46edo: Difference between revisions

Line 26:

! #

! Cents

! Approximate Ratios<ref name="interval ratios" group="note">~~Based on treating 46edo as a~~ 2.3.5.7.11.13.17.23 ~~subgroup, without ratios of 15 (except the superparticulars).~~ 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, 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}} Note that 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, 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 steps is slightly closer to 15/13 using direct approximation, but 10 steps 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" | [[SKULO interval names| SKULO notation]] (K or S = 1, U = 2)

@@ Line 26: / Line 26: @@
 ! #
 ! Cents
-! Approximate Ratios<ref name="interval ratios" group="note">Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, 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]]&mdash;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}} Note that 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, 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]]&mdash;9 steps is slightly closer to 15/13 using direct approximation, but 10 steps 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" | [[SKULO interval names| SKULO notation]] (K or S = 1, U = 2)