1506edo: Difference between revisions

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The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {~~4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250~~}~~, and for the 17-limit commas,~~ {~~4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625~~}.

[[~~Category:Equal divisions of the octave~~|#~~###~~]]

1506edo is a very strong 13- and 17-limit system, since it is the first past [[494edo|494]] with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is [[consistency|distinctly consistent]] through the [[17-odd-limit]]. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit [[comma]]s is {[[4096/4095]], [[6656/6655]], [[9801/9800]], 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, [[4914/4913]], [[5832/5831]], 6656/6655, 9801/9800, [[28561/28560]], 105644/105625}.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 1506 factors into {{factorization|1506}}, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.

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-The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+edo is a very strong 13- and 17-limit system, since it is the first past [[494edo|494]] with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is [[consistency|distinctly consistent]] through the [[17-odd-limit]]. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit [[comma]]s is {[[4096/4095]], [[6656/6655]], [[9801/9800]], 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, [[4914/4913]], [[5832/5831]], 6656/6655, 9801/9800, [[28561/28560]], 105644/105625}.
+=== Prime harmonics ===
+{{Harmonics in equal|1506|columns=11}}
+=== Subsets and supersets ===
+Since 1506 factors into {{factorization|1506}}, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.