Father–3 equivalence continuum/Godtone's approach: Difference between revisions
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Therefore, if ''n'' = ''a''/''b'' is a rational with ''b'' > 1 and ''b'' not a multiple of 3 (so that 3''a''/''b'' + 2 doesn't simplify), we reach prime 3 in a fractional number of generators of ~5/4, which means that the generator is not ~5/4 but rather ''b'' equal divisions of some octave-equivalent of ~5/4 or ~8/5, which as a result means that we reach prime 3 in ''b''(3''a''/''b'' + 2) = 3''a'' + 2''b'' generators, and also means that ~128/125 is split into ''b'' equal parts. | Therefore, if ''n'' = ''a''/''b'' is a rational with ''b'' > 1 and ''b'' not a multiple of 3 (so that 3''a''/''b'' + 2 doesn't simplify), we reach prime 3 in a fractional number of generators of ~5/4, which means that the generator is not ~5/4 but rather ''b'' equal divisions of some octave-equivalent of ~5/4 or ~8/5, which as a result means that we reach prime 3 in ''b''(3''a''/''b'' + 2) = 3''a'' + 2''b'' generators, and also means that ~128/125 is split into ''b'' equal parts. | ||
The just value of ''n'' is {{nowrap|log(25/24) / log(128/125) {{=}} 1.72125…}} where {{nowrap|''n'' {{=}} 2}} corresponds to the [[Würschmidt comma]].{| class="wikitable center-1" | The just value of ''n'' is {{nowrap|log(25/24) / log(128/125) {{=}} 1.72125…}} where {{nowrap|''n'' {{=}} 2}} corresponds to the [[Würschmidt comma]]. | ||
{| class="wikitable center-1" | |||
|+ style="font-size: 105%;" | Temperaments with integer ''n'' | |+ style="font-size: 105%;" | Temperaments with integer ''n'' | ||
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