1517edo: Difference between revisions

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 {{Infobox ET}}
-The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.
+{{ED intro}}
-== Theory ==
+edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large. To start with, we may consider the [[patent val]] and 1517d [[val]] up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 [[subgroup]] with optional additions of either [[13/1|13]] or [[19/1|19]].
-edo, despite its size, is a dual fifths system with a consistency limit of only 5.
+For higher harmonics, the first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo| 18 -12  2  1 1  0 }}, {{monzo| 44  -4 -9  1 0 -1 }}}.
-[[Category:Equal divisions of the octave|####]]
+=== Odd harmonics ===
-<!-- 4-digit number -->
+{{Harmonics in equal|1517}}
+=== Subsets and supersets ===
+Since 1517 factors into {{factorization|1517}}, 1517edo contains [[37edo]] and [[41edo]] as subsets.