46edo: Difference between revisions
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→Intervals: added the EUs. fixed the monzos somewhat, could be better. removed unnecessary nowraps inside a table |
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! Approximate ratios<ref name="interval ratios" group="note">{{sg|limit=2.3.5.7.11.13.17.23 subgroup}} However, ratios of 15 are not included here, as except for 15/8 and 16/15 themselves 46edo has intervals involving the 15th harmonic poorly approximated in general. This is because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger. This prevents it from being [[consistent]] in the [[15-odd-limit]], as there is a discrepancy approximating [[15/13]] and [[26/15]]—9\46 is closer to 15/13 by a hair, but 10\46 represents the difference between 46edo's 15/8 and 13/8 and is more likely to appear in chords actually functioning as 15/13.</ref> | ! Approximate ratios<ref name="interval ratios" group="note">{{sg|limit=2.3.5.7.11.13.17.23 subgroup}} However, ratios of 15 are not included here, as except for 15/8 and 16/15 themselves 46edo has intervals involving the 15th harmonic poorly approximated in general. This is because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger. This prevents it from being [[consistent]] in the [[15-odd-limit]], as there is a discrepancy approximating [[15/13]] and [[26/15]]—9\46 is closer to 15/13 by a hair, but 10\46 represents the difference between 46edo's 15/8 and 13/8 and is more likely to appear in chords actually functioning as 15/13.</ref> | ||
! colspan="3" | [[Ups and downs notation]] | ! colspan="3" | [[Ups and downs notation]] | ||
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^^d2) | |||
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2) | ! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2) | ||
! colspan="2" | [[Solfege]] | ! colspan="2" | [[Solfege]] | ||
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| downminor | | downminor | ||
| zo | | zo | ||
| | | [a, b, 0, 1> | ||
| 7/6, 7/4 | | 7/6, 7/4 | ||
|- | |- | ||
| minor | | minor | ||
| fourthward wa | | fourthward wa | ||
| | | [a, b>, b < −1 | ||
| 32/27, 16/9 | | 32/27, 16/9 | ||
|- | |- | ||
| upminor | | upminor | ||
| gu | | gu | ||
| | | [a, b, −1> | ||
| 6/5, 9/5 | | 6/5, 9/5 | ||
|- | |- | ||
| dupminor | | dupminor | ||
| ilo | | ilo | ||
| | | [a, b, 0, 0, 1> | ||
| 11/9, 11/6 | | 11/9, 11/6 | ||
|- | |- | ||
| dudmajor | | dudmajor | ||
| lu | | lu | ||
| | | [a, b, 0, 0, −1> | ||
| 12/11, 18/11 | | 12/11, 18/11 | ||
|- | |- | ||
| downmajor | | downmajor | ||
| yo | | yo | ||
| | | [a, b, 1> | ||
| 5/4, 5/3 | | 5/4, 5/3 | ||
|- | |- | ||
| major | | major | ||
| fifthward wa | | fifthward wa | ||
| | | [a, b>, b > 1 | ||
| 9/8, 27/16 | | 9/8, 27/16 | ||
|- | |- | ||
| upmajor | | upmajor | ||
| ru | | ru | ||
| | | [a, b, 0, −1> | ||
| 9/7, 12/7 | | 9/7, 12/7 | ||
|} | |} |