User:2^67-1/Ed12: Difference between revisions

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The '''equal division of ~~√12~~ (~~ed√12)~~''' is a tuning obtained by dividing the [[~~hemipyth]~~]~~[10~~] ~~perfect 18-step (√12)~~ in a certain number of ~~equal steps. ned√12 is also equivalent to 2n~~[[~~ed12~~]].

''Disclaimer: written a la MMTM''

The '''equal division of 12/1''' ('''ed12/1''') is a [[tuning]] obtained by dividing the [[12/1|twelfth harmonic (12/1)]] in a certain number of [[equal]] steps.

==Properties==

Division of ~~√12~~ into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of this interval as an equivalence, despite being irrational, is that it serves as an upper bound of the range of most peoples' voices. ~~While [[hemipyth]] chords can~~ be ~~used~~, ~~due~~ to the ~~wider equave wider~~, ~~sparser chord spacings can be utilized~~.

Division of 12 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of this interval as an equivalence, despite being irrational, is that it serves as two times the upper bound of the range of most peoples' voices, which the author takes to be about √12. The twelfth harmonic is pretty far as much as equivalences go, so here pure 3-smooth scales are required, leading the ratios to be square roots of 3-smooth integers or fractions. Taking √12 as the period gives us 2, 3, 4, 7, 11, and 18 note MOS-scales within the √12, or 4, 6, 8, 14, 22, or 36 note MOS-scales within the 12/1. This is the ''pochhammeroid temperament'', named by Cole.

==Proposed names for 12/1-equivalent temperaments==

''Explanation of notation: the notation a&b refers to the temperament shared by ED12s a and b, which is similar to the x31eq notation, and thus the MOS scales aL bs or bL as.''

'''Cole's names'''

==Proposed names for 12/1-equivalent MOS scales==

'''Cole's names'''

~~Octodecatonic MOSses are particularly natural with this equave, with [[User:2^67~~-~~1/7L 11s (√12-equivalent)|7L 11s]] particularly being reminiscent of hemipyth.~~

* 14L 22s - Pochhammeroid

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-The '''equal division of √12 (ed√12)''' is a tuning obtained by dividing the [[hemipyth]][10] perfect 18-step (√12) in a certain number of equal steps. ned√12 is also equivalent to 2n[[ed12]].
+''Disclaimer: written a la MMTM''
+The '''equal division of 12/1''' ('''ed12/1''') is a [[tuning]] obtained by dividing the [[12/1|twelfth harmonic (12/1)]] in a certain number of [[equal]] steps.
 ==Properties==
-Division of √12 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of this interval as an equivalence, despite being irrational, is that it serves as an upper bound of the range of most peoples' voices. While [[hemipyth]] chords can be used, due to the wider equave wider, sparser chord spacings can be utilized.
+Division of 12 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of this interval as an equivalence, despite being irrational, is that it serves as two times the upper bound of the range of most peoples' voices, which the author takes to be about √12. The twelfth harmonic is pretty far as much as equivalences go, so here pure 3-smooth scales are required, leading the ratios to be square roots of 3-smooth integers or fractions. Taking √12 as the period gives us 2, 3, 4, 7, 11, and 18 note MOS-scales within the √12, or 4, 6, 8, 14, 22, or 36 note MOS-scales within the 12/1. This is the ''pochhammeroid temperament'', named by Cole.
+==Proposed names for 12/1-equivalent temperaments==
+''Explanation of notation: the notation a&b refers to the temperament shared by ED12s a and b, which is similar to the x31eq notation, and thus the MOS scales aL bs or bL as.''
+'''Cole's names'''
+==Proposed names for 12/1-equivalent MOS scales==
+'''Cole's names'''
-Octodecatonic MOSses are particularly natural with this equave, with [[User:2^67-1/7L 11s (√12-equivalent)|7L 11s]] particularly being reminiscent of hemipyth.
+* 14L 22s - Pochhammeroid