Septischismic: Difference between revisions

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

<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 isn't 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 comes from the fact that 135edo is next in the line of cassandra, but halving it results in 270edo, so the latter is used.

== Notation ==

Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to ~~highly~~ accurate (217, 270, 311, ~~…).~~

Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to extremely accurate (217, 270, 311, ''581, 851…'').

~~As an example, we can use up and down arrows with shafts (↑/↓) for the comma step~~, ~~and arrows without shafts (^/v~~) ~~for the aberschisma step. In this scheme, 4:5:6:7:9:11:13 on a C is notated as C–^↓E–G–↓B♭–D–↑↑F–v↑↑A♭~~.

As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.

{| class="wikitable" style="text-align:center; vertical-align:middle;"

|+Nomenclature of selected intervals

!Ratio

!Example on C

|-

|3/2

|C–G (perfect fifth)

|-

|5/4

|C–^↓E (upsubmajor third)

|-

|7/4

|C–↓Bb (subminor seventh)

|-

|11/8

|C–↑↑F (hyperfourth)

|-

|13/8

|C–v↑↑Ab (downhyperminor sixth)

|-

|19/16

|C–^Eb (upminor third)

|}

[[Category:Cassaschismic| ]]

[[Category:Rank-3 temperaments]]

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-<nowiki/>* In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced
+<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 isn't 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 comes from the fact that 135edo is next in the line of cassandra, but halving it results in 270edo, so the latter is used.
 == Notation ==
-Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to highly accurate (217, 270, 311, …).
+Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to extremely accurate (217, 270, 311, ''581, 851…'').
-As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step. In this scheme, 4:5:6:7:9:11:13 on a C is notated as C–^↓E–G–↓B♭–D–↑↑F–v↑↑A♭.
+As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.
+{| class="wikitable" style="text-align:center; vertical-align:middle;"
+|+Nomenclature of selected intervals
+!Ratio
+!Example on C
+|-
+|3/2
+|C–G (perfect fifth)
+|-
+|5/4
+|C–^↓E (upsubmajor third)
+|-
+|7/4
+|C–↓Bb (subminor seventh)
+|-
+|11/8
+|C–↑↑F (hyperfourth)
+|-
+|13/8
+|C–v↑↑Ab (downhyperminor sixth)
+|-
+|19/16
+|C–^Eb (upminor third)
+|}
 [[Category:Cassaschismic| ]] <!-- main article -->
 [[Category:Rank-3 temperaments]]