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41edo: Difference between revisions

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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
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ET parameter name, cleanup
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
→Commas: rework commatable, long ratios missing
Line 692: Line 692:
== Commas ==
== Commas ==


41 EDO tempers out the following commas using its patent val, {{val|41 65 95 115 142 152 168 174 185 199 203}}.
41 EDO [[tempers out]] the following [[comma]]s using its patent [[val]], {{val|41 65 95 115 142 152 168 174 185 199 203}}.


{| class="wikitable center-1 center-2 right-3 center-6"
{| class="wikitable center-1 center-2 right-3 center-6"
! [[Prime limit|Prime <br> limit]]
! [[Prime limit|Prime <br> limit]]
! [[Ratio]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Cents]]
! [[Cents]]
! [[Monzo]]
! [[Monzo]]
! colspan="2" | [[Color notation/Temperament Names|Color name]]
! colspan="2" | [[Color name]]
! Name
! Name
|-
|-
Line 718: Line 718:
| shibboleth
| shibboleth
|-
|-
| "
| 5
|  
|  
| 31.57
| 31.57
Line 726: Line 726:
| Ampersand's comma
| Ampersand's comma
|-
|-
| "
| 5
| 3125/3072
| [[3125/3072]]
| 29.61
| 29.61
| {{Monzo| -10 -1 5 }}
| {{Monzo| -10 -1 5 }}
Line 734: Line 734:
| small diesis, magic comma
| small diesis, magic comma
|-
|-
| "
| 5
| 20000/19683
| [[20000/19683]]
| 27.66
| 27.66
| {{Monzo| 5 -9 4 }}
| {{Monzo| 5 -9 4 }}
Line 742: Line 742:
| minimal diesis, tetracot comma
| minimal diesis, tetracot comma
|-
|-
| "
| 5
|  
|  
| 25.71
| 25.71
Line 750: Line 750:
| roda
| roda
|-
|-
| "
| 5
| 32805/32768
| [[32805/32768]]
| 1.95
| 1.95
| {{Monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
Line 759: Line 759:
|-
|-
| 7
| 7
| 15625/15309
| [[15625/15309]]
| 35.37
| 35.37
| {{Monzo| 0 -7 6 -1 }}
| {{Monzo| 0 -7 6 -1 }}
Line 766: Line 766:
| great BP diesis
| great BP diesis
|-
|-
| "
| 7
|  
|  
| 22.41
| 22.41
Line 774: Line 774:
| blackjackisma
| blackjackisma
|-
|-
| "
| 7
| 875/864
| [[875/864]]
| 21.90
| 21.90
| {{Monzo| -5 -3 3 1 }}
| {{Monzo| -5 -3 3 1 }}
Line 782: Line 782:
| keema
| keema
|-
|-
| "
| 7
| 3125/3087
| [[3125/3087]]
| 21.18
| 21.18
| {{Monzo| 0 -2 5 -3 }}
| {{Monzo| 0 -2 5 -3 }}
Line 790: Line 790:
| major BP diesis, gariboh
| major BP diesis, gariboh
|-
|-
| "
| 7
|  
|  
| 19.95
| 19.95
Line 798: Line 798:
| tolerma
| tolerma
|-
|-
| "
| 7
| 33075/32768
| [[33075/32768]]
| 16.14
| 16.14
| {{Monzo| -15 3 2 2 }}
| {{Monzo| -15 3 2 2 }}
Line 806: Line 806:
| mirwomo comma
| mirwomo comma
|-
|-
| "
| 7
| 245/243
| [[245/243]]
| 14.19
| 14.19
| {{Monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
Line 814: Line 814:
| minor BP diesis, sensamagic
| minor BP diesis, sensamagic
|-
|-
| "
| 7
| 4000/3969
| [[4000/3969]]
| 13.47
| 13.47
| {{Monzo| 5 -4 3 -2 }}
| {{Monzo| 5 -4 3 -2 }}
Line 822: Line 822:
| septimal semicomma, octagar
| septimal semicomma, octagar
|-
|-
| "
| 7
|  
|  
| 9.15
| 9.15
Line 830: Line 830:
| quince
| quince
|-
|-
| "
| 7
| 1029/1024
| [[1029/1024]]
| 8.43
| 8.43
| {{Monzo| -10 1 0 3 }}
| {{Monzo| -10 1 0 3 }}
Line 838: Line 838:
| gamelan residue, gamelisma
| gamelan residue, gamelisma
|-
|-
| "
| 7
| 225/224
| [[225/224]]
| 7.71
| 7.71
| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
Line 846: Line 846:
| septimal kleisma, marvel comma
| septimal kleisma, marvel comma
|-
|-
| "
| 7
| 16875/16807
| [[16875/16807]]
| 6.99
| 6.99
| {{Monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
Line 854: Line 854:
| small BP diesis, mirkwai
| small BP diesis, mirkwai
|-
|-
| "
| 7
| 10976/10935
| [[10976/10935]]
| 6.48
| 6.48
| {{Monzo| 5 -7 -1 3 }}
| {{Monzo| 5 -7 -1 3 }}
Line 862: Line 862:
| hemimage
| hemimage
|-
|-
| "
| 7
| 5120/5103
| [[5120/5103]]
| 5.76
| 5.76
| {{Monzo| 10 -6 1 -1 }}
| {{Monzo| 10 -6 1 -1 }}
Line 870: Line 870:
| Beta 5, Garibaldi comma, hemifamity
| Beta 5, Garibaldi comma, hemifamity
|-
|-
| "
| 7
|  
|  
| 3.80
| 3.80
Line 878: Line 878:
| Beta 2, septimal schisma, garischisma
| Beta 2, septimal schisma, garischisma
|-
|-
| "
| 7
| 2401/2400
| [[2401/2400]]
| 0.72
| 0.72
| {{Monzo| -5 -1 -2 4 }}
| {{Monzo| -5 -1 -2 4 }}
Line 894: Line 894:
| thuja comma
| thuja comma
|-
|-
| "
| 11
| 245/242
| [[245/242]]
| 21.33
| 21.33
| {{Monzo| -1 0 1 2 -2 }}
| {{Monzo| -1 0 1 2 -2 }}
Line 902: Line 902:
| cassacot
| cassacot
|-
|-
| "
| 11
| 100/99
| [[100/99]]
| 17.40
| 17.40
| {{Monzo| 2 -2 2 0 -1 }}
| {{Monzo| 2 -2 2 0 -1 }}
Line 910: Line 910:
| Ptolemy's comma, ptolemisma
| Ptolemy's comma, ptolemisma
|-
|-
| "
| 11
| 1344/1331
| [[1344/1331]]
| 16.83
| 16.83
| {{Monzo| 6 1 0 1 -3 }}
| {{Monzo| 6 1 0 1 -3 }}
Line 918: Line 918:
| hemimin
| hemimin
|-
|-
| "
| 11
| 896/891
| [[896/891]]
| 9.69
| 9.69
| {{Monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
Line 926: Line 926:
| undecimal semicomma, pentacircle (minthma * gentle)
| undecimal semicomma, pentacircle (minthma * gentle)
|-
|-
| "
| 11
| 65536/65219
| [[65536/65219]]
| 8.39
| 8.39
| {{Monzo| 16 0 0 -2 -3 }}
| {{Monzo| 16 0 0 -2 -3 }}
Line 934: Line 934:
| orgonisma
| orgonisma
|-
|-
| "
| 11
| 243/242
| [[243/242]]
| 7.14
| 7.14
| {{Monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
Line 942: Line 942:
| neutral third comma, rastma
| neutral third comma, rastma
|-
|-
| "
| 11
| 385/384
| [[385/384]]
| 4.50
| 4.50
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
Line 950: Line 950:
| undecimal kleisma, keenanisma
| undecimal kleisma, keenanisma
|-
|-
| "
| 11
| 441/440
| [[441/440]]
| 3.93
| 3.93
| {{Monzo| -3 2 -1 2 -1 }}
| {{Monzo| -3 2 -1 2 -1 }}
Line 958: Line 958:
| Werckmeister's undecimal septenarian schisma, werckisma
| Werckmeister's undecimal septenarian schisma, werckisma
|-
|-
| "
| 11
| 1375/1372
| [[1375/1372]]
| 3.78
| 3.78
| {{Monzo| -2 0 3 -3 1 }}
| {{Monzo| -2 0 3 -3 1 }}
Line 966: Line 966:
| moctdel
| moctdel
|-
|-
| "
| 11
| 540/539
| [[540/539]]
| 3.21
| 3.21
| {{Monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
Line 974: Line 974:
| Swets' comma, swetisma
| Swets' comma, swetisma
|-
|-
| "
| 11
| 3025/3024
| [[3025/3024]]
| 0.57
| 0.57
| {{Monzo| -4 -3 2 -1 2 }}
| {{Monzo| -4 -3 2 -1 2 }}
Line 982: Line 982:
| Lehmerisma
| Lehmerisma
|-
|-
| "
| 11
|  
|  
| 0.15
| 0.15
Line 991: Line 991:
|-
|-
| 13
| 13
| 105/104
| [[105/104]]
| 16.57
| 16.57
| {{Monzo| -3 1 1 1 0 -1 }}
| {{Monzo| -3 1 1 1 0 -1 }}
Line 998: Line 998:
| small tridecimal comma, animist
| small tridecimal comma, animist
|-
|-
| "
| 13
| 28672/28431
| [[28672/28431]]
| 14.61
| 14.61
| {{Monzo| 12 -7 0 1 0 -1 }}
| {{Monzo| 12 -7 0 1 0 -1 }}
Line 1,006: Line 1,006:
| secorian
| secorian
|-
|-
| "
| 13
| 275/273
| [[275/273]]
| 12.64
| 12.64
| {{Monzo| 0 -1 2 -1 1 -1 }}
| {{Monzo| 0 -1 2 -1 1 -1 }}
Line 1,014: Line 1,014:
| gassorma
| gassorma
|-
|-
| "
| 13
| 144/143
| [[144/143]]
| 12.06
| 12.06
| {{Monzo| 4 2 0 0 -1 -1 }}
| {{Monzo| 4 2 0 0 -1 -1 }}
Line 1,022: Line 1,022:
| grossma
| grossma
|-
|-
| "
| 13
| 196/195
| [[196/195]]
| 8.86
| 8.86
| {{Monzo| 2 -1 -1 2 0 -1 }}
| {{Monzo| 2 -1 -1 2 0 -1 }}
Line 1,030: Line 1,030:
| mynucuma
| mynucuma
|-
|-
| "
| 13
| 640/637
| [[640/637]]
| 8.13
| 8.13
| {{Monzo| 7 0 1 -2 0 -1 }}
| {{Monzo| 7 0 1 -2 0 -1 }}
Line 1,038: Line 1,038:
| huntma
| huntma
|-
|-
| "
| 13
| 1188/1183
| [[1188/1183]]
| 7.30
| 7.30
| {{Monzo| 2 3 0 -1 1 -2 }}
| {{Monzo| 2 3 0 -1 1 -2 }}
Line 1,046: Line 1,046:
| kestrel comma
| kestrel comma
|-
|-
| "
| 13
| 325/324
| [[325/324]]
| 5.34
| 5.34
| {{Monzo| -2 -4 2 0 0 1 }}
| {{Monzo| -2 -4 2 0 0 1 }}
Line 1,054: Line 1,054:
| marveltwin
| marveltwin
|-
|-
| "
| 13
| 352/351
| [[352/351]]
| 4.93
| 4.93
| {{Monzo| 5 -3 0 0 1 -1 }}
| {{Monzo| 5 -3 0 0 1 -1 }}
Line 1,062: Line 1,062:
| minthma
| minthma
|-
|-
| "
| 13
| 364/363
| [[364/363]]
| 4.76
| 4.76
| {{Monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| 2 -1 0 1 -2 1 }}
Line 1,070: Line 1,070:
| gentle comma
| gentle comma
|-
|-
| "
| 13
| 847/845
| [[847/845]]
| 4.09
| 4.09
| {{Monzo| 0 0 -1 1 2 -2 }}
| {{Monzo| 0 0 -1 1 2 -2 }}
Line 1,078: Line 1,078:
| cuthbert
| cuthbert
|-
|-
| "
| 13
| 729/728
| [[729/728]]
| 2.38
| 2.38
| {{Monzo| -3 6 0 -1 0 -1 }}
| {{Monzo| -3 6 0 -1 0 -1 }}
Line 1,086: Line 1,086:
| squbema
| squbema
|-
|-
| "
| 13
| 4096/4095
| [[4096/4095]]
| 0.42
| 0.42
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
Line 1,094: Line 1,094:
| tridecimal schisma, Sagittal schismina
| tridecimal schisma, Sagittal schismina
|-
|-
| "
| 13
| 10648/10647
| [[10648/10647]]
| 0.16
| 0.16
| {{Monzo| 3 -2 0 -1 3 -2 }}
| {{Monzo| 3 -2 0 -1 3 -2 }}
Line 1,103: Line 1,103:
|-
|-
| 17
| 17
| 2187/2176
| [[2187/2176]]
| 8.73
| 8.73
| {{Monzo| -7 7 0 0 0 0 -1 }}
| {{Monzo| -7 7 0 0 0 0 -1 }}
Line 1,110: Line 1,110:
| septendecimal comma
| septendecimal comma
|-
|-
| "
| 17
| 256/255
| [[256/255]]
| 6.78
| 6.78
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
Line 1,118: Line 1,118:
| septendecimal kleisma
| septendecimal kleisma
|-
|-
| "
| 17
| 715/714
| [[715/714]]
| 2.42
| 2.42
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
Line 1,127: Line 1,127:
|-
|-
| 19
| 19
| 210/209
| [[210/209]]
| 8.26
| 8.26
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
Line 1,134: Line 1,134:
| spleen comma
| spleen comma
|-
|-
| "
| 19
| 361/360
| [[361/360]]
| 4.80
| 4.80
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
Line 1,142: Line 1,142:
| go comma
| go comma
|-
|-
| "
| 19
| 513/512
| [[513/512]]
| 3.38
| 3.38
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
Line 1,150: Line 1,150:
| undevicesimal comma, Boethius' comma
| undevicesimal comma, Boethius' comma
|-
|-
| "
| 19
| 1216/1215
| [[1216/1215]]
| 1.42
| 1.42
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
Line 1,159: Line 1,159:
|-
|-
| 23
| 23
| 736/729
| [[736/729]]
| 16.54
| 16.54
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
Line 1,167: Line 1,167:
|-
|-
| 29
| 29
| 145/144
| [[145/144]]
| 11.98
| 11.98
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
Line 1,174: Line 1,174:
| 29th-partial chroma
| 29th-partial chroma
|}
|}
<references/>


== Temperaments ==
== Temperaments ==
Retrieved from "https://en.xen.wiki/w/41edo"