26edo: Difference between revisions
| Line 739: | Line 739: | ||
{{main|List of MOS scales in 26edo}} | {{main|List of MOS scales in 26edo}} | ||
; 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) | ||
| Line 750: | Line 750: | ||
* [[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) | ||
; Additional mos scales | |||
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). | ||
| Line 775: | Line 764: | ||
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). | ||
=== | === 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 | ||