A-team: Difference between revisions

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==A-Team tuning spectrum==

==="Meantone" tunings: the 13edo-to-31edo range===

==="Meantone" A-Team tunings===

Generator size ranges from 13edo's 461.54 to 18edo's 466.67 cents. This range offers the best ratio of large to small melodic steps too: ranging from 13edo's L:s = 2:1 to 18edo's L:s = 3:1.

====the 13edo-to-31edo range====

'''tl;dr:''' [[44edo]] good

Occupies the flat end of the spectrum, from 461.54 to 464.52 cents.

Occupies the flat end of the spectrum, from 13edo's 461.54 cents to 31edo's 464.52 cents.

Surprisingly, A-Team tunings in this range can approximate some high-limit JI chords, owing to the generator being close to the 17/13 ratio and three of them approximating both 9/8 and 10/9, thus approximating their [[mediant]] 19/17. The 11th harmonic makes an appearance too, because it is approximated by both 13edo and 31edo. Thus A-Team can be viewed as representing the no-3, no-7 19-odd limit. If you optimize for this 19 limit harmony you also get the 23rd harmonic for free.

@@ Line 12: / Line 12: @@
 ==A-Team tuning spectrum==
-==="Meantone" tunings: the 13edo-to-31edo range===
+==="Meantone" A-Team tunings===
+Generator size ranges from 13edo's 461.54 to 18edo's 466.67 cents. This range offers the best ratio of large to small melodic steps too: ranging from 13edo's L:s = 2:1 to 18edo's L:s = 3:1.
+====the 13edo-to-31edo range====
 '''tl;dr:''' [[44edo]] good
-Occupies the flat end of the spectrum, from 461.54 to 464.52 cents.
+Occupies the flat end of the spectrum, from 13edo's 461.54 cents to 31edo's 464.52 cents.
 Surprisingly, A-Team tunings in this range can approximate some high-limit JI chords, owing to the generator being close to the 17/13 ratio and three of them approximating both 9/8 and 10/9, thus approximating their [[mediant]] 19/17. The 11th harmonic makes an appearance too, because it is approximated by both 13edo and 31edo. Thus A-Team can be viewed as representing the no-3, no-7 19-odd limit. If you optimize for this 19 limit harmony you also get the 23rd harmonic for free.