Large comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 555733535 - Original comment: ** |
Contribution (talk | contribs) No edit summary |
||
| (100 intermediate revisions by 20 users not shown) | |||
| Line 1: | Line 1: | ||
A '''large comma''' is a [[comma]] whose size is approximately 100 cents and larger. As intervals, these commas are steps or even skips. | |||
For commas under 100 cents, see [[Medium comma]] for commas in between 30 and 100 cents or [[Small comma]] for commas under 30 cents. For commas under 3.5 cents, see [[Unnoticeable comma]]. | |||
Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is [[tempered out]]. | |||
The commas might be numerous, but there is no need to memorise all the names. For pretty much all use cases, it is perfectly acceptable – preferred, even – to just refer to a comma by the monzo or ratio, whichever is simpler. | |||
== Disputed status == | |||
To varying degrees, the status of each of the commas on this page as "a comma" is disputed. Due to their large size in [[cents]], many of these commas lead to high-[[damage]] temperaments when tempered out. Which calls into question whether they can actually be used as commas. | |||
Those which have a highly complex monzo and ratio tend to distribute their error more thinly across a wide number of [[JI]] intervals, making them more 'comma-like' than the others on this page. Some still dispute this due to their perhaps limited ability to make [[comma pump]]s. However they are more widely accepted than the ones on this page with simpler monzos and ratios. | |||
== List of commas, by prime limit == | |||
=== 3-limit commas === | |||
{{See also| Table of 3-limit commas }} | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| [[26-comma]] | |||
| 26wM, Thebiwama | |||
| 26wM | |||
| 2541865828329 / 2199023255552 | |||
| {{Monzo| -41 26 }} | |||
| 250.83 | |||
|- | |||
| 27-comma | |||
| 27wama | |||
| 27wM | |||
| 8796093022208 / 7625597484987 | |||
| {{Monzo| 43 -27 }} | |||
| 247.21 | |||
|- | |||
| [[9/8|Pythagorean whole tone]] | |||
| Wabima | |||
| w2M | |||
| 9 / 8 | |||
| {{Monzo| -3 2 }} | |||
| 203.91 | |||
|- | |||
| 43-comma | |||
| 43wama | |||
| 43wM | |||
| | |||
| {{Monzo| -68 43 }} | |||
| 184.07 | |||
|- | |||
| 63-comma | |||
| 63wama | |||
| 63wM | |||
| | |||
| {{Monzo| 100 -63 }} | |||
| 176.83 | |||
|- | |||
| [[31-comma]] | |||
| 31wama, Thiwewama | |||
| 31wM | |||
| 617673396283947 / <br>562949953421312 | |||
| {{Monzo| -49 31 }} | |||
| 160.61 | |||
|- | |||
| 22-comma | |||
| 22wama, Lebiwama | |||
| 22wM | |||
| 34359738368 / <br>31381059609 | |||
| {{Monzo| 35 -22 }} | |||
| 156.99 | |||
|- | |||
| [[19-comma]] | |||
| 19wama, Newama | |||
| 19wM | |||
| 1162261467 / 1073741824 | |||
| {{Monzo| -30 19 }} | |||
| 137.15 | |||
|- | |||
| [[2187/2048|Pythagorean apotome]], whitewood comma | |||
| Lawama | |||
| LwM | |||
| 2187 / 2048 | |||
| {{Monzo| -11 7 }} | |||
| 113.69 | |||
|- | |||
| 46-comma | |||
| 46wama | |||
| 46wM | |||
| | |||
| {{Monzo| 73 -46 }} | |||
| 110.07 | |||
|} | |||
=== 5-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| [[Shallowtone comma]] | |||
| Lalayobi | |||
| LLy1 | |||
| 295245 / 262144 | |||
| {{Monzo| -18 10 1 }} | |||
| 205.86 | |||
|- | |||
| Delorean comma | |||
| Tribigu | |||
| 6g3 | |||
| 17496 / 15625 | |||
| {{Monzo| 3 7 -6 }} | |||
| 195.80 | |||
|- | |||
| 31-3/5-comma | |||
| Thiwegu | |||
| 31g7 | |||
| | |||
| {{Monzo| 23 31 -31 }} | |||
| 184.88 | |||
|- | |||
| [[10/9|Minor whole tone]] | |||
| Yo | |||
| y2 | |||
| 10 / 9 | |||
| {{Monzo| 1 -2 1 }} | |||
| 182.40 | |||
|- | |||
| 5-cycle major second, hexadecathird comma | |||
| Lala-quadquadyo | |||
| LL16y-4 | |||
| 152587890625 / <br>137438953472 | |||
| {{Monzo| -37 0 16 }} | |||
| 181.02 | |||
|- | |||
| [[Nadir comma]] | |||
| Lalatrigu | |||
| LL3g1 | |||
| 1162261467 / 1048576000 | |||
| {{Monzo| -23 19 -3 }} | |||
| 178.20 | |||
|- | |||
<!-- until it gets a name | |||
| | |||
| Legu | |||
| 11g4 | |||
| 53747712 / 48828125 | |||
| {{Monzo| 13 8 -11 }} | |||
| 166.19 | |||
|- | |||
--> | |||
| Enipucrop comma | |||
| Latriyobi | |||
| L3y1 | |||
| 1125 / 1024 | |||
| {{Monzo| -10 2 3 }} | |||
| 162.85 | |||
|- | |||
| [[800/729|Supersharp comma]] | |||
| Sayoyo | |||
| syy2 | |||
| 800 / 729 | |||
| {{Monzo| 5 -6 2 }} | |||
| 160.90 | |||
|- | |||
| [[Nether comma]] | |||
| Lala-gugu | |||
| LLgg1 | |||
| 14348907 / 13107200 | |||
| {{Monzo| -19 15 -2 }} | |||
| 156.70 | |||
|- | |||
| [[Rarity comma]] | |||
| Quadla-theyo | |||
| 4L13y-5 | |||
| | |||
| {{Monzo| -57 17 13 }} | |||
| 155.31 | |||
|- | |||
| Laconic comma | |||
| Latrigubi | |||
| L3g2 | |||
| 2187 / 2000 | |||
| {{Monzo| -4 7 -3 }} | |||
| 154.74 | |||
|- | |||
| [[2048/1875|Smate, symbolic comma]] | |||
| Saquadgu | |||
| s4g3 | |||
| 2048 / 1875 | |||
| {{Monzo| 11 -1 -4 }} | |||
| 152.79 | |||
|- | |||
| [[Submerged comma]] | |||
| | |||
| | |||
| 146484375/134217728 | |||
| {{Monzo| -27 1 11 }} | |||
| 151.41 | |||
|- | |||
| Acute limma | |||
| Trila-neyobi | |||
| 3L19y-5 | |||
| 19073486328125 / <br>17592186044416 | |||
| {{Monzo| -44 0 19 }} | |||
| 139.96 | |||
|- | |||
| 31-15-comma | |||
| Tritrila-thiweyo | |||
| 9L31y-11 | |||
| | |||
| {{Monzo| -121 31 31 }} | |||
| 136.33 | |||
|- | |||
| [[177147/163840|Deeptone comma]], Tragicomma | |||
| Lagu | |||
| Lg1 | |||
| 177147 / 163840 | |||
| {{Monzo| -15 11 -1 }} | |||
| 135.19 | |||
|- | |||
| [[27/25|Bug comma]] | |||
| Gugu | |||
| gg2 | |||
| 27 / 25 | |||
| {{Monzo| 0 3 -2 }} | |||
| 133.24 | |||
|- | |||
| 11-3/5-comma | |||
| Leyo | |||
| 11y-2 | |||
| 48828125 / 45349632 | |||
| {{Monzo| -8 -11 11 }} | |||
| 127.95 | |||
|- | |||
| 27-3/5-comma | |||
| Tritritrigu | |||
| 27g6 | |||
| | |||
| {{Monzo| 20 27 -27 }} | |||
| 122.31 | |||
|- | |||
| Lemba comma | |||
| Latribiyo | |||
| L6y-2 | |||
| 140625 / 131072 | |||
| {{Monzo| -17 2 6 }} | |||
| 121.79 | |||
|- | |||
| 87-15-comma | |||
| | |||
| | |||
| | |||
| {{Monzo| 340 -87 -87 }} | |||
| 120.62 | |||
|- | |||
| [[3125/2916|Sixix comma]] | |||
| Quinyo | |||
| 5y1 | |||
| 3125 / 2916 | |||
| {{Monzo| -2 -6 5 }} | |||
| 119.84 | |||
|- | |||
| Diesma | |||
| Lathegu | |||
| L13g3 | |||
| 10460353203 / <br>9765625000 | |||
| {{Monzo| -3 21 -13 }} | |||
| 118.98 | |||
|- | |||
| Comic comma | |||
| Saquadyobi | |||
| s4y2 | |||
| 5120000 / 4782969 | |||
| {{Monzo| 13 -14 4 }} | |||
| 117.88 | |||
|- | |||
| [[16/15|Father comma]] | |||
| Gubi | |||
| g2 | |||
| 16 / 15 | |||
| {{Monzo| 4 -1 -1 }} | |||
| 111.73 | |||
|- | |||
| Beatles comma | |||
| Sasa-gugu | |||
| ssgg3 | |||
| 524288 / 492075 | |||
| {{Monzo| 19 -9 -2 }} | |||
| 109.78 | |||
|- | |||
| 300-3/5-comma | |||
| | |||
| | |||
| | |||
| {{Monzo| -221 -300 300 }} | |||
| 107.61 | |||
|- | |||
| Wronecki comma | |||
| Latribigu | |||
| L6g2 | |||
| 531441 / 500000 | |||
| {{Monzo| -5 12 -6 }} | |||
| 105.58 | |||
|- | |||
|[[82944/78125|Migmag comma]] | |||
|Sepgu 3rd | |||
|g^7 3 | |||
|82944 / 78125 | |||
|[10 4 -7⟩ | |||
|103.62 | |||
|- | |||
| [[Wesley comma]] | |||
| Lasepyobi | |||
| L7y-2 | |||
| 78125 / 73728 | |||
| {{monzo| -13 -2 7 }} | |||
| 100.29 | |||
|} | |||
=== 7-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| Hexatone comma, 6-7-comma | |||
| Satribiru | |||
| s6r-2 | |||
| 131072 / 117649 | |||
| {{Monzo| 17 0 0 -6 }} | |||
| 187.04 | |||
|- | |||
| 45-7/5-comma | |||
| Quintritriruyo | |||
| 45ry-27 | |||
| | |||
| {{Monzo| 22 0 45 -45 }} | |||
| 186.95 | |||
|- | |||
| 63-35-comma | |||
| Tritribila-septritrizoyo | |||
| 18L63zy8 | |||
| | |||
| {{Monzo| -323 0 63 63 }} | |||
| 173.80 | |||
|- | |||
| 8-21-comma | |||
| Lala-quadbizo | |||
| LL8z4 | |||
| 37822859361 / <br>34359738368 | |||
| {{Monzo| -35 8 0 8 }} | |||
| 166.25 | |||
|- | |||
| 46-7-comma | |||
| Sepla-twethebizobi | |||
| 7L46z18 | |||
| | |||
| {{Monzo| -129 0 0 46 }} | |||
| 165.99 | |||
|- | |||
| 25-7/5-comma | |||
| Quinquinzogu | |||
| 25zg17 | |||
| | |||
| {{Monzo| -12 0 -25 25 }} | |||
| 162.80 | |||
|- | |||
| 43-21-comma | |||
| Quadtrisa-fotherubi | |||
| 12s43r-11 | |||
| | |||
| {{Monzo| 189 -43 0 -43 }} | |||
| 156.42 | |||
|- | |||
| [[35/32|Septimal neutral second]], octave-reduced 35th harmonic | |||
| Zoyo | |||
| zy2 | |||
| 35 / 32 | |||
| {{monzo| -5 0 1 1 }} | |||
| 155.14 | |||
|- | |||
| 43-7/5-comma | |||
| Fotheruyo | |||
| 43ry-26 | |||
| | |||
| {{Monzo| 21 0 43 -43 }} | |||
| 151.98 | |||
|- | |||
| [[49/45|Swetismic neutral second]] | |||
| Zozogu | |||
| zzg3 | |||
| 49 / 45 | |||
| {{Monzo| 0 -2 -1 2 }} | |||
| 147.43 | |||
|- | |||
<!-- until it gets a name | |||
| [[160/147]] | |||
| Ruruyobi | |||
| rry1 | |||
| 160 / 147 | |||
| {{Monzo| 5 -1 1 -2 }} | |||
| 146.71 | |||
--> | |||
|- | |||
| Hendecatone comma, 11-7-comma | |||
| Sasa-leru | |||
| ss11r-4 | |||
| 2147483648 / 1977326743 | |||
| {{Monzo| 31 0 0 -11 }} | |||
| 142.92 | |||
|- | |||
| [[243/224|Septimal subtone]] | |||
| Larubi | |||
| Lr1 | |||
| 243 / 224 | |||
| {{Monzo| -5 5 0 -1 }} | |||
| 140.95 | |||
|- | |||
| 55-35-comma | |||
| Quadquadla-lequinzoyobi | |||
| 16L55zy7 | |||
| | |||
| {{Monzo| -282 0 55 55 }} | |||
| 132.68 | |||
|- | |||
| 27-7/5-comma | |||
| Tritritrizogu | |||
| 27zg18 | |||
| | |||
| {{Monzo| -13 0 -27 27 }} | |||
| 127.83 | |||
|- | |||
| 41-7-comma | |||
| Tribila-fowezo | |||
| 6L41z16 | |||
| | |||
| {{Monzo| -115 0 0 41 }} | |||
| 121.86 | |||
|- | |||
| 13-21-comma | |||
| Quadla-thezobi | |||
| 4L13z5 | |||
| | |||
| {{Monzo| -57 13 0 13 }} | |||
| 120.15 | |||
|- | |||
| [[15/14|Septimal major semitone]] | |||
| Ruyo | |||
| ry1 | |||
| 15 / 14 | |||
| {{Monzo| -1 1 1 -1 }} | |||
| 119.44 | |||
|- | |||
| [[Primate comma]] | |||
| Saru | |||
| sr2 | |||
| 16384 / 15309 | |||
| {{Monzo| 14 -7 0 -1 }} | |||
| 117.49 | |||
|- | |||
| 41-7/5-comma | |||
| Foweruyo | |||
| 41ry-25 | |||
| | |||
| {{Monzo| 20 0 41 -41 }} | |||
| 117.00 | |||
|- | |||
| 7-35-comma | |||
| Sasa-seprugu | |||
| ss7rg1 | |||
| 68719476736 / <br>64339296875 | |||
| {{Monzo| 36 0 -7 -7 }} | |||
| 114.02 | |||
|- | |||
| 38-21-comma | |||
| Lesa-nebiru | |||
| 11s38r-10 | |||
| | |||
| {{Monzo| 167 -38 0 -38 }} | |||
| 110.33 | |||
|- | |||
| 3-9/7-comma | |||
| Triru | |||
| 3r-2 | |||
| 729 / 686 | |||
| {{Monzo| -1 6 0 -3 }} | |||
| 105.25 | |||
|} | |||
=== 11-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| 11-cycle major second prote, 33-11-comma | |||
| Quinla-letrilobi | |||
| 5L33(1o)-7 | |||
| | |||
| {{Monzo| -114 0 0 0 33 }} | |||
| 193.49 | |||
|- | |||
| 4/5-tone, Ptolemy's second | |||
| Logu | |||
| 1og2 | |||
| [[11/10|11 / 10]] | |||
| {{Monzo| -1 0 -1 0 1 }} | |||
| 165.00 | |||
|- | |||
| 11-enipucrop, 9-11-comma | |||
| Latritrilo | |||
| L9(1o)-2 | |||
| 2357947691 / 2147483648 | |||
| {{Monzo| -31 0 0 0 9 }} | |||
| 161.86 | |||
|- | |||
| 3/4-tone, undecimal neutral second | |||
| Lu | |||
| 1u2 | |||
| [[12/11|12 / 11]] | |||
| {{Monzo| 2 1 0 0 -1 }} | |||
| 150.64 | |||
|- | |||
| [[77/72|Undecimal secor]] | |||
| Lozo | |||
| 1oz2 | |||
| [[77/72|77 / 72]] | |||
| {{Monzo| -3 -2 0 1 1 }} | |||
| 116.23 | |||
|} | |||
=== 13-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| 13-cycle neutral second | |||
| Quadbila-fithethobi | |||
| 8L53(3o)7 | |||
| | |||
| {{Monzo| -196 0 0 0 0 53 }} | |||
| 147.97 | |||
|- | |||
| Large tridecimal 2/3-tone, tridecimal neutral second | |||
| Tho | |||
| 3o2 | |||
| [[13/12|13 / 12]] | |||
| {{Monzo| -2 -1 0 0 0 1 }} | |||
| 138.57 | |||
|- | |||
| Small tridecimal 2/3-tone, tridecimal limma, trienthird | |||
| Thuzo | |||
| 3uz2 | |||
| [[14/13|14 / 13]] | |||
| {{Monzo| 1 0 0 1 0 -1 }} | |||
| 128.30 | |||
|- | |||
| Heptasixth comma, 13-cycle secor | |||
| Sasepthu | |||
| s7(3u)1 | |||
| 67108864 / 62748517 | |||
| {{monzo| 26 0 0 0 0 -7 }} | |||
| 116.31 | |||
|- | |||
| Heptadecasixth comma, neutral thirteenth comma | |||
| Sasa-sethubi | |||
| ss17(3u)-2 | |||
| | |||
| {{Monzo| 63 0 0 0 0 -17 }} | |||
| 111.03 | |||
|} | |||
=== 17-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| 17-limit rational eventone | |||
| Sogubi | |||
| 17og3 | |||
| [[17/15|17 / 15]] | |||
| {{Monzo| 0 -1 -1 0 0 0 1 }} | |||
| 216.69 | |||
|- | |||
| Large septendecimal semitone, octave-reduced 17th harmonic | |||
| Iso | |||
| 17o2 | |||
| [[17/16|17 / 16]] | |||
| {{Monzo| -4 0 0 0 0 0 1 }} | |||
| 104.96 | |||
|} | |||
=== 19-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| 19-cycle meantone prima | |||
| Tribila-foweno | |||
| 6L41(19o)13 | |||
| | |||
| {{Monzo| -174 0 0 0 0 0 0 41 }} | |||
| 198.03 | |||
|- | |||
| Undevicesimal rational meantone | |||
| Nosu | |||
| 19o17u2 | |||
| [[19/17|19 / 17]] | |||
| {{Monzo| 0 0 0 0 0 0 -1 1 }} | |||
| 192.56 | |||
|- | |||
| 19-cycle meantone secunda | |||
| Tribila-quintritrino | |||
| 6L45(19o)14 | |||
| | |||
| {{Monzo| -191 0 0 0 0 0 0 45 }} | |||
| 188.09 | |||
|- | |||
| 19-cycle minor tone | |||
| Sepla-sepsepno | |||
| 7L49(19o)15 | |||
| | |||
| {{Monzo| -208 0 0 0 0 0 0 49 }} | |||
| 178.14 | |||
|- | |||
| Undevicesimal rational submajor second | |||
| Nuzo | |||
| 19uz2 | |||
| [[21/19|21 / 19]] | |||
| {{Monzo| 0 1 0 1 0 0 0 -1 }} | |||
| 173.27 | |||
|- | |||
| 19-cycle submajor second | |||
| Quadbila-fithenobi | |||
| 8L53(19o)16 | |||
| | |||
| {{Monzo| -225 0 0 0 0 0 0 53 }} | |||
| 168.19 | |||
|- | |||
| [[81/76|Dog comma]] | |||
| Inu | |||
| 19u1 | |||
| 81 / 76 | |||
| {{Monzo| -2 4 0 0 0 0 0 -1 }} | |||
| 110.31 | |||
|} | |||
=== 23-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| Large vicesimotertial neutral second | |||
| Twethoru | |||
| 23or2 | |||
| [[23/21|23 / 21]] | |||
| {{Monzo| 0 -1 0 -1 0 0 0 0 1 }} | |||
| 157.49 | |||
|- | |||
| Small vicesimotertial neutral second | |||
| Twethuyoyo | |||
| 23uyy1 | |||
| [[25/23|25 / 23]] | |||
| {{Monzo| 0 0 2 0 0 0 0 0 -1 }} | |||
| 144.35 | |||
|- | |||
| Octave-reduced 69th harmonic | |||
| Twetho | |||
| 23o2 | |||
| [[69/64|69 / 64]] | |||
| {{monzo| -6 1 0 0 0 0 0 0 1 }} | |||
| 130.23 | |||
|} | |||
=== Higher-limit commas === | |||
{| class="wikitable" | |||
|- | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation|Color name]] | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |||
| Octave-reduced 29th subharmonic | |||
| Twenu | |||
| 29u2 | |||
| [[32/29|32 / 29]] | |||
| 2.29 {{monzo| 5 -1 }} | |||
| 170.42 | |||
|- | |||
<!-- until it gets a name | |||
| [[47/44]] | |||
| Fosolu | |||
| 47o1u2 | |||
| 47 / 44 | |||
| 2.11.47 {{monzo| -2 -1 1 }} | |||
| 114.19 | |||
--> | |||
|} | |||
[[Category:Large commas| ]] <!-- main article --> | |||
[[Category:Lists of commas]] | |||
{{todo|complete table|add color name}} | |||