Ed4: Difference between revisions
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The same approach can also be taken with respect to [[regular temperament]]s, and this would suggest using only square ratios, meaning that [[subgroup]]s are composed of prime squares like 4.9.25 rather than [[prime]]s themselves. There is a tetratave-repeating "squared counterpart" to every octave-repeating temperament in a prime subgroup of any rank, created by squaring both the basis elements and the commas. The [[generator]]s of the temperament are also squared, and the general structure and any MOS scales will be the same, but with extreme stretching in place, creating a very distinct harmonic and melodic quality compared to the original temperament (see also [[macrodiatonic and microdiatonic scales]]). For example, [[meansquared]] is the counterpart of [[meantone]], tempering out [[81/80]]<sup>2</sup> and generated by ~[[4/1]] and ~[[9/4]] instead of ~[[2/1]] and ~[[3/2]] | The same approach can also be taken with respect to [[regular temperament]]s, and this would suggest using only square ratios, meaning that [[subgroup]]s are composed of prime squares like 4.9.25 rather than [[prime]]s themselves. There is a tetratave-repeating "squared counterpart" to every octave-repeating temperament in a prime subgroup of any rank, created by squaring both the basis elements and the commas. The [[generator]]s of the temperament are also squared, and the general structure and any MOS scales will be the same, but with extreme stretching in place, creating a very distinct harmonic and melodic quality compared to the original temperament (see also [[macrodiatonic and microdiatonic scales]]). For example, [[meansquared]] is the counterpart of [[meantone]], tempering out [[81/80]]<sup>2</sup> and generated by ~[[4/1]] and ~[[9/4]] instead of ~[[2/1]] and ~[[3/2]] | ||
== Individual pages for ED4's = | == Individual pages for ED4's == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||