46edo: Difference between revisions
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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]] | ||
| Line 613: | Line 614: | ||
| 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 | ||
|} | |} | ||
| Line 664: | Line 665: | ||
| zo | | zo | ||
| 6:7:9 | | 6:7:9 | ||
| | | 0–10–27 | ||
| C vEb G | | C vEb G | ||
| Cvm | | Cvm | ||
| Line 671: | Line 672: | ||
| gu | | gu | ||
| 10:12:15 | | 10:12:15 | ||
| | | 0–12–27 | ||
| C ^Eb G | | C ^Eb G | ||
| C^m | | C^m | ||
| Line 678: | Line 679: | ||
| ilo | | ilo | ||
| 18:22:27 | | 18:22:27 | ||
| | | 0–13–27 | ||
| C ^^Eb G | | C ^^Eb G | ||
| C^^m | | C^^m | ||
| Line 685: | Line 686: | ||
| lu | | lu | ||
| 22:27:33 | | 22:27:33 | ||
| | | 0–14–27 | ||
| C vvE G | | C vvE G | ||
| Cvv | | Cvv | ||
| Line 692: | Line 693: | ||
| yo | | yo | ||
| 4:5:6 | | 4:5:6 | ||
| | | 0–15–27 | ||
| C vE G | | C vE G | ||
| Cv | | Cv | ||
| Line 699: | Line 700: | ||
| ru | | ru | ||
| 14:18:21 | | 14:18:21 | ||
| | | 0–17–27 | ||
| C ^E G | | C ^E G | ||
| C^ | | C^ | ||
| Line 777: | Line 778: | ||
For the 23rd-octave temperament that 46edo supports which combines all above 23-note circles, see [[icositritonic]]. | For the 23rd-octave temperament that 46edo supports which combines all above 23-note circles, see [[icositritonic]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||