Schismatic family: Difference between revisions

Line 37:

=== Overview to extensions ===

The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at. [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]]. [[#Grackle|~~Grackle~~]] adds {{monzo| -44 26 0 1 }}. [[#Pontiac|~~Pontiac~~]] adds {{monzo| -59 39 0 -1 }}. [[#Schism|~~Schism~~]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]]. Those all have a fifth as generator.

The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at. [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]], [[#Grackle|grackle]] adds {{monzo| -44 26 0 1 }}, [[#Pontiac|pontiac]] adds {{monzo| -59 39 0 -1 }}, and [[#Schism|schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]]. Those all have a fifth as generator.

[[#Bischismic|Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period. [[#Salsa|Salsa]] adds [[parahemif comma|{{monzo| 15 -13 0 2 }}]] and has a hemififth generator. [[#Hemischis|Hemischis]] adds {{monzo| -34 25 0 -2 }} and has a hemitwelfth generator. [[Gamelismic clan #Guiron|Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. [[#Term|Term]] adds {{monzo| -94 54 0 3 }} with a 1/3-octave period. [[#Squirrel|Squirrel]], [[#Tertiaschis|tertiaschis]], and [[#Countertertiaschis|countertertiaschis]] each has a generator that is 1/3 of the fourth. [[#Quadrant|Quadrant]] adds {{monzo| -119 68 0 4 }} with a 1/4-octave period. [[#Kleischismic|Kleischismic]] adds {{monzo| 49 -38 0 4 }} with a half-octave period and also a bisect generator. [[#Sesquiquartififths|Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four.

Line 552:

* [[WE]]: ~2 = 1200.0989{{c}}, ~3/2 = 701.8145{{c}}

: [[error map]]: {{val| +0.099 -0.042 -0.138 -0.038 }}

* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.7579{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7579{{c}}

: error map: {{val| 0.000 -0.197 -0.377 -0.268 }}

Line 945:

* [[WE]]: ~2 = 1199.7974{{c}}, ~3/2 = 701.1210{{c}}

: [[error map]]: {{val| -0.203 -1.037 +3.300 -1.618 }}

* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.2465{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2465{{c}}

: error map: {{val| 0.000 -0.709 +3.715 -1.234 }}

Line 1,075:

Badness (Sintel): 2.01

== Quasipyth ==

Quasipyth tempers out the [[nanisma]], and the 7/4 is found at −67 fifths, represented by the nonuple-diminished 13th.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 32805/32768, 390625/387072

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.257{{c}}, ~3/2 = 702.115{{c}}

: [[error map]]: {{val| +0.257 +0.417 -1.434 +0.268 }}

* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.961{{c}}

: error map: {{val| 0.000 +0.006 -2.005 -0.244 }}

[[Badness]] (Sintel): 5.041

== Schism ==

@@ Line 37: / Line 37: @@
 === Overview to extensions ===
-The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at. [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]]. [[#Grackle|Grackle]] adds {{monzo| -44 26 0 1 }}. [[#Pontiac|Pontiac]] adds {{monzo| -59 39 0 -1 }}. [[#Schism|Schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]]. Those all have a fifth as generator.
+The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at. [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]], [[#Grackle|grackle]] adds {{monzo| -44 26 0 1 }}, [[#Pontiac|pontiac]] adds {{monzo| -59 39 0 -1 }}, and [[#Schism|schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]]. Those all have a fifth as generator.
 [[#Bischismic|Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period. [[#Salsa|Salsa]] adds [[parahemif comma|{{monzo| 15 -13 0 2 }}]] and has a hemififth generator. [[#Hemischis|Hemischis]] adds {{monzo| -34 25 0 -2 }} and has a hemitwelfth generator. [[Gamelismic clan #Guiron|Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. [[#Term|Term]] adds {{monzo| -94 54 0 3 }} with a 1/3-octave period. [[#Squirrel|Squirrel]], [[#Tertiaschis|tertiaschis]], and [[#Countertertiaschis|countertertiaschis]] each has a generator that is 1/3 of the fourth. [[#Quadrant|Quadrant]] adds {{monzo| -119 68 0 4 }} with a 1/4-octave period. [[#Kleischismic|Kleischismic]] adds {{monzo| 49 -38 0 4 }} with a half-octave period and also a bisect generator. [[#Sesquiquartififths|Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four.
@@ Line 552: / Line 552: @@
 * [[WE]]: ~2 = 1200.0989{{c}}, ~3/2 = 701.8145{{c}}
 : [[error map]]: {{val| +0.099 -0.042 -0.138 -0.038 }}
-* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.7579{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7579{{c}}
 : error map: {{val| 0.000 -0.197 -0.377 -0.268 }}
@@ Line 945: / Line 945: @@
 * [[WE]]: ~2 = 1199.7974{{c}}, ~3/2 = 701.1210{{c}}
 : [[error map]]: {{val| -0.203 -1.037 +3.300 -1.618 }}
-* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.2465{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2465{{c}}
 : error map: {{val| 0.000 -0.709 +3.715 -1.234 }}
@@ Line 1,075: / Line 1,075: @@
 Badness (Sintel): 2.01
+== Quasipyth ==
+Quasipyth tempers out the [[nanisma]], and the 7/4 is found at −67 fifths, represented by the nonuple-diminished 13th.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 32805/32768, 390625/387072
+{{Mapping|legend=1| 1 0 15 109 | 0 1 -8 -67 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.257{{c}}, ~3/2 = 702.115{{c}}
+: [[error map]]: {{val| +0.257 +0.417 -1.434 +0.268 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.961{{c}}
+: error map: {{val| 0.000 +0.006 -2.005 -0.244 }}
+{{Optimal ET sequence|legend=1| 53, 200, 253, 306c }}
+[[Badness]] (Sintel): 5.041
 == Schism ==