Ragismic microtemperaments: Difference between revisions

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 435.082

=== Semisupermajor ===

{{Optimal ET sequence|legend=1| 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf }}

== Enneadecal ==

{{Mapping|legend=1| 19 0 14 -37 | 0 1 1 3 }}

[[Optimal tuning]] ([[CTE]]): ~28/27 = 1\19, ~3/2 = 701.9275 (~225/224 = 7.1907)

{{Optimal ET sequence|legend=1| 19, …, 152, 171, 665, 836, 1007, 2185, 3192c }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 19, 133d, 152, 323e, 475de, 627de }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19, 133df, 152f, 323ef }}

=== Hemienneadecal ===

Mapping: {{mapping| 38 0 28 -74 11 | 0 1 1 3 2 }}

Optimal tuning (CTE): ~55/54 = 1\38, ~3/2 = 701.9351 (~225/224 = 7.1983)

{{Optimal ET sequence|legend=1| 152, 342, 836, 1178, 2014, 3192ce, 5206ce }}

==== Hemienneadecalis ====

{{Optimal ET sequence|legend=1| 152f, 342f, 494 }}

==== Hemienneadec ====

{{Optimal ET sequence|legend=1| 152, 342, 494, 1330, 1824, 2318d }}

==== Semihemienneadecal ====

Mapping: {{mapping| 38 1 29 -71 13 111 | 0 2 2 6 4 1 }}

Optimal tuning (CTE): ~429/250 = 935.1789 (~144/143 = 12.1895)

{{Optimal ET sequence|legend=1| 190, 304d, 494, 684, 1178, 2850, 4028ce }}

=== Kalium ===

{{Optimal ET sequence|legend=1| 855, 988, 1843 }}

== Semidimi ==

{{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}

== Brahmagupta ==

{{Mapping|legend=1| 7 2 -8 53 | 0 3 8 -11 }}

[[Optimal tuning]] ([[POTE]]): ~1157625/1048576 = 1\7, ~27/20 = 519.716

=== 11-limit ===

{{Optimal ET sequence|legend=1| 7, 217, 224, 441, 665, 1771ee }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 7, 217, 224, 441, 665, 1771eef }}

== Abigail ==

{{Mapping|legend=1| 2 7 13 -1 | 0 -11 -24 19 }}

[[Optimal tuning]] ([[POTE]]): ~46305/32768 = 1\2, ~6912/6125 = 208.899

{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 764 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 46, 178, 224, 270, 494, 764, 1258 }}

== Gamera ==

{{Mapping|legend=1| 1 6 10 3 | 0 -23 -40 -1 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 230.336

{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 422, 745d }}

=== Hemigamera ===

Mapping: {{mapping| 2 12 20 6 5 | 0 -23 -40 -1 5 }}

Optimal tuning (POTE): ~99/70 = 1\2, ~8/7 = 230.3370

{{Optimal ET sequence|legend=1| 26, 198, 224, 422, 646, 1068d }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 26, 198, 224, 422, 646f, 1068df }}

=== Semigamera ===

Mapping: {{mapping| 1 6 10 3 12 | 0 -46 -80 -2 -89 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.1642

{{Optimal ET sequence|legend=1| 73, 125, 198, 323, 521 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 73f, 125f, 198, 323, 521 }}

== Crazy ==

{{Mapping|legend=1| 2 1 6 -15 | 0 8 -5 76 }}

[[Optimal tuning]]s:  

{{Optimal ET sequence|legend=1| 118, 376, 494, 612, 1106, 1718 }}

=== 11-limit ===

{{Optimal ET sequence|legend=0| 118, 376, 494, 612, 1106, 2824, 3930e }}

== Orga ==

{{Mapping|legend=1| 2 21 36 5 | 0 -29 -51 1 }}

[[Optimal tuning]] ([[POTE]]): ~7411887/5242880 = 1\2, ~8/7 = 231.104

{{Optimal ET sequence|legend=1| 26, 244, 270, 836, 1106, 1376, 2482 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 26, 244, 270, 566, 836, 1106 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 26, 244, 270, 566, 836f, 1106f }}

== Seniority ==

{{Optimal ET sequence|legend=1| 26, 145, 171, 1513d, 1684d, 1855d, 2026d, 2197d, 2368d, 2539d, 2710d }}

=== Senator ===

{{Optimal ET sequence|legend=1| 26, 119c, 145, 171, 316e, 487ee }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 26, 119c, 145, 171, 316ef, 487eef }}

==== 17-limit ====

{{Optimal ET sequence|legend=1| 26, 119c, 145, 171, 316ef, 487eef }}

== Monzismic ==

{{Optimal ET sequence|legend=1| 53, …, 559, 612, 1277, 1889 }}

=== Monzism ===

{{Optimal ET sequence|legend=1| 53, 559, 612 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 53, 559, 612 }}

== Semidimfourth ==

{{Optimal ET sequence|legend=1| 8d, 91, 99, 289, 388, 875, 1263d, 1651d }}

=== Neusec ===

{{Optimal ET sequence|legend=1| 8d, 190, 388 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 8d, 190, 198, 388 }}

== Acrokleismic ==

{{Optimal ET sequence|legend=1| 19, …, 251, 270, 2449c, 2719c, 2989bc }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 19, 251, 270, 829, 1099, 1369, 1639 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19, 251, 270 }}

=== Counteracro ===

{{Optimal ET sequence|legend=1| 19e, 251e, 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19e, 251e, 270, 1331c, 1601c, 1871bcf, 2141bcf }}

== Quasithird ==

{{Mapping|legend=1| 4 0 -11 | 0 5 16 }}

[[Optimal tuning]] ([[POTE]]): ~51200000/43046721, ~1594323/1280000 = 380.395

{{Optimal ET sequence|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}

=== 7-limit ===

{{Optimal ET sequence|legend=1| 60d, 164, 224, 388, 612, 1448, 2060 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 60d, 164, 224, 388, 612, 836, 1448 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 60d, 164, 224, 388, 612, 836, 1448f, 2284f }}

== Deca ==

{{Mapping|legend=1| 10 4 9 2 | 0 5 6 11 }}

[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~6/5 = 315.577

Badness (Sintel): 0.695

Subgroup: 2.3.5.7.11.13.19

{{Mapping|legend=1| 1 2 3 3 | 0 -112 -183 -52 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 21 3 1 -10 }} = 4.4465

{{Optimal ET sequence|legend=1| 270, 1079, 1349, 1619, 1889, 2159, 4048, 18081cd }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 270, 1349, 1619, 1889, 2159, 11065, 13224 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 270, 1079, 1349, 1619, 1889, 4048 }}

== Aluminium ==

Aluminium is named after the 13th element, and tempers out the {{monzo| 92 -39 -13 }} comma which sets [[135/128]] interval to be equal to 1/13th of the octave.

[[Subgroup]]: 2.3.5.7

[[Mapping]]: {{mapping| 13 0 92 -355 | 0 1 -3 19 }}

[[Optimal tuning]] ([[CTE]]): ~135/128 = 1\13, ~3/2 = 702.0024

{{Optimal ET sequence|legend=1| 494, 1053, 1547, 8788, 10335, 11882, 13429b, 14976b }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 494, 1053, 1547, 3588e, 5135e }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 494, 1547, 2041, 4576def }}

== Countritonic ==

{{Mapping|legend=1| 1 6 19 -33 | 0 -9 -34 73 }}

[[Optimal tuning]] (CTE): ~2 = 1\1, ~45927/32768 = 588.6216

{{Optimal ET sequence|legend=1| 53, 210d, 263, 316, 369, 422, 791, 1213cd, 2004bcdd }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 53, 316e, 369, 422, 791e, 1213cde }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 53, 316ef, 369f, 422, 1213cdeff, 1635bcdefff }}

== Quatracot ==

{{Mapping|legend=1| 2 7 7 23 | 0 -13 -8 -59 }}

[[Optimal tuning]] ([[POTE]]): ~2278125/1605632 = 1\2, ~448/405 = 176.805

{{Optimal ET sequence|legend=1| 190, 224, 414, 638, 1052c, 1690bcc }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 190, 224, 414, 638, 1052c }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 190, 224, 414, 638, 1690bcc, 2328bccde }}

== Moulin ==

{{Mapping|legend=1| 1 57 38 248 | 0 -73 -47 -323 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6422528/3796875 = 910.9323

{{Optimal ET sequence|legend=1| 494, 1125, 1619 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 494, 1125, 1619, 2113 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 494, 1125, 1619, 2113 }}

== Palladium ==

{{Mapping|legend=1| 46 0 -39 202 | 0 1 2 -1 }}

[[Optimal tuning]] ([[POTE]]): ~83349/81920 = 1\46, ~3/2 = 701.6074

{{Optimal ET sequence|legend=1| 46, 368, 414, 460, 874d }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 46, 368, 414, 460, 874de }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 46, 368, 414, 460, 874de, 1334de }}

=== 17-limit ===

{{Optimal ET sequence|legend=1| 46, 368, 414, 460, 874de, 1334deg }}

== Oviminor ==

{{Mapping|legend=1| 1 50 51 147 | 0 -184 -185 -548 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 315.7501

{{Optimal ET sequence|legend=1| 19, …, 1600, 1619, 4838, 6457c }}

== Octoid ==

{{Mapping|legend=1| 8 1 3 3 | 0 3 4 5 }}

[[Optimal tuning]] ([[POTE]]): ~49/45 = 1\8, ~7/5 = 583.940

{{Optimal ET sequence|legend=1| 8d, 72, 152, 224 }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152, 224 }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152f, 224 }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152fg, 224, 296, 520g }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152fg, 224 }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152, 224f }}

Scales: [[octoid72]], [[octoid80]]

{{Optimal ET sequence|legend=1| 72, 152, 224fg, 296ffg }}

Scales: [[Octoid72]], [[Octoid80]]

{{Optimal ET sequence|legend=1| 72, 152, 224fg, 376ffgh }}

Scales: [[Octoid72]], [[Octoid80]]

{{Optimal ET sequence|legend=1| 80, 144, 224 }}

===== 17-limit =====

{{Optimal ET sequence|legend=1| 80, 144, 224, 528dg }}

===== 19-limit =====

{{Optimal ET sequence|legend=1| 80, 144, 224, 304dh, 528dghh }}

== Parakleismic ==

{{Optimal ET sequence|legend=1| 19, 61, 80, 99, 118, 453, 571, 689, 1496 }}

=== 7-limit ===

{{Optimal ET sequence|legend=1| 19, 80, 99, 217, 316, 415 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 19, 99, 118 }}

=== Paralytic ===

{{Optimal ET sequence|legend=1| 19e, 99e, 118, 217, 335, 552d, 887dd }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 99e, 118, 217, 552d, 769de }}

==== Paraklein ====

{{Optimal ET sequence|legend=1| 19e, 99ef, 118, 217ff, 335ff }}

=== Parkleismic ===

{{Optimal ET sequence|legend=1| 19e, 80, 179, 259cd }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19e, 80, 179 }}

=== Paradigmic ===

{{Optimal ET sequence|legend=1| 19, 61d, 80, 99e, 179e }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19, 61d, 80, 99e, 179e }}

=== Semiparakleismic ===

{{Optimal ET sequence|legend=1| 80, 118, 198, 316, 514c, 830c }}

==== Semiparamint ====

{{Optimal ET sequence|legend=1| 80, 118, 198 }}

==== Semiparawolf ====

{{Optimal ET sequence|legend=1| 80, 118f, 198f }}

== Counterkleismic ==

{{Mapping|legend=1| 1 20 20 61 | 0 -25 -24 -79 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.060

{{Optimal ET sequence|legend=1| 19, 205, 224, 243, 467 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 19, 205, 224 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19, 205, 224, 1587cde, 1811ccdef, 2035ccddeef, 2259ccddeef, 2483ccddeef, 2707ccddeef }}

=== Counterlytic ===

{{Optimal ET sequence|legend=1| 19e, 205e, 224 }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 19e, 205e, 224 }}

== Quincy ==

{{Optimal ET sequence|legend=1| 72, 217, 289 }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 72, 217, 289 }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 72, 145, 217, 289 }}

=== 17-limit ===

{{Optimal ET sequence|legend=1| 72, 145, 217, 289 }}

=== 19-limit ===

{{Optimal ET sequence|legend=1| 72, 145, 217 }}

== Sfourth ==

{{Optimal ET sequence|legend=1| 45, 46, 91, 137d }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 45e, 46, 91e, 137de }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 45ef, 46, 91ef, 137def }}

=== Sfour ===

{{Optimal ET sequence|legend=1| 45, 46, 91, 137d }}

==== 13-limit ====

{{Optimal ET sequence|legend=1| 45, 46, 91, 137d }}

== Trideci ==

The trideci temperament (26 & 65) has a period of 1/13 octave and tempers out 245/242 and 385/384 in the 11-limit. It tempers out the same 5-limit comma as the [[Octagar temperaments #Tridecatonic|tridecatonic temperament]], but with the ragisma (4375/4374) rather than the octagar (4000/3969) tempered out. The name ''trideci'' comes from "tridecim" (Latin for "[[wikipedia:13|thirteen]]").

{{Optimal ET sequence|legend=1| 26, 65, 91, 156d, 247cdd }}

=== 11-limit ===

{{Optimal ET sequence|legend=1| 26, 65, 91, 156d, 247cdde }}

=== 13-limit ===

{{Optimal ET sequence|legend=1| 26, 65f, 91f, 156dff }}

== Counterorson ==

{{Optimal ET sequence|legend=1| 53, …, 1612, 1665, 1718 }}

== Notes ==