Diaschismic family: Difference between revisions

Overthink (talk | contribs)
Septimal diaschismic: + a few notes
Overthink (talk | contribs)
7-limit extensions: note pajara tempers 50/49
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To get the 7-limit extensions, we add another comma:
To get the 7-limit extensions, we add another comma:
* Septimal diaschismic adds [[126/125]], the starling comma, to obtain 7-limit harmony by more complex methods than pajara, but with greater accuracy.  
* Septimal diaschismic adds [[126/125]], the starling comma, to obtain 7-limit harmony by more complex methods than pajara, but with greater accuracy.  
* Pajara derives from [[64/63]] and is a popular and well-known choice.  
* Pajara adds [[50/49]] or [[64/63]] and is a popular and well-known choice.  
* Srutal adds [[4375/4374]], the ragisma, which is about as accurate as septimal diaschismic but has a much more complex mapping of 7.  
* Srutal adds [[4375/4374]], the ragisma, which is about as accurate as septimal diaschismic but has a much more complex mapping of 7.  
* Keen adds [[875/864]].  
* Keen adds [[875/864]].  
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Those all keep the same half-octave period and fifth generator.  
Those all keep the same half-octave period and fifth generator.  


Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original  generator in four.  
Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original  generator in four.


==== Subgroup extensions ====
==== Subgroup extensions ====