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}.

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}.

=== Prime harmonics ===

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

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 {{Infobox ET}}
-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}.
+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}.
+=== Prime harmonics ===
+{{Harmonics in equal|1506|columns=11}}
 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->