Gravity family: Difference between revisions

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{{Technical data page}}~~ ~~

The '''gravity family''' tempers out [[graviton]], the 5-limit comma 129140163/128000000 = {{monzo| -13 17 -6 }}. The graviton equals (81/80)4/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of [[~]][[40/27]], and hence the name. It is part of the [[syntonic–chromatic equivalence continuum]], whereby (81/80)''k'' = 25/24.

== Gravity ==

[[Subgroup]]: 2.3.5

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There is also an unnamed 58 & 65d extension by tempering [[176/175]] to extend larry to include prime 7 and tempering [[847/845]] to extend it to the 13-limit, with an [[S-expression]]-based comma list of {[[5120/5103|S8/S9]], [[8019/8000|S9/S10]], [[4000/3993|S10/S11]], ([[847/845|S11/S13]],) [[144/143|S12]]}.

=== ~~Larry~~ ===

=== 2.3.5.11 subgroup (larry) ===

Subgroup: 2.3.5.11

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~~{{Multival|legend=1| 6 17 46 13 56 59 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.694

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Mapping: {{mapping| 1 5 12 29 12 | 0 -6 -17 -46 -15 }}

~~{{Multival|legend=1| 6 17 46 15 13 56 3 59 -24 -117 }}~~

Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.699

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Mapping: {{mapping| 1 5 12 29 12 39 | 0 -6 -17 -46 -15 -62 }}

~~{{Multival|legend=1| 6 17 46 15 62 13 56 3 76 59 -24 81 -117 4 159 }}~~

Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.730

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~~{{Multival|legend=1| 6 17 -26 13 -58 -108 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.702

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~~{{Multival|legend=1| 6 17 39 13 45 43 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 517.140

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Harry adds the [[breedsma]], 2401/2400, and the [[cataharry comma]], 19683/19600, to the set of commas, and may be described as the 58 & 72 temperament. The [[period]] is half an [[octave]], and the generator ~21/20, with generator tunings of [[130edo|9\130]] or [[202edo|14\202]] being good choices. [[Mos]] of size 14, 16, 30, 44 or 58 are among the scale choices.

It becomes much more interesting as we move to the 11-limit, where we can add [[243/242]], [[441/440]] and [[540/539]] to the set of commas. 9\130 and especially 14\202 still make for good tuning choices~~, and the octave part of the wedgie is {{multival| 12 34 20 30 … }}~~.

It becomes much more interesting as we move to the 11-limit, where we can add [[243/242]], [[441/440]] and [[540/539]] to the set of commas. 9\130 and especially 14\202 still make for good tuning choices.

Similar comments apply to the 13-limit, where we can add [[351/350]], [[364/363]], and [[729/728]] to the commas~~, with {{multival| 12 34 20 30 52 … }} as the octave wedgie~~. 130edo is again a good tuning choice, but even better might be tuning the harmonic 7 justly, which can be done via a generator of 83.1174 [[cent]]s. 72 notes of harry gives plenty of room even for the 13-limit harmonies.

Similar comments apply to the 13-limit, where we can add [[351/350]], [[364/363]], and [[729/728]] to the commas. 130edo is again a good tuning choice, but even better might be tuning the harmonic 7 justly, which can be done via a generator of 83.1174 [[cent]]s. 72 notes of harry gives plenty of room even for the 13-limit harmonies.

[[Subgroup]]: 2.3.5.7

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: mapping generators: ~567/400, ~21/20

~~{{Multival|legend=1| 12 34 20 26 -2 -49 }}~~

[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/20 = 516.844 (~21/20 = 83.156)

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Gravity family| ]]

[[Category:Gravity| ]]

[[Category:Rank 2]]

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-{{Technical data page}}<br><br>
+{{Technical data page}}
 The '''gravity family''' tempers out [[graviton]], the 5-limit comma 129140163/128000000 = {{monzo| -13 17 -6 }}. The graviton equals (81/80)<sup>4</sup>/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of [[~]][[40/27]], and hence the name. It is part of the [[syntonic&ndash;chromatic equivalence continuum]], whereby (81/80)<sup>''k''</sup> = 25/24.
 == Gravity ==
+{{main|Gravity}}
 [[Subgroup]]: 2.3.5
@@ Line 22: / Line 24: @@
 There is also an unnamed 58 & 65d extension by tempering [[176/175]] to extend larry to include prime 7 and tempering [[847/845]] to extend it to the 13-limit, with an [[S-expression]]-based comma list of {[[5120/5103|S8/S9]], [[8019/8000|S9/S10]], [[4000/3993|S10/S11]], ([[847/845|S11/S13]],) [[144/143|S12]]}.
-=== Larry ===
+=== 2.3.5.11 subgroup (larry) ===
 Subgroup: 2.3.5.11
@@ Line 45: / Line 47: @@
 {{Mapping|legend=1| 1 5 12 29 | 0 -6 -17 -46 }}
-{{Multival|legend=1| 6 17 46 13 56 59 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.694
@@ Line 60: / Line 60: @@
 Mapping: {{mapping| 1 5 12 29 12 | 0 -6 -17 -46 -15 }}
-{{Multival|legend=1| 6 17 46 15 13 56 3 59 -24 -117 }}
 Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.699
@@ Line 75: / Line 73: @@
 Mapping: {{mapping| 1 5 12 29 12 39 | 0 -6 -17 -46 -15 -62 }}
-{{Multival|legend=1| 6 17 46 15 62 13 56 3 76 59 -24 81 -117 4 159 }}
 Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.730
@@ Line 90: / Line 86: @@
 {{Mapping|legend=1| 1 5 12 -12 | 0 -6 -17 26 }}
-{{Multival|legend=1| 6 17 -26 13 -58 -108 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.702
@@ Line 131: / Line 125: @@
 {{Mapping|legend=1| 1 5 12 25 | 0 -6 -17 -39 }}
-{{Multival|legend=1| 6 17 39 13 45 43 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 517.140
@@ Line 158: / Line 150: @@
 Harry adds the [[breedsma]], 2401/2400, and the [[cataharry comma]], 19683/19600, to the set of commas, and may be described as the 58 &amp; 72 temperament. The [[period]] is half an [[octave]], and the generator ~21/20, with generator tunings of [[130edo|9\130]] or [[202edo|14\202]] being good choices. [[Mos]] of size 14, 16, 30, 44 or 58 are among the scale choices.
-It becomes much more interesting as we move to the 11-limit, where we can add [[243/242]], [[441/440]] and [[540/539]] to the set of commas. 9\130 and especially 14\202 still make for good tuning choices, and the octave part of the wedgie is {{multival| 12 34 20 30 … }}.
+It becomes much more interesting as we move to the 11-limit, where we can add [[243/242]], [[441/440]] and [[540/539]] to the set of commas. 9\130 and especially 14\202 still make for good tuning choices.
-Similar comments apply to the 13-limit, where we can add [[351/350]], [[364/363]], and [[729/728]] to the commas, with {{multival| 12 34 20 30 52 … }} as the octave wedgie. 130edo is again a good tuning choice, but even better might be tuning the harmonic 7 justly, which can be done via a generator of 83.1174 [[cent]]s. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
+Similar comments apply to the 13-limit, where we can add [[351/350]], [[364/363]], and [[729/728]] to the commas. 130edo is again a good tuning choice, but even better might be tuning the harmonic 7 justly, which can be done via a generator of 83.1174 [[cent]]s. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
 [[Subgroup]]: 2.3.5.7
@@ Line 169: / Line 161: @@
 : mapping generators: ~567/400, ~21/20
-{{Multival|legend=1| 12 34 20 26 -2 -49 }}
 [[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/20 = 516.844 (~21/20 = 83.156)
@@ Line 218: / Line 208: @@
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Gravity family| ]] <!-- main article -->
 [[Category:Gravity| ]] <!-- key article -->
 [[Category:Rank 2]]