Xenharmonic Wiki

Ragismic microtemperaments: Difference between revisions

← Older edit
VisualWikitext
Move chlorine back according to XW:TEMPCAT now that everything is sorted out
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,634 edits
No edit summary
 
(8 intermediate revisions by 2 users not shown)
Line 25: Line 25:
* [[Parakleismic]] (+3136/3125) → [[Parakleismic family #Septimal parakleismic|Parakleismic family]]
* [[Parakleismic]] (+3136/3125) → [[Parakleismic family #Septimal parakleismic|Parakleismic family]]
* ''[[Vishnu]]'' (+29360128/29296875) → [[Vishnu family #Septimal vishnu|Vishnu family]]
* ''[[Vishnu]]'' (+29360128/29296875) → [[Vishnu family #Septimal vishnu|Vishnu family]]
* ''[[Maja]]'' (+2430/2401 or 3125/3087) → [[Maja family #Septimal maja|Maja family]]
* ''[[Maja]]'' (+2430/2401 or 3125/3087) → [[Nuwell temperaments #Maja|Nuwell temperaments]]
* ''[[Mitonic]]'' (+2100875/2097152) → [[Minortone family #Mitonic|Minortone family]]
* ''[[Mitonic]]'' (+2100875/2097152) → [[Minortone family #Mitonic|Minortone family]]
* ''[[Vacuum]]'' (+{{monzo| -68 18 17 }}) → [[Vavoom family #Vacuum|Vavoom family]]
* ''[[Vacuum]]'' (+{{monzo| -68 18 17 }}) → [[Vavoom family #Vacuum|Vavoom family]]
* [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
* [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
* ''[[Dzelic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Dzelic|37th-octave temperaments]]
* [[Octoid]] (+16875/16807) → [[Stearnsmic clan #Octoid|Stearnsmic clan]]
* ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]]


Considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, octoid, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, and palladium.  
Considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, and palladium.  


== Supermajor ==
== Supermajor ==
Line 58: Line 59:
Comma list: 3025/3024, 4375/4374, 35156250/35153041
Comma list: 3025/3024, 4375/4374, 35156250/35153041


Mapping: {{mapping| 2 -7 -8 -15 -6 | 0 37 46 75 47 }}
{{Mapping|legend=0| 2 -7 -8 -15 -6 | 0 37 46 75 47 }}
: mapping generators: ~99/70, ~11/10
: mapping generators: ~99/70, ~11/10


Line 98: Line 99:
Comma list: 540/539, 4375/4374, 16384/16335
Comma list: 540/539, 4375/4374, 16384/16335


Mapping: {{mapping| 19 0 14 -37 126 | 0 1 1 3 -2 }}
{{Mapping|legend=0| 19 0 14 -37 126 | 0 1 1 3 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 113: Line 114:
Comma list: 540/539, 625/624, 729/728, 2205/2197
Comma list: 540/539, 625/624, 729/728, 2205/2197


Mapping: {{mapping| 19 0 14 -37 126 -20 | 0 1 1 3 -2 3 }}
{{Mapping|legend=0| 19 0 14 -37 126 -20 | 0 1 1 3 -2 3 }}


Optimal tunings:  
Optimal tunings:  
Line 128: Line 129:
Comma list: 3025/3024, 4375/4374, 234375/234256
Comma list: 3025/3024, 4375/4374, 234375/234256


Mapping: {{mapping| 38 0 28 -74 11 | 0 1 1 3 2 }}
{{Mapping|legend=0| 38 0 28 -74 11 | 0 1 1 3 2 }}
: mapping generators: ~55/54, ~3
: mapping generators: ~55/54, ~3


Line 144: Line 145:
Comma list: 1716/1715, 2080/2079, 3025/3024, 234375/234256
Comma list: 1716/1715, 2080/2079, 3025/3024, 234375/234256


Mapping: {{mapping| 38 0 28 -74 11 -281 | 0 1 1 3 2 7 }}
{{Mapping|legend=0| 38 0 28 -74 11 -281 | 0 1 1 3 2 7 }}


Optimal tunings:  
Optimal tunings:  
Line 159: Line 160:
Comma list: 3025/3024, 4096/4095, 4375/4374, 31250/31213
Comma list: 3025/3024, 4096/4095, 4375/4374, 31250/31213


Mapping: {{mapping| 38 0 28 -74 11 502 | 0 1 1 3 2 -6 }}
{{Mapping|legend=0| 38 0 28 -74 11 502 | 0 1 1 3 2 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 174: Line 175:
Comma list: 3025/3024, 4225/4224, 4375/4374, 78125/78078
Comma list: 3025/3024, 4225/4224, 4375/4374, 78125/78078


Mapping: {{mapping| 38 1 29 -71 13 111 | 0 2 2 6 4 1 }}
{{Mapping|legend=0| 38 1 29 -71 13 111 | 0 2 2 6 4 1 }}
: mapping generators: ~55/54, ~429/250
: mapping generators: ~55/54, ~429/250


Line 192: Line 193:
Comma list: 2500/2499, 3250/3249, 4225/4224, 4375/4374, 11016/11011, 57375/57344
Comma list: 2500/2499, 3250/3249, 4225/4224, 4375/4374, 11016/11011, 57375/57344


Mapping: {{mapping| 19 3 17 -28 82 92 159 78 | 0 10 10 30 -6 -8 -30 1 }}
{{Mapping|legend=0| 19 3 17 -28 82 92 159 78 | 0 10 10 30 -6 -8 -30 1 }}


Optimal tunings:  
Optimal tunings:  
Line 251: Line 252:
Comma list: 4000/3993, 4375/4374, 131072/130977
Comma list: 4000/3993, 4375/4374, 131072/130977


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


Optimal tunings:  
Optimal tunings:  
Line 266: Line 267:
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374


Mapping: {{mapping| 7 2 -8 53 3 35 | 0 3 8 -11 7 -3 }}
{{Mapping|legend=0| 7 2 -8 53 3 35 | 0 3 8 -11 7 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 305: Line 306:
Comma list: 3025/3024, 4375/4374, 131072/130977
Comma list: 3025/3024, 4375/4374, 131072/130977


Mapping: {{mapping| 2 -4 -11 18 18 | 0 11 24 -19 -17 }}
{{Mapping|legend=0| 2 -4 -11 18 18 | 0 11 24 -19 -17 }}


Optimal tunings:  
Optimal tunings:  
Line 320: Line 321:
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095


Mapping: {{mapping| 2 -4 -11 18 18 25 | 0 11 24 -19 -17 -27 }}
{{Mapping|legend=0| 2 -4 -11 18 18 25 | 0 11 24 -19 -17 -27 }}


Optimal tunings:  
Optimal tunings:  
Line 353: Line 354:
Comma list: 3025/3024, 4375/4374, 589824/588245
Comma list: 3025/3024, 4375/4374, 589824/588245


Mapping: {{mapping| 2 -11 -20 5 10 | 0 23 40 1 -5 }}
{{Mapping|legend=0| 2 -11 -20 5 10 | 0 23 40 1 -5 }}
: mapping generators: ~99/70, ~99/80
: mapping generators: ~99/70, ~99/80


Line 369: Line 370:
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024


Mapping: {{mapping| 2 -11 -20 5 10 -8 | 0 23 40 1 -5 25 }}
{{Mapping|legend=0| 2 -11 -20 5 10 -8 | 0 23 40 1 -5 25 }}


Optimal tunings:  
Optimal tunings:  
Line 384: Line 385:
Comma list: 4375/4374, 14641/14580, 15488/15435
Comma list: 4375/4374, 14641/14580, 15488/15435


Mapping: {{mapping| 1 -40 -70 1 -77 | 0 46 80 2 89 }}
{{Mapping|legend=0| 1 -40 -70 1 -77 | 0 46 80 2 89 }}
: mapping generators: ~2, ~144/77
: mapping generators: ~2, ~144/77


Line 400: Line 401:
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580


Mapping: {{mapping| 1 -40 -70 1 -77 -131 | 0 46 80 2 89 149 }}
{{Mapping|legend=0| 1 -40 -70 1 -77 -131 | 0 46 80 2 89 149 }}


Optimal tunings:  
Optimal tunings:  
Line 439: Line 440:
Comma list: 3025/3024, 4375/4374, 2791309312/2790703125
Comma list: 3025/3024, 4375/4374, 2791309312/2790703125


Mapping: {{mapping| 2 1 6 -15 -8 | 0 8 -5 76 55 }}
{{Mapping|legend=0| 2 1 6 -15 -8 | 0 8 -5 76 55 }}


Optimal tunings:
Optimal tunings:
Line 474: Line 475:
Comma list: 3025/3024, 4375/4374, 5767168/5764801
Comma list: 3025/3024, 4375/4374, 5767168/5764801


Mapping: {{mapping| 2 -8 -15 6 10 | 0 29 51 -1 -8 }}
{{Mapping|legend=0| 2 -8 -15 6 10 | 0 29 51 -1 -8 }}


Optimal tunings:  
Optimal tunings:  
Line 489: Line 490:
Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360
Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360


Mapping: {{mapping| 2 -8 -15 6 10 -3 | 0 29 51 -1 -8 27 }}
{{Mapping|legend=0| 2 -8 -15 6 10 -3 | 0 29 51 -1 -8 27 }}


Optimal tunings:  
Optimal tunings:  
Line 501: Line 502:
== Chlorine ==
== Chlorine ==
: ''For the 5-limit version, see [[17th-octave temperaments #Chlorine]].''
: ''For the 5-limit version, see [[17th-octave temperaments #Chlorine]].''
Chlorine (named after the 17th element) tempers out the [[septendecima]] in the 5-limit, and {{monzo| -49 4 22 -3 }} as well as the ragisma in the 7-limit. It has a 1/17-octave period, and can be described as {{nowrap| 289 & 323 }} temperament. Not only the semitwelfth, but also the ~5/4 can be used as a generator.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 523: Line 526:
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192


Mapping: {{mapping| 17 0 26 -87 207 | 0 2 1 10 -11 }}
{{Mapping|legend=0| 17 0 26 -87 207 | 0 2 1 10 -11 }}


Optimal tunings:  
Optimal tunings:  
Line 532: Line 535:


Badness (Sintel): 2.11
Badness (Sintel): 2.11
== Octoid ==
: {{Main| Octoid }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Octoid]].''
The octoid temperament has a period of 1/8 octave and tempers out 4375/4374 ([[4375/4374|ragisma]]) and 16875/16807 ([[16875/16807|mirkwai comma]]). In the 11-limit, it tempers out [[540/539]], [[1375/1372]], and [[6250/6237]]. In this temperament, one period gives ~[[12/11]], two give ~[[25/21]], three give ~[[35/27]], and four give [[99/70]]~[[140/99]].
The [[11-limit]] is the last place where all the extensions of octoid shown here agree in the mappings of primes. [[80edo]] is an alternative tuning for octoid in the 11-limit; though [[72edo]] does better for minimizing the average damage on the [[11-odd-limit]], 80edo damages prime 7 in favor of practically-just [[17/16]]'s, [[11/10]]'s and [[9/7]]'s. In higher limits, the mapping supported by 80edo is octopus – not octoid – as 80edo does not temper out [[324/323]], [[375/374]], [[495/494]], [[625/624]], [[715/714]] or [[729/728]].
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 4375/4374, 16875/16807
{{Mapping|legend=1| 8 1 3 3 | 0 3 4 5 }}
: mapping generators: ~49/45, ~7/5
[[Optimal tuning]]s:
* [[WE]]: ~49/45 = 150.0003{{c}}, ~7/5 = 583.9416{{c}}
: [[error map]]: {{val| +0.002 -0.130 -0.547 +0.883 }}
* [[CWE]]: ~49/45 = 150.0000{{c}}, ~7/5 = 583.9411{{c}}
: error map: {{val| 0.000 -0.132 -0.549 +0.880 }}
[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~7/5 = [578.571, 600.000] (27\56 to 4\8)
* 9-odd-limit diamond monotone: ~7/5 = [581.250, 586.364] (31\64 to 43\88)
* 7-odd-limit [[diamond tradeoff]]: ~7/5 = [582.512, 584.359]
* 9-odd-limit diamond tradeoff: ~7/5 = [582.512, 585.084]
{{Optimal ET sequence|legend=1| 8d, …, 72, 152, 224 }}
[[Badness]] (Sintel): 1.08
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 4000/3993
Mapping: {{mapping| 8 1 3 3 16 | 0 3 4 5 3 }}
Optimal tunings:
* WE: ~12/11 = 149.9932{{c}}, ~7/5 = 583.9356{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9477{{c}}
Tuning ranges:
* 11-odd-limit diamond monotone: ~7/5 = [581.250, 586.364] (31\64, 43\88)
* 11-odd-limit diamond tradeoff: ~7/5 = [582.512, 585.084]
{{Optimal ET sequence|legend=0| 8d, …, 72, 152, 224, 824d }}
Badness (Sintel): 0.466
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 729/728, 1375/1372
Mapping: {{mapping| 8 1 3 3 16 -21 | 0 3 4 5 3 13 }}
Optimal tunings:
* WE: ~12/11 = 150.0005{{c}}, ~7/5 = 583.9066{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9052{{c}}
{{Optimal ET sequence|legend=0| 72, 152f, 224 }}
Badness (Sintel): 0.631
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 375/374, 540/539, 625/624, 715/714, 729/728
Mapping: {{mapping| 8 1 3 3 16 -21 -14 | 0 3 4 5 3 13 12 }}
Optimal tunings:
* WE: ~12/11 = 150.0064{{c}}, ~7/5 = 583.8666{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.8489{{c}}
{{Optimal ET sequence|legend=0| 72, 152fg, 224, 296, 520g }}
Badness (Sintel): 0.729
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 375/374, 400/399, 495/494, 540/539, 715/714
Mapping: {{mapping| 8 1 3 3 16 -21 -14 34 | 0 3 4 5 3 13 12 0 }}
Optimal tunings:
* WE: ~12/11 = 149.9785{{c}}, ~7/5 = 583.8482{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9138{{c}}
{{Optimal ET sequence|legend=0| 72, 152fg, 224 }}
Badness (Sintel): 0.975
==== Octopus ====
A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4 = 300{{c}}.
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 364/363, 540/539
Mapping: {{mapping| 8 1 3 3 16 14 | 0 3 4 5 3 4 }}
Optimal tunings:
* WE: ~12/11 = 150.0313{{c}}, ~7/5 = 584.0134{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9583{{c}}
{{Optimal ET sequence|legend=0| 8d, …, 72, 152, 224f }}
Badness (Sintel): 0.896
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 289/288, 325/324, 540/539
Mapping: {{mapping| 8 1 3 3 16 14 21 | 0 3 4 5 3 4 3 }}
Optimal tunings:
* WE: ~12/11 = 150.0528{{c}}, ~7/5 = 584.0161{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9166{{c}}
{{Optimal ET sequence|legend=0| 8d, …, 72, 152, 224fg, 296ffg }}
Badness (Sintel): 0.795
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 221/220, 286/285, 289/288, 325/324, 400/399
Mapping: {{mapping| 8 1 3 3 16 14 21 34 | 0 3 4 5 3 4 3 0 }}
Optimal tunings:
* WE: ~12/11 = 150.0049{{c}}, ~7/5 = 584.0833{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~7/5 = 584.0712{{c}}
{{Optimal ET sequence|legend=0| 8d, 72, 152 }}
Badness (Sintel): 0.993
Scales: [[Octoid72]], [[Octoid80]]
==== Hexadecoid ====
{{See also| 16th-octave temperaments }}
Hexadecoid (80 & 144) has a period of 1/16 octave and tempers out 4225/4224.
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1375/1372, 4000/3993, 4225/4224
Mapping: {{mapping| 16 2 6 6 32 67 | 0 3 4 5 3 -1 }}
: mapping generators: ~448/429, ~7/5
Optimal tunings:
* WE: ~448/429 = 74.9943{{c}}, ~7/5 = 583.9408{{c}}
* CWE: ~448/429 = 75.0000{{c}}, ~7/5 = 583.9709{{c}}
{{Optimal ET sequence|legend=0| 80, 144, 224 }}
Badness (Sintel): 1.27
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 715/714, 936/935, 4000/3993, 4225/4224
Mapping: {{mapping| 16 2 6 6 32 67 81 | 0 3 4 5 3 -1 -2 }}
Optimal tunings:
* WE: ~117/112 = 74.9865{{c}}, ~7/5 = 583.9626{{c}}
* CWE: ~117/112 = 75.0000{{c}}, ~7/5 = 584.0463{{c}}
{{Optimal ET sequence|legend=0| 80, 144, 224, 528dg }}
Badness (Sintel): 1.46
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 400/399, 540/539, 715/714, 936/935, 1331/1330, 1445/1444
Mapping: {{mapping| 16 2 6 6 32 67 81 68 | 0 3 4 5 3 -1 -2 0 }}
Optimal tunings:
* WE: ~117/112 = 74.9865{{c}}, ~7/5 = 583.9642{{c}}
* CWE: ~117/112 = 75.0000{{c}}, ~7/5 = 584.0803{{c}}
{{Optimal ET sequence|legend=0| 80, 144, 224, 304dh, 528dghh }}
Badness (Sintel): 1.44


== Seniority ==
== Seniority ==
Line 756: Line 565:
Comma list: 441/440, 4375/4374, 65536/65219
Comma list: 441/440, 4375/4374, 65536/65219


Mapping: {{mapping| 1 -24 -43 5 2 | 0 35 62 -3 2 }}
{{Mapping|legend=0| 1 -24 -43 5 2 | 0 35 62 -3 2 }}


Optimal tunings:  
Optimal tunings:  
Line 771: Line 580:
Comma list: 364/363, 441/440, 2200/2197, 4375/4374
Comma list: 364/363, 441/440, 2200/2197, 4375/4374


Mapping: {{mapping| 1 -24 -43 5 2 -27 | 0 35 62 -3 2 42 }}
{{Mapping|legend=0| 1 -24 -43 5 2 -27 | 0 35 62 -3 2 42 }}


Optimal tunings:  
Optimal tunings:  
Line 786: Line 595:
Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197
Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197


Mapping: {{mapping| 1 -24 -43 5 2 -27 -31 | 0 35 62 -3 2 42 48 }}
{{Mapping|legend=0| 1 -24 -43 5 2 -27 -31 | 0 35 62 -3 2 42 48 }}


Optimal tunings:  
Optimal tunings:  
Line 823: Line 632:
Comma list: 4375/4374, 41503/41472, 184549376/184528125
Comma list: 4375/4374, 41503/41472, 184549376/184528125


Mapping: {{mapping| 1 0 -27 109 -159 | 0 2 37 -134 205 }}
{{Mapping|legend=0| 1 0 -27 109 -159 | 0 2 37 -134 205 }}


Optimal tunings:  
Optimal tunings:  
Line 838: Line 647:
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625


Mapping: {{mapping| 1 0 -27 109 -159 -70 | 0 2 37 -134 205 93 }}
{{Mapping|legend=0| 1 0 -27 109 -159 -70 | 0 2 37 -134 205 93 }}


Optimal tunings:  
Optimal tunings:  
Line 875: Line 684:
Comma list: 3025/3024, 4375/4374, 235298/234375
Comma list: 3025/3024, 4375/4374, 235298/234375


Mapping: {{mapping| 2 -20 -26 -34 -17 | 0 31 41 53 32 }}
{{Mapping|legend=0| 2 -20 -26 -34 -17 | 0 31 41 53 32 }}
: mapping generators: ~99/70, ~35/27
: mapping generators: ~99/70, ~35/27


Line 891: Line 700:
Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374
Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374


Mapping: {{mapping| 2 -20 -26 -34 -17 -21 | 0 31 41 53 32 38 }}
{{Mapping|legend=0| 2 -20 -26 -34 -17 -21 | 0 31 41 53 32 38 }}


Optimal tunings:  
Optimal tunings:  
Line 924: Line 733:
Comma list: 4375/4374, 41503/41472, 172032/171875
Comma list: 4375/4374, 41503/41472, 172032/171875


Mapping: {{mapping| 1 -22 -22 -65 58 | 0 32 33 92 -74 }}
{{Mapping|legend=0| 1 -22 -22 -65 58 | 0 32 33 92 -74 }}


Optimal tunings:  
Optimal tunings:  
Line 939: Line 748:
Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976
Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976


Mapping: {{mapping| 1 -22 -22 -65 58 -56 | 0 32 33 92 -74 81 }}
{{Mapping|legend=0| 1 -22 -22 -65 58 -56 | 0 32 33 92 -74 81 }}


Optimal tunings:  
Optimal tunings:  
Line 954: Line 763:
Comma list: 4375/4374, 5632/5625, 117649/117612
Comma list: 4375/4374, 5632/5625, 117649/117612


Mapping: {{mapping| 1 -22 -22 -65 -141 | 0 32 33 92 196 }}
{{Mapping|legend=0| 1 -22 -22 -65 -141 | 0 32 33 92 196 }}


Optimal tunings:  
Optimal tunings:  
Line 969: Line 778:
Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374
Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374


Mapping: {{mapping| 1 -22 -22 -65 -141 -56 | 0 32 33 92 196 81 }}
{{Mapping|legend=0| 1 -22 -22 -65 -141 -56 | 0 32 33 92 196 81 }}


Optimal tunings:  
Optimal tunings:  
Line 1,006: Line 815:
Comma list: 3025/3024, 4375/4374, 4296700485/4294967296
Comma list: 3025/3024, 4375/4374, 4296700485/4294967296


Mapping: {{mapping| 4 0 -11 48 43 | 0 5 16 -29 -23 }}
{{Mapping|legend=0| 4 0 -11 48 43 | 0 5 16 -29 -23 }}


Optimal tunings:  
Optimal tunings:  
Line 1,021: Line 830:
Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374
Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374


Mapping: {{mapping| 4 0 -11 48 43 11 | 0 5 16 -29 -23 3 }}
{{Mapping|legend=0| 4 0 -11 48 43 11 | 0 5 16 -29 -23 3 }}


Optimal tunings:  
Optimal tunings:  
Line 1,054: Line 863:
Comma list: 441/440, 4000/3993, 4375/4374
Comma list: 441/440, 4000/3993, 4375/4374


Mapping: {{mapping| 1 2 3 3 4 | 0 -30 -49 -14 -39 }}
{{Mapping|legend=0| 1 2 3 3 4 | 0 -30 -49 -14 -39 }}


Optimal tunings:  
Optimal tunings:  
Line 1,069: Line 878:
Comma list: 364/363, 441/440, 676/675, 4375/4374
Comma list: 364/363, 441/440, 676/675, 4375/4374


Mapping: {{mapping| 1 2 3 3 4 5 | 0 -30 -49 -14 -39 -94 }}
{{Mapping|legend=0| 1 2 3 3 4 5 | 0 -30 -49 -14 -39 -94 }}


Optimal tunings:  
Optimal tunings:  
Line 1,084: Line 893:
Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155
Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155


Mapping: {{mapping| 1 2 3 3 4 5 5 | 0 -30 -49 -14 -39 -94 -66 }}
{{Mapping|legend=0| 1 2 3 3 4 5 5 | 0 -30 -49 -14 -39 -94 -66 }}


Optimal tunings:  
Optimal tunings:  
Line 1,099: Line 908:
Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675
Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675


Mapping: {{mapping| 1 2 3 3 4 5 5 4 | 0 -30 -49 -14 -39 -94 -66 18 }}
{{Mapping|legend=0| 1 2 3 3 4 5 5 4 | 0 -30 -49 -14 -39 -94 -66 18 }}


Optimal tunings:  
Optimal tunings:  
Line 1,136: Line 945:
Comma list: 3025/3024, 4375/4374, 391314/390625
Comma list: 3025/3024, 4375/4374, 391314/390625


Mapping: {{mapping| 10 4 9 2 18 | 0 5 6 11 7 }}
{{Mapping|legend=0| 10 4 9 2 18 | 0 5 6 11 7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,151: Line 960:
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374


Mapping: {{mapping| 10 4 9 2 18 37 | 0 5 6 11 7 0 }}
{{Mapping|legend=0| 10 4 9 2 18 37 | 0 5 6 11 7 0 }}


Optimal tunings:  
Optimal tunings:  
Line 1,166: Line 975:
Comma list: 1001/1000, 1521/1520, 3025/3024, 4225/4224, 4375/4374
Comma list: 1001/1000, 1521/1520, 3025/3024, 4225/4224, 4375/4374


Mapping: {{mapping| 10 4 9 2 18 37 33 | 0 5 6 11 7 0 4 }}
{{Mapping|legend=0| 10 4 9 2 18 37 33 | 0 5 6 11 7 0 4 }}


Optimal tunings:  
Optimal tunings:  
Line 1,201: Line 1,010:
Comma list: 4375/4374, 117649/117612, 67110351/67108864
Comma list: 4375/4374, 117649/117612, 67110351/67108864


Mapping: {{mapping| 1 2 3 3 3 | 0 -112 -183 -52 124 }}
{{Mapping|legend=0| 1 2 3 3 3 | 0 -112 -183 -52 124 }}


Optimal tunings:  
Optimal tunings:  
Line 1,216: Line 1,025:
Comma list: 4225/4224, 4375/4374, 6656/6655, 117649/117612
Comma list: 4225/4224, 4375/4374, 6656/6655, 117649/117612


Mapping: {{mapping| 1 2 3 3 3 3 | 0 -112 -183 -52 124 189 }}
{{Mapping|legend=0| 1 2 3 3 3 3 | 0 -112 -183 -52 124 189 }}


Optimal tunings:  
Optimal tunings:  
Line 1,253: Line 1,062:
Comma list: 540/539, 4375/4374, 2097152/2096325
Comma list: 540/539, 4375/4374, 2097152/2096325


Mapping: {{mapping| 1 -5 -4 -18 19 | 0 25 24 79 -59 }}
{{Mapping|legend=0| 1 -5 -4 -18 19 | 0 25 24 79 -59 }}


Optimal tunings:  
Optimal tunings:  
Line 1,268: Line 1,077:
Comma list: 540/539, 625/624, 729/728, 10985/10976
Comma list: 540/539, 625/624, 729/728, 10985/10976


Mapping: {{mapping| 1 -5 -4 -18 19 -15 | 0 25 24 79 -59 71 }}
{{Mapping|legend=0| 1 -5 -4 -18 19 -15 | 0 25 24 79 -59 71 }}


Optimal tunings:  
Optimal tunings:  
Line 1,283: Line 1,092:
Comma list: 1375/1372, 4375/4374, 496125/495616
Comma list: 1375/1372, 4375/4374, 496125/495616


Mapping: {{mapping| 1 -5 -4 -18 -40 | 0 25 24 79 165 }}
{{Mapping|legend=0| 1 -5 -4 -18 -40 | 0 25 24 79 165 }}


Optimal tunings:  
Optimal tunings:  
Line 1,298: Line 1,107:
Comma list: 625/624, 729/728, 1375/1372, 10985/10976
Comma list: 625/624, 729/728, 1375/1372, 10985/10976


Mapping: {{mapping| 1 -5 -4 -18 -40 -15 | 0 25 24 79 165 71 }}
{{Mapping|legend=0| 1 -5 -4 -18 -40 -15 | 0 25 24 79 165 71 }}


Optimal tunings:  
Optimal tunings:  
Line 1,333: Line 1,142:
Comma list: 121/120, 441/440, 4375/4374
Comma list: 121/120, 441/440, 4375/4374


Mapping: {{mapping| 1 2 3 3 4 | 0 -19 -31 -9 -25 }}
{{Mapping|legend=0| 1 2 3 3 4 | 0 -19 -31 -9 -25 }}


Optimal tunings:  
Optimal tunings:  
Line 1,348: Line 1,157:
Comma list: 121/120, 169/168, 325/324, 441/440
Comma list: 121/120, 169/168, 325/324, 441/440


Mapping: {{mapping| 1 2 3 3 4 4 | 0 -19 -31 -9 -25 -14 }}
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -19 -31 -9 -25 -14 }}


Optimal tunings:  
Optimal tunings:  
Line 1,363: Line 1,172:
Comma list: 385/384, 2401/2376, 4375/4374
Comma list: 385/384, 2401/2376, 4375/4374


Mapping: {{mapping| 1 2 3 3 3 | 0 -19 -31 -9 21 }}
{{Mapping|legend=0| 1 2 3 3 3 | 0 -19 -31 -9 21 }}


Optimal tunings:  
Optimal tunings:  
Line 1,378: Line 1,187:
Comma list: 196/195, 364/363, 385/384, 4375/4374
Comma list: 196/195, 364/363, 385/384, 4375/4374


Mapping: {{mapping| 1 2 3 3 3 3 | 0 -19 -31 -9 21 32 }}
{{Mapping|legend=0| 1 2 3 3 3 3 | 0 -19 -31 -9 21 32 }}


Optimal tunings:  
Optimal tunings:  
Line 1,415: Line 1,224:
Comma list: 4375/4374, 234375/234256, 2097152/2096325
Comma list: 4375/4374, 234375/234256, 2097152/2096325


Mapping: {{mapping| 13 0 92 -355 148 | 0 1 -3 19 -5 }}
{{Mapping|legend=0| 13 0 92 -355 148 | 0 1 -3 19 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 1,430: Line 1,239:
Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078
Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078


Mapping: {{mapping| 13 0 92 -355 148 419 | 0 1 -3 19 -5 -18 }}
{{Mapping|legend=0| 13 0 92 -355 148 419 | 0 1 -3 19 -5 -18 }}


Optimal tunings:  
Optimal tunings:  
Line 1,469: Line 1,278:
Comma list: 4375/4374, 5632/5625, 2621440/2614689
Comma list: 4375/4374, 5632/5625, 2621440/2614689


Mapping: {{mapping| 1 -3 -15 40 -75 | 0 9 34 -73 154 }}
{{Mapping|legend=0| 1 -3 -15 40 -75 | 0 9 34 -73 154 }}


Optimal tunings:  
Optimal tunings:  
Line 1,484: Line 1,293:
Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625
Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625


Mapping: {{mapping| 1 -3 -15 40 -75 -34 | 0 9 34 -73 154 74 }}
{{Mapping|legend=0| 1 -3 -15 40 -75 -34 | 0 9 34 -73 154 74 }}


Optimal tunings:  
Optimal tunings:  
Line 1,519: Line 1,328:
Comma list: 3025/3024, 4375/4374, 1265625/1261568
Comma list: 3025/3024, 4375/4374, 1265625/1261568


Mapping: {{mapping| 2 -6 -1 -36 -22 | 0 13 8 59 41 }}
{{Mapping|legend=0| 2 -6 -1 -36 -22 | 0 13 8 59 41 }}


Optimal tunings:  
Optimal tunings:  
Line 1,534: Line 1,343:
Comma list: 625/624, 729/728, 1575/1573, 2200/2197
Comma list: 625/624, 729/728, 1575/1573, 2200/2197


Mapping: {{mapping| 2 -6 -1 -36 -22 -6 | 0 13 8 59 41 19 }}
{{Mapping|legend=0| 2 -6 -1 -36 -22 -6 | 0 13 8 59 41 19 }}


Optimal tunings:  
Optimal tunings:  
Line 1,571: Line 1,380:
Comma list: 245/242, 385/384, 4375/4374
Comma list: 245/242, 385/384, 4375/4374


Mapping: {{mapping| 13 0 -11 57 45 | 0 1 2 -1 0 }}
{{Mapping|legend=0| 13 0 -11 57 45 | 0 1 2 -1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 1,586: Line 1,395:
Comma list: 169/168, 245/242, 325/324, 385/384
Comma list: 169/168, 245/242, 325/324, 385/384


Mapping: {{mapping| 13 0 -11 57 45 48 | 0 1 2 -1 0 0 }}
{{Mapping|legend=0| 13 0 -11 57 45 48 | 0 1 2 -1 0 0 }}


Optimal tunings:  
Optimal tunings:  
Line 1,621: Line 1,430:
Comma list: 4375/4374, 759375/758912, 100663296/100656875
Comma list: 4375/4374, 759375/758912, 100663296/100656875


Mapping: {{mapping| 1 -16 -9 -75 9 | 0 73 47 323 -23 }}
{{Mapping|legend=0| 1 -16 -9 -75 9 | 0 73 47 323 -23 }}


Optimal tunings:  
Optimal tunings:  
Line 1,636: Line 1,445:
Comma list: 4225/4224, 4375/4374, 6656/6655, 78125/78078
Comma list: 4225/4224, 4375/4374, 6656/6655, 78125/78078


Mapping: {{mapping| 1 -16 -9 -75 9 9 | 0 73 47 323 -23 -22 }}
{{Mapping|legend=0| 1 -16 -9 -75 9 9 | 0 73 47 323 -23 -22 }}


Optimal tunings:  
Optimal tunings:  
Line 1,673: Line 1,482:
Comma list: 3025/3024, 4375/4374, 134775333/134217728
Comma list: 3025/3024, 4375/4374, 134775333/134217728


Mapping: {{mapping| 46 0 -39 202 232 | 0 1 2 -1 -1 }}
{{Mapping|legend=0| 46 0 -39 202 232 | 0 1 2 -1 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,688: Line 1,497:
Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364
Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364


Mapping: {{mapping| 46 0 -39 202 232 316 | 0 1 2 -1 -1 -2 }}
{{Mapping|legend=0| 46 0 -39 202 232 316 | 0 1 2 -1 -1 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 1,703: Line 1,512:
Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224
Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224


Mapping: {{mapping| 46 0 -39 202 232 316 188 | 0 1 2 -1 -1 -2 0 }}
{{Mapping|legend=0| 46 0 -39 202 232 316 188 | 0 1 2 -1 -1 -2 0 }}


Optimal tunings:  
Optimal tunings:  
Retrieved from "https://en.xen.wiki/w/Ragismic_microtemperaments"