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{{Harmonics in equal|43}}
{{Harmonics in equal|43}}
{{Harmonics in equal|43|start=12|columns=9|collapsed=true|title=Approximation of prime harmonics in 43edo (continued)}}
{{Harmonics in equal|43|start=12|columns=9|collapsed=true|title=Approximation of prime harmonics in 43edo (continued)}}
Although not [[consistent]], 43edo performs quite well in very high prime limits. It has unambiguous mappings for all prime harmonics up to ''113'' (after which the demands on its pitch resolution finally become too great), with the sole exceptions of 23, 71, 89, and 103, making a great [[#Ringer 43|Ringer scale]]. Mappings for ratios between these prime harmonics can then be derived from those for the primes themselves, allowing for a complete set of approximations to the first 16 harmonics in the harmonic series and an almost-complete approximation of the first 32 harmonics, although the limited consistency will give some unusual results. Indeed, one step of 43edo is very close to the [[64/63|septimal comma (64/63)]]; similarly, two steps is close to [[32/31]], and four steps tunes [[16/15]] almost perfectly.
Although not [[consistent]], 43edo performs quite well in very high prime limits. It has unambiguous mappings for all prime harmonics up to ''113'' (after which the demands on its pitch resolution finally become too great), with the sole exceptions of 23, 71, 89, and 103, making a great [[#Ringer 43|Ringer scale]]. Mappings for ratios between these prime harmonics can then be derived from those for the primes themselves, allowing for a complete set of approximations to the first 16 harmonics in the harmonic series and an almost-complete approximation of the first 32 harmonics, although the limited consistency will give some unusual results. Indeed, one step of 43edo is very close to the [[64/63|septimal comma (64/63)]]; similarly, two steps is close to [[32/31]], and four steps tunes [[16/15]] almost perfectly.


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== Intervals ==
== Intervals ==
The distance from C to C♯ is 3 edosteps (or keys, frets). Thus one edostep equals one third of a sharp.  
The distance from C to C♯ is 3 edosteps (or keys, frets). Thus one edostep equals one third of a sharp.  
{{Interval table}}
{| class="wikitable center-all right-2 left-3"
|-
! #
! Cents
! Approximate ratios*
! colspan="3" | [[Ups and downs notation]]
|-
| 0
| 0.000
| 1/1
| P1
| perfect unison
| D
|-
| 1
| 27.907
| ''36/35'', 50/49, 64/63, 65/64, 66/65
| ^1, d2
| up unison, dim 2nd
| ^D, Ebb
|-
| 2
| 55.814
| ''49/48'', 33/32
| vA1, ^d2
| downaug unison, updim 2nd
| vD#, ^Ebb
|-
| 3
| 83.721
| 25/24, 21/20, ''28/27'', 22/21, ''18/17''
| A1, vm2
| aug 1sn, downminor 2nd
| D#, vEb
|-
| 4
| 111.628
| 16/15, 15/14, 17/16
| m2
| minor 2nd
| Eb
|-
| 5
| 139.535
| 12/11, 13/12, 14/13
| ^m2
| upminor 2nd
| ^Eb
|-
| 6
| 167.442
| 11/10
| vM2
| downmajor 2nd
| vE
|-
| 7
| 195.349
| 9/8, 10/9
| M2
| major 2nd
| E
|-
| 8
| 223.256
| 8/7
| ^M2, d3
| upmajor 2nd, dim 3rd
| ^E, Fb
|-
| 9
| 251.163
| 15/13
| vA2, ^d3
| downaug 2nd, updim 3rd
| vE#, ^Fb
|-
| 10
| 279.070
| 7/6, 13/11
| A2, vm3
| aug 2nd, downminor 3rd
| E#, vF
|-
| 11
| 306.977
| 6/5
| m3
| minor 3rd
| F
|-
| 12
| 334.884
| 39/32, 17/14
| ^m3
| upminor 3rd
| ^F
|-
| 13
| 362.791
| 16/13, 21/17, ''11/9''
| vM3
| downmajor 3rd
| vF#
|-
| 14
| 390.698
| 5/4
| M3
| major 3rd
| F#
|-
| 15
| 418.605
| ''9/7'', 14/11
| ^M3, d4
| upmajor 3rd, dim 4th
| ^F#, Gb
|-
| 16
| 446.512
| 13/10
| vA3, ^d4
| downaug 3rd, updim 4th
| vFx, ^Gb
|-
| 17
| 474.419
| 21/16
| v4
| down 4th
| vG
|-
| 18
| 502.326
| 4/3
| P4
| perfect 4th
| G
|-
| 19
| 530.233
| 15/11
| ^4
| up 4th
| ^G
|-
| 20
| 558.140
| 11/8, 18/13
| vA4
| downaug 4th
| vG#
|-
| 21
| 586.047
| 45/32, 7/5, 24/17
| A4, vd5
| aug 4th, downdim 5th
| G#, ^Ab
|-
| 22
| 613.953
| 64/45, 10/7, 17/12
| ^A4, d5
| upaug 4th, dim 5th
| ^G#, Ab
|-
| 23
| 641.860
| 16/11, 13/9
| ^d5
| updim 5th
| ^Ab
|-
| 24
| 669.767
| 22/15
| v5
| down 5th
| vA
|-
| 25
| 697.674
| 3/2
| P5
| perfect 5th
| A
|-
| 26
| 725.581
| 32/21
| ^5
| up 5th
| ^A
|-
| 27
| 753.488
| 20/13
| vA5, ^d6
| downaug 5th, updim 6th
| vA#, ^Bbb
|-
| 28
| 781.395
| ''14/9'', 11/7
| A5, vm6
| aug 5th, downminor 6th
| A#, vBb
|-
| 29
| 809.302
| 8/5
| m6
| minor 6th
| Bb
|-
| 30
| 837.209
| 13/8, 34/21, ''18/11''
| ^m6
| upminor 6th
| ^Bb
|-
| 31
| 865.116
| 64/39, 28/17
| vM6
| downmajor 6th
| vB
|-
| 32
| 893.023
| 5/3
| M6
| major 6th
| B
|-
| 33
| 920.930
| 12/7, 22/13
| ^M6, d7
| upmajor 6th, dim 7th
| ^B, Cb
|-
| 34
| 948.837
| 26/15
| vA6, ^d7
| downaug 6th, updim 7th
| vB#, ^Cb
|-
| 35
| 976.744
| 7/4
| A6, vm7
| aug 6th, downminor 7th
| B#, vC
|-
| 36
| 1004.651
| 16/9, 9/5
| m7
| minor 7th
| C
|-
| 37
| 1032.558
| 20/11
| ^m7
| upminor 7th
| ^C
|-
| 38
| 1060.465
| 11/6, 24/13, 13/7
| vM7
| downmajor 7th
| vC#
|-
| 39
| 1088.372
| 15/8, 28/15, 32/17
| M7
| major 7th
| C#
|-
| 40
| 1116.279
| 48/25, 40/21, ''27/14'', 21/11, ''17/9''
| ^M7, d8
| upmajor 7th, dim 8ve
| ^C#, Db
|-
| 41
| 1144.186
| ''96/49'', 64/33
| vA7, ^d8
| downaug 7th, updim 8ve
| vCx, ^Db
|-
| 42
| 1172.093
| ''35/18'', 49/25, 63/32, 65/33, 128/65
| A7, v8
| aug 7th, down 8ve
| Cx, vD
|-
| 43
| 1200.000
| 2/1
| P8
| perfect 8ve
| D
|}
 
<nowiki>*</nowiki> As a 17-limit system


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chords and Chord Progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
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