Father–3 equivalence continuum/Godtone's approach: Difference between revisions
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The 3 & 118 microtemperament [[squarschmidt]] 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 [[squarschmidt]] 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 | 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 (7) indicates that 128/125 is split into 7 equal parts, while the numerator indicates that each (128/125)<sup>1/7</sup> part represents (25/24)<sup>1/12</sup>, that is, a twelfth of 25/24. | ||
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