Septischismic clan: Difference between revisions

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The second comma of the comma list determines which full 7-limit or 11-limit family member we are looking at. Garibaldi adds the [[schisma]], or equivalently [[225/224]] and finds 5/4 at the diminished fourth. Cotoneum adds [[10976/10935]] and finds 5/4 at the septuple-diminished octave. These are generated by the fifth as is gary.

Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five.

Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five. Heptacot adds [[703125/702464]], slicing the fifth in seven. Finally, garitritonic adds 95703125/95551488 ({{monzo| -17 -6 9 2 }}), slicing the 24th harmonic in nine.

Temperaments discussed elsewhere are:

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Badness (Sintel): 1.82

== Heptacot ==

: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Heptacot (5-limit)]].''

Heptacot tempers out the [[meter]] and may be described as the {{nowrap| 12 & 311 }} temperament.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 703125/702464, 33554432/33480783

: mapping generators: ~2, ~1323/1250

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9434{{c}}, ~1323/1250 = 100.3096{{c}}

: [[error map]]: {{val| -0.057 +0.155 -0.274 +0.215 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~1323/1250 = 100.3148{{c}}

: error map: {{val| 0.000 +0.249 -0.165 +0.324 }}

{{Optimal ET sequence|legend=1| 12, …, 299, 311, 323, 634, 957, 1591 }}

[[Badness]] (Sintel): 3.06

== Garitritonic ==

: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''

Garitritonic may be described as the {{nowrap| 53 & 581 }} temperament, splitting the [[24/1|24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[634edo]] makes for a strong tuning.

Garitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''gary'' and ''tritonic''.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 33554432/33480783, 95703125/95551488

: mapping generators: ~2, ~4375/3072

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9678{{c}}, ~4375/3072 = 611.3417{{c}}

: [[error map]]: {{val| -0.032 +0.217 -0.213 -0.036 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~4375/3072 = 611.3582{{c}}

: error map: {{val| 0.000 +0.268 -0.136 +0.045 }}

{{Optimal ET sequence|legend=1| 53, 422d, 475, 528, 581, 634, 1215 }}

[[Badness]] (Sintel): 6.12

[[Category:Temperament clans]]

[[Category:Garischismic clan| ]]

[[Category:Rank 2]]

@@ Line 28: / Line 28: @@
 The second comma of the comma list determines which full 7-limit or 11-limit family member we are looking at. Garibaldi adds the [[schisma]], or equivalently [[225/224]] and finds 5/4 at the diminished fourth. Cotoneum adds [[10976/10935]] and finds 5/4 at the septuple-diminished octave. These are generated by the fifth as is gary.
-Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five.
+Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five. Heptacot adds [[703125/702464]], slicing the fifth in seven. Finally, garitritonic adds 95703125/95551488 ({{monzo| -17 -6 9 2 }}), slicing the 24th harmonic in nine.
 Temperaments discussed elsewhere are:
@@ Line 523: / Line 523: @@
 Badness (Sintel): 1.82
+== Heptacot ==
+: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Heptacot (5-limit)]].''
+Heptacot tempers out the [[meter]] and may be described as the {{nowrap| 12 & 311 }} temperament.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 703125/702464, 33554432/33480783
+{{Mapping|legend=1| 1 1 6 11 | 0 7 -44 -98 }}
+: mapping generators: ~2, ~1323/1250
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9434{{c}}, ~1323/1250 = 100.3096{{c}}
+: [[error map]]: {{val| -0.057 +0.155 -0.274 +0.215 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~1323/1250 = 100.3148{{c}}
+: error map: {{val| 0.000 +0.249 -0.165 +0.324 }}
+{{Optimal ET sequence|legend=1| 12, …, 299, 311, 323, 634, 957, 1591 }}
+[[Badness]] (Sintel): 3.06
+== Garitritonic ==
+: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''
+Garitritonic may be described as the {{nowrap| 53 & 581 }} temperament, splitting the [[24/1|24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[634edo]] makes for a strong tuning.
+Garitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''gary'' and ''tritonic''.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 33554432/33480783, 95703125/95551488
+{{Mapping|legend=1| 1 -3 -15 67 | 0 9 34 -126 }}
+: mapping generators: ~2, ~4375/3072
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9678{{c}}, ~4375/3072 = 611.3417{{c}}
+: [[error map]]: {{val| -0.032 +0.217 -0.213 -0.036 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~4375/3072 = 611.3582{{c}}
+: error map: {{val| 0.000 +0.268 -0.136 +0.045 }}
+{{Optimal ET sequence|legend=1| 53, 422d, 475, 528, 581, 634, 1215 }}
+[[Badness]] (Sintel): 6.12
 [[Category:Temperament clans]]
 [[Category:Garischismic clan| ]] <!-- main article -->
 [[Category:Rank 2]]