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72edo: Difference between revisions

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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m formatting
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
→Commas: started comma table, not sure if this is not overkill
Line 728: Line 728:
Commas tempered out by 72edo include…
Commas tempered out by 72edo include…


{| class="wikitable"
{| class="wikitable center-1 center-2 right-4"
! [[Harmonic limit|Prime<br>Limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cents]]
! Name(s)
|-
|-
! | 3-limit
| 3
| [[531441/524288|(12 digits)]]
| {{Monzo|-19 12 }}
| 23.46
| Pythagorean comma
|-
|-
| |<nowiki> Pythagorean comma = 531441/524288 = |-19 12</nowiki>&gt;
| 5
|}
| [[15625/15552]]
| {{Monzo| -6 -5 6 }}
| 8.11
| Kleisma
|-
| 5
| [[34171875/33554432|(16 digits)]]
| {{Monzo| -25 7 6 }}
| 31.57
| [[Ampersand]]
|-
| 5
| [[129140163/128000000|(18 digits)]]
| {{Monzo| -13 17 -6 }}
| 15.35
| [[Graviton]]
|-
| 5
| <abbr title="7629394531250/7625597484987">(26 digits)</abbr>
| {{Monzo| 1 -27 18 }}
| 0.86
| [[Ennealimma]]
|-
| 7
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
| 7.71
| Septimal kleisma, Marvel comma
|-
| 7
| [[1029/1024]]
|
|
|
|-
| 7
| [[2401/2400]]
| {{Monzo| -5 -1 -2 4 }}
| 0.72
| Breedsma
|-
| 7
| [[4375/4374]]
| {{Monzo| -1 -7 4 1 }}
| 0.40
| Ragisma
|-
| 7
| [[16875/16807]]
|
|
|
|-
| 7
| [[19683/19600]]
|
|
|
|-
| 7
| [[420175/419904]]
|
|
|
|-
| 7
| [[250047/250000]]
|
|
|
|-
| 11
| [[243/242]]
| {{Monzo| -1 5 0 0 -2}}
| 7.14
| Rastma
|-
| 11
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| 4.50
| Keenanisma
|-
| 11
| [[441/440]]
|
|
|
|-
| 11
| [[540/539]]
|
|
|
|-
| 11
| [[1375/1372]]
|
|
|
|-
| 11
| [[3025/3024]]
| {{Monzo| -4 -3 2 -1 2 }}
| 0.57
| Lehmerisma
|-
| 11
| [[4000/3993]]
|
|
|
|-
| 11
| [[6250/6237]]
|
|
|
|-
| 11
| [[9801/9800]]
| {{Monzo| -3 4 -2 -2 2 }}
| 0.18
| Kalisma, Gauss' comma
|-
| 13
| [[169/168]]
|
|
|
|-
| 13
| [[325/324]]
| {{Monzo| -2 -4 2 0 0 1 }}
| 5.34
| Marveltwin comma
|-
| 13
| [[351/350]]
| {{Monzo| -1 3 -2 -1 0 1 }}
| 4.94
| Ratwolfsma
|-
| 13
| [[364/363]]
| {{Monzo| 2 -1 0 1 -2 1 }}
| 4.76
| Gentle comma
|-
| 13
| [[625/624]]
|
|
|
|-
| 13
| [[676/675]]
| {{Monzo| 2 -3 -2 0 0 2 }}
| 2.56
| Island comma, Parizeksma


{| class="wikitable"
|-
|-
! | 5-limit
| 13
| [[729/728]]
|
|
|
|-
| 13
| [[1001/1000]]
|
|
|
|-
|-
| |<nowiki> kleisma = 15625/15552 = |-6 -5 6</nowiki>&gt;
| 13
 
| [[1575/1573]]
ampersand = 34171875/33554432 = |-25 7 6&gt;
|
 
|
graviton = 129140163/128000000 = |-13 17 -6&gt;
|
 
|-
ennealimma = 7629394531250/7625597484987 = |1 -27 18&gt;
| 13
|}
| [[1716/1715]]
 
|
{| class="wikitable"
|
|
|-
|-
! | 7-limit
| 13
! | 11-limit
| [[2080/2079]]
! | 13-limit
|
|
|
|-
|-
| | ...............................
| 13
 
| [[6656/6655]]
225/224
|
 
|
1029/1024
|
 
2401/2400
 
4375/4374
 
16875/16807
 
19683/19600
 
420175/419904
 
250047/250000
| | .......................
 
243/242
 
385/384
 
441/440
 
540/539
 
1375/1372
 
3025/3024
 
4000/3993
 
6250/6237
 
9801/9800
| | .......................
 
169/168
 
325/324
 
351/350
 
364/363
 
625/624
 
676/675
 
729/728
 
1001/1000
 
1575/1573
 
1716/1715
 
2080/2079
 
6656/6655
|}
|}


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