Stearnsmic clan: Difference between revisions

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== No-5 stearnsmic ==

This temperament is generated by a very slightly flat [[~]][[9/7]] major third, three of which minus a [[semi-octave]] period give the [[3/2|perfect fifth]]. Its [[ploidacot]] is diploid alpha-tricot.

[[Subgroup]]: 2.3.7

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=== 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]], as well as [[9801/9800]], so that [[11/10]] and [[9/7]] add up to the ~~semioctave~~.

The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.

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.

All of them extend naturally to the 11-limit via tempering out both [[540/539]] and [[4000/3993]], as well as [[9801/9800]], so that [[11/10]] and [[9/7]] add up to the semi-octave period.

Stearnsmic temperaments not listed include:

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== Pogo ==

~~{{See also| Schismatic family }}~~

The pogo temperament tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It may be described as 94 & 130, and is the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.

The pogo temperament ~~(94 & 130)~~ tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is ~~also~~ the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.

[[Subgroup]]: 2.3.5.7

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== Supers ==

Supers tempers out 5120/5103, the [[aberschisma]], and may be described as the {{nowrap| 58 & 94 }} temperament.

[[Subgroup]]: 2.3.5.7

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== Stearnscape ==

Stearnscape tempers out 250047/250000, the [[landscape comma]], with a period of 1/6 octave, and may be described as the {{nowrap| 72 & 282 }} temperament.

[[Subgroup]]: 2.3.5.7

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== Garistearn ==

The garistearn temperament (94 & 282) ~~has a period of 1/94-octave and~~ tempers out ~~118098/117649 and~~ the [[~~garischisma~~]]~~, 33554432~~/~~33480783~~.

The garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].

[[Subgroup]]: 2.3.5.7

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The decistearn temperament ~~(80 & 130)~~ has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]].

The decistearn temperament has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]]. It may be described as 80 & 130.

[[Subgroup]]: 2.3.5.7

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 == No-5 stearnsmic ==
+This temperament is generated by a very slightly flat [[~]][[9/7]] major third, three of which minus a [[semi-octave]] period give the [[3/2|perfect fifth]]. Its [[ploidacot]] is diploid alpha-tricot.
 [[Subgroup]]: 2.3.7
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 === 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]], as well as [[9801/9800]], so that [[11/10]] and [[9/7]] add up to the semioctave.
+The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.
+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.
+All of them extend naturally to the 11-limit via tempering out both [[540/539]] and [[4000/3993]], as well as [[9801/9800]], so that [[11/10]] and [[9/7]] add up to the semi-octave period.
 Stearnsmic temperaments not listed include:
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 == Pogo ==
-{{See also| Schismatic family }}
+The pogo temperament tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It may be described as 94 & 130, and is the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.
-The pogo temperament (94 & 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is also the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.
 [[Subgroup]]: 2.3.5.7
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 == Supers ==
+Supers tempers out 5120/5103, the [[aberschisma]], and may be described as the {{nowrap| 58 & 94 }} temperament.
 [[Subgroup]]: 2.3.5.7
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 == Stearnscape ==
+Stearnscape tempers out 250047/250000, the [[landscape comma]], with a period of 1/6 octave, and may be described as the {{nowrap| 72 & 282 }} temperament.
 [[Subgroup]]: 2.3.5.7
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 == Garistearn ==
-The garistearn temperament (94 & 282) has a period of 1/94-octave and tempers out 118098/117649 and the [[garischisma]], 33554432/33480783.
+The garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].
 [[Subgroup]]: 2.3.5.7
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 {{See also| Trisedodge family }}
-The decistearn temperament (80 & 130) has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]].
+The decistearn temperament has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]]. It may be described as 80 & 130.
 [[Subgroup]]: 2.3.5.7