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== Temperaments ==

Tempering out this comma in the 17-limit results in the rank-6 '''sperasmic''' temperament, or in the the 2.3.5.7.17 subgroup, the rank-4 '''speric''' temperament. You may find a list of good equal temperaments that support these temperaments below.

=== Speric ===

[[Subgroup]]: 2.3.5.7.17

{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }}

: mapping generators: ~2, ~3, ~5, ~7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}

{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }}

[[Badness]] (Sintel): 0.122

=== Sperasmic ===

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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.~~9677~~{{c}}, ~5/4 = 386.~~2047~~{{c}}, ~7/4 - 968.~~9056~~{{c}}, ~11/8, ~13/8

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}, ~11/8 = 551.3474{{c}}, ~13/8 = 840.5571{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}, ~11/8 = 551.3352{{c}}, ~13/8 = 840.5461{{c}}

{{Optimal ET sequence|legend=1| 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477 }}

~~=== Speric ===~~

[[Badness]] (Sintel): 1.13

[[~~Subgroup]]: 2.3.5.7.17~~

~~{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }}~~

~~: mapping generators: ~2, ~3, ~5, ~7~~

~~[[Optimal tuning~~]] (~~[[CTE]]~~): ~~~2 = 1200.0000{{c}}, ~3/2 = 701.9677{{c}}, ~5/4 = 386~~.~~2047{{c}}, ~7/4 = 968.9056{{c}}~~

~~{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }}~~

== Etymology ==

@@ Line 26: / Line 26: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit results in the rank-6 '''sperasmic''' temperament, or in the the 2.3.5.7.17 subgroup, the rank-4 '''speric''' temperament. You may find a list of good equal temperaments that support these temperaments below.
+=== Speric ===
+[[Subgroup]]: 2.3.5.7.17
+{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}
+{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }}
+[[Badness]] (Sintel): 0.122
 === Sperasmic ===
@@ Line 47: / Line 61: @@
 : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9677{{c}}, ~5/4 = 386.2047{{c}}, ~7/4 - 968.9056{{c}}, ~11/8, ~13/8
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}, ~11/8 = 551.3474{{c}}, ~13/8 = 840.5571{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}, ~11/8 = 551.3352{{c}}, ~13/8 = 840.5461{{c}}
 {{Optimal ET sequence|legend=1| 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477 }}
-=== Speric ===
+[[Badness]] (Sintel): 1.13
-[[Subgroup]]: 2.3.5.7.17
-{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }}
-: mapping generators: ~2, ~3, ~5, ~7
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9677{{c}}, ~5/4 = 386.2047{{c}}, ~7/4 = 968.9056{{c}}
-{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }}
 == Etymology ==