Archytas clan: Difference between revisions

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=== Overview to extensions ===

~~Adding~~ [[~~245~~/~~243~~]] ~~to the list~~ of ~~commas gives superpyth~~; [[2430/2401]] ~~gives quasisuper~~; [[36/35]] ~~gives dominant~~; ~~360~~/~~343 gives schism~~; 6860/6561 ~~gives ultrapyth; 33614/32805 gives quasiultra~~; [[16/15]] ~~gives mother~~. These all use the same generators as archy.

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

The second comma in the comma list defines which [[7-limit]] family member we are looking at:

* [[#Schism|Schism]] adds 360/343, for an [[exotemperament]] well tuned around [[12edo]];

* Dominant adds [[36/35]], for a tuning flat of [[17edo|17c-edo]];

* [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];

* [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];

* [[#Quasiultra|Quasiultra]] adds 33614/32805, for a tuning between 27edo and [[32edo]];

* [[#Ultrapyth|Ultrapyth]] adds 6860/6561, for a tuning sharp of 32edo;

* Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].

These all use the same generators as archy.

[[686/675]] gives beatles, splitting the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blacksmith with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.

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Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

==== Subgroup extensions ====

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–Gb). This is called supra, given right below.

=== Supra ===

@@ Line 32: / Line 32: @@
 === Overview to extensions ===
-Adding [[245/243]] to the list of commas gives superpyth; [[2430/2401]] gives quasisuper; [[36/35]] gives dominant; 360/343 gives schism; 6860/6561 gives ultrapyth; 33614/32805 gives quasiultra; [[16/15]] gives mother. These all use the same generators as archy.
+==== 7-limit extensions ====
+The second comma in the comma list defines which [[7-limit]] family member we are looking at:
+* [[#Schism|Schism]] adds 360/343, for an [[exotemperament]] well tuned around [[12edo]];
+* Dominant adds [[36/35]], for a tuning flat of [[17edo|17c-edo]];
+* [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
+* [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
+* [[#Quasiultra|Quasiultra]] adds 33614/32805, for a tuning between 27edo and [[32edo]];
+* [[#Ultrapyth|Ultrapyth]] adds 6860/6561, for a tuning sharp of 32edo;
+* Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].
+These all use the same generators as archy.
 [[686/675]] gives beatles, splitting the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blacksmith with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.
@@ Line 52: / Line 62: @@
 Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.
+==== Subgroup extensions ====
+Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–Gb). This is called supra, given right below.
 === Supra ===