit; in the 11-limit it tempers 3025/3024, 9801/9800 and 14641/14580; and in the 13-limit 352/351, 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.
It is the optimal patent val for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as hemimist, namaka and semicanou. It is distinctly consistent through the 15-odd-limit. It factors into 2 × 32 × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
Primary intervals
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