Ed4: Difference between revisions

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Ed4 scales also have the feature that they ascend the pitch continuum twice as fast as edo systems. 37 tones of 37edo is one octave, while 37 tones of 37ed4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.

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 quality compared to the original temperament (see also [[macrodiatonic and microdiatonic]]). 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 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 =

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 Ed4 scales also have the feature that they ascend the pitch continuum twice as fast as edo systems. 37 tones of 37edo is one octave, while 37 tones of 37ed4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.
-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 quality compared to the original temperament (see also [[macrodiatonic and microdiatonic]]). 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 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 =