A-team: Difference between revisions

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#As every other note of the third-fifths pergen (P8, P5/3). This is backwards compatible with having fifths.

==~~JI interpretations~~==

==A-team tuning spectrum==

===~~Meantone spectrum (13&31)~~===

===The 13edo-to-31edo range===

Occupies the flat end of the spectrum, 461 to about 465 cents. 18edo is an edge case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo and 44edo.

Surprisingly, A-Team tunings can have good approximations of some high-limit JI chords. The most plentiful consonant triad is 4:9:21 or 8:18:21, followed by 4:5:9. The following tuning (and the 44edo tuning) of A-Team[13] has five copies of 4:5:9:13:17:21, three copies of 4:5:9:11, two copies of 4:5:9:(11):13, two copies of 4:5:9:13:19:21, and one copy of 4:9:(15):21:23. The 13-note [[MODMOS]] given by flattening just the seventh and eighth degrees of the LsLssLsLssLss mode of A-Team[13] by the 13-generator interval (~25.5 cents) gives the entire 4:5:9:11:13:17:19:21:23 otonal chord over a single root.

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(***) 65/64 and other commas only tempered out by 13edo

===~~Non-meantone~~ tunings for A-Team===

===Sharper generator tunings for A-Team===

23edo...

~~18edo is a borderline case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo and 44edo.~~

@@ Line 10: / Line 10: @@
 #As every other note of the third-fifths pergen (P8, P5/3). This is backwards compatible with having fifths.
-==JI interpretations==
+==A-team tuning spectrum==
-===Meantone spectrum (13&31)===
+===The 13edo-to-31edo range===
+Occupies the flat end of the spectrum, 461 to about 465 cents. 18edo is an edge case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo and 44edo.
 Surprisingly, A-Team tunings can have good approximations of some high-limit JI chords. The most plentiful consonant triad is 4:9:21 or 8:18:21, followed by 4:5:9. The following tuning (and the 44edo tuning) of A-Team[13] has five copies of 4:5:9:13:17:21, three copies of 4:5:9:11, two copies of 4:5:9:(11):13, two copies of 4:5:9:13:19:21, and one copy of 4:9:(15):21:23. The 13-note [[MODMOS]] given by flattening just the seventh and eighth degrees of the LsLssLsLssLss mode of A-Team[13] by the 13-generator interval (~25.5 cents) gives the entire 4:5:9:11:13:17:19:21:23 otonal chord over a single root.
@@ Line 157: / Line 159: @@
 (***) 65/64 and other commas only tempered out by 13edo
-===Non-meantone tunings for A-Team===
+===Sharper generator tunings for A-Team===
 edo...
-edo is a borderline case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo and 44edo.