198edo: Difference between revisions
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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. | 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. | ||
=== | === Prime intervals === | ||
{{Primes in edo|198|prec=2|columns=11}} | {{Primes in edo|198|prec=2|columns=11}} | ||
Revision as of 11:09, 17 March 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.
Prime intervals
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