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

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==Properties==
==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 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.
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 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.


==Proposed names for 12/1-equivalent temperaments==
==MOSes==
 
===25-note MOSes===
''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.''
This is equivalent to 7-note MOSes in the 2/1.
 
* 18L 7s and 7L 18s: Greater Diatonic and Greater Mavila
'''Cole's names'''
* 14L 11s and 11L 14s: Greater Smitonic and Greater Mosh
 
===36-note MOSes===
==Proposed names for 12/1-equivalent MOS scales==
This is equivalent to 10-note MOSes in the 2/1.
 
* 29L 7s and 7L 29s: Hexacontapental and Antihexacontapental
'''Cole's names'''
* 27L 9s and 9L 27s: Unquic and Antiunquic
 
* 25L 11s and 11L 25s: Greater Dichotic and Greater Sephiroid
* 14L 22s - Pochhammeroid
* 22L 14s and 14L 22s: Anticolian and Colian
* 18L 18s: Grenadilla

Latest revision as of 03:10, 11 April 2025

Disclaimer: written a la MMTM

The equal division of 12/1 (ed12/1) is a tuning obtained by dividing the 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 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.

MOSes

25-note MOSes

This is equivalent to 7-note MOSes in the 2/1.

  • 18L 7s and 7L 18s: Greater Diatonic and Greater Mavila
  • 14L 11s and 11L 14s: Greater Smitonic and Greater Mosh

36-note MOSes

This is equivalent to 10-note MOSes in the 2/1.

  • 29L 7s and 7L 29s: Hexacontapental and Antihexacontapental
  • 27L 9s and 9L 27s: Unquic and Antiunquic
  • 25L 11s and 11L 25s: Greater Dichotic and Greater Sephiroid
  • 22L 14s and 14L 22s: Anticolian and Colian
  • 18L 18s: Grenadilla
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