46edo: Difference between revisions

! Approximate ratios<ref name="interval ratios" group="note">{{sg|limit=2.3.5.7.11.13.17.23&nbsp;subgroup}} This list does not include ratios of 15, since 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves. 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]]&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>

! colspan="3" | [[Ups and downs notation]]

! colspan="2" | [[Solfege]]

|-

| 0

| [[1/1]]

| perfect unison

|-

| 1

| [[81/80]], [[64/63]], [[49/48]]

| up unison

| ^1

| ^D

| K1, S1

| KD, SD

|-

| 2

| [[28/27]], [[36/35]], [[33/32]]

| downminor 2nd

|-

| 3

| [[25/24]], [[21/20]], [[22/21]], [[24/23]], [[23/22]]

| minor 2nd

| m2

| Eb

| m2, kkA1

| Eb, kkD#

|-

| 4

| [[16/15]], [[17/16]], [[18/17]]

| upminor 2nd

| ^m2

| ^Eb

| Km2, kA1

| KEb, kD#

|-

| 5

| [[13/12]], [[14/13]], [[15/14]]

| dupminor 2nd

|-

| 6

| [[12/11]], [[11/10]], [[23/21]]

| dudmajor 2nd

| vvM2

| vvE

| N2, sA1

| uE, sD#

|-

| 7

| [[10/9]]

| downmajor 2nd

|-

| 8

| [[9/8]]

| major 2nd

|-

| 9

| [[8/7]], [[23/20]]

| upmajor 2nd

|-

| 10

| [[7/6]]

| downminor 3rd

|-

| 11

| [[13/11]], [[20/17]]

| minor 3rd

|-

| 12

| [[6/5]]

| upminor 3rd

|-

| 13

| [[11/9]], [[17/14]], [[28/23]]

| dupminor 3rd

|-

| 14

| [[16/13]], [[26/21]], [[21/17]]

| dudmajor 3rd

|-

| 15

| [[5/4]]

| downmajor 3rd

|-

| 16

| [[14/11]], [[23/18]]

| major 3rd

|-

| 17

| [[9/7]], [[13/10]], [[22/17]]

| upmajor 3rd

|-

| 18

| [[21/16]], [[17/13]]

| down 4th

|-

| 19

| [[4/3]]

| perfect 4th

|-

| 20

| [[27/20]], [[23/17]]

| up 4th

|-

| 21

| [[11/8]]

| dup 4th

|-

| 22

| [[7/5]], [[18/13]], [[32/23]]

| vvA4, d5

| vvG#, Ab

|-

| 23

| [[17/12]], [[24/17]]

| downaug 4th, updim 5th

| vA4, ^d5

| vG#, ^Ab

| kA4, Kd5

| kG#, KAb

|-

| 24

| [[10/7]], [[13/9]], [[23/16]]

| aug 4th, dupdim 5th

| A4, ^^d5

| G#, ^^Ab

| A4, KKd5

| G#, KKAb

|-

| 25

| [[16/11]]

| dud 5th

| vv5

| vvA

| SA4, u5

| SG#, uA

|-

| 26

| [[40/27]], [[34/23]]

| down 5th

|-

| 27

| [[3/2]]

| perfect 5th

|-

| 28

| [[32/21]], [[26/17]]

| up 5th

|-

| 29

| [[14/9]], [[20/13]], [[17/11]]

| downminor 6th

|-

| 30

| [[11/7]]

| minor 6th

|-

| 31

| [[8/5]]

| upminor 6th

|-

| 32

| [[13/8]], [[21/13]], [[34/21]]

| dupminor 6th

|-

| 33

| [[18/11]], [[28/17]], [[23/14]]

| dudmajor 6th

|-

| 34

| [[5/3]]

| downmajor 6th

|-

| 35

| [[22/13]], [[17/10]]

| major 6th

|-

| 36

| [[12/7]]

| upmajor 6th

|-

| 37

| [[7/4]], [[40/23]]

| downminor 7th

|-

| 38

| [[16/9]], [[23/13]]

| minor 7th

|-

| 39

| [[9/5]]

| upminor 7th

|-

| 40

| [[11/6]], [[20/11]], [[42/23]]

| dupminor 7th

|-

| 41

| [[24/13]], [[13/7]], [[28/15]]

| dudmajor 7th

|-

| 42

| [[15/8]], [[32/17]], [[17/9]]

| downmajor 7th

|-

| 43

| [[48/25]], [[40/21]], [[21/11]], [[23/12]], [[44/23]]

| major 7th

| M7

| C#

| M7, KKd8

| C#, KKDb

|-

| 44

| [[27/14]], [[35/18]], [[64/33]]

| upmajor 7th

|-

| 45

| [[160/81]], [[63/32]], [[96/49]]

| down 8ve

|-

| 46

| [[2/1]]

| perfect 8ve

| minor

| fourthward wa

| 32/27, 16/9

|-

| major

| fifthward wa

| 9/8, 27/16

|-

| C upmajor or C up

|}

== Notation ==