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Gravity family: Difference between revisions

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


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.844
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~27/20 = 516.844{{c}}


{{Optimal ET sequence|legend=1| 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469 }}
{{Optimal ET sequence|legend=1| 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469 }}


[[Badness]]: 0.093184
[[Badness]] (Smith): 0.093184


=== Overview to extensions ===
=== Overview to extensions ===
Full 7-limit extensions of gravity include marvo (65d & 72), zarvo (65 & 72), gravid (58 & 65), and harry (58 & 72), all considered below. A notable subgroup extension is larry.
Full 7-limit extensions of gravity include marvo ({{nowrap| 65d & 72 }}), zarvo ({{nowrap| 65 & 72 }}), gravid ({{nowrap| 58 & 65 }}), and harry ({{nowrap| 58 & 72 }}), all considered below. A notable subgroup extension is larry.


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]]}.
There is also an unnamed {{nowrap| 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]]}.


=== 2.3.5.11 subgroup (larry) ===
=== 2.3.5.11 subgroup (larry) ===
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Comma list: 243/242, 4000/3993
Comma list: 243/242, 4000/3993


Sval mapping: {{mapping| 1 5 12 12 | 0 -6 -17 -15 }}
Subgrop-val mapping: {{mapping| 1 5 12 12 | 0 -6 -17 -15 }}


Gencom mapping: {{mapping| 1 5 12 0 12 | 0 -6 -17 0 -15 }}
Gencom mapping: {{mapping| 1 5 12 0 12 | 0 -6 -17 0 -15 }}


: gencom: [2 40/27; 243/242 4000/3993]
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 516.834{{c}}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.834
{{Optimal ET sequence|legend=0| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}


{{Optimal ET sequence|legend=1| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}
Badness (Smith): 0.0125
 
Badness: 0.0125


== Marvo ==
== Marvo ==
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{{Mapping|legend=1| 1 5 12 29 | 0 -6 -17 -46 }}
{{Mapping|legend=1| 1 5 12 29 | 0 -6 -17 -46 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.694
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~27/20 = 516.694{{c}}


{{Optimal ET sequence|legend=1| 65d, 72, 137, 209, 281, 569bcc }}
{{Optimal ET sequence|legend=1| 65d, 72, 137, 209, 281, 569bcc }}


[[Badness]]: 0.097627
[[Badness]] (Smith): 0.097627


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 5 12 29 12 | 0 -6 -17 -46 -15 }}
Mapping: {{mapping| 1 5 12 29 12 | 0 -6 -17 -46 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.699
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 516.699{{c}}


{{Optimal ET sequence|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}
{{Optimal ET sequence|legend=0| 65d, 72, 281, 353c, 425bc, 497bc }}


Badness: 0.031685
Badness (Smith): 0.031685


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 5 12 29 12 39 | 0 -6 -17 -46 -15 -62 }}
Mapping: {{mapping| 1 5 12 29 12 39 | 0 -6 -17 -46 -15 -62 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.730
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 516.730{{c}}


{{Optimal ET sequence|legend=1| 65d, 72, 137, 209, 281f, 490bcf }}
{{Optimal ET sequence|legend=0| 65d, 72, 137, 209, 281f, 490bcf }}


Badness: 0.026882
Badness (Smith): 0.026882


== Zarvo ==
== Zarvo ==
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{{Mapping|legend=1| 1 5 12 -12 | 0 -6 -17 26 }}
{{Mapping|legend=1| 1 5 12 -12 | 0 -6 -17 26 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 516.702
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~27/20 = 516.702{{c}}


{{Optimal ET sequence|legend=1| 65, 72, 281d, 353cd, 425bcdd, 497bcdd }}
{{Optimal ET sequence|legend=1| 65, 72, 281d, 353cd, 425bcdd, 497bcdd }}


[[Badness]]: 0.096840
[[Badness]] (Smith): 0.096840


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 5 12 -12 12 | 0 -6 -17 26 -15 }}
Mapping: {{mapping| 1 5 12 -12 12 | 0 -6 -17 26 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.691
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 516.691{{c}}


{{Optimal ET sequence|legend=1| 65, 72, 353cd }}
{{Optimal ET sequence|legend=0| 65, 72, 353cd }}


Badness: 0.034773
Badness (Smith): 0.034773


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 5 12 -12 12 -2 | 0 -6 -17 26 -15 10 }}
Mapping: {{mapping| 1 5 12 -12 12 -2 | 0 -6 -17 26 -15 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.667
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 516.667{{c}}


{{Optimal ET sequence|legend=1| 65f, 72 }}
{{Optimal ET sequence|legend=0| 65f, 72 }}


Badness: 0.027584
Badness (Smith): 0.027584


== Gravid ==
== Gravid ==
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{{Mapping|legend=1| 1 5 12 25 | 0 -6 -17 -39 }}
{{Mapping|legend=1| 1 5 12 25 | 0 -6 -17 -39 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/20 = 517.140
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~27/20 = 517.140{{c}}


{{Optimal ET sequence|legend=1| 58, 123, 181c }}
{{Optimal ET sequence|legend=1| 58, 123, 181c }}


[[Badness]]: 0.131153
[[Badness]] (Smith): 0.131153


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 5 12 25 12 | 0 -6 -17 -39 -15 }}
Mapping: {{mapping| 1 5 12 25 12 | 0 -6 -17 -39 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 517.155
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/20 = 517.155{{c}}


{{Optimal ET sequence|legend=1| 58, 123, 181ce }}
{{Optimal ET sequence|legend=0| 58, 123, 181ce }}


Badness: 0.047283
Badness (Smith): 0.047283


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


[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/20 = 516.844 (~21/20 = 83.156)
[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~27/20 = 516.844{{c}} (~21/20 = 83.156{{c}})


{{Optimal ET sequence|legend=1| 14c, 58, 72, 130, 202, 534, 736b, 938b }}
{{Optimal ET sequence|legend=1| 14c, 58, 72, 130, 202, 534, 736b, 938b }}


[[Badness]]: 0.034077
[[Badness]] (Smith): 0.034077


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 4 7 7 9 | 0 -6 -17 -10 -15 }}
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 tuning (POTE): ~99/70 = 600.000{{c}}, ~27/20 = 516.833{{c}} (~21/20 = 83.167{{c}})


{{Optimal ET sequence|legend=1| 14c, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=0| 14c, 58, 72, 130, 202 }}


Badness: 0.015867
Badness (Smith): 0.015867


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 2 4 7 7 9 11 | 0 -6 -17 -10 -15 -26 }}
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 tuning (POTE): ~55/39 = 600.000{{c}}, ~27/20 = 516.884{{c}} (~21/20 = 83.116{{c}})


{{Optimal ET sequence|legend=1| 14cf, 58, 72, 130, 332f, 462ef }}
{{Optimal ET sequence|legend=0| 14cf, 58, 72, 130, 332f, 462ef }}


Badness: 0.013046
Badness (Smith): 0.013046


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 2 4 7 7 9 11 9 | 0 -6 -17 -10 -15 -26 -6 }}
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 tuning (POTE): ~17/12 = 600.000{{c}}, ~27/20 = 516.832{{c}} (~21/20 = 83.168{{c}})


{{Optimal ET sequence|legend=1| 14cf, 58, 72, 130, 202g }}
{{Optimal ET sequence|legend=0| 14cf, 58, 72, 130, 202g }}


Badness: 0.012657
Badness (Smith): 0.012657


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Gravity_family"