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{{Technical data page}}
= Gravity =
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.
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-chromatic equivalence continuum]], whereby (81/80)<sup>''n''-2</sup> = 25/24.


Comma: 129140163/128000000
== Gravity ==
{{main|Gravity}}


POTE generator: ~40/27 = 683.156
[[Subgroup]]: 2.3.5


Map: [&lt;1 5 12|, &lt;0 -6 -17|]
[[Comma list]]: 129140163/128000000


EDOs: {{EDOs| 7, 58, 65, 137, 202, 267, 469 }}
{{Mapping|legend=1| 1 5 12 | 0 -6 -17 }}


Badness: 0.0932
: mapping generators: ~2, ~40/27


=Harry=
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.844
[[Harry]] temperament can be described as 58&amp;72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between [[21/20]] and [[22/21]]. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.


Commas: 2401/2400, 19683/19600
{{Optimal ET sequence|legend=1| 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469 }}


POTE generator: ~21/20 = 83.156
[[Badness]]: 0.093184


Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
=== Overview to extensions ===
Full 7-limit extensions of gravity include marvo (65d &amp; 72), zarvo (65 &amp; 72), gravid (58 &amp; 65), and harry (58 &amp; 72), all considered below. A notable subgroup extension is larry.


Wedgie: &lt;&lt;12 34 20 26 -2 -49||
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]]}.


EDOs: 58, 72, 130, 202, 534
=== 2.3.5.11 subgroup (larry) ===
Subgroup: 2.3.5.11


Badness: 0.0341
Comma list: 243/242, 4000/3993


==11-limit==
Sval mapping: {{mapping| 1 5 12 12 | 0 -6 -17 -15 }}
Commas: 243/242, 441/440, 4000/3993


POTE generator: ~21/20 = 83.167
Gencom mapping: {{mapping| 1 5 12 0 12 | 0 -6 -17 0 -15 }}


Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
: gencom: [2 40/27; 243/242 4000/3993]


EDOs: 58, 72, 130, 202
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.834


Badness: 0.0159
{{Optimal ET sequence|legend=1| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}


==13-limit==
Badness: 0.0125
Commas: 243/242, 351/350, 364/363, 441/440


POTE generator: ~21/20 = 83.116
== Marvo ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
[[Comma list]]: 225/224, 78125000/78121827


EDOs: 58, 72, 130
{{Mapping|legend=1| 1 5 12 29 | 0 -6 -17 -46 }}


Badness: 0.0130
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.694


==17-limit==
{{Optimal ET sequence|legend=1| 65d, 72, 137, 209, 281, 569bcc }}
Commas: 221/220, 243/242, 289/288, 351/350, 441/440


POTE generator: ~21/20 = 83.168
[[Badness]]: 0.097627


Map: [&lt;2 4 7 7 9 11 9|, &lt;0 -6 -17 -10 -15 -26 -6|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: 58, 72, 130
Comma list: 225/224, 243/242, 4000/3993


Badness: 0.0127
Mapping: {{mapping| 1 5 12 29 12 | 0 -6 -17 -46 -15 }}


=Gravid=
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.699
Commas: 126/125, 1605632/1594323


POTE generator: ~27/20 = 517.140
{{Optimal ET sequence|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}


Map: [&lt;1 -1 -5 -14|, &lt;0 6 17 39|]
Badness: 0.031685


Wedgie: &lt;&lt;6 17 39 13 45 43||
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 7d, 58, 65, 123, 181c
Comma list: 225/224, 243/242, 351/350, 1625/1617


Badness: 0.1312
Mapping: {{mapping| 1 5 12 29 12 39 | 0 -6 -17 -46 -15 -62 }}


==11-limit==
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.730
Commas: 126/125, 243/242, 896/891


POTE generator: ~27/20 = 517.155
{{Optimal ET sequence|legend=1| 65d, 72, 137, 209, 281f, 490bcf }}


Map: [&lt;1 -1 -5 -14 -3|, &lt;0 6 17 39 15|]
Badness: 0.026882


EDOs: 7d, 58, 65, 123, 181ce
== Zarvo ==
[[Subgroup]]: 2.3.5.7


Badness: 0.0473
[[Comma list]]: 4375/4374, 33075/32768


=Zarvo=
{{Mapping|legend=1| 1 5 12 -12 | 0 -6 -17 26 }}
Commas: 4375/4374, 33075/32768


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


Map: [&lt;1 -1 -5 14|, &lt;0 6 17 -26|]
{{Optimal ET sequence|legend=1| 65, 72, 281d, 353cd, 425bcdd, 497bcdd }}


Wedgie: &lt;&lt;6 17 -26 13 -58 -108||
[[Badness]]: 0.096840


EDOs: 7, 65, 72
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0968
Comma list: 243/242, 385/384, 4000/3993


==11-limit==
Mapping: {{mapping| 1 5 12 -12 12 | 0 -6 -17 26 -15 }}
Commas: 243/242, 385/384, 4000/3993


POTE generator: ~27/20 = 516.691
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.691


Map: [&lt;1 -1 -5 14 -3|, &lt;0 6 17 -26 15|]
{{Optimal ET sequence|legend=1| 65, 72, 353cd }}


EDOs: 7, 65, 72
Badness: 0.034773


Badness: 0.0348
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 169/168, 243/242, 325/324, 385/384
Commas: 169/168, 243/242, 325/324, 385/384


POTE generator: ~27/20 = 516.667
Mapping: {{mapping| 1 5 12 -12 12 -2 | 0 -6 -17 26 -15 10 }}


Map: [&lt;1 -1 -5 14 -3 8|, &lt;0 6 17 -26 15 -10|]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.667


EDOs: 7, 65f, 72, 79
{{Optimal ET sequence|legend=1| 65f, 72 }}


Badness: 0.0276
Badness: 0.027584


[[Category:Theory]]
== Gravid ==
[[Category:Temperament family]]
[[Subgroup]]: 2.3.5.7
[[Category:Gravity]]
 
[[Comma list]]: 126/125, 1605632/1594323
 
{{Mapping|legend=1| 1 5 12 25 | 0 -6 -17 -39 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 517.140
 
{{Optimal ET sequence|legend=1| 58, 123, 181c }}
 
[[Badness]]: 0.131153
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 243/242, 896/891
 
Mapping: {{mapping| 1 5 12 25 12 | 0 -6 -17 -39 -15 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 517.155
 
{{Optimal ET sequence|legend=1| 58, 123, 181ce }}
 
Badness: 0.047283
 
== Harry ==
{{Main| Harry }}
 
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.
 
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
 
[[Comma list]]: 2401/2400, 19683/19600
 
{{Mapping|legend=1| 2 4 7 7 | 0 -6 -17 -10 }}
 
: mapping generators: ~567/400, ~21/20
 
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/20 = 516.844 (~21/20 = 83.156)
 
{{Optimal ET sequence|legend=1| 14c, 58, 72, 130, 202, 534, 736b, 938b }}
 
[[Badness]]: 0.034077
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 441/440, 4000/3993
 
Mapping: {{mapping| 2 4 7 7 9 | 0 -6 -17 -10 -15 }}
 
Optimal tuning (POTE): ~99/70 = 1\2, ~27/20 = 516.833 (~21/20 = 83.167)
 
{{Optimal ET sequence|legend=1| 14c, 58, 72, 130, 202 }}
 
Badness: 0.015867
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 243/242, 351/350, 364/363, 441/440
 
Mapping: {{mapping| 2 4 7 7 9 11 | 0 -6 -17 -10 -15 -26 }}
 
Optimal tuning (POTE): ~55/39 = 1\2, ~27/20 = 516.884 (~21/20 = 83.116)
 
{{Optimal ET sequence|legend=1| 14cf, 58, 72, 130, 332f, 462ef }}
 
Badness: 0.013046
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 221/220, 243/242, 289/288, 351/350, 441/440
 
Mapping: {{mapping| 2 4 7 7 9 11 9 | 0 -6 -17 -10 -15 -26 -6 }}
 
Optimal tuning (POTE): ~17/12 = 1\2, ~27/20 = 516.832 (~21/20 = 83.168)
 
{{Optimal ET sequence|legend=1| 14cf, 58, 72, 130, 202g }}
 
Badness: 0.012657
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Gravity family| ]] <!-- main article -->
[[Category:Gravity| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Gravity_family"