Cassaschismic: Difference between revisions

Review (3/): many cleanups and fixes
m + category. - notice. Fix section title
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{{Idiosyncratic terms|Many of the information and terminology here has been ported and adapted from Eufalesio's user page "Ultimate".}}
{{Todo|inline=1|review|comment= Replace idiosyncratic terms with conventional ones. }}
{{Infobox regtemp
{{Infobox regtemp
| Title = Cassaschismic
| Title = Cassaschismic
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See [[Garischismic family #Cassaschismic]] for technical data.
See [[Garischismic family #Cassaschismic]] for technical data.


== Interval chain ==
== Interval lattice ==
Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.   
Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.   


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


[[Category:Cassaschismic| ]] <!-- main article -->
[[Category:Rank-3 temperaments]]
[[Category:Rank-3 temperaments]]
[[Category:Microtemperaments]]
[[Category:Microtemperaments]]
[[Category:Garischismic family]]
[[Category:Garischismic family]]
[[Category:Olympic clan]]
[[Category:Olympic clan]]