Diaschismic family: Difference between revisions

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=== Overview to extensions ===

==== 7-limit extensions ====

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.

* Pajara derives from [[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.

* Keen adds [[875/864]].

* Bidia adds [[3136/3125]], the hemimean comma.

* Echidna adds [[1728/1715]], the orwellisma.

* Shrutar adds [[245/243]], the sensamagic comma.

Pajara, diaschismic, srutal and keen keep the same half-octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as [[36/35]], the septimal quarter-tone) and echidna has a generator of 9/7. Bidia has a quarter-octave period and a fifth generator.

==== Subgroup extensions ====

Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', documented right below. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.

=== Srutal archagall ===

Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup, resulting in ''srutal archagall''. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.

Subgroup: 2.3.5.17

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~~=== Overview to extensions ===~~

~~To get the 7-limit extensions, we add another comma:~~