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__FORCETOC__
{{interwiki
-----
| de = 46-EDO
| en = 46edo
| es =
| ja =
}}
{{Infobox ET}}
{{ED intro}}


=<span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span>=
== Theory ==
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[Octave|octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent|cent]]s, an interval close in size to [[66/65|66/65]], the interval from [[13/11|13/11]] to [[6/5|6/5]].
In the opinion of some, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]] or [[53edo]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison. 46edo is not a [[zeta peak edo]], but it is a [[zeta gap edo]]. It is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]].


46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank_two_temperaments|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit|11-limit]] [[Target_tunings|minimax]] tuning for [[Starling_family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit|13-limit]], though others award that distinction to [[41edo|41edo]]. In fact, while 41 is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] but not a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]], 46 is zeta gap but not zeta integral.
46edo is also notable for being the smallest edo to approximate odd harmonics 1–13 with less than 25% [[relative interval error|relative error]].


The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just_fifth|just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
[[Magic22 as srutis #Shrutar.5B22.5D_as_srutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.


46edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.
=== Prime harmonics ===
{{Harmonics in equal|46|columns=11}}
{{Harmonics in equal|46|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 46edo (continued)}}


=46edo srutis=
=== As a tuning of other temperaments ===
[[Magic22_as_srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian|Indian]] music.
46edo is a superb tuning for [[sensi]] and [[leapday]]. It also [[support]]s but tunes less optimally [[valentine]], [[shrutar]], [[rodan]], and [[unidec]]. The [[11-odd-limit]] [[minimax tuning]] for valentine, (11/7)<sup>1/10</sup>, is only 0.01 cents flat of 3\46, but [[77edo]] has a lower average error overall.  


=Intervals=
=== Subsets and supersets ===
46edo can be treated as two circles of [[23edo]] separated by an interval of 26.087 cents. Supersets [[414edo]] and [[460edo]] are also notable for their high consistency.


{| class="wikitable"
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4 left-7"
|-
|-
! | degrees of 46edo
! #
! | solfege
! Cents
! | cents value
! Approximate ratios<ref name="interval ratios" group="note">{{safesubst:Subgroup note|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]]&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
! [[Kite's ups and downs notation|Ups and downs notation]]
 
in the [[17-limit|17-limit]]
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]]
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | do
| 0.0
| | 0.00
| [[1/1]]
| | 1/1
| {{UDnote|step=0}}
| style="text-align:center;" | perfect unison
| style="text-align:center;" | P1
| style="text-align:center;" | D
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | di
| 26.1
| | 26.087
| [[49/48]], [[64/63]], [[81/80]]
| |
| {{UDnote|step=1}}
| style="text-align:center;" | up unison
| style="text-align:center;" | ^1
| style="text-align:center;" | D^
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | ro
| 52.2
| | 52.174
| [[28/27]], [[33/32]], [[36/35]]
| |
| {{UDnote|step=2}}
| style="text-align:center;" | downminor 2nd
| style="text-align:center;" | vm2
| style="text-align:center;" | Ebv
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | rih
| 78.3
| | 78.261
| [[21/20]], [[22/21]], [[24/23]], [[23/22]], [[25/24]]
| |
| {{UDnote|step=3}}
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | m2
| style="text-align:center;" | Eb
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | ra
| 104.3
| | 104.348
| [[16/15]], [[17/16]], [[18/17]]
| | 16/15, 17/16, 18/17
| {{UDnote|step=4}}
| style="text-align:center;" | upminor 2nd
| style="text-align:center;" | ^m2
| style="text-align:center;" | Eb^
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | ru (as in supraminor)
| 130.4
| | 130.435
| [[13/12]], [[14/13]], [[15/14]]
| | 13/12, 14/13, 15/14
| {{UDnote|step=5}}
| style="text-align:center;" | downmid 2nd
| style="text-align:center;" | v~2
| style="text-align:center;" | Eb^^
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | ruh (as in submajor)
| 156.5
| | 156.522
| [[11/10]], [[12/11]], [[23/21]]
| | 12/11, 11/10
| {{UDnote|step=6}}
| style="text-align:center;" | upmid 2nd
| style="text-align:center;" | ^~2
| style="text-align:center;" | Evv
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | reh
| 182.6
| | 182.609
| [[10/9]]
| | 10/9
| {{UDnote|step=7}}
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | vM2
| style="text-align:center;" | Ev
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | re
| 208.7
| | 208.696
| [[9/8]]
| | 9/8, 17/15
| {{UDnote|step=8}}
| style="text-align:center;" | major 2nd
| style="text-align:center;" | M2
| style="text-align:center;" | E
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | ri
| 234.8
| | 234.783
| [[8/7]], [[23/20]]
| | 8/7, 15/13*
| {{UDnote|step=9}}
| style="text-align:center;" | upmajor 2nd
| style="text-align:center;" | ^M2
| style="text-align:center;" | E^
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | ma
| 260.9
| | 260.87
| [[7/6]]
| | 7/6, 15/13*
| {{UDnote|step=10}}
| style="text-align:center;" | downminor 3rd
| style="text-align:center;" | vm3
| style="text-align:center;" | Fv
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | meh
| 287.0
| | 286.957
| [[13/11]], [[20/17]]
| | 13/11, 20/17
| {{UDnote|step=11}}
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | m3
| style="text-align:center;" | F
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | me
| 313.0
| | 313.043
| [[6/5]]
| | 6/5
| {{UDnote|step=12}}
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | ^m3
| style="text-align:center;" | F^
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | mu
| 339.1
| | 339.13
| [[11/9]], [[17/14]], [[28/23]]
| | 11/9, 17/14
| {{UDnote|step=13}}
| style="text-align:center;" | downmid 3rd
| style="text-align:center;" | v~3
| style="text-align:center;" | F^^
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | muh
| 365.2
| | 365.217
| [[16/13]], [[21/17]], [[26/21]]
| | 16/13
| {{UDnote|step=14}}
| style="text-align:center;" | upmid 3rd
| style="text-align:center;" | ^~3
| style="text-align:center;" | F#vv
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | mi
| 391.3
| | 391.304
| [[5/4]]
| | 5/4
| {{UDnote|step=15}}
| style="text-align:center;" | downmajor 3rd
| style="text-align:center;" | vM3
| style="text-align:center;" | F#v
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | maa
| 417.4
| | 417.391
| [[14/11]], [[23/18]]
| | 14/11
| {{UDnote|step=16}}
| style="text-align:center;" | major 3rd
| style="text-align:center;" | M3
| style="text-align:center;" | F#
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | mo
| 443.5
| | 443.478
| [[9/7]], [[13/10]], [[22/17]]
| | 9/7, 13/10, 22/17
| {{UDnote|step=17}}
| style="text-align:center;" | upmajor 3rd
| style="text-align:center;" | ^M3
| style="text-align:center;" | F#^
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | fe
| 469.6
| | 469.565
| [[17/13]], [[21/16]]
| | 17/13
| {{UDnote|step=18}}
| style="text-align:center;" | down 4th
| style="text-align:center;" | v4
| style="text-align:center;" | Gv
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | fa
| 495.7
| | 495.652
| [[4/3]]
| | 4/3
| {{UDnote|step=19}}
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | P4
| style="text-align:center;" | G
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | fih
| 521.7
| | 521.739
| [[23/17]], [[27/20]]
| |
| {{UDnote|step=20}}
| style="text-align:center;" | up 4th
| style="text-align:center;" | ^4
| style="text-align:center;" | G^
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | fu
| 547.8
| | 547.826
| [[11/8]]
| | 11/8, 15/11
| {{UDnote|step=21}}
| style="text-align:center;" | double-up 4th
| style="text-align:center;" | ^^4
| style="text-align:center;" | G^^
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | fi
| 573.9
| | 573.913
| [[7/5]], [[18/13]], [[32/23]]
| | 7/5, 18/13
| {{UDnote|step=22}}
| style="text-align:center;" | double-down aug 4th,
 
dim 5th
| style="text-align:center;" | vvA4, d5
| style="text-align:center;" | G#vv, Ab
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | seh
| 600.0
| | 600
| [[17/12]], [[24/17]]
| | 17/12, 24/17
| {{UDnote|step=23}}
| style="text-align:center;" | downaug 4th, updim 5th
| style="text-align:center;" | vA4, ^d5
| style="text-align:center;" | G#v, Ab^
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | se
| 626.1
| | 626.087
| [[10/7]], [[13/9]], [[23/16]]
| | 10/7, 13/9
| {{UDnote|step=24}}
| style="text-align:center;" | aug 4th, double-up dim 5th
| style="text-align:center;" | A4, ^^d5
| style="text-align:center;" | G#, Ab^^
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:center;" | su
| 652.2
| | 652.174
| [[16/11]]
| | 16/11, 22/15
| {{UDnote|step=25}}
| style="text-align:center;" | double-down 5th
| style="text-align:center;" | vv5
| style="text-align:center;" | Avv
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | sih
| 678.3
| | 678.261
| [[34/23]], [[40/27]]
| |
| {{UDnote|step=26}}
| style="text-align:center;" | down 5th
| style="text-align:center;" | v5
| style="text-align:center;" | Av
|-
|-
| style="text-align:center;" | 27
| 27
| style="text-align:center;" | sol
| 704.3
| | 704.348
| [[3/2]]
| | 3/2
| {{UDnote|step=27}}
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | P5
| style="text-align:center;" | A
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | si
| 730.4
| | 730.435
| [[26/17]], [[32/21]]
| | 26/17
| {{UDnote|step=28}}
| style="text-align:center;" | up 5th
| style="text-align:center;" | ^5
| style="text-align:center;" | A^
|-
|-
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | lo
| 756.5
| | 756.522
| [[14/9]], [[17/11]], [[20/13]]
| | 14/9, 20/13, 17/11
| {{UDnote|step=29}}
| style="text-align:center;" | downminor 6th
| style="text-align:center;" | vm6
| style="text-align:center;" | Bbv
|-
|-
| style="text-align:center;" | 30
| 30
| style="text-align:center;" | leh
| 782.6
| | 782.609
| [[11/7]]
| | 11/7
| {{UDnote|step=30}}
| style="text-align:center;" | minor 6th
| style="text-align:center;" | m6
| style="text-align:center;" | Bb
|-
|-
| style="text-align:center;" | 31
| 31
| style="text-align:center;" | le
| 808.7
| | 808.696
| [[8/5]]
| | 8/5
| {{UDnote|step=31}}
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | ^m6
| style="text-align:center;" | Bb^
|-
|-
| style="text-align:center;" | 32
| 32
| style="text-align:center;" | lu
| 834.8
| | 834.783
| [[13/8]], [[21/13]], [[34/21]]
| | 13/8
| {{UDnote|step=32}}
| style="text-align:center;" | downmid 6th
| style="text-align:center;" | v~6
| style="text-align:center;" | Bb^^
|-
|-
| style="text-align:center;" | 33
| 33
| style="text-align:center;" | luh
| 860.9
| | 860.87
| [[18/11]], [[23/14]], [[28/17]]
| | 18/11, 28/17
| {{UDnote|step=33}}
| style="text-align:center;" | upmid 6th
| style="text-align:center;" | ^~6
| style="text-align:center;" | Bvv
|-
|-
| style="text-align:center;" | 34
| 34
| style="text-align:center;" | la
| 887.0
| | 886.957
| [[5/3]]
| | 5/3
| {{UDnote|step=34}}
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | vM6
| style="text-align:center;" | Bv
|-
|-
| style="text-align:center;" | 35
| 35
| style="text-align:center;" | laa
| 913.0
| | 913.043
| [[17/10]], [[22/13]]
| | 22/13, 17/10
| {{UDnote|step=35}}
| style="text-align:center;" | major 6th
| style="text-align:center;" | M6
| style="text-align:center;" | B
|-
|-
| style="text-align:center;" | 36
| 36
| style="text-align:center;" | li
| 939.1
| | 939.13
| [[12/7]]
| | 12/7, 26/15*
| {{UDnote|step=36}}
| style="text-align:center;" | upmajor 6th
| style="text-align:center;" | ^M6
| style="text-align:center;" | B^
|-
|-
| style="text-align:center;" | 37
| 37
| style="text-align:center;" | ta
| 965.2
| | 965.217
| [[7/4]], [[40/23]]
| | 7/4, 26/15*
| {{UDnote|step=37}}
| style="text-align:center;" | downminor 7th
| style="text-align:center;" | vm7
| style="text-align:center;" | Cv
|-
|-
| style="text-align:center;" | 38
| 38
| style="text-align:center;" | teh
| 991.3
| | 991.304
| [[16/9]], [[23/13]]
| | 16/9, 30/17
| {{UDnote|step=38}}
| style="text-align:center;" | minor 7th
| style="text-align:center;" | m7
| style="text-align:center;" | C
|-
|-
| style="text-align:center;" | 39
| 39
| style="text-align:center;" | te
| 1017.4
| | 1017.391
| [[9/5]]
| | 9/5
| {{UDnote|step=39}}
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | ^m7
| style="text-align:center;" | C^
|-
|-
| style="text-align:center;" | 40
| 40
| style="text-align:center;" | tu
| 1043.5
| | 1043.478
| [[11/6]], [[20/11]], [[42/23]]
| | 11/6, 20/11
| {{UDnote|step=40}}
| style="text-align:center;" | downmid 7th
| style="text-align:center;" | v~7
| style="text-align:center;" | C^^
|-
|-
| style="text-align:center;" | 41
| 41
| style="text-align:center;" | tuh
| 1069.6
| | 1069.565
| [[13/7]], [[24/13]], [[28/15]]
| | 24/13, 13/7, 28/15
| {{UDnote|step=41}}
| style="text-align:center;" | upmid 7th
| style="text-align:center;" | ^~7
| style="text-align:center;" | C#vv
|-
|-
| style="text-align:center;" | 42
| 42
| style="text-align:center;" | ti
| 1095.7
| | 1095.652
| [[15/8]], [[17/9]], [[32/17]]
| | 15/8, 32/17, 17/9
| {{UDnote|step=42}}
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | vM7
| style="text-align:center;" | C#v
|-
|-
| style="text-align:center;" | 43
| 43
| style="text-align:center;" | taa
| 1121.7
| | 1121.739
| [[21/11]], [[23/12]], [[40/21]], [[44/23]], [[48/25]]
| |
| {{UDnote|step=43}}
| style="text-align:center;" | major 7th
| style="text-align:center;" | M7
| style="text-align:center;" | C#
|-
|-
| style="text-align:center;" | 44
| 44
| style="text-align:center;" | to
| 1147.8
| | 1147.826
| [[27/14]], [[35/18]], [[64/33]]
| |
| {{UDnote|step=44}}
| style="text-align:center;" | upmajor 7th
| style="text-align:center;" | ^M7
| style="text-align:center;" | C#^
|-
|-
| style="text-align:center;" | 45
| 45
| style="text-align:center;" | da
| 1173.9
| | 1173.913
| [[63/32]], [[96/49]], [[160/81]]
| |
| {{UDnote|step=45}}
| style="text-align:center;" | down 8ve
| style="text-align:center;" | v8
| style="text-align:center;" | Dv
|-
|-
| style="text-align:center;" | 46
| 46
| style="text-align:center;" | do
| 1200.0
| | 1200
| [[2/1]]
| | 2/1
| {{UDnote|step=46}}
| style="text-align:center;" | perfect 8ve
| style="text-align:center;" | P8
| style="text-align:center;" | D
|}
|}
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not [[consistent|consistent]] in the [[15-limit|15-limit]].
<references group="note" />


Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
=== Proposed interval names and solfèges ===
 
{| class="wikitable center-all right-2 left-2 left-3 left-6 mw-collapsible mw-collapsed"
{| class="wikitable"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]<br>([[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="2" | [[Solfège]]s
|-
| 0
| 0.0
| perfect unison
| P1
| D
| Perfect unison
| P1
| D
| da
| do
|-
| 1
| 26.1
| up unison
| ^1
| ^D
| comma-wide unison, <br>super unison
| K1, S1
| KD, SD
| du
| di
|-
| 2
| 52.2
| downminor 2nd
| vm2
| vEb
| subminor 2nd, uber unison
| sm2, U1
| sEb, UD
| fro
| ro
|-
| 3
| 78.3
| minor 2nd
| m2
| Eb
| minor 2nd, <br>classic augmented unison
| m2, kkA1
| Eb, kkD#
| fra
| rih
|-
| 4
| 104.3
| upminor 2nd
| ^m2
| ^Eb
| classic minor 2nd, <br>comma-narrow aug unison
| Km2, kA1
| KEb, kD#
| fru
| ra
|-
| 5
| 130.4
| dupminor 2nd
| ^^m2
| ^^Eb
| lesser neutral second, augmented unison
| n2, A1
| UEb, D#
| fri
| ru<ref name="intervals2" group="note">/u/ as in s'''u'''praminor</ref>
|-
| 6
| 156.5
| dudmajor 2nd
| vvM2
| vvE
| greater neutral second, <br>super aug unison
| N2, sA1
| uE, sD#
| ri
| ruh<ref name="intervals3" group="note">/ʌ/ as in s'''u'''bmajor</ref>
|-
|-
! | quality
| 7
! | color
| 182.6
! | monzo format
| downmajor 2nd
! | examples
| vM2
| vE
| classic/comma-narrow major 2nd
| kM2
| kE
| ro
| reh
|-
|-
| style="text-align:center;" | downminor
| 8
| style="text-align:center;" | blue
| 208.7
| style="text-align:center;" | {a, b, 0, 1}
| major 2nd
| style="text-align:center;" | 7/6, 7/4
| M2
| E
| major 2nd
| M2
| E
| ra
| re
|-
|-
| style="text-align:center;" | minor
| 9
| style="text-align:center;" | fourthward white
| 234.8
| style="text-align:center;" | {a, b}, b &lt; -1
| upmajor 2nd
| style="text-align:center;" | 32/27, 16/9
| ^M2
| ^E
| supermajor 2nd
| SM2
| SE
| ru
| ri
|-
|-
| style="text-align:center;" | upminor
| 10
| style="text-align:center;" | green
| 260.9
| style="text-align:center;" | {a, b, -1}
| downminor 3rd
| style="text-align:center;" | 6/5, 9/5
| vm3
| vF
| subminor 3rd
| sm3
| sF
| no
| ma
|-
|-
| style="text-align:center;" | downmid
| 11
| style="text-align:center;" | jade
| 287.0
| style="text-align:center;" | {a, b, 0, 0, 1}
| minor 3rd
| style="text-align:center;" | 11/9, 11/6
| m3
| F
| minor 3rd
| m3
| F
| na
| meh
|-
|-
| style="text-align:center;" | upmid
| 12
| style="text-align:center;" | amber
| 313.0
| style="text-align:center;" | {a, b, 0, 0, -1}
| upminor 3rd
| style="text-align:center;" | 12/11, 18/11
| ^m3
| ^F
| classic minor 3rd
| Km3
| KF
| nu
| me
|-
|-
| style="text-align:center;" | downmajor
| 13
| style="text-align:center;" | yellow
| 339.1
| style="text-align:center;" | {a, b, 1}
| dupminor 3rd
| style="text-align:center;" | 5/4, 5/3
| ^^m3
| ^^F
| lesser neutral 3rd
| n3
| UF
| ni
| mu<ref name="intervals2" group="note" />
|-
|-
| style="text-align:center;" | major
| 14
| style="text-align:center;" | fifthward white
| 365.2
| style="text-align:center;" | {a, b}, b &gt; 1
| dudmajor 3rd
| style="text-align:center;" | 9/8, 27/16
| vvM3
| vvF#
| greater neutral 3rd
| N3
| uF#
| mi
| muh<ref name="intervals3" group="note" />
|-
|-
| style="text-align:center;" | upmajor
| 15
| style="text-align:center;" | red
| 391.3
| style="text-align:center;" | {a, b, 0, -1}
| downmajor 3rd
| style="text-align:center;" | 9/7, 12/7
| vM3
|}
| vF#
All 46edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
| classic major 3rd
 
| kM3
{| class="wikitable"
| kF#
| mo
| mi
|-
|-
! | color of the 3rd
| 16
! | JI chord
| 417.4
! | notes as edosteps
| major 3rd
! | notes of C chord
| M3
! | written name
| F#
! | spoken name
| major 3rd
| M3
| F#
| ma
| maa
|-
|-
| style="text-align:center;" | blue
| 17
| style="text-align:center;" | 6:7:9
| 443.5
| style="text-align:center;" | 0-10-27
| upmajor 3rd
| style="text-align:center;" | C Ebv G
| ^M3
| style="text-align:center;" | C.vm
| ^F#
| style="text-align:center;" | C downminor
| supermajor 3rd
| SM3
| SF#
| mu
| mo
|-
|-
| style="text-align:center;" | green
| 18
| style="text-align:center;" | 10:12:15
| 469.6
| style="text-align:center;" | 0-12-27
| down 4th
| style="text-align:center;" | C Eb^ G
| v4
| style="text-align:center;" | C.^m
| vG
| style="text-align:center;" | C upminor
| sub 4th
| s4
| sG
| fo
| fe
|-
|-
| style="text-align:center;" | jade
| 19
| style="text-align:center;" | 18:22:27
| 495.7
| style="text-align:center;" | 0-13-27
| perfect 4th
| style="text-align:center;" | C Eb^^ G
| P4
| style="text-align:center;" | C.v~
| G
| style="text-align:center;" | C downmid
| perfect 4th
| P4
| G
| fa
| fa
|-
|-
| style="text-align:center;" | yellow
| 20
| style="text-align:center;" | 4:5:6
| 521.7
| style="text-align:center;" | 0-15-27
| up 4th
| style="text-align:center;" | C Ev G
| ^4
| style="text-align:center;" | C.v
| ^G
| style="text-align:center;" | C downmajor or C dot down
| comma-wide 4th
| K4
| KG
| fu
| fih
|-
|-
| style="text-align:center;" | red
| 21
| style="text-align:center;" | 14:18:27
| 547.8
| style="text-align:center;" | 0-17-27
| dup 4th
| style="text-align:center;" | C E^ G
| ^^4
| style="text-align:center;" | C.^
| ^^G
| style="text-align:center;" | C upmajor or C dot up
| uber 4th, sub diminished 5th
|}
| U4, sd5
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
| UG, sAb
 
| fi/sho
==Selected just intervals by error==
| fu
The following table shows how [[Just-24|some prominent just intervals]] are represented in 46edo (ordered by absolute error).
 
{| class="wikitable"
|-
|-
! | Interval, complement
| 22
! | Error (abs., in [[cent|cents]])
| 573.9
| dudaug 4th, <br>dim 5th
| vvA4, d5
| vvG#, Ab
| classic augmented 4th, diminished 5th
| kkA4, d5
| kkG#, Ab
| pi/sha
| fi
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| 23
| style="text-align:center;" | 0.103
| 600.0
| downaug 4th, updim 5th
| vA4, ^d5
| vG#, ^Ab
| comma-narrow aug 4th, <br>comma-wide dim 5th
| kA4, Kd5
| kG#, KAb
| po/shu
| seh
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| 24
| style="text-align:center;" | 0.962
| 626.1
| aug 4th, dupdim 5th
| A4, ^^d5
| G#, ^^Ab
| augmented 4th, <br>classic diminished 5th
| A4, KKd5
| G#, KKAb
| pa/shi
| se
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| 25
| style="text-align:center;" | 1.097
| 652.2
| dud 5th
| vv5
| vvA
| super augmented 4th, <br>unter 5th
| SA4, u5
| SG#, uA
| pu/si
| su
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| 26
| style="text-align:center;" | 2.438
| 678.3
| down 5th
| v5
| vA
| comma-narrow 5th
| k5
| kA
| so
| sih
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| 27
| style="text-align:center;" | 3.318
| 704.3
| perfect 5th
| P5
| A
| perfect 5th
| P5
| A
| sa
| sol
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| 28
| style="text-align:center;" | 3.422
| 730.4
| up 5th
| ^5
| ^A
| super 5th
| S5
| SA
| su
| si
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| 29
| style="text-align:center;" | 3.534
| 756.5
| downminor 6th
| vm6
| vBb
| subminor 6th
| sm6
| sBb
| flo
| lo
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| 30
| style="text-align:center;" | 4.281
| 782.6
| minor 6th
| m6
| Bb
| minor 6th
| m6
| Bb
| fla
| leh
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| 31
| style="text-align:center;" | 4.384
| 808.7
| upminor 6th
| ^m6
| ^Bb
| classic minor 6th
| Km6
| KBb
| flu
| le
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| 32
| style="text-align:center;" | 5.243
| 834.8
| dupminor 6th
| ^^m6
| ^^Bb
| lesser neutral 6th
| n6
| UBb
| fli
| lu<ref name="intervals2" group="note" />
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| 33
| style="text-align:center;" | 6.718
| 860.9
| dudmajor 6th
| vvM6
| vvB
| greater neutral 6th
| N6
| uB
| li
| luh<ref name="intervals3" group="note" />
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| 34
| style="text-align:center;" | 6.822
| 887.0
| downmajor 6th
| vM6
| vB
| classic major 6th
| kM6
| kB
| lo
| la
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| 35
| style="text-align:center;" | 7.702
| 913.0
| major 6th
| M6
| B
| major 6th
| M6
| B
| la
| laa
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| 36
| style="text-align:center;" | 7.815
| 939.1
| upmajor 6th
| ^M6
| ^B
| supermajor 6th
| SM6
| SB
| lu
| li
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| 37
| style="text-align:center;" | 7.918
| 965.2
| downminor 7th
| vm7
| vC
| subminor 7th
| sm7
| sC
| tho
| ta
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| 38
| style="text-align:center;" | 8.561
| 991.3
| minor 7th
| m7
| C
| minor 7th
| m7
| C
| tha
| teh
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| 39
| style="text-align:center;" | 8.665
| 1017.4
| upminor 7th
| ^m7
| ^C
| classic/comma-wide minor 7th
| Km7
| KC
| thu
| te
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| 40
| style="text-align:center;" | 10.140
| 1043.5
| dupminor 7th
| ^^m7
| ^^C
| lesser neutral 7th, sub diminished 8ve
| n7, sd8
| UC, sDb
| thi
| tu<ref name="intervals2" group="note" />
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| 41
| style="text-align:center;" | 11.102
| 1069.6
| dudmajor 7th
| vvM7
| vvC#
| greater neutral 7th,
diminished 8ve
| N7, d8
| uC#, Db
| ti
| tuh<ref name="intervals3" group="note" />
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| 42
| style="text-align:center;" | 11.237
| 1095.7
| downmajor 7th
| vM7
| vC#
| classic major 7th,
comma-wide dim 8ve
| kM7, Kd8
| kC#, KDb
| to
| ti
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| 43
| style="text-align:center;" | 12.199
| 1121.7
| major 7th
| M7
| C#
| major 7th, <br>classic diminished 8ve
| M7, KKd8
| C#, KKDb
| ta
| taa
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| 44
| style="text-align:center;" | 12.945
| 1147.8
| upmajor 7th
| ^M7
| ^C#
| supermajor 7th, unter 8ve
| SM7, u8
| SC#, uD
| tu
| to
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| 45
| style="text-align:center;" | 15.383
| 1173.9
| down 8ve
| v8
| vD
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| do
| da
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| 46
| style="text-align:center;" | 16.479
| 1200.0
| perfect 8ve
| P8
| D
| perfect 8ve
| P8
| D
| da
| do
|}
|}


=Linear temperaments=
=== Interval quality and chord names in color notation ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable"
{| class="wikitable center-all"
|-
! Quality
! Color
! Monzo format
! Examples
|-
| downminor
| zo
| {{Monzo| ''a'' ''b'' 0 1 }}
| 7/6, 7/4
|-
| minor
| fourthward wa
| {{Monzo| ''a'' ''b'' }}, ''b'' < −1
| 32/27, 16/9
|-
| upminor
| gu
| {{Monzo| ''a'' ''b'' −1 }}
| 6/5, 9/5
|-
| dupminor
| ilo
| {{Monzo| ''a'' ''b'' 0 0 1 }}
| 11/9, 11/6
|-
|-
! | Periods
| dudmajor
| lu
| {{Monzo| ''a'' ''b'' 0 0 −1 }}
| 12/11, 18/11
|-
| downmajor
| yo
| {{Monzo| ''a'' ''b'' 1 }}
| 5/4, 5/3
|-
| major
| fifthward wa
| {{Monzo| ''a'' ''b'' }}, ''b'' > 1
| 9/8, 27/16
|-
| upmajor
| ru
| {{Monzo| ''a'' ''b'' 0 −1 }}
| 9/7, 12/7
|}
All 46edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. Ups or downs immediately after the chord root affect the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, ilo, lu, yo and ru triads:


per octave
{| class="wikitable center-all"
! | Generator
|-
! | Cents
! Color of the 3rd
! | Temperaments
! JI chord
! | MOS/DE Scales available
! Notes as edosteps
! | L:s
! Notes of C chord
! Written name
! Spoken name
|-
|-
| | 1
| zo
| | 1\46
| 6:7:9
| | 26.087
| 0–10–27
| |
| C vEb G
| |
| Cvm
| |
| C downminor
|-
|-
| | 1
| gu
| | 3\46
| 10:12:15
| | 78.261
| 0–12–27
| | [[Valentine|Valentine]]
| C ^Eb G
| | 1L 14s (15-tone)
| C^m
 
| C upminor
15L 1s (16-tone)
|-
 
| ilo
16L 15s (31-tone)
| 18:22:27
| | 4:3 ~ [[Maximal_evenness|quasi-equal]]
| 0–13–27
 
| C ^^Eb G
3:1
| C^^m
 
| C dupminor
2:1 ~ QE
|-
| lu
| 22:27:33
| 0–14–27
| C vvE G
| Cvv
| C dudmajor or C dud
|-
| yo
| 4:5:6
| 0–15–27
| C vE G
| Cv
| C downmajor or C down
|-
|-
| | 1
| ru
| | 5\46
| 14:18:21
| | 130.435
| 0–17–27
| | [[Twothirdtonic|Twothirdtonic]]
| C ^E G
| | [[1L_8s|1L 8s]] (9-tone)
| C^
| C upmajor or C up
|}
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].


[[9L_1s|9L 1s]] (10-tone)
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp5-szg}}


9L 10s (19-tone)
=== Kite's ups and downs notation ===
46edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp, etc., and likewise down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
{{Ups and downs sharpness}}


9L 19s (28-tone)
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[39edo #Sagittal notation|39edo]].


9L 28s (37-tone)
==== Evo flavor ====
| | 6:5 ~ QE
{{Sagittal chart|Evo}}


5:1
==== Revo flavor ====
{{Sagittal chart}}


4:1
== Approximation to JI ==
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]


3:1
=== 17-odd-limit interval mappings ===
{{Q-odd-limit intervals|46|17}}


2:1 ~ QE
=== Consistent circles ===
46edo is home to a number of [[consistent circle]]s, both ones closing after generating all 46 notes and ones closing after generating 23edo.
{| class="wikitable center-1 center-2 center-3"
|+ style="font-size: 105%;" | 46-note circles by gen. with related temperaments organized by period
|-
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! 1\1 !! 1\2
|-
| [[68/65]] || 25.9% || Normal || [[Valentine]] || [[Semivalentine]]
|-
|-
| | 1
| [[10/9]] || 36.1% || Normal || [[Mitonic]] || [[Unidec]], [[hendec]]
| | 7\46
|-
| | 182.609
| [[31/24]] || 70.2% || Weak || [[Sensible]], [[sensi]] add-31 || [[Bison]] add-31, [[bisensi]] add-31
| | [[Minortone|Minortone]]
|}
| | [[1L_5s|1L 5s]] (6-tone)


[[6L_1s|6L 1s]] (7-tone)
{| class="wikitable center-all left-4"
|+ style="font-size: 105%;" | 23-note circles by gen. with related half-octave temperaments
|-
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! Temperaments
|-
| [[17/16]] || 53.5% || Weak || [[Diaschismic]]
|-
| [[23/21]] || 85.7% || Weak || [[Bison]]
|-
| [[44/39]] || 12.3% || Super-strong || [[Abigail]]
|-
| [[21/17]] || 53.6% || Weak || ?
|-
| [[14/11]] || 10.2% || Super-strong || ?
|-
| [[21/16]] || 107% || Sub-weak || ?
|}


7L 6s (13-tone)
For the 23rd-octave temperament that 46edo supports which combines all above 23-note circles, see [[icositritonic]].


13L 7s (20-tone)
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 73 -46 }}
| {{mapping| 46 73 }}
| −0.755
| 0.75
| 2.89
|-
| 2.3.5
| 2048/2025, 78732/78125
| {{mapping| 46 73 107 }}
| −1.219
| 0.90
| 3.45
|-
| 2.3.5.7
| 126/125, 245/243, 1029/1024
| {{mapping| 46 73 107 129 }}
| −0.595
| 1.34
| 5.12
|-
| 2.3.5.7.11
| 121/120, 126/125, 176/175, 245/243
| {{mapping| 46 73 107 129 159 }}
| −0.274
| 1.36
| 5.20
|-
| 2.3.5.7.11.13
| 91/90, 121/120, 169/168, 176/175, 245/243
| {{mapping| 46 73 107 129 159 170 }}
| +0.030
| 1.41
| 5.42
|-
| 2.3.5.7.11.13.17
| 91/90, 121/120, 154/153, 169/168, 176/175, 245/243
| {{mapping| 46 73 107 129 159 170 188 }}
| +0.047
| 1.31
| 5.02
|-
| 2.3.5.7.11.13.17.23
| 91/90, 121/120, 154/153, 169/168, 176/175, 208/207, 231/230
| {{mapping| 46 73 107 129 159 170 188 208 }}
| +0.101
| 1.23
| 4.72
|}
* 46et is lower in relative error than any previous equal temperaments in the 17-, 19-, 23-limit, and others. The next equal temperaments doing better in the aforementioned subgroups are 72, 72, 94, respectively. 46et is even more prominent in the no-19 23-limit, and the next equal temperament doing better in this subgroup is 140.


13L 20s (33-tone)
=== Commas ===
| | 11:7
This is a partial list of the [[commas]] that 46et [[tempering out|tempers out]] with its [[patent val]], {{val| 24 38 56 67 83 89 }}.


7:4
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 5
| <abbr title="50331648/48828125">(16 digits)</abbr>
| {{monzo| 24 1 -11 }}
| 52.50
| Salegu
| [[Magus comma]]
|-
| 5
| <abbr title="1990656/1953125">(14 digits)</abbr>
| {{monzo| 13 5 -9 }}
| 32.95
| Satritrigu
| [[Valentine comma]]
|-
| 5
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
| 5
| <abbr title="1600000/1594323">(14 digits)</abbr>
| {{monzo| 9 -13 5 }}
| 6.15
| Saquinyo
| [[Amity comma]]
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
| 7
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.80
| Zotrigu
| Starling comma
|-
| 7
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
| 7
| [[5120/5103]]
| {{monzo| 10 -6 1 -1 }}
| 5.76
| Saruyo
| Hemifamity comma, aberschisma
|-
| 7
| <abbr title="2147483648/2144153025">(20 digits)</abbr>
| {{monzo| 31 -6 -2 -6 }}
| 2.69
| Sasa-tribiru-agugu
| [[Pessoalisma]]
|-
| 7
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
| 11
| [[121/120]]
| {{monzo|-3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
| 11
| [[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
| 9.86
| Lorugugu
| Valinorsma
|-
| 11
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
| 11
| [[385/384]]
| {{monzo|-7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 11
| [[441/440]]
| {{monzo| -3 2 -1 2 -1 }}
| 3.93
| Luzozogu
| Werckisma
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
| 13
| [[169/168]]
| {{monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
| 13
| [[196/195]]
| {{monzo| 2 -1 -1 2 0 -1 }}
| 8.86
| Thuzozogu
| Mynucuma
|-
| 13
| [[507/500]]
| {{monzo| -2 1 -3 0 0 2 }}
| 24.07
| Thothotrigu
|
|-
| 13
| [[351/350]]
| {{Monzo| -1 3 -2 -1 0 1 }}
| 4.94
| Thorugugu
| Ratwolfsma
|-
| 13
| [[352/351]]
| {{monzo| 5 -3 0 0 1 -1 }}
| 4.93
| Thulo
| Minor minthma
|-
| 17
| [[256/255]]
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| 6.78
| Sugu
| Charisma, septendecimal kleisma
|-
| 17
| [[289/288]]
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| Soso
| Semitonisma
|}
<references group="note" />


4:3 ~ QE
=== Rank-2 temperaments ===
 
{| class="wikitable center-1 center-2 center-3 center-4"
3:1
|-
 
! Periods<br>per 8ve
2:1 ~ QE
! Generator
! Cents
! Temperaments
! MOS scales
! L:s
|-
| rowspan="11" | 1
| 1\46
| 26.087
| [[Sfourth]]
|
|
|-
| 3\46
| 78.261
| [[Valentine]]
| 1L&nbsp;14s (15-tone)<br>15L&nbsp;1s (16-tone)<br>16L&nbsp;15s (31-tone)
| 4:3 ~ [[Maximal evenness|quasi-equal]]<br>3:1<br>2:1 ~ QE
|-
| 5\46
| 130.435
| [[Twothirdtonic]]
| [[1L&nbsp;8s]] (9-tone)<br>[[9L&nbsp;1s]] (10-tone)<br>9L&nbsp;10s (19-tone)<br>9L&nbsp;19s (28-tone)<br>9L&nbsp;28s (37-tone)
| 6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 7\46
| 182.609
| [[Minortone]] / [[mitonic]]
| [[1L&nbsp;5s]] (6-tone)<br>[[6L&nbsp;1s]] (7-tone)<br>7L&nbsp;6s (13-tone)<br>13L&nbsp;7s (20-tone)<br>13L&nbsp;20s (33-tone)
| 11:7<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
|-
| 9\46
| 234.783
| [[Rodan]]
| [[1L&nbsp;4s]] (5-tone)<br>[[1L&nbsp;5s]] (6-tone)<br>[[5L&nbsp;6s]] (11-tone)<br>5L&nbsp;11s (16-tone)<br>5L&nbsp;16s (21-tone)<br>5L&nbsp;21s (26-tone)<br>5L&nbsp;26s (31-tone)<br>5L&nbsp;31s (36-tone)<br>5L&nbsp;36s (41-tone)
| 10:9 ~QE<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 11\46
| 286.957
| [[Amity_family#Gamity|Gamity]]
| [[4L&nbsp;1s]] (5-tone)<br>[[4L&nbsp;5s]] (9-tone)<br>4L&nbsp;9s (13-tone)<br>4L&nbsp;13s (17-tone)<br>4L&nbsp;17s (21-tone)<br>21L&nbsp;4s (25-tone)
| 11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 13\46
| 339.130
| [[Amity]] / [[Amity_family#Hitchcock|Hitchcock]]
| [[4L&nbsp;3s]] (7-tone)<br>[[7L&nbsp;4s]] (11-tone)<br>7L&nbsp;11s (18-tone)<br>7L&nbsp;18s (25-tone)<br>7L&nbsp;25s (32-tone)<br>7L&nbsp;32s (39-tone)
| 7:6 ~ QE<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 15\46
| 391.304
| [[Magus]] / [[amigo]]
| [[1L&nbsp;2s]] (3-tone)<br>[[3L&nbsp;1s]] (4-tone)<br>[[3L&nbsp;4s]] (7-tone)<br>[[3L&nbsp;7s]] (10-tone)<br>3L&nbsp;10s (13-tone)<br>3L&nbsp;13s (16-tone)<br>3L&nbsp;16s (19-tone)<br>3L&nbsp;19s (21-tone)<br>3L&nbsp;21s (24-tone)<br>3L&nbsp;24s (27-tone)<br>3L&nbsp;27s (30-tone)<br>3L&nbsp;30s (33-tone)<br>3L&nbsp;33s (36-tone)<br>3L&nbsp;36s (39-tone)<br>3L&nbsp;39s (42-tone)
| 16:15 ~ QE<br>15:1<br>14:1<br>13:1<br>12:1<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 17\46
| 443.478
| [[Sensi]]
| [[3L&nbsp;2s]] (5-tone)<br>[[3L&nbsp;5s]] (8-tone)<br>[[8L&nbsp;3s]] (11-tone)<br>8L&nbsp;11s (19-tone)<br>19L&nbsp;8s (27-tone)
| 12:5<br>7:5<br>5:2<br>3:2 ~ QE, Golden<br>2:1
|-
| 19\46
| 495.652
| [[Leapday]]
| [[2L&nbsp;3s]] (5-tone)<br>[[5L&nbsp;2s]] (7-tone)<br>[[5L&nbsp;7s]] (12-tone)<br>12L&nbsp;5s (17-tone)<br>17L&nbsp;12s (29-tone)
| 11:8<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 21\46
| 547.826
| [[Heinz]]
| [[2L&nbsp;3s]] (5-tone)<br>[[2L&nbsp;5s]] (7-tone)<br>[[2L&nbsp;7s]] (9-tone)<br>[[2L&nbsp;9s]] (11-tone)<br>11L&nbsp;2s (13-tone)<br>11L&nbsp;13s (24-tone)<br>11L&nbsp;24s (35-tone)
| 17:4<br>13:4<br>9:4<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
|-
| rowspan="11" | 2
| 1\46
| 26.087
| [[Ketchup]]
|
|
|-
| 2\46
| 52.174
| [[Shrutar]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[2L&nbsp;10s]] (12-tone)<br>2L&nbsp;12s (14-tone)<br>2L&nbsp;14s (16-tone)<br>2L&nbsp;16s (18-tone)<br>2L&nbsp;18s (20-tone)<br>2L&nbsp;20s (22-tone)<br>22L&nbsp;2s (24-tone)
| 21:2<br>19:2<br>17:2<br>15:2<br>13:2<br>11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 3\46
| 78.261
| [[Semivalentine]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[2L&nbsp;10s]] (12-tone)<br>2L&nbsp;12s (14-tone)<br>14L&nbsp;2s (16-tone)<br>16L&nbsp;14s (30-tone)
| 20:3<br>17:3<br>14:3<br>11:3<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
|-
| | 1
| 4\46
| | 9\46
| 104.348
| | 234.783
| [[Srutal]] / [[diaschismic]]
| | [[Rodan|Rodan]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[10L&nbsp;2s]] (12-tone)<br>12L&nbsp;10s (22-tone)<br>12L&nbsp;22s (34-tone)
| | [[1L_4s|1L 4s]] (5-tone)
| 19:4<br>15:4<br>11:4<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
 
[[1L_5s|1L 5s]] (6-tone)
 
[[5L_6s|5L 6s]] (11-tone)
 
5L 11s (16-tone)
 
5L 16s (21-tone)
 
5L 21s (26-tone)
 
5L 26s (31-tone)
 
5L 31s (36-tone)
 
5L 36s (41-tone)
| | 10:9 ~QE
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 1
| 5\46
| | 11\46
| 130.435
| | 286.957
|  
| |  
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[8L&nbsp;2s]] (10-tone)<br>8L&nbsp;10s (18-tone)<br>18L&nbsp;10s (28-tone)
| | [[4L_1s|4L 1s]] (5-tone)
| 18:5<br>13:5<br>8:5 ~ Golden<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
 
[[4L_5s|4L 5s]] (9-tone)
 
4L 9s (13-tone)
 
4L 13s (17-tone)
 
4L 17s (21-tone)
 
21L 4s (25-tone)
| | 11:2
 
9:2
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 1
| 6\46
| | 13\46
| 156.522
| | 339.13
| [[Bison]]
| | [[Amity|Amity]]/[[Hitchcock|hitchcock]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>8L&nbsp;6s (14-tone)<br>8L&nbsp;14s (22-tone)<br>8L&nbsp;22s (30-tone)<br>8L&nbsp;30s (38-tone
| | [[4L_3s|4L 3s]] (7-tone)
| 17:6<br>11:6<br>6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
 
[[7L_4s|7L 4s]] (11-tone)
 
7L 11s (18-tone)
 
7L 18s (25-tone)
 
7L 25s (32-tone)
 
7L 32s (39-tone)
| | 7:6 ~ QE
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 1
| 7\46
| | 15\46
| 182.609
| | 391.304
| [[Unidec]] / [[hendec]]
| | [[amigo|Amigo]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>6L&nbsp;8s (14-tone)<br>6L&nbsp;14s (20-tone)<br>20L&nbsp;6s (26-tone)
| | [[1L_2s|1L 2s]] (3-tone)
| 16:7<br>9:7<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
 
[[3L_1s|3L 1s]] (4-tone)
 
[[3L_4s|3L 4s]] (7-tone)
 
[[3L_7s|3L 7s]] (10-tone)
 
3L 10s (13-tone)
 
3L 13s (16-tone)
 
3L 16s (19-tone)
 
3L 19s (21-tone)
 
3L 21s (24-tone)
 
3L 24s (27-tone)
 
3L 27s (30-tone)
 
3L 30s (33-tone)
 
3L 33s (36-tone)
 
3L 36s (39-tone)
 
3L 39s (42-tone)
| | 16:15 ~ QE
 
15:1
 
14:1
 
13:1
 
12:1
 
11:1
 
10:1
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 1
| 8\46
| | 17\46
| 208.696
| | 443.478
| [[Abigail]]
| | [[Sensi|Sensi]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>6L&nbsp;8s (14-tone)<br>6L&nbsp;14s (20-tone)<br>6L&nbsp;20s (26-tone)<br>6L&nbsp;26s (32-tone)<br>6L&nbsp;32s (38-tone)<br>6L&nbsp;38s (44-tone)
| | [[3L_2s|3L 2s]] (5-tone)
| 15:8<br>8:7 ~ QE<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
 
[[3L_5s|3L 5s]] (8-tone)
 
[[8L_3s|8L 3s]] (11-tone)
 
8L 11s (19-tone)
 
19L 8s (27-tone)
| | 12:5
 
7:5
 
5:2
 
3:2 ~ QE, Golden
 
2:1
|-
|-
| | 1
| 9\46
| | 19\46
| 234.783
| | 495.652
| [[Echidnic]]
| | [[Leapday|Leapday]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[6L&nbsp;4s]] (10-tone)<br>10L&nbsp;6s (16-tone)<br>10L&nbsp;16s (26-tone)<br>10L&nbsp;26s (36-tone)
| | [[2L_3s|2L 3s]] (5-tone)
| 14:9<br>9:5<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
 
[[5L_2s|5L 2s]] (7-tone)
 
[[5L_7s|5L 7s]] (12-tone)
 
12L 5s (17-tone)
 
17L 12s (29-tone)
| | 11:8
 
8:3
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 1
| 10\46
| | 21\46
| 260.87
| | 547.826
| [[Bamity]]
| | [[Heinz|Heinz]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[4L&nbsp;6s]] (10-tone)<br>4L&nbsp;10s (14-tone)<br>14L&nbsp;4s (18-tone)<br>14L&nbsp;18s (32-tone)
| | [[2L_3s|2L 3s]] (5-tone)
| 13:10<br>10:3<br>7:3<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
 
[[2L_5s|2L 5s]] (7-tone)
 
[[2L_7s|2L 7s]] (9-tone)
 
[[2L_9s|2L 9s]] (11-tone)
 
11L 2s (13-tone)
 
11L 13s (24-tone)
 
11L 24s (35-tone)
| | 17:4
 
13:4
 
9:4
 
5:4 ~ QE
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
| 11\46
| | 1\46
| 286.957
| | 26.087
| [[Vines]]
| | [[Ketchup|Ketchup]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[4L&nbsp;6s]] (10-tone)<br>4L&nbsp;10s (14-tone)<br>4L&nbsp;14s (18-tone)<br>4L&nbsp;18s (22-tone)<br>4L&nbsp;22s (26-tone)<br>4L&nbsp;26s (30-tone)<br>4L&nbsp;30s (34-tone)<br>4L&nbsp;34s (38-tone)<br>4L&nbsp;38s (42-tone)
| |
| 12:11 ~ QE<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
| |
|-
|-
| | 2
| 23
| | 2\46
| 1\46
| | 52.174
| 26.087
| | [[Shrutar|Shrutar]]
| [[Icositritonic]]
| | 2L 2s (4-tone)
|  
 
|  
[[2L_4s|2L 4s]] (6-tone)
|}
 
[[2L_6s|2L 6s]] (8-tone)
 
[[2L_8s|2L 8s]] (10-tone)
 
[[2L_10s|2L 10s]] (12-tone)
 
2L 12s (14-tone)
 
2L 14s (16-tone)
 
2L 16s (18-tone)
 
2L 18s (20-tone)
 
2L 20s (22-tone)
 
22L 2s (24-tone)
| | 21:2
 
19:2
 
17:2
 
15:2


13:2
== Scales ==
{{Main| List of MOS scales in 46edo }}


11:2
* [[Plum]]
* [[Compdye]]
* [[Smi2s]]


9:2
; Sensi
* [[Sensi5]]
* [[Sensi8]]
* [[Sensi11]]
* [[Sensi19]]


7:2
; Elfleapday
* [[Elfleapday7]]
* [[Elfleapday8d]]
* [[Elfleapday9]]
* [[Elfleapday10]]
* [[Elfleapday12]]
* [[Elfleapday12f]]


5:2
; Elfsensus
* [[Elfsensus7]]
* [[Elfsensus8d]]
* [[Elfsensus9]]
* [[Elfsensus10]]
* [[Elfsensus12]]
* [[Elfsensus12f]]


3:2 ~ QE, Golden
=== Harmonic scales ===
46edo represents [[harmonic series|overtones]] 8 through 16 (written as [[JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. This corresponds to scale steps of 8, 7, 6, 6, 5, 5, 5, 4.
* 8\46 (208.696{{c}}) stands in for frequency ratio [[9/8]] (203.910{{c}}).
* 7\46 (182.609{{c}}) stands in for [[10/9]] (182.404{{c}}).
* 6\46 (156.522{{c}}) stands in for [[11/10]] (165.004{{c}}) and [[12/11]] (150.637{{c}}).
* 5\46 (130.435{{c}}) stands in for [[13/12]] (138.573{{c}}), [[14/13]] (128.298{{c}}) and [[15/14]] (119.443{{c}}).
* 4\46 (104.348{{c}}) stands in for [[16/15]] (111.731{{c}}).


2:1 ~ QE
{| class="wikitable center-all"
|-
|-
| | 2
! Harmonic
| | 3\46
! Note (starting from C)
| | 78.261
| | [[Semivalentine|Semivalentine]]
| | 2L 2s (4-tone)
 
[[2L_4s|2L 4s]] (6-tone)
 
[[2L_6s|2L 6s]] (8-tone)
 
[[2L_8s|2L 8s]] (10-tone)
 
[[2L_10s|2L 10s]] (12-tone)
 
2L 12s (14-tone)
 
14L 2s (16-tone)
 
16L 14s (30-tone)
| | 20:3
 
17:3
 
14:3
 
11:3
 
8:3
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 2
! 1
| | 4\46
| style="font-size: 16px;" | C
| | 104.348
| | [[Srutal|Srutal]]/[[Diaschismic|diaschismic]]
| | 2L 2s (4-tone)
 
[[2L_4s|2L 4s]] (6-tone)
 
[[2L_6s|2L 6s]] (8-tone)
 
[[2L_8s|2L 8s]] (10-tone)
 
[[10L_2s|10L 2s]] (12-tone)
 
12L 10s (22-tone)
 
12L 22s (34-tone)
| | 19:4
 
15:4
 
11:4
 
7:4
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
! 3
| | 5\46
| style="font-size: 16px;" | G
| | 130.435
| |
| | 2L 2s (4-tone)
 
[[2L_4s|2L 4s]] (6-tone)
 
[[2L_6s|2L 6s]] (8-tone)
 
[[8L_2s|8L 2s]] (10-tone)
 
8L 10s (18-tone)
 
18L 10s (28-tone)
| | 18:5
 
13:5
 
8:5 ~ Golden
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 2
! 5
| | 6\46
| style="font-size: 16px;" | E{{naturaldown|40}}
| | 156.522
| | [[Bison|Bison]]
| | 2L 2s (4-tone)
 
[[2L_4s|2L 4s]] (6-tone)
 
[[6L_2s|6L 2s]] (8-tone)
 
8L 6s (14-tone)
 
8L 14s (22-tone)
 
8L 22s (30-tone)
 
8L 30s (38-tone
| | 17:6
 
11:6
 
6:5 ~ QE
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
! 7
| | 7\46
| style="font-size: 16px;" | G&#x1D12A;, B{{flatdown|40}}
| | 182.609
| | [[Unidec|Unidec]]/[[Hendec|hendec]]
| | 2L 2s (4-tone)
 
[[2L_4s|2L 4s]] (6-tone)
 
[[6L_2s|6L 2s]] (8-tone)
 
6L 8s (14-tone)
 
6L 14s (20-tone)
 
20L 6s (26-tone)
| | 16:7
 
9:7
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 2
! 9
| | 8\46
| style="font-size: 16px;" | D
| | 208.696
| | [[Abigail|Abigail]]
| | 2L 2s (4-tone)
 
[[4L_2s|4L 2s]] (6-tone)
 
[[6L_2s|6L 2s]] (8-tone)
 
6L 8s (14-tone)
 
6L 14s (20-tone)
 
6L 20s (26-tone)
 
6L 26s (32-tone)
 
6L 32s (38-tone)
 
6L 38s (44-tone)
| | 15:8
 
8:7 ~ QE
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
! 11
| | 9\46
| style="font-size: 16px;" | E&#x266F;, F{{naturalup2|40}}
| | 234.783
| | [[Echidnic|Echidnic]]
| | 2L 2s (4-tone)
 
[[4L_2s|4L 2s]] (6-tone)
 
[[6L_4s|6L 4s]] (10-tone)
 
10L 6s (16-tone)
 
10L 16s (26-tone)
 
10L 26s (36-tone)
| | 14:9
 
9:5
 
5:4 ~ QE
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
! 13
| | 10\46
| style="font-size: 16px;" | G&#x266F;, A{{flatup2|40}}
| | 260.87
| | [[Bamity|Bamity]]
| | 2L 2s (4-tone)
 
[[4L_2s|4L 2s]] (6-tone)
 
[[4L_6s|4L 6s]] (10-tone)
 
4L 10s (14-tone)
 
14L 4s (18-tone)
 
14L 18s (32-tone)
| | 13:10
 
10:3
 
7:3
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| | 2
! 15
| | 11\46
| style="font-size: 16px;" | B{{naturaldown|40}}
| | 286.957
|}
| | [[Vines|Vines]]
| | 2L 2s (4-tone)


[[4L_2s|4L 2s]] (6-tone)
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 46edo]]


[[4L_6s|4L 6s]] (10-tone)
=== Skip fretting ===
'''[[Skip fretting system 46 2 11]]''' is a [[skip fretting]] system for playing 46-edo on a 23-edo stringed instrument.


4L 10s (14-tone)


4L 14s (18-tone)
'''Skip fretting system 46 7 11''' is another skip fretting system for 46edo. The examples on this page are for 7-string [[guitar]].


4L 18s (22-tone)
; Harmonics
1/1: string 2 open


4L 22s (26-tone)
2/1: string 3 fret 5


4L 26s (30-tone)
3/2: not easily accessible


4L 30s (34-tone)
5/4: string 5 fret 4


4L 34s (38-tone)
== Music ==
=== Modern renditions ===
; {{W|Johann Sebastian Bach}}
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3 Sonata No. 3 in G minor, BWV 1029]{{dead link}} (late 1730s – early 1740s) – arranged and rendered by Claudi Meneghin
* [https://www.youtube.com/watch?v=wMEdFl2puL0 "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – with syntonic-comma adjustment, rendered by Claudi Meneghin (2025)
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080]{{dead link}} (1742–1749) – arranged and rendered by Claudi Meneghin
* "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – arranged and rendered by Claudi Meneghin
** [https://www.youtube.com/watch?v=4yetEubmIk0 organ rendering] (2024) · [https://www.youtube.com/watch?v=fwGBD-oGNxI harpsichord rendering] (2025)


4L 38s (42-tone)
; {{W|Nicolaus Bruhns}}
| | 12:11 ~ QE
* [https://www.youtube.com/watch?v=_YiCc81ktBI ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
 
11:1
 
10:1
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
| | 23
| | 1\46
| | 26.087
| |
| |
| |
|}


=Approximation to Mode 8 of the Harmonic Series=
; {{W|Frederick Chopin}}
* [https://www.youtube.com/shorts/nCKtRb7fD2w ''Prelude op. 28 no. 7 in A major''] (1836) – rendered by Claudi Meneghin (2025)
* ''"Waterfall" Étude from 12 Études, op. 10'' (1829–1832) – with syntonic comma adjustment, rendered with fortepiano tone by Claudi Meneghin (2025)
** [https://www.youtube.com/shorts/AkKCmAtAQCg ''fortepiano rendering'']
** [https://www.youtube.com/shorts/QCN0H2Gnmk4 ''sine wave rendering'']


46edo represents [[overtone|overtone]]s 8 through 16 (written as [[JI|JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.
; {{W|Scott Joplin}}
* ''Maple Leaf Rag'' (1899) – arranged for harpsichord and rendered by Claudi Meneghin
** with syntonic comma adjustment ([https://www.youtube.com/watch?v=GXIoWsvFMzI 2024], [https://www.youtube.com/watch?v=55iWVqnaox8&lc=Ugz472kn24J1Bw_vHtV4AaABAg 2025])
** without syntonic comma adjustment (super-Pythagorean) ([https://www.youtube.com/shorts/2OOXUO2H9qA 2026])


8\46edo (208.70¢) stands in for frequency ratio [[9/8|9:8]] (203.91¢).
; Claude Larson ({{W|Klaus Netzle|German Wikipedia|s=de}})
* [https://www.youtube.com/shorts/fxEWnqvZtjY "Memory Image" from ''Soundscapes Vol.2''] (1986) – covered by [[Bryan Deister]] (2025)


7\46edo (182.61¢) stands in for [[10/9|10:9]] (182.40¢).
; {{W|Akira Yamaoka}}
* [https://www.youtube.com/shorts/WyY-7Im0zkw ''Lakeview Hotel Music Box''] via ''{{W|Silent Hill 2}}'' (2001) – microtonal cover in 46edo by [[Bryan Deister]] (2026)


6\46edo (156.52¢) stands in for [[11/10|11:10]] (165.00¢) and [[12/11|12:11]] (150.64¢).
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=SCpbbov1fSQ ''music box 46edo''] (2025)
* [https://www.youtube.com/shorts/K-Gu_YkjYS4 ''46edo improv''] (2025)
* [https://www.youtube.com/shorts/IWYJPyWE_Ao ''46edo waltz''] (2025)


5\46edo (130.43¢) stands in for [[13/12|13:12]] (138.57¢), [[14/13|14:13]] (128.30¢) and [[15/14|15:14]] (119.44¢).
; [[Jake Freivald]] ([https://soundcloud.com/jdfreivald site])
* [https://soundcloud.com/jdfreivald/a-seed-planted-yet-another ''A Seed Planted''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3 play]{{dead link}}


4\46edo (104.35¢) stands in for [[16/15|16:15]] (111.73¢).
; [[groundfault]]
* "Glimmer Extrication", from ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/track/glimmer-extrication-46edo-2 Bandcamp] | [https://www.youtube.com/watch?v=rrjuGmmodn0&t=969 YouTube (16:09–21:11)]


=Scales=
; [[Andrew Heathwaite]]
<ul><li>[[plum|plum]]</li><li>[[sensi5|sensi5]]</li><li>[[sensi8|sensi8]]</li><li>[[sensi11|sensi11]]</li><li>[[sensi19|sensi19]]</li></ul>
* [https://andrewheathwaite.bandcamp.com/track/rats ''Rats''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/tumbledown-stew ''Tumbledown Stew''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1 ''Hypnocloudsmack 1''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 ''Hypnocloudsmack 2''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 ''Hypnocloudsmack 3''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play]{{dead link}} (2012)


=Music=
; [[Aaron Krister Johnson]]
by [[Aaron_Krister_Johnson|Aaron Krister Johnson:]]
* [https://aaronkristerjohnson.bandcamp.com/track/satiesque ''Satiesque''] (2014)


[http://aaronkristerjohnson.bandcamp.com/track/satiesque Satiesque]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=-6ORgyqom5M ''Les Regrets''] (2019) – chaconne & fugue a 5, for recorder, cornett, viola da braccio, bassoon, gamba, and continuo.
* [https://www.youtube.com/watch?v=1r55c2nppe8 ''El Rossinyol''] (2020) – for organ
* [https://www.youtube.com/watch?v=JwjoT6ceU20 ''Arietta with 5 Variations''] (2020) – for organ
* [https://www.youtube.com/watch?v=rmgWC_jruSg ''Sensi Fugue''] (2024) – fugue for two organs, in sensi, 46edo tuning
* [https://www.youtube.com/shorts/iZQElKqq6Hw "Closing Jingle"], from [https://www.youtube.com/playlist?list=PLC6ZSKWKnVz14UQd32K1sXc2zvstkPN6V ''Mikrokosmos''] (2026)


by [[Gene_Ward_Smith|Gene Ward Smith:]]
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/light-at-the-end ''Light at the End''] (2020)


[http://www.archive.org/details/Chromosounds Chromosounds] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play]
; [[Joseph Monzo]]
* [https://www.youtube.com/watch?v=gL90m2ri5kw ''I Love the Blackness (unfinished)''] (2008)


[http://www.archive.org/details/MusicForYourEars Music For Your Ears] [http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] The central portion is in [[27edo|27edo]], the rest in 46edo.
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=QDFLKyTXZgs ''Fugue in 46EDO Bohlen-Pierce-Stearns 9 (Sensi Extension) LssLsLsLs "Lambda"'']


by [[Andrew_Heathwaite|Andrew Heathwaite]]: [http://andrewheathwaite.bandcamp.com/track/rats Rats], [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3 play] [http://andrewheathwaite.bandcamp.com/track/tumbledown-stew Tumbledown Stew] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play], [http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1 Hypnocloudsmack 1] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play], [http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 Hypnocloudsmack 2] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play], [http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 Hypnocloudsmack 3] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play]
; [[Gene Ward Smith]]
* [https://www.archive.org/details/Chromosounds ''Chromosounds''] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play]
* [https://www.archive.org/details/MusicForYourEars ''Music For Your Ears''] [https://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] – The central portion is in [[27edo]]; the rest is in 46edo.


[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3 Bach BWV 1029 in 46 equal] Claudi Meneghin version
; [[Tristan Bay]]
* [https://www.youtube.com/watch?v=s61YY80E_IA ''Catalyst''] (2025)


[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 Bach Contrapunctus 4] Claudi Meneghin version
; [[vivi mouse]]
* ''valentine's day'', from ''2025'' (2025) – [https://soundcloud.com/vivi-mouse-emoji/valentines-day SoundCloud] | [https://vivimouse.bandcamp.com/track/valentines-day Bandcamp] – in valentine, 46edo tuning


[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3 A Seed Planted - (Yet another version: 46 EDO)] by [https://soundcloud.com/jdfreivald/a-seed-planted-yet-another Jake Freivald]      [[Category:46edo]]
[[Category:Chromosounds]]
[[Category:chromosounds]]
[[Category:Leapday]]
[[Category:edo]]
[[Category:Sensi]]
[[Category:leapday]]
[[Category:Shrutar]]
[[Category:listen]]
[[Category:Valentine]]
[[Category:sensi]]
[[Category:Quartismic]]
[[Category:shrutar]]
[[Category:Listen]]
[[Category:todo:unify_precision]]
[[Category:Diaschismic]]
[[Category:valentine]]
Retrieved from "https://en.xen.wiki/w/46edo"