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 = 31/22 = 24/17, 26/19 = 41/30, 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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== Intervals ==

{| class="wikitable center-1 right-2"

! Number of LGT (*1)

! Number of LGT(*1)

! Cents value (*2)

! Cents value(*2)

! Approximate Ratios

|-

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| 2

| 10.714

| 144/143, 145/144, 153/152, ~~ ~~154/153, 155/154, 156/155, 161/160, 162/161, 165/164, ~~ ~~169/168, 170/169, 171/170, 185/184, 186/185, 187/186, ~~ ~~190/189, 196/195

| 144/143, 145/144, 153/152, 154/153, 155/154, 156/155, 161/160, 162/161, 165/164, 169/168, 170/169, 171/170, 185/184, 186/185, 187/186, 190/189, 196/195, 204/203

|-

| 4

| 21.428

| 77/76, 78/77, 81/80, 82/81, ~~ ~~85/84, 88/87, 91/90, 93/92

| 77/76, 78/77, 81/80, 82/81, 85/84, 88/87, 91/90, 93/92

|-

| 6

| 32.142

| 52/51, 55/54, 56/55, 57/56

| 50/49, 52/51, 55/54, 56/55, 57/56

|-

| 8

| 42.856

| 39/38, 40/39, 41/40, 42/41

| 39/38, 40/39, 41/40, 42/41

|-

| 10

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{| class="wikitable center-1 right-2"

! Number of SGT (*3)

! Number of SGT(*3)

! Cents value (*4)

! Cents value(*4)

! Approximate Ratios

|-

| 1

| 594.643

| 24/17, 31/22, 38/27, 55/39

| 24/17, 31/22, 38/27, 55/39

|-

| 3

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== See also ==

* [[Mirkwai clan]]

* [[Very high accuracy temperaments]]

* [[Unnoticeable comma]]

[[Category: Mirkwai clan]]

[[Category:Gaster| ]]

~~{{IoT}}~~

[[Category:Rank-2 temperaments]]

[[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 = 31/22 = 24/17, 26/19 = 41/30, 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 57: / Line 57: @@
 == Intervals ==
 {| class="wikitable center-1 right-2"
-! Number of <br>LGT (*1)
+! Number of <br>LGT(*1)
-! Cents <br>value (*2)
+! Cents <br>value(*2)
 ! Approximate Ratios
 |-
@@ Line 67: / Line 67: @@
 | 2
 | 10.714
-| 144/143, 145/144, 153/152, <br>154/153, 155/154, 156/155, <br>161/160, 162/161, 165/164, <br>169/168, 170/169, 171/170, <br>185/184, 186/185, 187/186, <br>190/189, 196/195
+| 144/143, 145/144, <br>153/152, 154/153, <br>155/154, 156/155, <br>161/160, 162/161, <br>165/164, 169/168, <br>170/169, 171/170, <br>185/184, 186/185, <br>187/186, 190/189, <br>196/195, 204/203
 |-
 | 4
 | 21.428
-| 77/76, 78/77, 81/80, 82/81, <br>85/84, 88/87, 91/90, 93/92
+| 77/76, 78/77, 81/80, <br>82/81, 85/84, 88/87, <br>91/90, 93/92
 |-
 | 6
 | 32.142
-| 52/51, 55/54, 56/55, 57/56
+| 50/49, 52/51, 55/54, <br>56/55, 57/56
 |-
 | 8
 | 42.856
-| 39/38, 40/39, 41/40, 42/41
+| 39/38, 40/39, 41/40, <br>42/41
 |-
 | 10
@@ Line 232: / Line 232: @@
 {| class="wikitable center-1 right-2"
-! Number of <br>SGT (*3)
+! Number of <br>SGT(*3)
-! Cents <br>value (*4)
+! Cents <br>value(*4)
 ! Approximate Ratios
 |-
 | 1
 | 594.643
-| 24/17, 31/22, 38/27, 55/39
+| 24/17, 31/22, 38/27, <br>55/39
 |-
 | 3
@@ Line 408: / Line 408: @@
 == See also ==
 * [[Mirkwai clan]]
+* [[Very high accuracy temperaments]]
+* [[Unnoticeable comma]]
-[[Category: Mirkwai clan]]
+[[Category:Gaster| ]] <!-- main article -->
-{{IoT}}
+[[Category:Rank-2 temperaments]]
+[[Category:Mirkwai clan]]