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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>''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>''k''</sup> = 25/24.
Temperaments not discussed here include [[Marvel temperaments #marvo|marvo]].


== Gravity  ==
== Gravity  ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 129140163/128000000
[[Comma list]]: 129140163/128000000


[[Mapping]]: [{{val|1 5 12}}, {{val|0 -6 -17}}]
[[Mapping]]: [{{val| 1 5 12 }}, {{val| 0 -6 -17 }}]


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


{{Val list| 7, 58, 65, 137, 202, 267, 469 }}
{{Val list|legend=1| 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469 }}


[[Badness]]: 0.093184
[[Badness]]: 0.093184


== Harry ==
=== Extensions ===
{{main|Harry}}
Extensions of gravity include harry, gravid and zarvo, considered below, as well as these temperaments discussed elsewhere:
{{see also|Breedsmic temperaments #Harry}}
* ''[[marvo]]'', {225/224, 78125000/78121827} → [[Marvel temperaments #marvo]]
 
== Harry ==
{{main| Harry }}
{{see also| Breedsmic temperaments #Harry }}


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.
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.
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[[Badness]]: 0.034077
[[Badness]]: 0.034077


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 49: Line 51:
Badness: 0.015867
Badness: 0.015867


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 62: Line 64:
Badness: 0.013046
Badness: 0.013046


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 75: Line 77:
Badness: 0.012657
Badness: 0.012657


== Gravid ==
== Gravid ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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[[Mapping]]: [{{val|1 -1 -5 -14}}, {{val|0 6 17 39}}]
[[Mapping]]: [{{val|1 -1 -5 -14}}, {{val|0 6 17 39}}]


[[Wedgie]]: {{multival|6 17 39 13 45 43}}
{{Multival|legend=1| 6 17 39 13 45 43 }}


[[POTE generator]]: ~27/20 = 517.140
[[POTE generator]]: ~27/20 = 517.140


{{Val list|legend=1| 7d, 58, 65, 123, 181c }}
{{Val list|legend=1| 7d, 44cdd, 51cd, 58, 123, 181c }}


[[Badness]]: 0.131153
[[Badness]]: 0.131153


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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POTE generator: ~27/20 = 517.155
POTE generator: ~27/20 = 517.155


Vals: {{Val list| 7d, 58, 65, 123, 181ce }}
Vals: {{Val list| 7d, 44cdde, 51cde, 58, 123, 181ce }}


Badness: 0.047283
Badness: 0.047283


== Zarvo ==
== Zarvo ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 110: Line 112:
[[Mapping]]: [{{val|1 -1 -5 14}}, {{val|0 6 17 -26}}]
[[Mapping]]: [{{val|1 -1 -5 14}}, {{val|0 6 17 -26}}]


[[Wedgie]]: {{multival|6 17 -26 13 -58 -108}}
{{Multival|legend=1| 6 17 -26 13 -58 -108 }}


[[POTE generator]]: ~27/20 = 516.702
[[POTE generator]]: ~27/20 = 516.702


{{Val list|lenegd=1| 7, 65, 72 }}
{{Val list|legend=1| 7, 65, 72, 281d, 353cd, 425bcdd, 497bcdd }}


[[Badness]]: 0.096840
[[Badness]]: 0.096840


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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POTE generator: ~27/20 = 516.691
POTE generator: ~27/20 = 516.691


Vals: {{Val list| 7, 65, 72 }}
Vals: {{Val list| 7, 65, 72, 353cd }}


Badness: 0.034773
Badness: 0.034773


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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POTE generator: ~27/20 = 516.667
POTE generator: ~27/20 = 516.667


Vals: {{Val list| 7, 65f, 72, 79 }}
Vals: {{Val list| 7, 65f, 72 }}


Badness: 0.027584
Badness: 0.027584


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Gravity]]
[[Category:Gravity]]
[[Category:Gravity family| ]] <!-- main article -->
[[Category:Gravity family| ]] <!-- main article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Gravity_family"