Subgroup temperaments: Difference between revisions

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 [[Tp tuning #T2 tuning|RMS error]]: 0.0586 cents
+=== Mercy ===
+Two generators make an [[8/7]]; seven generators make a [[8/5]]. Mercy can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]], and is the no-threes or elevens version of [[miracle]].
+Subgroup: 2.5.7
+[[Comma]]: 823543/819200
+[[Gencom]]: [2 2744/2560; 823543/819200]
+[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 }}, {{val|0 0 -7 -2}}]
+[[Mapping|Sval mapping]]: [{{val|1 3 3 }}, {{val|0 -7 -2}}]
+[[Tp tuning|POL2 generator]]: ~2744/2560 = 116.291
+{{Val list|legend=1| 10, 21, 31}}
+==== '''2.5.7.13''' ====
+Subgroup: 2.5.7.13
+[[Comma list]]: 343/338, 640/637
+[[Gencom]]: [2 14/13; 343/338 640/637]
+[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4}}, {{val|0 0 -7 -2 -3}}]
+[[Mapping|Sval mapping]]: [{{val|1 3 3 4}}, {{val|0 -7 -2 -3}}]
+[[Tp tuning|POL2 generator]]: ~14/13 = 116.094
+{{Val list|legend=1| 10, 21, 31}}
+==== 2.5.7.13.17 ====
+Subgroup: 2.5.7.13.17
+[[Comma list]]: 170/169, 224/221, 640/637
+[[Gencom]]: [2 14/13; 170/169 224/221 640/637]
+[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4}}, {{val|0 0 -7 -2 -3 1}}]
+[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4}}, {{val|0 -7 -2 -3 1}}]
+[[Tp tuning|POL2 generator]]: ~14/13 = 115.769
+{{Val list|legend=1| 10, 21, 31}}
+==== 2.5.7.13.17.19 ====
+Subgroup: 2.5.7.13.17.19
+[[Comma list]]: 170/169, 343/338, 640/637, 16384/16055
+[[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055]
+[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4 3}}, {{val|0 0 -7 -2 -3 1 13}}]
+[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4 3}}, {{val|0 -7 -2 -3 1 13}}]
+[[Tp tuning|POL2 generator]]: ~14/13 = 115.716
+{{Val list|legend=1| 10, 21, 31, 52f}}
 == 2.9.7.11 subgroup ==

Subgroup temperaments: Difference between revisions

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