5L 3s: Difference between revisions

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The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes (but the generator can be viewed as a 21/16 ~~making~~ 4:9:21 chords plentiful, and the 5\13 to 12\31 range gives various higher limit JI harmonies; see [[A-Team]]).

The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes (but the generator can be viewed as a 21/16, three of which make a 9/8, which makes 4:9:21 chords plentiful; and the 5\13 to 12\31 range gives various higher limit JI harmonies; see [[A-Team]]).

By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce|Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.

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-The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes (but the generator can be viewed as a 21/16 making 4:9:21 chords plentiful, and the 5\13 to 12\31 range gives various higher limit JI harmonies; see [[A-Team]]).
+The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes (but the generator can be viewed as a 21/16, three of which make a 9/8, which makes 4:9:21 chords plentiful; and the 5\13 to 12\31 range gives various higher limit JI harmonies; see [[A-Team]]).
 By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce|Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.