155edo: Difference between revisions

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~~'''~~155edo~~''' is the [[EDO|equal division of the octave]] into 155 parts of 7.7419 cents each. It~~ is closely related to [[31edo]], but the patent ~~vals~~ differ on the mapping for 3. It tempers out 15625/15552 (kleisma) and ~~4398046511104/4236443047215~~ in the 5-limit; 245/243, 3136/3125, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 385/384, 896/891, 1331/1323, and 3773/3750 in the 11-limit; 196/195, 325/324, 625/624, and 1001/1000 in the 13-limit.

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

155edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 42 -25 -1 }} in the 5-limit; [[245/243]], [[3136/3125]], and 823543/819200 in the 7-limit, supporting [[clyde]]. Using the patent val, it tempers out [[385/384]], [[896/891]], 1331/1323, and 3773/3750 in the 11-limit; [[196/195]], [[325/324]], [[625/624]], and [[1001/1000]] in the 13-limit.

155edo is additionally notable for having an extremely precise (about 0.0006 cents sharp) approximation of [[15/13]], being the denominator of a convergent to its logarithm, the last one before [[8743edo]], having 28-strong [[telicity]] for this interval.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 155 factors into {{factorization|155}}, 155edo contains [[5edo]] and [[31edo]] as subsets.

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 {{Infobox ET}}
-'''155edo''' is the [[EDO|equal division of the octave]] into 155 parts of 7.7419 cents each. It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 15625/15552 (kleisma) and 4398046511104/4236443047215 in the 5-limit; 245/243, 3136/3125, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 385/384, 896/891, 1331/1323, and 3773/3750 in the 11-limit; 196/195, 325/324, 625/624, and 1001/1000 in the 13-limit.
+{{ED intro}}
-{{stub}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 42 -25 -1 }} in the 5-limit; [[245/243]], [[3136/3125]], and 823543/819200 in the 7-limit, supporting [[clyde]]. Using the patent val, it tempers out [[385/384]], [[896/891]], 1331/1323, and 3773/3750 in the 11-limit; [[196/195]], [[325/324]], [[625/624]], and [[1001/1000]] in the 13-limit.
+edo is additionally notable for having an extremely precise (about 0.0006 cents sharp) approximation of [[15/13]], being the denominator of a convergent to its logarithm, the last one before [[8743edo]], having 28-strong [[telicity]] for this interval.
+=== Odd harmonics ===
+{{Harmonics in equal|155}}
+=== Subsets and supersets ===
+Since 155 factors into {{factorization|155}}, 155edo contains [[5edo]] and [[31edo]] as subsets.