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#REDIRECT [[Quartonic]]
{{Technical data page}}
The '''quartonic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[quartonic comma]] ({{monzo|legend=1| 3 -18 11 }}, [[ratio]]: 390 625 000 / 387 420 489).
 
== Quartonic ==
The name ''quartonic'' refers to the [[quartertone]], since a somewhat flattened quartertone (representing the triptolemaic chromatic semitone, i.e. [[porcupine comma]]) is the [[generator]] of this temperament. The [[ploidacot]] for the temperament is omega-hendecacot, with eleven generator steps giving the [[4/3|perfect fourth]]. It is a member of the [[schismic–Mercator equivalence continuum]], with equivalence number ''n'' = 11/2.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 390625000/387420489
 
{{Mapping|legend=1| 1 2 3 | 0 -11 -18 }}
: mapping generators: ~2, ~250/243
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9709{{c}}, ~250/243 = 45.2318{{c}}
: [[error map]]: {{val| -0.029 +0.437 -0.574 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~250/243 = 45.2349{{c}}
: error map: {{val| 0.000 +0.461 -0.541 }}
 
{{Optimal ET sequence|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
 
[[Badness]] (Sintel): 2.75
 
=== Overview to extensions ===
The second comma of the [[Normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at.
* [[1728/1715]] or [[4000/3969]] gives septimal quartonic, with interpretation of the generator ~36/35. It also tempers out [[4375/4374]].
* [[10976/10935]] gives yarman I (80 & 159) and slices the quartonic generator in three.
* 5359375/5308416 gives yarman II (79 & 159) and slices the quartonic generator in three.
* [[2401/2400]] gives tertiseptisix (27 & 212) with generator ~875/729, three of them give ~12/7, and four give ~250/243 with octave reduction.
* [[250047/250000]] gives triquart (27 & 159) with 1/3-octave period.
* [[390625/388962]] or [[4802000/4782969]] gives quartiquart (80 & 212) with 1/4-octave period.
* [[16875/16807]] gives quintiquart (80 & 265) with 1/5-octave period.
 
== Septimal quartonic ==
Septimal quartonic tempers out the [[orwellisma]], the [[octagar comma]], as well as the [[ragisma]], and may be described as the {{nowrap| 26 & 27 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 4000/3969
 
{{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.1424{{c}}, ~36/35 = 45.1064{{c}}
: [[error map]]: {{val| -0.858 +0.160 -0.801 +3.069 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 45.1881{{c}}
: error map: {{val| 0.000 +0.976 +0.301 +5.234 }}
 
{{Optimal ET sequence|legend=1| 26, 27, 53, 80, 133d, 186d, 319dd }}
 
[[Badness]] (Sintel): 1.08
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 540/539, 2200/2187
 
{{Mapping|legend=0| 1 2 3 3 5 | 0 -11 -18 -5 -41 }}
 
Optimal tunings:
* WE: ~2 = 1198.8787{{c}}, ~36/35 = 44.9994{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 45.0863{{c}}
 
{{Optimal ET sequence|legend=0| 26e, 27e, 53, 80 }}
 
Badness (Sintel): 1.13
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 176/175, 325/324, 540/539
 
{{Mapping|legend=0| 1 2 3 3 5 4 | 0 -11 -18 -5 -41 -8 }}
 
Optimal tunings:
* WE: ~2 = 1199.2991{{c}}, ~36/35 = 45.0539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 45.1049{{c}}
 
{{Optimal ET sequence|legend=0| 26e, 27e, 53, 80, 133d }}
 
Badness (Sintel): 0.987
 
=== Quarto ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 245/242, 864/847
 
{{Mapping|legend=0| 1 2 3 3 4 | 0 -11 -18 -5 -14 }}
 
Optimal tunings:
* WE: ~2 = 1198.3094{{c}}, ~36/35 = 45.0688{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 45.2329{{c}}
 
{{Optimal ET sequence|legend=0| 26, 27e, 53e, 80ee }}
 
Badness (Sintel): 1.38
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 78/77, 100/99, 144/143, 245/242
 
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -11 -18 -5 -14 -8 }}
 
Optimal tunings:
* WE: ~2 = 1198.9315{{c}}, ~36/35 = 45.1650{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 45.2640{{c}}
 
{{Optimal ET sequence|legend=0| 26, 27e, 53e }}
 
Badness (Sintel): 1.14
 
=== Quartz ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 385/384, 4000/3969
 
{{Mapping|legend=0| 1 2 3 3 3 | 0 -11 -18 -5 12 }}
 
Optimal tunings:
* WE: ~2 = 1200.5082{{c}}, ~33/32 = 45.4047{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 45.3739{{c}}
 
{{Optimal ET sequence|legend=0| 26, 53 }}
 
Badness (Sintel): 1.76
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 99/98, 169/168, 275/273, 385/384
 
{{Mapping|legend=0| 1 2 3 3 3 4 | 0 -11 -18 -5 12 -8 }}
 
Optimal tunings:
* WE: ~2 = 1200.5899{{c}}, ~33/32 = 45.4096{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 45.3739{{c}}
 
{{Optimal ET sequence|legend=0| 26, 53 }}
 
Badness (Sintel): 1.19
 
=== Biquartonic ===
Subgroup: 2.3.5.7.11
 
Comma list: 1728/1715, 2420/2401, 2560/2541
 
{{Mapping|legend=0| 2 4 6 6 7 | 0 -11 -18 -5 -1 }}
: mapping generators: ~99/70, ~36/35
 
Optimal tunings:
* WE: ~99/70 = 599.5389{{c}}, ~36/35 = 45.0947{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~36/35 = 45.1692{{c}}
 
{{Optimal ET sequence|legend=0| 26, 54c, 80, 186de, 266dde }}
 
Badness (Sintel): 2.01
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 364/363, 640/637
 
{{Mapping|legend=0| 2 4 6 6 7 8 | 0 -11 -18 -5 -1 -8 }}
 
Optimal tunings:
* WE: ~55/39 = 599.6870{{c}}, ~40/39 = 45.1293{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~40/39 = 45.1789{{c}}
 
{{Optimal ET sequence|legend=0| 26, 54c, 80, 106 }}
 
Badness (Sintel): 1.65
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 289/288, 325/324, 544/539
 
{{Mapping|legend=0| 2 4 6 6 7 8 9 | 0 -11 -18 -5 -1 -8 -11 }}
 
Optimal tunings:
* WE: ~17/12 = 599.7706{{c}}, ~40/39 = 45.1427{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~40/39 = 45.1790{{c}}
 
{{Optimal ET sequence|legend=0| 26, 54c, 80, 106 }}
 
Badness (Sintel): 1.43
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 169/168, 221/220, 289/288, 325/324, 544/539, 400/399
 
{{Mapping|legend=0| 2 4 6 6 7 8 9 10 | 0 -11 -18 -5 -1 -8 -11 -20 }}
 
Optimal tunings:
* WE: ~17/12 = 599.7848{{c}}, ~39/38 = 45.1288{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~39/38 = 45.1634{{c}}
 
{{Optimal ET sequence|legend=0| 26, 54ch, 80, 106 }}
 
Badness (Sintel): 1.30
 
=== Yarm ===
Subgroup: 2.3.5.7.11
 
Comma list: 1331/1323, 1728/1715, 4000/3969
 
{{Mapping|legend=0| 1 2 3 3 4 | 0 -33 -54 -15 -43 }}
 
Optimal tunings:
* WE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0363{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0617{{c}}
 
{{Optimal ET sequence|legend=0| 79, 80, 239dd }}
 
Badness (Sintel): 3.30
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 640/637, 1331/1323
 
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -33 -54 -15 -43 -24 }}
 
Optimal tunings:
* WE: ~2 = 1199.5798{{c}}, ~100/99 = 15.0551{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0681{{c}}
 
{{Optimal ET sequence|legend=0| 79, 80 }}
 
Badness (Sintel): 2.55
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
 
{{Mapping|legend=0| 1 2 3 3 4 4 4 | 0 -33 -54 -15 -43 -24 7 }}
 
Optimal tunings:
* WE: ~2 = 1199.6800{{c}}, ~100/99 = 15.0624{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0705{{c}}
 
{{Optimal ET sequence|legend=0| 79, 80 }}
 
Badness (Sintel): 2.38
 
== Yarman I ==
Yarman I is the first interpretation of [[Ozan Yarman]]'s proposed tuning for the Turkish makam.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 10976/10935, 244140625/243045684
 
{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}
: mapping generators: ~2, ~126/125
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8726{{c}}, ~126/125 = 15.0651{{c}}
: [[error map]]: {{val| -0.127 +0.641 -0.213 -0.523 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~126/125 = 15.0689{{c}}
: error map: {{val| 0.000 +0.771 -0.036 -0.374 }}
 
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239, 637, 876b }}
 
[[Badness]] (Sintel): 4.89
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 4000/3993, 10976/10935
 
{{Mapping|legend=0| 1 2 3 4 4 | 0 -33 -54 -95 -43 }}
 
Optimal tunings:
* WE: ~2 = 1199.8339{{c}}, ~100/99 = 15.0637{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0685{{c}}
 
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 876be }}
 
Badness (Sintel): 1.63
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 364/363, 1001/1000, 10976/10935
 
{{Mapping|legend=0| 1 2 3 4 4 4 | 0 -33 -54 -95 -43 -24 }}
 
Optimal tunings:
* WE: ~2 = 1200.1080{{c}}, ~100/99 = 15.0766{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0737{{c}}
 
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f }}
 
Badness (Sintel): 1.69
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935
 
{{Mapping|legend=0| 1 2 3 4 4 4 4 | 0 -33 -54 -95 -43 -24 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.0222{{c}}, ~100/99 = 15.0718{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0713{{c}}
 
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f }}
 
Badness (Sintel): 1.58
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 325/324, 361/360, 364/363, 595/594, 969/968, 1001/1000
 
{{Mapping|legend=0| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}
 
Optimal tunings:
* WE: ~2 = 1200.0698{{c}}, ~100/99 = 15.0722{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0706{{c}}
 
{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 398fh }}
 
Badness (Sintel): 1.41
 
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 325/324, 361/360, 364/363, 460/459, 507/506, 529/528, 760/759
 
{{Mapping|legend=0| 1 2 3 4 4 4 4 5 5 | 0 -33 -54 -95 -43 -24 7 -60 -38 }}
 
Optimal tunings:
* WE: ~2 = 1200.0946{{c}}, ~100/99 = 15.0732{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0710{{c}}
 
{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 398fh }}
 
Badness (Sintel): 1.27
 
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 325/324, 361/360, 364/363, 406/405, 460/459, 494/493, 507/506, 529/528
 
{{Mapping|legend=0| 1 2 3 4 4 4 4 5 5 6 | 0 -33 -54 -95 -43 -24 7 -60 -38 -91 }}
 
Optimal tunings:
* WE: ~2 = 1200.0995{{c}}, ~100/99 = 15.0726{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0703{{c}}
 
{{Optimal ET sequence|legend=0| 79dhj, 80, 159, 239, 398fh }}
 
Badness (Sintel): 1.19
 
== Yarman II ==
Yarman II is the other interpretation of [[Ozan Yarman]]'s proposed tuning for the Turkish makam.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 5359375/5308416, 390625000/387420489
 
{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}
: mapping generators: ~2, ~875/864
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4734{{c}}, ~875/864 = 15.1122{{c}}
: [[error map]]: {{val| +0.473 +0.291 -0.950 -0.701 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~875/864 = 15.1048{{c}}
: error map: {{val| 0.000 -0.412 -1.971 -2.121 }}
 
{{Optimal ET sequence|legend=1| 79, 159, 397cd, 556cd, 715ccdd }}
 
[[Badness]] (Sintel): 16.6
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 4000/3993, 78121827/77948684
 
{{Mapping|legend=0| 1 2 3 2 4 | 0 -33 -54 64 -43 }}
 
Optimal tunings:
* WE: ~2 = 1200.4357{{c}}, ~100/99 = 15.1126{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1054{{c}}
 
{{Optimal ET sequence|legend=0| 79, 159, 397cd, 556cd }}
 
Badness (Sintel): 4.74
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 385/384, 1575/1573, 85683/85184
 
{{Mapping|legend=0| 1 2 3 2 4 4 | 0 -33 -54 64 -43 -24 }}
 
Optimal tunings:
* WE: ~2 = 1200.5028{{c}}, ~100/99 = 15.1135{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1052{{c}}
 
{{Optimal ET sequence|legend=0| 79, 159, 397cdff, 556cdff }}
 
Badness (Sintel): 2.82
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913
 
{{Mapping|legend=0| 1 2 3 2 4 4 4 | 0 -33 -54 64 -43 -24 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.3840{{c}}, ~100/99 = 15.1086{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1025{{c}}
 
{{Optimal ET sequence|legend=0| 79, 159 }}
 
Badness (Sintel): 2.60
 
== Tertiseptisix ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 390625000/387420489
 
{{Mapping|legend=1| 1 -31 -51 -32 | 0 44 72 47 }}
: mapping generators: ~2, ~1458/875
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0156{{c}}, ~1458/875 = 888.7028{{c}}
: [[error map]]: {{val| +0.016 +0.485 -0.507 -0.293 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1458/875 = 888.6915{{c}}
: error map: {{val| 0.000 +0.472 -0.523 -0.324 }}
 
{{Optimal ET sequence|legend=1| 27, …, 212, 239, 451 }}
 
[[Badness]] (Sintel): 3.95
 
== Triquart ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 117649/116640, 250047/250000
 
{{Mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}
: mapping generators: ~63/50, ~250/243
 
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 400.0521{{c}}, ~250/243 = 45.2373{{c}}
: [[error map]]: {{val| +0.156 +0.747 -0.117 -1.628 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~250/243 = 45.2204{{c}}
: error map: {{val| 0.000 +0.621 -0.281 -1.911 }}
 
{{Optimal ET sequence|legend=1| 27, 105cd, 132d, 159, 345d, 506d }}
 
[[Badness]] (Sintel): 4.30
 
== Quartiquart ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 390625/388962, 4802000/4782969
 
{{Mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}
: mapping generators: ~25/21, ~250/243
 
[[Optimal tuning]]s:
* [[WE]]: ~25/21 = 299.9955{{c}}, ~250/243 = 45.2382{{c}}
: [[error map]]: {{val| -0.018 +0.389 -0.655 +0.152 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~250/243 = 45.2400{{c}}
: error map: {{val| 0.000 +0.405 -0.634 +0.174 }}
 
{{Optimal ET sequence|legend=1| 80, 132d, 212, 292, 504 }}
 
[[Badness]] (Sintel): 5.04
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 1375/1372, 6250/6237, 14641/14580
 
{{Mapping|legend=0| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}
 
Optimal tunings:
* WE: ~25/21 = 300.0140{{c}}, ~77/75 = 45.2398{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~77/75 = 45.2342{{c}}
 
{{Optimal ET sequence|legend=0| 80, 132de, 212, 292, 504e }}
 
Badness (Sintel): 2.06
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 1001/1000, 1375/1372, 10648/10647
 
{{Mapping|legend=0| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}
 
Optimal tunings:
* WE: ~25/21 = 300.0805{{c}}, ~40/39 = 45.2812{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~40/39 = 45.2517{{c}}
 
{{Optimal ET sequence|legend=0| 80, 132de, 212 }}
 
Badness (Sintel): 1.86
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 289/288, 325/324, 561/560, 1001/1000, 10648/10647
 
{{Mapping|legend=0| 4 8 12 15 17 16 18 | 0 -11 -18 -25 -21 -8 -11 }}
 
Optimal tunings:
* WE: ~25/21 = 300.1108{{c}}, ~40/39 = 45.2990{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~40/39 = 45.2604{{c}}
 
{{Optimal ET sequence|legend=0| 80, 132deg, 212g }}
 
Badness (Sintel): 1.59
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 289/288, 325/324, 361/360, 561/560, 1001/1000, 1331/1330
 
{{Mapping|legend=0| 4 8 12 15 17 16 18 20 | 0 -11 -18 -25 -21 -8 -11 20 }}
 
Optimal tunings:
* WE: ~25/21 = 300.1212{{c}}, ~39/38 = 45.3015{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~39/38 = 45.2590{{c}}
 
{{Optimal ET sequence|legend=0| 80, 132degh, 212gh }}
 
Badness (Sintel): 1.36
 
== Quintiquart ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16875/16807, 390625000/387420489
 
{{Mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}
: mapping generators: ~35721/31250, ~250/243
 
[[Optimal tuning]]s:
* [[WE]]: ~35721/31250 = 239.9950{{c}}, ~250/243 = 45.2520{{c}}
: [[error map]]: {{val| -0.025 +0.223 -0.925 +0.792 }}
* [[CWE]]: ~35721/31250 = 240.0000{{c}}, ~250/243 = 45.2546{{c}}
: error map: {{val| 0.000 +0.244 -0.897 +0.826 }}
 
{{Optimal ET sequence|legend=1| 80, 185c, 265, 610d }}
 
[[Badness]] (Sintel): 9.04
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1375/1372, 390625000/387420489
 
{{Mapping|legend=0| 5 10 15 18 19 | 0 -11 -18 -21 -9 }}
 
Optimal tunings:
* WE: ~8019/7000 = 239.9613{{c}}, ~250/243 = 45.2270{{c}}
* CWE: ~8019/7000 = 240.0000{{c}}, ~250/243 = 45.2460{{c}}
 
{{Optimal ET sequence|legend=0| 80, 185c, 265, 345 }}
 
Badness (Sintel): 3.42
 
[[Category:Quartonic family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Quartonic_family"