Keemic temperaments: Difference between revisions

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: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''

Quasitemp is a full 7-limit strong extension of [[gariberttet]], the 2.5/3.7/3 subgroup temperament defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]] (which is equated to [[13/11]] in the 13-limit extension). In quasitemp, tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.

Quasitemp is a full 7-limit strong extension of [[gariberttet]], the 2.5/3.7/3 subgroup temperament defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]] (which is equated to [[13/11]] in the 13-limit extension). This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. In quasitemp, tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.

[[Subgroup]]: 2.3.5.7

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: Mapping generators: ~2, ~25/21

~~{{Multival|legend=1| 14 11 9 -15 -25 -10 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 292.710

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: Mapping generators: ~2, ~98/75

~~{{Multival|legend=1| 19 12 21 -25 -20 15 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 468.331

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: Mapping generators: ~2, ~6/5

~~{{Multival|legend=1| 17 16 3 -14 -43 -38 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 323.780

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[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Keemic temperaments| ]]

[[Category:Rank 2]]

@@ Line 17: / Line 17: @@
 : ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''
-Quasitemp is a full 7-limit strong extension of [[gariberttet]], the 2.5/3.7/3 subgroup temperament defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]] (which is equated to [[13/11]] in the 13-limit extension). In quasitemp, tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.
+Quasitemp is a full 7-limit strong extension of [[gariberttet]], the 2.5/3.7/3 subgroup temperament defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]] (which is equated to [[13/11]] in the 13-limit extension). This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. In quasitemp, tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.
 [[Subgroup]]: 2.3.5.7
@@ Line 26: / Line 26: @@
 : Mapping generators: ~2, ~25/21
-{{Multival|legend=1| 14 11 9 -15 -25 -10 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 292.710
@@ Line 115: / Line 113: @@
 : Mapping generators: ~2, ~98/75
-{{Multival|legend=1| 19 12 21 -25 -20 15 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 468.331
@@ Line 158: / Line 154: @@
 : Mapping generators: ~2, ~6/5
-{{Multival|legend=1| 17 16 3 -14 -43 -38 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 323.780
@@ Line 237: / Line 231: @@
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Keemic temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]