7L 1s: Difference between revisions

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There are ~~two~~ notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The ~~first~~ is [[Porcupine_family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic_pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

There are three notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The lowest accuracy one is [[Porcupine_family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[Chromatic_pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[Square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[Porcupine family#2.3.5.11 subgroup .28porkypine.29|porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)

== Modes ==

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 {{MOS intro}}
-There are two notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The first is [[Porcupine_family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic_pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.
+There are three notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The lowest accuracy one is [[Porcupine_family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[Chromatic_pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[Square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[Porcupine family#2.3.5.11 subgroup .28porkypine.29|porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)
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