Father–3 equivalence continuum/Godtone's approach: Difference between revisions
add third-integer continuum and more explanations |
m add one more temp to the microtemps table |
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| [[mutt comma]] | | [[mutt comma]] | ||
| {{ monzo| -44 -3 21 }} | | {{ monzo| -44 -3 21 }} | ||
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| 12/7 | |||
| {{nowrap|202 & 205 {{=}} 3 & 612}} | |||
| [[88817841970012523233890533447265625/88715259606372406434345277125033984|(70 digits)]] | |||
| {{ monzo| -105 -7 50 }} | |||
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| 7/4 | | 7/4 | ||
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The 3 & 118 microtemperament is at ''n'' = 7/4. Its generator is approximately 397{{cent}} so that four generators reaches 5/2, corresponding to the denominator of 4. The number of generators of ~(5/2)<sup>1/4</sup> needed to find prime 3 is thus four times the result of plugging ''n'' = 7/4 into 3''n'' + 2 , which is 3(7/4) + 2 = 21/4 + 8/4 = 29/4, that is, 29 generators. | The 3 & 118 microtemperament is at ''n'' = 7/4. Its generator is approximately 397{{cent}} so that four generators reaches 5/2, corresponding to the denominator of 4. The number of generators of ~(5/2)<sup>1/4</sup> needed to find prime 3 is thus four times the result of plugging ''n'' = 7/4 into 3''n'' + 2 , which is 3(7/4) + 2 = 21/4 + 8/4 = 29/4, that is, 29 generators. | ||
Finally, the 3 & 612 microtemperament at ''n'' = 12/7 is extremely complex, because to find prime 5, you need 7 times 3(12/7) + 2 = 36/7 + 14/7 = 50/7, that is, 50 generators, and is noted only because of being extremely close to the JIP and being supported by the 5-limit microtemperament [[612edo]]. The denominator of 7 indicates that 128/125 is split into 7 equal parts. | |||
{| class="wikitable center-1" | {| class="wikitable center-1" | ||