Vulture family: Difference between revisions

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 === Overview to extensions ===
-Temperaments discussed elsewhere include [[Buzzardsmic clan #Buzzard|buzzard]]. Considered below are septimal vulture, terture, condor, eagle, and turkey.
+Strong 7-limit extensions include septimal vulture (53 & 270), which tempers out [[4375/4374]], and buzzard (53 & 58), which tempers out [[1728/1715]].
+Terture adds [[250047/250000]] with a 1/3-octave period. Condor adds [[10976/10935]] and splits the generator in three. Eagle adds [[2401/2400]]. Turkey adds [[4802000/4782969]]. Those split the generator in four.
+Most of these temperaments extend naturally to the 11-limit via tempering out the [[symbiotic comma]] and [[seascape comma]], from 10485760000/10460353203 = (19712/19683)<sup>2</sup>/(160083/160000), and to the 13-limit via identifying the hemitwelfth as [[~]][[26/15]], tempering out the [[island comma]].
+Buzzard is discussed in its own clan (→ [[Buzzardsmic clan #Septimal buzzard]]). The rest are considered below.
 == Septimal vulture ==