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Xenwolf (talk | contribs)
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→Commas: rework commatable
Line 578: Line 578:
== Commas ==
== Commas ==


19 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] {{val| 19 30 44 53 66 70 }}.)
19 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 19 30 44 53 66 70 }}.)


{| class="wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>Limit]]
! [[Ratio]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
Line 589: Line 589:
|-
|-
| 5
| 5
| 16875/16384
| [[16875/16384]]
| {{Monzo| -14 3 4 }}
| {{Monzo| -14 3 4 }}
| 51.12
| 51.12
Line 595: Line 595:
| Negri comma, double augmentation diesis
| Negri comma, double augmentation diesis
|-
|-
| "
| 5
| 3125/3072
| [[3125/3072]]
| {{Monzo| -10 -1 5 }}
| {{Monzo| -10 -1 5 }}
| 29.61
| 29.61
Line 602: Line 602:
| Small diesis, magic comma
| Small diesis, magic comma
|-
|-
| "
| 5
| [[81/80]]
| [[81/80]]
| {{Monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
Line 609: Line 609:
| [[Syntonic comma]], Didymus comma, meantone comma
| [[Syntonic comma]], Didymus comma, meantone comma
|-
|-
| "
| 5
| 78732/78125
| [[78732/78125]]
| {{Monzo| 2 9 -7 }}
| {{Monzo| 2 9 -7 }}
| 13.40
| 13.40
Line 616: Line 616:
| Medium semicomma, sensipent comma
| Medium semicomma, sensipent comma
|-
|-
| "
| 5
| 15625/15552
| [[15625/15552]]
| {{Monzo| -6 -5 6 }}
| {{Monzo| -6 -5 6 }}
| 8.11
| 8.11
Line 623: Line 623:
| Kleisma, semicomma majeur
| Kleisma, semicomma majeur
|-
|-
| "
| 5
|  
| <abbr title="1224440064/1220703125">(20 digits)</abbr>
| {{Monzo| 8 14 -13 }}
| {{Monzo| 8 14 -13 }}
| 5.29
| 5.29
| Thegu
| Thegu
| Parakleisma
| [[Parakleisma]]
|-
|-
| "
| 5
|  
| <abbr title="19073486328125/19042491875328">(28 digits)</abbr>
| {{Monzo| -14 -19 19 }}
| {{Monzo| -14 -19 19 }}
| 2.82
| 2.82
| Neyo
| Neyo
| Enneadeca, 19-tone-comma
| [[Enneadeca]], 19-tone-comma
|-
|-
| 7
| 7
| 1029/1000
| [[1029/1000]]
| {{Monzo| -3 1 -3 3 }}
| {{Monzo| -3 1 -3 3 }}
| 49.49
| 49.49
Line 644: Line 644:
| Keega
| Keega
|-
|-
| "
| 7
| 525/512
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| {{Monzo| -9 1 2 1 }}
| 43.41
| 43.41
Line 651: Line 651:
| Avicennma, Avicenna's enharmonic diesis
| Avicennma, Avicenna's enharmonic diesis
|-
|-
| "
| 7
| [[49/48]]
| [[49/48]]
| {{Monzo| -4 -1 0 2 }}
| {{Monzo| -4 -1 0 2 }}
Line 658: Line 658:
| Slendro diesis
| Slendro diesis
|-
|-
| "
| 7
| 686/675
| [[686/675]]
| {{Monzo| 1 -3 -2 3 }}
| {{Monzo| 1 -3 -2 3 }}
| 27.99
| 27.99
Line 665: Line 665:
| Senga
| Senga
|-
|-
| "
| 7
| 875/864
| [[875/864]]
| {{Monzo| -5 -3 3 1 }}
| {{Monzo| -5 -3 3 1 }}
| 21.90
| 21.90
Line 672: Line 672:
| Keema
| Keema
|-
|-
| "
| 7
| [[245/243]]
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
Line 679: Line 679:
| Sensamagic
| Sensamagic
|-
|-
| "
| 7
| [[126/125]]
| [[126/125]]
| {{Monzo| 1 2 -3 1 }}
| {{Monzo| 1 2 -3 1 }}
Line 686: Line 686:
| Septimal semicomma, starling comma
| Septimal semicomma, starling comma
|-
|-
| "
| 7
| [[225/224]]
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
Line 693: Line 693:
| Septimal kleisma, marvel comma
| Septimal kleisma, marvel comma
|-
|-
| "
| 7
| 19683/19600
| [[19683/19600]]
| {{Monzo| -4 9 -2 -2 }}
| {{Monzo| -4 9 -2 -2 }}
| 7.32
| 7.32
Line 700: Line 700:
| Cataharry
| Cataharry
|-
|-
| "
| 7
| 10976/10935
| [[10976/10935]]
| {{Monzo| 5 -7 -1 3 }}
| {{Monzo| 5 -7 -1 3 }}
| 6.48
| 6.48
Line 707: Line 707:
| Hemimage
| Hemimage
|-
|-
| "
| 7
| 3136/3125
| [[3136/3125]]
| {{Monzo| 6 0 -5 2 }}
| {{Monzo| 6 0 -5 2 }}
| 6.08
| 6.08
Line 714: Line 714:
| Hemimean
| Hemimean
|-
|-
| "
| 7
|  
| <abbr title="703125/702464">(12 digits)</abbr>
| {{Monzo| -11 2 7 -3 }}
| {{Monzo| -11 2 7 -3 }}
| 1.63
| 1.63
| Latriru-asepyo
| Latriru-asepyo
| Meter
| [[Meter]]
|-
|-
| "
| 7
| 4375/4374
| [[4375/4374]]
| {{Monzo| -1 -7 4 1 }}
| {{Monzo| -1 -7 4 1 }}
| 0.40
| 0.40
Line 735: Line 735:
| Ptolemisma
| Ptolemisma
|-
|-
| "
| 11
| 896/891
| [[896/891]]
| {{Monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
| 9.69
| 9.69
Line 742: Line 742:
| Pentacircle
| Pentacircle
|-
|-
| "
| 11
| 65536/65219
| [[65536/65219]]
| {{Monzo| 16 0 0 -2 -3 }}
| {{Monzo| 16 0 0 -2 -3 }}
| 8.39
| 8.39
Line 749: Line 749:
| Orgonisma
| Orgonisma
|-
|-
| "
| 11
| [[385/384]]
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
Line 756: Line 756:
| Keenanisma
| Keenanisma
|-
|-
| "
| 11
| 540/539
| [[540/539]]
| {{Monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
| 3.21
| 3.21
Line 764: Line 764:
|-
|-
| 13
| 13
| 65/64
| [[65/64]]
| {{Monzo| -6 0 1 0 0 1 }}
| {{Monzo| -6 0 1 0 0 1 }}
| 26.84
| 26.84
Line 770: Line 770:
|  
|  
|-
|-
| "
| 13
| [[91/90]]
| [[91/90]]
| {{Monzo| -1 -2 -1 1 0 1 }}
| {{Monzo| -1 -2 -1 1 0 1 }}
Line 777: Line 777:
| Superleap
| Superleap
|-
|-
| "
| 13
| 676/675
| [[676/675]]
| {{Monzo| 2 -3 -2 0 0 2 }}
| {{Monzo| 2 -3 -2 0 0 2 }}
| 2.56
| 2.56
Line 784: Line 784:
| Parizeksma
| Parizeksma
|}
|}
<references/>


== Linear temperaments ==
== Linear temperaments ==
Retrieved from "https://en.xen.wiki/w/19edo"