Ragismic family: Difference between revisions

The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]].

* ''[[Sensigh]]'' → [[Sensamagic family #Sensigh|Sensamagic family]]

* ''[[Catakleismoid]]'' → [[Marvel family #Catakleismoid|Marvel family]]

* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]]

Considered below are beyla, ulmo, thor, heimdall, bragi, and vidar.

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }}

: mapping generators: ~2, ~3, ~5

[[Mapping to lattice]]: [{{val| 0 -1 -1 -3 }}, {{val| 0 -1 -2 1 }}]

* [[7-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

* [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

{{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}

[[Projection pair]]: ~7 = ~4374/625

Scales: [[Ragismic19]], [[Ragismic chromatic]]

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 385/384, 4375/4374

{{Mapping|legend=1| 1 0 0 1 6 | 0 1 0 7 -6 | 0 0 1 -4 3 }}

{{Optimal ET sequence|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}

[[Badness]]: 0.721 × 10^-3

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 385/384

Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }}

{{Optimal ET sequence|legend=1| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}

 

Badness: 0.840 × 10^-3

 

== Ulmo ==

[[Subgroup]]: 2.3.5.7.11

 

[[Comma list]]: 176/175, 2200/2187

 

{{Mapping|legend=1| 1 0 0 1 -3 | 0 1 0 7 7 | 0 0 1 -4 -2 }}

 

{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}

 

[[Badness]]: 1.23 × 10^-3

 

Subgroup: 2.3.5.7.11.13

 

Comma list: 169/168, 176/175, 325/324

 

Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }}

 

{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}

 

Badness: 0.932 × 10^-3

 

[[Subgroup]]: 2.3.5.7.11

 

[[Comma list]]: 3025/3024, 4375/4374

 

{{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }}

 

: mapping generators: ~99/70, ~3, ~5

 

* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5

 

{{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}

 

[[Badness]]: 0.0888 × 10^-3

 

[[Projection pair]]s: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11

 

=== Thunor ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 1716/1715, 2080/2079, 3025/3024

 

Mapping: {{mapping| 2 0 0 2 5 -3 | 0 1 0 7 5 15 | 0 0 1 -4 -3 -8 }}

 

Mapping to lattice: [{{val| 0 -1 -2 -3 -2 -7 }}, {{val| 0 -1 -2 1 1 1 }}] 

 

: 10/9 length = 0.4234, 6/5 length = 0.8426

: Angle (10/9, 6/5) = 84.126°

 

* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13

 

{{Optimal ET sequence|legend=1| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}

 

Badness: 0.341 × 10^-3

 

Subgroup: 2.3.5.7.11.13

 

Comma list: 3025/3024, 4096/4095, 4375/4374

 

Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }}

 

{{Optimal ET sequence|legend=1| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}

 

Badness: 0.549 × 10^-3

 

=== Donar ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 3025/3024, 4225/4224, 4375/4374

 

Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}

 

: mapping generators: ~99/70, ~3, ~220/117

 

Mapping to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 0 -1 -2 1 1 2 }}]

 

Lattice basis:

: 44/39 length = 0.3480, 6/5 length = 0.7828

: Angle (44/39, 6/5) = 85.3977°

 

Minimax tuning:

* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5

* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11

 

{{Optimal ET sequence|legend=1| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}

 

Badness: 0.322 × 10^-3

 

Scales: [[Donar46]]

 

== Heimdall ==

[[Subgroup]]: 2.3.5.7.11

 

[[Comma list]]: 4375/4374, 117649/117612

 

{{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }}

 

: mapping generators: ~2, ~343/198, ~5

 

{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}

 

 

[[Comma list]]: 4375/4374, 2097152/2096325

 

{{Mapping|legend=1| 1 0 2 -7 8 | 0 1 0 7 -3 | 0 0 3 -12 2 }}

 

: mapping generators: ~2, ~3, ~320/297

 

{{Optimal ET sequence|legend=1| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}

 

Subgroup: 2.3.5.7.11.13

 

Comma list: 2080/2079, 4375/4374, 10985/10976

 

Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }}

 

{{Optimal ET sequence|legend=1| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}

 

[[Subgroup]]: 2.3.5.7.11

 

 

{{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }}

 

: mapping generators: ~2, ~3, ~96/55

 

{{Optimal ET sequence|legend=1| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 4225/4224, 4375/4374, 6656/6655

 

Mapping: {{mapping| 1 0 0 1 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }}

 

{{Optimal ET sequence|legend=1| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}

 

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Ragismic family| ]] <!-- main article -->

[[Category:Ragismic| ]] <!-- key article -->

[[Category:Rank 3]]