Septischismic: Difference between revisions

Line 1:

~~[[Category:Rank-3 temperaments]]~~

{{Idiosyncratic terms|Many of the information and terminology here has been ported and adapted from Eufalesio's user page "Ultimate" and his own TAMNAMS extensions.}}

~~[[Category:Microtemperaments]]~~

{{Todo|inline=1|review|comment= Replace idiosyncratic terms with conventional ones. }}

~~[[Category:Garischismic family]]~~

{{Infobox regtemp

~~[[Category:Olympic clan]]~~

| Title = Cassaschismic

{{Infobox regtemp|Title=Cassaschismic|Subgroups=2.3.5.7.11.13.19|Comma basis=[[19712/19683]], [[41503/41472]]|Edo join 1=~~217~~|Edo join 2=270|Mapping=1; 0 1 0 -14 23 12 5; 0 0 1 0 0 -1 1|Generators=3/2|Generators tuning=~~TBA~~|Optimization method=~~TBA|MOS scales=[[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]~~|Pergen=(P8, P5, ^1)|Color name=Salozo & Sasaru|Odd limit 1=15|Mistuning 1=~~TBA~~|Complexity 1=TBD|Odd limit 2=13-limit 225|Mistuning 2=TBA|Complexity 2=TBD|Edo join 3=311|Ploidacot=Haploid monocot}}{{Idiosyncratic terms|Many of the information and terminology here has been ported and adapted from Eufalesio's user page "Ultimate" and his own TAMNAMS extensions.}}Cassaschismic is a rank-3 temperament for the 11-, 13-limit and beyond. It is a member of [[garischismic clan]] and [[olympic clan]]. It extends the chain-of-fifths sequence of [[gary]] into the full 11-limit by adding an independent generator for 5/4, which naturally can be then used for 13/8 and 19/16.

| Subgroups = 2.3.5.7.11, 2.3.5.7.11.13, 2.3.5.7.11.13.19

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

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

| Optimization method = CWE

| Pergen = (P8, P5, ^1)

| Color name = Salozo & Sasaru

| Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ?

}}

Cassaschismic is a rank-3 temperament for the 11-, 13-limit and beyond. It is a member of [[garischismic clan]] and [[olympic clan]]. It extends the chain-of-fifths sequence of [[gary]] into the full 11-limit by adding an independent generator for 5/4, which naturally can be then used for 13/8 and 19/16.

By moving the generators around, this generator can be instead taken to be a tiny 3~5c ''minicomma'' (from this point forward refered to as "MC") that represents 385/384, 352/351, 5120/5103, 513/512, the schisma... etc; acting as a rank-3 detemper of [[cassandra]], where cassandra mappings are modified by ±1 MC to reach the rest of primes.

Line 138:

Line 148:

It can be instead see as an "addition" to the schismic/garibaldi/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 accurate (41,53,94), to incredibly accurate (217,270,311...).

~~== Tunings ==~~

[[Category:Rank-3 temperaments]]

~~TBA~~

[[Category:Microtemperaments]]

[[Category:Garischismic family]]

[[Category:Olympic clan]]

@@ Line 1: / Line 1: @@
-[[Category:Rank-3 temperaments]]
+{{Idiosyncratic terms|Many of the information and terminology here has been ported and adapted from Eufalesio's user page "Ultimate" and his own TAMNAMS extensions.}}
-[[Category:Microtemperaments]]
+{{Todo|inline=1|review|comment= Replace idiosyncratic terms with conventional ones. }}
-[[Category:Garischismic family]]
+{{Infobox regtemp
-[[Category:Olympic clan]]
+| Title = Cassaschismic
-{{Infobox regtemp|Title=Cassaschismic|Subgroups=2.3.5.7.11.13.19|Comma basis=[[19712/19683]], [[41503/41472]]|Edo join 1=217|Edo join 2=270|Mapping=1; 0 1 0 -14 23 12 5; 0 0 1 0 0 -1 1|Generators=3/2|Generators tuning=TBA|Optimization method=TBA|MOS scales=[[2L&nbsp;3s]], [[5L&nbsp;2s]], [[5L&nbsp;7s]], [[12L&nbsp;5s]]|Pergen=(P8, P5, ^1)|Color name=Salozo & Sasaru|Odd limit 1=15|Mistuning 1=TBA|Complexity 1=TBD|Odd limit 2=13-limit 225|Mistuning 2=TBA|Complexity 2=TBD|Edo join 3=311|Ploidacot=Haploid monocot}}{{Idiosyncratic terms|Many of the information and terminology here has been ported and adapted from Eufalesio's user page "Ultimate" and his own TAMNAMS extensions.}}Cassaschismic is a rank-3 temperament for the 11-, 13-limit and beyond. It is a member of [[garischismic clan]] and [[olympic clan]]. It extends the chain-of-fifths sequence of [[gary]] into the full 11-limit by adding an independent generator for 5/4, which naturally can be then used for 13/8 and 19/16.
+| Subgroups = 2.3.5.7.11, 2.3.5.7.11.13, 2.3.5.7.11.13.19
+| 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
+| Generators = 3/2; 5/4 | Generators tuning = 702.2307; 386.3245
+| Optimization method = CWE
+| Pergen = (P8, P5, ^1)
+| Color name = Salozo & Sasaru
+| Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ?
+}}
+Cassaschismic is a rank-3 temperament for the 11-, 13-limit and beyond. It is a member of [[garischismic clan]] and [[olympic clan]]. It extends the chain-of-fifths sequence of [[gary]] into the full 11-limit by adding an independent generator for 5/4, which naturally can be then used for 13/8 and 19/16.
 By moving the generators around, this generator can be instead taken to be a tiny <span data-darkreader-inline-color="">3~5c ''minicomma'' (from this point forward refered to as "MC") that represents 385/384, 352/351, 5120/5103, 513/512, the schisma... etc; acting as a rank-3 detemper of [[cassandra]], where cassandra mappings are modified by ±1 MC to reach the rest of primes.</span>
@@ Line 138: / Line 148: @@
 It can be instead see as an "addition" to the schismic/garibaldi/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 accurate (41,53,94), to incredibly accurate (217,270,311...).
-== Tunings ==
+[[Category:Rank-3 temperaments]]
-TBA
+[[Category:Microtemperaments]]
+[[Category:Garischismic family]]
+[[Category:Olympic clan]]