Gaster: Difference between revisions

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'''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} (quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]].

'''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} ([[gaster comma]], quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Coincidentally, one of its commas involves stacking seventeen 9/8s, and 17 is a number associated with the character Gaster from Undertale. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]].

== Temperament data ==

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* 41-limit: ~2 = 1199.91875, ~24/17 = 594.60272

[[Optimal ~~GPV~~ sequence]]s:

[[Optimal ET sequence]]s:

* 7, 19 and 23-limit: {{~~Vals~~| 111, 224 }}

* 7, 19 and 23-limit: {{Optimal ET sequence| 111, 224 }}

* 11-limit: {{~~Vals~~| 111, 224, 783d, 1007d, 1231dd }}

* 11-limit: {{Optimal ET sequence| 111, 224, 783d, 1007d, 1231dd }}

* 13-limit: {{~~Vals~~| 111, 224, 783df, 1007df, 1231ddf }}

* 13-limit: {{Optimal ET sequence| 111, 224, 783df, 1007df, 1231ddf }}

* 17-limit: {{~~Vals~~| 111, 224, 559dgg }}

* 17-limit: {{Optimal ET sequence| 111, 224, 559dgg }}

* 29, 31, 37 and 41-limit: {{~~Vals~~| 111, 113, 224 }}

* 29, 31, 37 and 41-limit: {{Optimal ET sequence| 111, 113, 224 }}

[[Badness]]:

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|}

<nowiki>*</nowiki>3: SGT stands for smaller gassormic tritone.<br><nowiki>*</nowiki>4: in 41-limit POTE tuning

~~== Gaster comma ==~~

'''Gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu). Equal temperaments which temper out this comma include {{Vals| 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 }} and others.

~~=== 5-limit gaster temperament ===~~

~~<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">~~

~~<div style="line-height:1.6;">'''5-limit gaster temperament (559&1342)'''</div>~~

~~<div class="mw-collapsible-content">~~

~~Subgroup: 2.3.5~~

~~[[Comma]]: {{monzo|-70 72 -19}}~~

~~[[Mapping]]: [{{val|1 11 38}}, {{val|0 -19 -72}}]~~

~~[[POTE generator]]: ~1638400000/1162261467 = 594.63457~~

~~[[TOP tuning|TOP generator]]s: ~2 = 1200.00282, ~1638400000/1162261467 = 594.63596~~

~~{{Optimal GPV sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243 }}~~

~~[[Badness]]: 0.088530~~

~~</div></div>~~

== See also ==

* [[Mirkwai clan]]

* [[Very high accuracy temperaments]]

* [[Unnoticeable comma]]

[[Category: ~~Mirkwai clan~~]]

[[Category:Gaster| ]]

[[Category: ~~Index of~~ temperaments]]

[[Category:Rank-2 temperaments]]

[[Category: ~~Unnoticeable comma~~]]

[[Category:Mirkwai clan]]

@@ Line 1: / Line 1: @@
-'''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} (quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]].
+'''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} ([[gaster comma]], quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Coincidentally, one of its commas involves stacking seventeen 9/8s, and 17 is a number associated with the character Gaster from Undertale. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]].
 == Temperament data ==
@@ Line 35: / Line 35: @@
 * 41-limit: ~2 = 1199.91875, ~24/17 = 594.60272
-[[Optimal GPV sequence]]s:
+[[Optimal ET sequence]]s:
-* 7, 19 and 23-limit: {{Vals| 111, 224 }}
+* 7, 19 and 23-limit: {{Optimal ET sequence| 111, 224 }}
-* 11-limit: {{Vals| 111, 224, 783d, 1007d, 1231dd }}
+* 11-limit: {{Optimal ET sequence| 111, 224, 783d, 1007d, 1231dd }}
-* 13-limit: {{Vals| 111, 224, 783df, 1007df, 1231ddf }}
+* 13-limit: {{Optimal ET sequence| 111, 224, 783df, 1007df, 1231ddf }}
-* 17-limit: {{Vals| 111, 224, 559dgg }}
+* 17-limit: {{Optimal ET sequence| 111, 224, 559dgg }}
-* 29, 31, 37 and 41-limit: {{Vals| 111, 113, 224 }}
+* 29, 31, 37 and 41-limit: {{Optimal ET sequence| 111, 113, 224 }}
 [[Badness]]:
@@ Line 405: / Line 405: @@
 |}
 <nowiki>*</nowiki>3: SGT stands for smaller gassormic tritone.<br><nowiki>*</nowiki>4: in 41-limit POTE tuning
-== Gaster comma ==
-'''Gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu). Equal temperaments which temper out this comma include {{Vals| 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 }} and others.
-=== 5-limit gaster temperament ===
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
-<div style="line-height:1.6;">'''5-limit gaster temperament (559&amp;1342)'''</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5
-[[Comma]]: {{monzo|-70 72 -19}}
-[[Mapping]]: [{{val|1 11 38}}, {{val|0 -19 -72}}]
-[[POTE generator]]: ~1638400000/1162261467 = 594.63457
-[[TOP tuning|TOP generator]]s: ~2 = 1200.00282, ~1638400000/1162261467 = 594.63596
-{{Optimal GPV sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243 }}
-[[Badness]]: 0.088530
-</div></div>
 == See also ==
 * [[Mirkwai clan]]
+* [[Very high accuracy temperaments]]
 * [[Unnoticeable comma]]
-[[Category: Mirkwai clan]]
+[[Category:Gaster| ]] <!-- main article -->
-[[Category: Index of temperaments]]
+[[Category:Rank-2 temperaments]]
-[[Category: Unnoticeable comma]]
+[[Category:Mirkwai clan]]