1506edo: Difference between revisions

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~~The~~ 1506 ~~division divides the octave into 1506 parts of 0.7968 [[cent]]s each. It~~ is a very strong 13- and 17-limit system, 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-odd-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}.

1506edo is a very strong 13- and 17-limit system, 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-odd-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}.

=== Prime harmonics ===

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

=== Divisors ===

Since 1506 factors into 2 × 3 × 251, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.

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 {{Infobox ET}}
-The 1506 division divides the octave into 1506 parts of 0.7968 [[cent]]s each. It is a very strong 13- and 17-limit system, 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-odd-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}.
+{{EDO intro|1506}}
+edo is a very strong 13- and 17-limit system, 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-odd-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}.
 === Prime harmonics ===
 {{Harmonics in equal|1506|columns=11}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Divisors ===
+Since 1506 factors into 2 × 3 × 251, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.