2.3.7 subgroup: Difference between revisions

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The 1.3.7-odd-limit refers to a constraint on the selection of [[Just intonation|just]] [[Interval class|intervals]] for a scale or composition such that 3 and 7 are the only allowable odd numbers, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 1.3.7-odd-limit intervals within the octave is [[1/1]], [[8/7]], [[7/6]], [[4/3]], [[3/2]], [[12/7]], [[7/4]], and [[2/1]], which is known as the 1.3.7-limit tonality diamond.

The phrase "2.3.7-limit just intonation" usually refers to the 2.3.7~~-prime-limit~~ and includes primes 2, 3, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in 2-dimensional [[Harmonic lattice diagram|lattice diagrams]], each prime represented by a different dimension.

The phrase "2.3.7-limit just intonation" usually refers to the 2.3.7 subgroup and includes primes 2, 3, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in 2-dimensional [[Harmonic lattice diagram|lattice diagrams]], each prime represented by a different dimension.

== Scales ==

== Edos ==

A list of edos with progressively better tunings for the 2.3.7 subgroup: {{EDOs| 5, 12, 14, 17, 22, 31, 36, 77, 94, 130, 135, 171, 265, 306, 400, 571, 706, 1277 }} and so on.

Another list of edos which provides relatively good tunings for the 2.3.7 subgroup (relative error < 2.5%): {{EDOs| 36, 41, 77, 94, 99, 130, 135, 171, 207, 229, 265, 301, 306, 364, 400, 436, 441, 477, 494, 535, 571, 576, 607, 648, 665, 670, 701, 706, 742, 747, 783, 836, 841, 877, 913, 935, 971, 976, 1007, 1012, 1048, 1106, 1147, 1178, 1183, 1236, 1241, 1277 }} and so on.

== Rank-2 temperaments ==

== Notes ==

[[Category:7-limit]]

[[Category:Rank 3]]

[[Category:Stub]]

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 The 1.3.7-odd-limit refers to a constraint on the selection of [[Just intonation|just]] [[Interval class|intervals]] for a scale or composition such that 3 and 7 are the only allowable odd numbers, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 1.3.7-odd-limit intervals within the octave is [[1/1]], [[8/7]], [[7/6]], [[4/3]], [[3/2]], [[12/7]], [[7/4]], and [[2/1]], which is known as the 1.3.7-limit tonality diamond.
-The phrase "2.3.7-limit just intonation" usually refers to the 2.3.7-prime-limit and includes primes 2, 3, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in 2-dimensional [[Harmonic lattice diagram|lattice diagrams]], each prime represented by a different dimension.
+The phrase "2.3.7-limit just intonation" usually refers to the 2.3.7 subgroup and includes primes 2, 3, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in 2-dimensional [[Harmonic lattice diagram|lattice diagrams]], each prime represented by a different dimension.
 == Scales ==
 == Edos ==
+A list of edos with progressively better tunings for the 2.3.7 subgroup: {{EDOs| 5, 12, 14, 17, 22, 31, 36, 77, 94, 130, 135, 171, 265, 306, 400, 571, 706, 1277 }} and so on.
+Another list of edos which provides relatively good tunings for the 2.3.7 subgroup (relative error < 2.5%): {{EDOs| 36, 41, 77, 94, 99, 130, 135, 171, 207, 229, 265, 301, 306, 364, 400, 436, 441, 477, 494, 535, 571, 576, 607, 648, 665, 670, 701, 706, 742, 747, 783, 836, 841, 877, 913, 935, 971, 976, 1007, 1012, 1048, 1106, 1147, 1178, 1183, 1236, 1241, 1277 }} and so on.
 == Rank-2 temperaments ==
 == Notes ==
 <references />
 [[Category:7-limit]]
 [[Category:Rank 3]]
 [[Category:Stub]]