126edo: Difference between revisions

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126edo has a distinctly sharp tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the ~~large [[quill]]s~~ to 17 steps, and the ~~small~~ to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

126edo has a distinctly sharp tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the generators to 17 steps, and the smaller interval to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

=== Odd harmonics ===

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=== Subsets and supersets ===

It has ~~divisors~~ 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.

Since 126 factors into {{factorization|126}}, 126edo has subset edos {{EDOs| 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63 }}.

[[Category:Srutal]]

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 {{Infobox ET}}
-{{EDO intro|126}}
+{{ED intro}}
-edo has a distinctly sharp tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the large [[quill]]s to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.
+edo has a distinctly sharp tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the generators to 17 steps, and the smaller interval to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.
 === Odd harmonics ===
@@ Line 8: / Line 8: @@
 === Subsets and supersets ===
-It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
+Since 126 factors into {{factorization|126}}, 126edo has subset edos {{EDOs| 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63 }}.
 [[Category:Srutal]]