Large comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Spt3125 (talk | contribs)
autopatrolled, Sysops
523 edits
added some simple ratios; formatting fixes
Spt3125 (talk | contribs)
autopatrolled, Sysops
523 edits
m {{Monzo}}, etc
Line 1: Line 1:
Lists of commas over 100 cents in size.
See also:
* [[Comma]]
* [[Unnoticeable comma]]
==3-limit commas==
==3-limit commas==


{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | ratio
! ratio
! | monzo
! monzo
! | cents
! cents
|-
|-
| | whole tone
| whole tone
| | [[9/8|9 / 8]]
| [[9/8|9 / 8]]
| | | -3 2 >
| {{Monzo| -3 2 }}
| | 203.910
| 203.910
|-
|-
| | apotome
| apotome
| | [[2187/2048|2187 / 2048]]
| [[2187/2048|2187 / 2048]]
| | | -11 7 >
| {{Monzo| -11 7 }}
| | 113.685
| 113.685
|-
|-
| | 19-comma
| 19-comma
| | 1162261467 / 1073741824
| 1162261467 / 1073741824
| | | -30 19 >
| {{Monzo| -30 19 }}
| | 137.145
| 137.145
|-
|-
| | 22-comma
| 22-comma
| | 34359738368 / 31381059609
| 34359738368 / 31381059609
| | | 35 -22 >
| {{Monzo| 35 -22 }}
| | 156.990
| 156.990
|-
|-
| | [[31_comma_temperaments|31-comma]]
| [[31_comma_temperaments|31-comma]]
| | 617673396283947 / 562949953421312
| 617673396283947 / 562949953421312
| | | -49 31 >
| {{Monzo| -49 31 }}
| | 160.605
| 160.605
|-
|-
| | 43-comma
| 43-comma
| |  
|  
| | | -68 43 >
| {{Monzo| -68 43 }}
| | 184.065
| 184.065
|-
|-
| | 46-comma
| 46-comma
| |  
|  
| | | 73 -46 >
| {{Monzo| 73 -46 }}
| | 110.070
| 110.070
|-
|-
| | 63-comma
| 63-comma
| |  
|  
| | | 100 -63 >
| {{Monzo| 100 -63 }}
| | 176.835
| 176.835
|-
|-
| | 77-comma
| 77-comma
| |  
|  
| | | 122 -77 >
| {{Monzo| 122 -77 }}
| | 176.815
| 176.815
|}
|}


Line 58: Line 65:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | ratio
! ratio
! | monzo
! monzo
! | cents
! cents
|-
|-
| | minor whole tone
| minor whole tone
| | 10 / 9
| 10 / 9
| | | 1 -2 1 >
| {{Monzo| 1 -2 1 }}
| | 182.40
| 182.404
|-
|-
| | 5-cycle major second, hexadecathird comma
| 5-cycle major second, hexadecathird comma
| | 152587890625 / 137438953472
| 152587890625 / 137438953472
| | | -37 0 16 >
| {{Monzo| -37 0 16 }}
| | 181.019
| 181.019
|-
|-
| | acute limma
| acute limma
| | 19073486328125 / 17592186044416
| 19073486328125 / 17592186044416
| | | -44 0 19 >
| {{Monzo| -44 0 19 }}
| | 139.961
| 139.961
|-
|-
| | meantone Integer cents comma
| <strike>meantone Integer cents comma</strike>
| |  
|  
| | | -1393 0 600 &gt;
| {{Monzo| -1393 0 600 }}
| | 188.228
| 188.228
|-
|-
| | 31-15-comma
| 31-15-comma
| |  
|  
| | | 121 -31 -31 &gt;
| {{Monzo| 121 -31 -31 }}
| | 136.330
| 136.330
|-
|-
| | 87-15-comma
| 87-15-comma
| |  
|  
| | | 340 -87 -87 &gt;
| {{Monzo| 340 -87 -87 }}
| | 120.622
| 120.622
|-
|-
| | enipucrop
| enipucrop
| | 1125 / 1024
| 1125 / 1024
| | | -10 2 3 &gt;
| {{Monzo| -10 2 3 }}
| | 162.851
| 162.851
|-
|-
| | supersharp
| supersharp
| | 800 / 729
| 800 / 729
| | | 5 -6 2 &gt;
| {{Monzo| 5 -6 2 }}
| | 160.897
| 160.897
|-
|-
| | gorgo
| gorgo
| | 2187 / 2000
| 2187 / 2000
| | | -4 7 -3 &gt;
| {{Monzo| -4 7 -3 }}
| | 154.744
| 154.744
|-
|-
| | large limma
| large limma
| | [[27/25|27 / 25]]
| [[27/25|27 / 25]]
| | | 0 3 -2 &gt;
| {{Monzo| 0 3 -2 }}
| | 133.238
| 133.238
|-
|-
| | lemba
| lemba
| | 140625 / 131072
| 140625 / 131072
| | | -17 2 6 &gt;
| {{Monzo| -17 2 6 }}
| | 121.792
| 121.792
|-
|-
| | sixix
| sixix
| | 3125 / 2916
| 3125 / 2916
| | | -2 -6 5 &gt;
| {{Monzo| -2 -6 5 }}
| | 119.839
| 119.839
|-
|-
| | diesma
| diesma
| | 10460353203 / 9765625000
| 10460353203 / 9765625000
| | | -3 21 -13 &gt;
| {{Monzo| -3 21 -13 }}
| | 118.977
| 118.977
|-
|-
| | comic
| comic
| | 5120000 / 4782969
| 5120000 / 4782969
| | | 13 -14 4 &gt;
| {{Monzo| 13 -14 4 }}
| | 117.885
| 117.885
|-
|-
| | just diatonic semitone
| just diatonic semitone
| | [[16/15|16 / 15]]
| [[16/15|16 / 15]]
| | | 4 -1 -1 &gt;
| {{Monzo| 4 -1 -1 }}
| | 111.731
| 111.731
|-
|-
| | beatles
| beatles
| | 524288 / 492075
| 524288 / 492075
| | | 19 -9 -2 &gt;
| {{Monzo| 19 -9 -2 }}
| | 109.778
| 109.778
|-
|-
| | wronecki
| wronecki
| | 531441 / 500000
| 531441 / 500000
| | | -5 12 -6 &gt;
| {{Monzo| -5 12 -6 }}
| | 105.578
| 105.578
|-
|-
| | wesley
| wesley
| | 78125 / 73728
| 78125 / 73728
| | | -13 -2 7 &gt;
| {{Monzo| -13 -2 7 }}
| | 100.286
| 100.286
|-
|-
| | 11-3/5-comma
| 11-3/5-comma
| | 48828125 / 45349632
| 48828125 / 45349632
| | | -8 -11 11 &gt;
| {{Monzo| -8 -11 11 }}
| | 127.946
| 127.946
|-
|-
| | 27-3/5-comma
| 27-3/5-comma
| |  
|  
| | | 20 27 -27 &gt;
| {{Monzo| 20 27 -27 }}
| | 122.315
| 122.315
|-
|-
| | 31-3/5-comma
| 31-3/5-comma
| |  
|  
| | | 23 31 -31 &gt;
| {{Monzo| 23 31 -31 }}
| | 184.880
| 184.880
|-
|-
| | Keemun Integer cents comma
| 300-3/5-comma
| |  
|  
| | | 221 300 -300 &gt;
| {{Monzo| 221 300 -300 }}
| | 107.614
| 107.614
|}
|}


Line 178: Line 185:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | monzo
! monzo
! | cents
! cents
|-
|-
| | major diatonic semitone, 15/14
| major diatonic semitone, 15/14
| | | -1 1 1 -1 &gt;
| {{Monzo| -1 1 1 -1 }}
| | 119.443
| 119.443
|-
|-
| | hexatone comma, 6-7-comma
| hexatone comma, 6-7-comma
| | | 17 0 0 -6 &gt;
| {{Monzo| 17 0 0 -6 }}
| | 187.045
| 187.045
|-
|-
| | hendecatone comma, 11-7-comma
| hendecatone comma, 11-7-comma
| | | 31 0 0 -11 &gt;
| {{Monzo| 31 0 0 -11 }}
| | 142.915
| 142.915
|-
|-
| | 41-7-comma
| 41-7-comma
| | | -115 0 0 41 &gt;
| {{Monzo| -115 0 0 41 }}
| | 121.862
| 121.862
|-
|-
| | 46-7-comma
| 46-7-comma
| | | -129 0 0 46 &gt;
| {{Monzo| -129 0 0 46 }}
| | 165.992
| 165.992
|-
|-
| | 25-7/5-comma
| 25-7/5-comma
| | | -12 0 -25 25 &gt;
| {{Monzo| -12 0 -25 25 }}
| | 162.805
| 162.805
|-
|-
| | 27-7/5-comma
| 27-7/5-comma
| | | -13 0 -27 27 &gt;
| {{Monzo| -13 0 -27 27 }}
| | 127.829
| 127.829
|-
|-
| | 41-7/5-comma
| 41-7/5-comma
| | | 20 0 41 -41 &gt;
| {{Monzo| 20 0 41 -41 }}
| | 117.000
| 117.000
|-
|-
| | 43-7/5-comma
| 43-7/5-comma
| | | 21 0 43 -43 &gt;
| {{Monzo| 21 0 43 -43 }}
| | 151.976
| 151.976
|-
|-
| | 45-7/5-comma
| 45-7/5-comma
| | | 22 0 45 -45 &gt;
| {{Monzo| 22 0 45 -45 }}
| | 186.951
| 186.951
|-
|-
| | 8-21-comma
| 8-21-comma
| | | -35 8 0 8 &gt;
| {{Monzo| -35 8 0 8 }}
| | 166.247
| 166.247
|-
|-
| | 13-21-comma
| 13-21-comma
| | | -57 13 0 13 &gt;
| {{Monzo| -57 13 0 13 }}
| | 120.152
| 120.152
|-
|-
| | 38-21-comma
| 38-21-comma
| | | 167 -38 0 -38 &gt;
| {{Monzo| 167 -38 0 -38 }}
| | 110.3255
| 110.326
|-
|-
| | 43-21-comma
| 43-21-comma
| | | 189 -43 0 -43 &gt;
| {{Monzo| 189 -43 0 -43 }}
| | 156.421
| 156.421
|-
|-
| | 7-35-comma
| 7-35-comma
| | | 36 0 -7 -7 &gt;
| {{Monzo| 36 0 -7 -7 }}
| | 114.023
| 114.023
|-
|-
| | 55-35-comma
| 55-35-comma
| | | -282 0 55 55 &gt;
| {{Monzo| -282 0 55 55 }}
| | 132.679
| 132.679
|-
|-
| | 63-35-comma
| 63-35-comma
| | | -323 0 63 63 &gt;
| {{Monzo| -323 0 63 63 }}
| | 173.796
| 173.796
|}
|}


Line 255: Line 262:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | monzo
! monzo
! | cents
! cents
|-
|-
| | 12/11, 3/4-tone, undecimal neutral second
| 12/11, 3/4-tone, undecimal neutral second
| | | 2 1 0 0 -1 &gt;
| {{Monzo| 2 1 0 0 -1 }}
| | 150.637
| 150.637
|-
|-
| | 11/10, 4/5-tone, Ptolemy's second
| 11/10, 4/5-tone, Ptolemy's second
| | | -1 0 -1 0 1 &gt;
| {{Monzo| -1 0 -1 0 1 }}
| | 165.004
| 165.004
|-
|-
| | 11-enipucrop, 9-11-comma
| 11-enipucrop, 9-11-comma
| | | -31 0 0 0 9 &gt;
| {{Monzo| -31 0 0 0 9 }}
| | 161.8615
| 161.862
|-
|-
| | 11-cycle major second prote, 33-11-comma
| 11-cycle major second prote, 33-11-comma
| | | -114 0 0 0 33 &gt;
| {{Monzo| -114 0 0 0 33 }}
| | 193.492
| 193.492
|}
|}


Line 280: Line 287:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | monzo
! monzo
! | cents
! cents
|-
|-
| | 14/13, 2/3-tone
| 14/13, 2/3-tone
| | | 1 0 0 1 0 -1 &gt;
| {{Monzo| 1 0 0 1 0 -1 }}
| | 128.298
| 128.298
|-
|-
| | 13/12, tridecimal 2/3-tone
| 13/12, tridecimal 2/3-tone
| | | -2 -1 0 0 0 1 &gt;
| {{Monzo| -2 -1 0 0 0 1 }}
| | 138.573
| 138.573
|-
|-
| | heptasixth comma, 13-cycle secor
| heptasixth comma, 13-cycle secor
| | | 26 0 0 0 0 -7 &gt;
| {{Monzo| 26 0 0 0 0 -7 }}
| | 116.306
| 116.306
|-
|-
| | heptadecasixth comma, neutral thirteenth comma
| heptadecasixth comma, neutral thirteenth comma
| | | 63 0 0 0 0 -17 &gt;
| {{Monzo| 63 0 0 0 0 -17 }}
| | 111.030
| 111.030
|-
|-
| | 13-cycle neutral second
| 13-cycle neutral second
| | | -196 0 0 0 0 53 &gt;
| {{Monzo| -196 0 0 0 0 53 }}
| | 147.966
| 147.966
|}
|}


Line 309: Line 316:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | monzo
! monzo
! | cents
! cents
|-
|-
| | 17/16, 17th harmonic
| 17/16, 17th harmonic
| | | -4 0 0 0 0 0 1 &gt;
| {{Monzo| -4 0 0 0 0 0 1 }}
| | 104.955
| 104.955
|}
|}


Line 322: Line 329:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | name(s)
! name(s)
! | monzo
! monzo
! | cents
! cents
|-
|-
| | 19-cycle meantone prima
| 19-cycle meantone prima
| | | -174 0 0 0 0 0 0 41 &gt;
| {{Monzo| -174 0 0 0 0 0 0 41 }}
| | 198.034
| 198.034
|-
|-
| | 19-cycle meantone secunda
| 19-cycle meantone secunda
| | | -191 0 0 0 0 0 0 45 &gt;
| {{Monzo| -191 0 0 0 0 0 0 45 }}
| | 188.086
| 188.086
|-
|-
| | 19-cycle minor tone
| 19-cycle minor tone
| | | -208 0 0 0 0 0 0 49 &gt;
| {{Monzo| -208 0 0 0 0 0 0 49 }}
| | 178.138
| 178.138
|-
|-
| | 19-cycle submajor second
| 19-cycle submajor second
| | | -225 0 0 0 0 0 0 53 &gt;
| {{Monzo| -225 0 0 0 0 0 0 53 }}
| | 168.190
| 168.190
|}
|}

Revision as of 16:10, 23 November 2018

Lists of commas over 100 cents in size.

See also:


3-limit commas

name(s) ratio monzo cents
whole tone 9 / 8 [-3 2⟩ 203.910
apotome 2187 / 2048 [-11 7⟩ 113.685
19-comma 1162261467 / 1073741824 [-30 19⟩ 137.145
22-comma 34359738368 / 31381059609 [35 -22⟩ 156.990
31-comma 617673396283947 / 562949953421312 [-49 31⟩ 160.605
43-comma [-68 43⟩ 184.065
46-comma [73 -46⟩ 110.070
63-comma [100 -63⟩ 176.835
77-comma [122 -77⟩ 176.815

5-limit commas

name(s) ratio monzo cents
minor whole tone 10 / 9 [1 -2 1⟩ 182.404
5-cycle major second, hexadecathird comma 152587890625 / 137438953472 [-37 0 16⟩ 181.019
acute limma 19073486328125 / 17592186044416 [-44 0 19⟩ 139.961
meantone Integer cents comma [-1393 0 600⟩ 188.228
31-15-comma [121 -31 -31⟩ 136.330
87-15-comma [340 -87 -87⟩ 120.622
enipucrop 1125 / 1024 [-10 2 3⟩ 162.851
supersharp 800 / 729 [5 -6 2⟩ 160.897
gorgo 2187 / 2000 [-4 7 -3⟩ 154.744
large limma 27 / 25 [0 3 -2⟩ 133.238
lemba 140625 / 131072 [-17 2 6⟩ 121.792
sixix 3125 / 2916 [-2 -6 5⟩ 119.839
diesma 10460353203 / 9765625000 [-3 21 -13⟩ 118.977
comic 5120000 / 4782969 [13 -14 4⟩ 117.885
just diatonic semitone 16 / 15 [4 -1 -1⟩ 111.731
beatles 524288 / 492075 [19 -9 -2⟩ 109.778
wronecki 531441 / 500000 [-5 12 -6⟩ 105.578
wesley 78125 / 73728 [-13 -2 7⟩ 100.286
11-3/5-comma 48828125 / 45349632 [-8 -11 11⟩ 127.946
27-3/5-comma [20 27 -27⟩ 122.315
31-3/5-comma [23 31 -31⟩ 184.880
300-3/5-comma [221 300 -300⟩ 107.614

7-limit commas

name(s) monzo cents
major diatonic semitone, 15/14 [-1 1 1 -1⟩ 119.443
hexatone comma, 6-7-comma [17 0 0 -6⟩ 187.045
hendecatone comma, 11-7-comma [31 0 0 -11⟩ 142.915
41-7-comma [-115 0 0 41⟩ 121.862
46-7-comma [-129 0 0 46⟩ 165.992
25-7/5-comma [-12 0 -25 25⟩ 162.805
27-7/5-comma [-13 0 -27 27⟩ 127.829
41-7/5-comma [20 0 41 -41⟩ 117.000
43-7/5-comma [21 0 43 -43⟩ 151.976
45-7/5-comma [22 0 45 -45⟩ 186.951
8-21-comma [-35 8 0 8⟩ 166.247
13-21-comma [-57 13 0 13⟩ 120.152
38-21-comma [167 -38 0 -38⟩ 110.326
43-21-comma [189 -43 0 -43⟩ 156.421
7-35-comma [36 0 -7 -7⟩ 114.023
55-35-comma [-282 0 55 55⟩ 132.679
63-35-comma [-323 0 63 63⟩ 173.796

11-limit commas

name(s) monzo cents
12/11, 3/4-tone, undecimal neutral second [2 1 0 0 -1⟩ 150.637
11/10, 4/5-tone, Ptolemy's second [-1 0 -1 0 1⟩ 165.004
11-enipucrop, 9-11-comma [-31 0 0 0 9⟩ 161.862
11-cycle major second prote, 33-11-comma [-114 0 0 0 33⟩ 193.492

13-limit commas

name(s) monzo cents
14/13, 2/3-tone [1 0 0 1 0 -1⟩ 128.298
13/12, tridecimal 2/3-tone [-2 -1 0 0 0 1⟩ 138.573
heptasixth comma, 13-cycle secor [26 0 0 0 0 -7⟩ 116.306
heptadecasixth comma, neutral thirteenth comma [63 0 0 0 0 -17⟩ 111.030
13-cycle neutral second [-196 0 0 0 0 53⟩ 147.966

17-limit commas

name(s) monzo cents
17/16, 17th harmonic [-4 0 0 0 0 0 1⟩ 104.955

19-limit commas

name(s) monzo cents
19-cycle meantone prima [-174 0 0 0 0 0 0 41⟩ 198.034
19-cycle meantone secunda [-191 0 0 0 0 0 0 45⟩ 188.086
19-cycle minor tone [-208 0 0 0 0 0 0 49⟩ 178.138
19-cycle submajor second [-225 0 0 0 0 0 0 53⟩ 168.190
Retrieved from "https://en.xen.wiki/index.php?title=Large_comma&oldid=38568"