Gammic family: Difference between revisions

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A more interesting extension is to neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds [[2401/2400]] to the gammic comma, and may be described as the 68&171 temperament. The generator chain goes merrily on, stacking one 10/7 over another, until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. [[171edo]] makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending [[Carlos Gamma]].

Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the [[11-limit]], where (7/5)<sup>3</sup> equates to 11/4~~. This may be described as {{multival| 40 22 21 -3 … }} or 68 & 103, and 171 can still be used as a tuning, with [[val]] {{val| 171 271 397 480 591 }}~~.

Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the [[11-limit]], where (7/5)<sup>3</sup> equates to 11/4.

[[Gene Ward Smith]] once described [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_6001.html neptune as an analog of miracle].

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 A more interesting extension is to neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds [[2401/2400]] to the gammic comma, and may be described as the 68&amp;171 temperament. The generator chain goes merrily on, stacking one 10/7 over another, until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. [[171edo]] makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending [[Carlos Gamma]].
-Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the [[11-limit]], where (7/5)<sup>3</sup> equates to 11/4. This may be described as {{multival| 40 22 21 -3 … }} or 68 &amp; 103, and 171 can still be used as a tuning, with [[val]] {{val| 171 271 397 480 591 }}.
+Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the [[11-limit]], where (7/5)<sup>3</sup> equates to 11/4.
 [[Gene Ward Smith]] once described [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_6001.html neptune as an analog of miracle].