Small comma: Difference between revisions
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== Definition == | == Definition == | ||
A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 (0 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between [[10/9]] and [[9/8]], as well as [[81/64]] and [[5/4]], is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s. | A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 (0 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between [[10/9]] and [[9/8]], as well as [[81/64]] and [[5/4]], is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s. The [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos. | ||
For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]] | For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]] | ||
| Line 90: | Line 90: | ||
! [[Cents]] | ! [[Cents]] | ||
|- | |- | ||
| | | double large yoyo negative 2nd | ||
| lala-yoyo | | lala-yoyo | ||
| LLyy-2 | | LLyy-2 | ||
| Line 287: | Line 287: | ||
|- | |- | ||
| small diesis, [[magic comma]] | | small diesis, [[magic comma]] | ||
| | | laquinyo | ||
| Ly<sup>5</sup>-2 | | Ly<sup>5</sup>-2 | ||
| 3125 / 3072 | | 3125 / 3072 | ||
| Line 406: | Line 406: | ||
|- | |- | ||
| [[Würschmidt comma]] | | [[Würschmidt comma]] | ||
| | | saquadbigu | ||
| sg<sup>8</sup>3 | | sg<sup>8</sup>3 | ||
| 393216 / 390625 | | 393216 / 390625 | ||
| Line 504: | Line 504: | ||
|- | |- | ||
| 21-15-comma | | 21-15-comma | ||
| | |tribila-septriyo | ||
| | |L<sup>6</sup>y<sup>21</sup>-8 | ||
| | | | ||
| {{Monzo| -82 21 21 }} | | {{Monzo| -82 21 21 }} | ||
| Line 539: | Line 539: | ||
|- | |- | ||
| acute thirds comma | | acute thirds comma | ||
| | |quadsa-thirty-wegu | ||
| s<sup>4</sup>g<sup>31</sup>9 | | s<sup>4</sup>g<sup>31</sup>9 | ||
| | | | ||
| Line 546: | Line 546: | ||
|- | |- | ||
| 32-15-comma | | 32-15-comma | ||
| | |tritrila-quadquadbiyo | ||
| | |L<sup>9</sup>y<sup>32</sup>-12 | ||
| | | | ||
| {{Monzo| -125 32 32 }} | | {{Monzo| -125 32 32 }} | ||
| Line 553: | Line 553: | ||
|- | |- | ||
| 34-5-comma | | 34-5-comma | ||
| | |quinsa-sebigu | ||
| s<sup>5</sup>g<sup>34</sup>10 | | s<sup>5</sup>g<sup>34</sup>10 | ||
| | | | ||
| Line 575: | Line 575: | ||
| Schismic thirds chromatic semitone | | Schismic thirds chromatic semitone | ||
| | | | ||
| | | | ||
| | | | ||
| {{Monzo| -123 0 53 }} | | {{Monzo| -123 0 53 }} | ||
| Line 610: | Line 610: | ||
| 59-5-comma | | 59-5-comma | ||
| | | | ||
| | | | ||
| | | | ||
| {{Monzo| 137 0 -59 }} | | {{Monzo| 137 0 -59 }} | ||
| Line 639: | Line 639: | ||
| 84.467 | | 84.467 | ||
|- | |- | ||
| | | laruru negative 2nd | ||
| laruru | | laruru | ||
| Lrr-2 | | Lrr-2 | ||
| Line 745: | Line 745: | ||
|- | |- | ||
| blackjackisma | | blackjackisma | ||
| | | lasepru'aquadbiyo | ||
| Lr<sup>7</sup>y<sup>8</sup>-6 | | Lr<sup>7</sup>y<sup>8</sup>-6 | ||
| 854296875 / 843308032 | | 854296875 / 843308032 | ||
| Line 752: | Line 752: | ||
|- | |- | ||
| squalentine | | squalentine | ||
| | | laquadzo'atrigu | ||
| Lz<sup>4</sup>g<sup>3</sup>3 | | Lz<sup>4</sup>g<sup>3</sup>3 | ||
| 64827 / 64000 | | 64827 / 64000 | ||
| Line 766: | Line 766: | ||
|- | |- | ||
| gariboh | | gariboh | ||
| | | triru'aquinyo | ||
| r<sup>3</sup>y<sup>5</sup>-3 | | r<sup>3</sup>y<sup>5</sup>-3 | ||
| 3125 / 3087 | | 3125 / 3087 | ||
| Line 773: | Line 773: | ||
|- | |- | ||
| nuwell | | nuwell | ||
| | | quadru'ayo | ||
| r<sup>4</sup>y-3 | | r<sup>4</sup>y-3 | ||
| 2430 / 2401 | | 2430 / 2401 | ||
| Line 829: | Line 829: | ||
|- | |- | ||
| quince | | quince | ||
| | | lasepzo'agugu | ||
| Lz<sup>7</sup>gg4 | | Lz<sup>7</sup>gg4 | ||
| 823543 / 819200 | | 823543 / 819200 | ||
| Line 871: | Line 871: | ||
|- | |- | ||
| mirkwai | | mirkwai | ||
| | | quinru'aquadyo | ||
| r<sup>5</sup>y<sup>4</sup>-4 | | r<sup>5</sup>y<sup>4</sup>-4 | ||
| 16875 / 16807 | | 16875 / 16807 | ||
| Line 885: | Line 885: | ||
|- | |- | ||
| hemimage | | hemimage | ||
| | | satrizo'agu | ||
| sz<sup>3</sup>g3 | | sz<sup>3</sup>g3 | ||
| 10976 / 10935 | | 10976 / 10935 | ||
| Line 948: | Line 948: | ||
|- | |- | ||
| 8-35-comma | | 8-35-comma | ||
| lala- | | lala-quadbizoyo | ||
| LLz<sup>8</sup>y<sup>8</sup>2 | | LLz<sup>8</sup>y<sup>8</sup>2 | ||
| 2251875390625 / 2199023255552 | | 2251875390625 / 2199023255552 | ||
| Line 962: | Line 962: | ||
|- | |- | ||
| hexadecatone comma, 16-7-comma | | hexadecatone comma, 16-7-comma | ||
| sasa- | | sasa-quadquadru | ||
| ssr<sup>16</sup>-6 | | ssr<sup>16</sup>-6 | ||
| 35184372088832 / 33232930569601 | | 35184372088832 / 33232930569601 | ||
| Line 997: | Line 997: | ||
|- | |- | ||
| quarter tone comma | | quarter tone comma | ||
| | | | ||
| | | | ||
| | | | ||
| Line 1,153: | Line 1,153: | ||
| 80.537 | | 80.537 | ||
|- | |- | ||
| | | lalu unison | ||
| lalu | | lalu | ||
| L1u1 | | L1u1 | ||
| Line 1,203: | Line 1,203: | ||
|- | |- | ||
| thuja comma | | thuja comma | ||
| | | saquinlu'ayo | ||
| s1u<sup>5</sup>y2 | | s1u<sup>5</sup>y2 | ||
| 163840 / 161051 | | 163840 / 161051 | ||
| Line 1,280: | Line 1,280: | ||
|- | |- | ||
| orgonisma | | orgonisma | ||
| | | satrilu'aruru | ||
| s1u<sup>3</sup>rr1 | | s1u<sup>3</sup>rr1 | ||
| 65536 / 65219 | | 65536 / 65219 | ||
| Line 1,572: | Line 1,572: | ||
| 50.184 | | 50.184 | ||
|- | |- | ||
| | |solu 2nd | ||
| solu | | solu | ||
| 17o1u2 | | 17o1u2 | ||
| Line 1,586: | Line 1,586: | ||
| 34.283 | | 34.283 | ||
|- | |- | ||
| | |sutho unison | ||
| sutho | | sutho | ||
| 17u3o1 | | 17u3o1 | ||
| Line 1,593: | Line 1,593: | ||
| 33.617 | | 33.617 | ||
|- | |- | ||
| | |soruyo unison | ||
| soruyo | | soruyo | ||
| 17ory1 | | 17ory1 | ||
| Line 1,607: | Line 1,607: | ||
| 14.730 | | 14.730 | ||
|- | |- | ||
| | |suruyo comma | ||
| suruyo | | suruyo | ||
| 17ury-2 | | 17ury-2 | ||
| Line 1,701: | Line 1,701: | ||
| 88.801 | | 88.801 | ||
|- | |- | ||
| | |nutho unison | ||
| nutho | | nutho | ||
| 19u3o1 | | 19u3o1 | ||
| Line 1,708: | Line 1,708: | ||
| 44.970 | | 44.970 | ||
|- | |- | ||
| | |noru unison | ||
| noru | | noru | ||
| 19or1 | | 19or1 | ||
| Line 1,715: | Line 1,715: | ||
| 30.642 | | 30.642 | ||
|- | |- | ||
| | |nuruyo comma | ||
| nuruyo | | nuruyo | ||
| 19ury-2 | | 19ury-2 | ||
| Line 1,722: | Line 1,722: | ||
| 25.840 | | 25.840 | ||
|- | |- | ||
| | |nogugu 2nd | ||
| nogugu | | nogugu | ||
| 19ogg2 | | 19ogg2 | ||
| Line 1,743: | Line 1,743: | ||
| 18.128 | | 18.128 | ||
|- | |- | ||
| | |noluzo 2nd | ||
| noluzo | | noluzo | ||
| 19o1uz2 | | 19o1uz2 | ||
| Line 1,757: | Line 1,757: | ||
| 11.352 | | 11.352 | ||
|- | |- | ||
| | |nosugu unison | ||
| nosugu | | nosugu | ||
| 19o17ug1 | | 19o17ug1 | ||
| Line 1,778: | Line 1,778: | ||
| 8.2637 | | 8.2637 | ||
|- | |- | ||
| | |nusu comma | ||
| nusu | | nusu | ||
| 19u17u-2 | | 19u17u-2 | ||