Stearnsmic clan: Difference between revisions

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The pogo temperament (94 &~~amp;~~ 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma.

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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: mapping generators: ~343/243, ~9/7

[[Optimal tuning]] ([[POTE]]): ~343/243 = ~~1\2~~, ~9/7 = 433.901

[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}

[[Badness]]: 0.079635

[[Badness]] (Smith): 0.079635

=== 11-limit ===

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Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}

Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~9/7 = 433.911

Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}

Badness: 0.031857

Badness (Smith): 0.031857

=== 13-limit ===

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Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}

Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~9/7 = 433.911

Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}

Badness: 0.017514

Badness (Smith): 0.017514

== Supers ==

@@ Line 33: / Line 33: @@
 {{See also| Schismatic family #Pogo }}
-The pogo temperament (94 &amp; 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma.
+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
@@ Line 40: / Line 40: @@
 {{Mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}
+: mapping generators: ~343/243, ~9/7
-[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.901
+[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}
 {{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
-[[Badness]]: 0.079635
+[[Badness]] (Smith): 0.079635
 === 11-limit ===
@@ Line 54: / Line 55: @@
 Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354, 578 }}
+{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness: 0.031857
+Badness (Smith): 0.031857
 === 13-limit ===
@@ Line 67: / Line 68: @@
 Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354, 578 }}
+{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness: 0.017514
+Badness (Smith): 0.017514
 == Supers ==