Cassaschismic: Difference between revisions

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| Comma basis = [[19712/19683]], [[41503/41472]] (11-limit); <br>[[2080/2079]], [[4096/4095]], [[19712/19683]] (13-limit); <br>[[1216/1215]], [[1540/1539]], [[1729/1728]], <br>[[2080/2079]] (2.3.5.7.11.13.19)

| Edo join 1 = 41 | Edo join 2 = 53 | Edo join 3 = 270

| Mapping = 1; 0 1 0 -14 23 12 5; 0 0 1 0 0 -1 1

| Mapping = 1; 1 0 -14 23 12 5; 0 1 0 0 -1 1

| Generators = 3/2; 5/4 | Generators tuning = 702.2307; 386.3245

| Optimization method = CWE

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|}

<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced

[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo|harmonic mode 8]] (green), and [[5L 7s]] 6|5 (red). The purple line on 12 is patent val p11, which is not used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in the line of cassandra; since halving it results in 270edo, it is used instead, also to showcase the use of aberschismas to reach primes 5, 13, and 19.

== Notation ==

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| C–^Eb (upminor third)

|}

== See also ==

* [[User:Eufalesio/Ultimate]] – An opinion-based derivation of cassaschismic

== External links ==

* [https://www.desmos.com/calculator/pbyqpjgrrn] A [https://www.desmos.com/calculator Desmos] graph showing cassaschismic edos up to 311, [[8afdo|harmonic mode 8]] (green), and [[5L 7s]] 6|5 (red). The purple line on 12 is the [[patent val]] prime 11, which is not used in cassaschismic. The blue dots indicate going up and down by Pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.

[[Category:Cassaschismic| ]]

[[Category:Rank-3 temperaments]]

@@ Line 4: / Line 4: @@
 | Comma basis = [[19712/19683]], [[41503/41472]] (11-limit); <br>[[2080/2079]], [[4096/4095]], [[19712/19683]] (13-limit); <br>[[1216/1215]], [[1540/1539]], [[1729/1728]], <br>[[2080/2079]] (2.3.5.7.11.13.19)
 | Edo join 1 = 41 | Edo join 2 = 53 | Edo join 3 = 270
-| Mapping = 1; 0 1 0 -14 23 12 5; 0 0 1 0 0 -1 1
+| Mapping = 1; 1 0 -14 23 12 5; 0 1 0 0 -1 1
 | Generators = 3/2; 5/4 | Generators tuning = 702.2307; 386.3245
 | Optimization method = CWE
@@ Line 195: / Line 195: @@
 |}
 <nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced
-[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo|harmonic mode 8]] (green), and [[5L 7s]] 6|5 (red). The purple line on 12 is patent val p11, which is not used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in the line of cassandra; since halving it results in 270edo, it is used instead, also to showcase the use of aberschismas to reach primes 5, 13, and 19.
 == Notation ==
@@ Line 226: / Line 224: @@
 | C–^Eb (upminor third)
 |}
+== See also ==
+* [[User:Eufalesio/Ultimate]] – An opinion-based derivation of cassaschismic
+== External links ==
+* [https://www.desmos.com/calculator/pbyqpjgrrn] A [https://www.desmos.com/calculator Desmos] graph showing cassaschismic edos up to 311, [[8afdo|harmonic mode 8]] (green), and [[5L 7s]] 6|5 (red). The purple line on 12 is the [[patent val]] prime 11, which is not used in cassaschismic. The blue dots indicate going up and down by Pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.
 [[Category:Cassaschismic| ]] <!-- main article -->
 [[Category:Rank-3 temperaments]]