26edo: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
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== Scales ==
== Scales ==
=== Orgone temperament ===
=== MOS scales ===
{{main|List of MOS scales in 26edo}}
 
Important mos scales include (in addition to ones found in [[13edo]]):
* [[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]][19] (enharmonic) 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 (15\26, 1\1)
* [[Orgone]][7] 5 5 2 5 2 5 2 (7\26, 1\1)
* [[Orgone]][11] 3 2 3 2 2 3 2 2 3 2 2 (7\26, 1\1)
* [[Orgone]][15] 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 (7\26, 1\1)
* [[Lemba]][6] 5 5 3 5 5 3 (5\26, 1\2)
* [[Lemba]][10] 3 2 3 2 3 3 2 3 2 3 (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 ====
[[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:
[[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 degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L_3s|4L 3s (mish)]].
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[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]


=== Additional scalar bases available ===
==== 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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* 8L+1s (3 3 3 3 3 3 3 3 2)
* 8L+1s (3 3 3 3 3 3 3 3 2)
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).
=== MOS scales ===
{{main|List of MOS scales in 26edo}}
Important mos scales include (in addition to ones found in [[13edo]]):
* [[Flattone]][7] (diatonic) 4 4 4 3 4 4 3 (15\26, 1\1)
* [[Flattone]][12] (chromatic) 3 1 3 1 3 1 3 3 1 3 1 3 (15\26, 1\1)
* [[Flattone]][19] (enharmonic) 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 (15\26, 1\1)
* [[Orgone]][7] 5 5 2 5 2 5 2 (7\26, 1\1)
* [[Orgone]][11] 3 2 3 2 2 3 2 2 3 2 2 (7\26, 1\1)
* [[Orgone]][15] 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 (7\26, 1\1)
* [[Lemba]][6] 5 5 3 5 5 3 (5\26, 1\2)
* [[Lemba]][10] 3 2 3 2 3 3 2 3 2 3 (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)


== Instruments ==
== Instruments ==