26edo: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
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{{main|List of MOS scales in 26edo}}
{{main|List of MOS scales in 26edo}}


Important mos scales include (in addition to ones found in [[13edo]]):
; Most important [[mos scale]]s
* [[Flattone]][7] (diatonic) 4 4 4 3 4 4 3 (15\26, 1\1) (quasi-[[equiheptatonic]])
* [[Flattone]][7] (diatonic) 4 4 4 3 4 4 3 (15\26, 1\1) (quasi-[[equiheptatonic]])
* [[Flattone]][12] (chromatic) 3 1 3 1 3 1 3 3 1 3 1 3 (15\26, 1\1)
* [[Flattone]][12] (chromatic) 3 1 3 1 3 1 3 3 1 3 1 3 (15\26, 1\1)
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* [[Lemba]][16] 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 (5\26, 1\2)
* [[Lemba]][16] 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 (5\26, 1\2)


==== Orgone temperament ====
; Additional mos scales
[[Andrew Heathwaite]] first proposed [[Orgonia|orgone]] temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
* The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L_3s|4L 3s (mish)]].
* The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.
* The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. [[MOSScales|MOS]] of type [[4L_7s|4L 7s]].
* The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108 1200.
 
The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
 
[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
 
==== Additional scalar bases available ====
Since the perfect 5th in 26edo spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12).  
Since the perfect 5th in 26edo spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12).  


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and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (though further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).
and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (though further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).


=== Non-MOS scales ===
=== Orgone temperament ===
[[Andrew Heathwaite]] first proposed [[Orgonia|orgone]] temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
* The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L_3s|4L 3s (mish)]].
* The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.
* The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. [[MOSScales|MOS]] of type [[4L_7s|4L 7s]].
* The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108 1200.
 
The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
 
[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
 
=== Other scales ===
* Approximate [[5afdo]]: 4 4 7 6 5
* Approximate [[5afdo]]: 4 4 7 6 5
* Approximate [[6afdo]]: 6 5 4 4 4 3
* Approximate [[6afdo]]: 6 5 4 4 4 3