Stearnsmic clan: Difference between revisions

Line 1:

The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649.

~~Stearnsmic temperaments not listed include:~~

* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Porcupine family #Hedgehog|Porcupine family]]

* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]

* ''[[Echidna]]'' (+1728/1715 or 2048/2025) → [[Diaschismic family #Echidna|Diaschismic family]]

* [[Harry]] (+2401/2400 or 19683/19600) → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]

* ''[[Octoid]]'' (+4375/4374 or 16875/16807 → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]

* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]

~~Considered below are pogo, supers, stearnscape, garistearn and decistearn.~~

== No-five stearnsmic ==

Line 25:

Line 15:

{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}

=== Overview to extensions ===

The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo adds [[32805/32768]], supers [[5120/5103]], echidna [[1728/1715]], and hedgehog [[50/49]]. Those are strong extensions. The others are weak. Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] and splits the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five. They all have neat extensions to the 11-limit via tempering out both [[540/539]] and [[4000/3993]].

Stearnsmic temperaments not listed include:

* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Porcupine family #Hedgehog|Porcupine family]]

* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]

* ''[[Echidna]]'' (+1728/1715 or 2048/2025) → [[Diaschismic family #Echidna|Diaschismic family]]

* [[Harry]] (+2401/2400 or 19683/19600) → [[Gravity family #Harry|Gravity family]]

* ''[[Octoid]]'' (+4375/4374 or 16875/16807) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]

* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]

Considered below are pogo, supers, stearnscape, garistearn and decistearn.

== Pogo ==

@@ Line 1: / Line 1: @@
 The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649.
-Stearnsmic temperaments not listed include:
-* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Porcupine family #Hedgehog|Porcupine family]]
-* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
-* ''[[Echidna]]'' (+1728/1715 or 2048/2025) → [[Diaschismic family #Echidna|Diaschismic family]]
-* [[Harry]] (+2401/2400 or 19683/19600) → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
-* ''[[Octoid]]'' (+4375/4374 or 16875/16807 → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
-* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]
-Considered below are pogo, supers, stearnscape, garistearn and decistearn.
 == No-five stearnsmic ==
@@ Line 25: / Line 15: @@
 {{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
+=== Overview to extensions ===
+The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo adds [[32805/32768]], supers [[5120/5103]], echidna [[1728/1715]], and hedgehog [[50/49]]. Those are strong extensions. The others are weak. Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] and splits the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five. They all have neat extensions to the 11-limit via tempering out both [[540/539]] and [[4000/3993]].
+Stearnsmic temperaments not listed include:
+* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Porcupine family #Hedgehog|Porcupine family]]
+* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
+* ''[[Echidna]]'' (+1728/1715 or 2048/2025) → [[Diaschismic family #Echidna|Diaschismic family]]
+* [[Harry]] (+2401/2400 or 19683/19600) → [[Gravity family #Harry|Gravity family]]
+* ''[[Octoid]]'' (+4375/4374 or 16875/16807) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
+* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]
+Considered below are pogo, supers, stearnscape, garistearn and decistearn.
 == Pogo ==