1308edo: Difference between revisions

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'''1308edo''' is the [[EDO|equal division of the octave]] into 1308 parts of 0.917431 cents each. It is consistent to the 21-limit distinctly, tempering out |37 25 -33> (whoosh comma) and |-46 51 -15> (171&453 comma) in the 5-limit; 250047/250000, 2460375/2458624, and |47 4 0 -19> in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

1308edo is the 15th [[~~The Riemann Zeta Function and Tuning|~~zeta gap edo]].

1308edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.

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

It [[tempering out|tempers out]] {{monzo| 37 25 -33 }} (whoosh comma) and {{monzo| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 1308 factors into {{factorization|1308}}, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.

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-'''1308edo''' is the [[EDO|equal division of the octave]] into 1308 parts of 0.917431 cents each. It is consistent to the 21-limit distinctly, tempering out |37 25 -33&gt; (whoosh comma) and |-46 51 -15&gt; (171&amp;453 comma) in the 5-limit; 250047/250000, 2460375/2458624, and |47 4 0 -19&gt; in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.
+{{Infobox ET}}
+{{ED intro}}
-edo is the 15th [[The Riemann Zeta Function and Tuning|zeta gap edo]].
+edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+It [[tempering out|tempers out]] {{monzo| 37 25 -33 }} (whoosh comma) and {{monzo| -46 51 -15 }} (171 &amp; 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|1308|columns=12}}
+=== Subsets and supersets ===
+Since 1308 factors into {{factorization|1308}}, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.