A-team: Difference between revisions

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==="Superpythagorean" tunings===

In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad. Apart from that, there's little common JI interpretation shared by these sharper tunings. One tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically distinct, much like 22edo superpyth[7].

In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad. Apart from that, there's little common JI interpretation shared by these sharper tunings. One possible tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically distinct, much like 22edo superpyth[7].

~~[[23edo]] (469.57 cents) and [[41edo]] (468.29 cents): two tones represent 14/11 rather than 5/4, and J-O# (4 large steps + 1 small step) becomes a 5/3 rather than a 13/8~~.

Using a pure 21/16 of 470.78¢ results in an extremely lopsided oneirotonic scale with L/s = 4.60. Harmonically this results in a 9/8 of 212.342722 which is very much in the superpyth range (for comparison, 17edo's 9/8 is 211.765 cents). The "major tritone" in oneirotonic (J-N in Kentaku notation) will be a very flat fifth of 683.123 cents, constrasting with the very sharp 40/21 fifth (729.2 cents). The flat fifths give shimmery detuned versions of zo (subminor) triads 6:7:9 and sus2 triads 8:9:12. All these intervals contribute to the scale's overall gently shimmery quality which the 23edo version shares too.

[[Category:Temperament]]

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 ==="Superpythagorean" tunings===
-In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad.  Apart from that, there's little common JI interpretation shared by these sharper tunings. One tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically distinct, much like 22edo superpyth[7].
+In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad.  Apart from that, there's little common JI interpretation shared by these sharper tunings. One possible tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically distinct, much like 22edo superpyth[7].
-[[23edo]] (469.57 cents) and [[41edo]] (468.29 cents): two tones represent 14/11 rather than 5/4, and J-O# (4 large steps + 1 small step) becomes a 5/3 rather than a 13/8.
 Using a pure 21/16 of 470.78¢ results in an extremely lopsided oneirotonic scale with L/s  = 4.60. Harmonically this results in a 9/8 of 212.342722 which is very much in the superpyth range (for comparison, 17edo's 9/8 is 211.765 cents). The "major tritone" in oneirotonic (J-N in Kentaku notation) will be a very flat fifth of 683.123 cents, constrasting with the very sharp 40/21 fifth (729.2 cents). The flat fifths give shimmery detuned versions of zo (subminor) triads 6:7:9 and sus2 triads 8:9:12. All these intervals contribute to the scale's overall gently shimmery quality which the 23edo version shares too.
 [[Category:Temperament]]