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{{Infobox ET
{{interwiki
| Prime factorization = 2 × 23
| de = 46-EDO
| Step size = 26.087¢
| en = 46edo
| Fifth = 27\46 = 704.348¢
| es =  
| Major 2nd = 8\46 = 209¢
| ja =  
| Minor 2nd = 3\46 = 78¢
| Augmented 1sn = 5\46 = 130¢
}}
}}
{{Infobox ET}}
{{ED intro}}


The '''46 equal temperament''', often abbreviated '''46-tET''', '''46-EDO''', or '''46-ET''', is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent|cents]], an interval close in size to [[66/65]], the interval from [[13/11]] to [[6/5]].
== Theory ==
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]].
 
46edo is also notable for being the smallest edo to approximate odd harmonics 1–13 with less than 25% [[relative interval error|relative error]].
 
[[Magic22 as srutis #Shrutar.5B22.5D_as_srutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.
 
=== 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)}}
 
=== As a tuning of other temperaments ===
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.
 
=== 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.


== Theory ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all right-2 left-3 left-4 left-7"
! colspan="2" | <!-- empty cell -->
|-
! prime 2
! #
! prime 3
! Cents
! prime 5
! 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>
! prime 7
! [[Kite's ups and downs notation|Ups and downs notation]]
! prime 11
! prime 13
! prime 17
! prime 19
! prime 23
|-
|-
! rowspan="2" | Error
| 0
! absolute (¢)
| 0.0
| 0.0
| +2.4
| [[1/1]]
| +5.0
| {{UDnote|step=0}}
| -3.6
|-
| -3.5
| 1
| -5.7
| 26.1
| -0.6
| [[49/48]], [[64/63]], [[81/80]]
| -10.6
| {{UDnote|step=1}}
| -2.1
|-
| 2
| 52.2
| [[28/27]], [[33/32]], [[36/35]]
| {{UDnote|step=2}}
|-
| 3
| 78.3
| [[21/20]], [[22/21]], [[24/23]], [[23/22]], [[25/24]]
| {{UDnote|step=3}}
|-
| 4
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| {{UDnote|step=4}}
|-
| 5
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| {{UDnote|step=5}}
|-
| 6
| 156.5
| [[11/10]], [[12/11]], [[23/21]]
| {{UDnote|step=6}}
|-
| 7
| 182.6
| [[10/9]]
| {{UDnote|step=7}}
|-
| 8
| 208.7
| [[9/8]]
| {{UDnote|step=8}}
|-
| 9
| 234.8
| [[8/7]], [[23/20]]
| {{UDnote|step=9}}
|-
|-
! [[Relative error|relative]] (%)
| 10
| 0
| 260.9
| +9
| [[7/6]]
| +19
| {{UDnote|step=10}}
| -14
|-
| -13
| 11
| -22
| 287.0
| -2
| [[13/11]], [[20/17]]
| -40
| {{UDnote|step=11}}
| -8
|-
| 12
| 313.0
| [[6/5]]
| {{UDnote|step=12}}
|-
| 13
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| {{UDnote|step=13}}
|-
| 14
| 365.2
| [[16/13]], [[21/17]], [[26/21]]
| {{UDnote|step=14}}
|-
|-
! colspan="2" | [[nearest edomapping]]
| 46
| 27
| 15
| 15
| 37
| 391.3
| [[5/4]]
| {{UDnote|step=15}}
|-
| 16
| 417.4
| [[14/11]], [[23/18]]
| {{UDnote|step=16}}
|-
| 17
| 443.5
| [[9/7]], [[13/10]], [[22/17]]
| {{UDnote|step=17}}
|-
| 18
| 469.6
| [[17/13]], [[21/16]]
| {{UDnote|step=18}}
|-
| 19
| 495.7
| [[4/3]]
| {{UDnote|step=19}}
|-
| 20
| 521.7
| [[23/17]], [[27/20]]
| {{UDnote|step=20}}
|-
| 21
| 21
| 547.8
| [[11/8]]
| {{UDnote|step=21}}
|-
| 22
| 573.9
| [[7/5]], [[18/13]], [[32/23]]
| {{UDnote|step=22}}
|-
| 23
| 600.0
| [[17/12]], [[24/17]]
| {{UDnote|step=23}}
|-
| 24
| 626.1
| [[10/7]], [[13/9]], [[23/16]]
| {{UDnote|step=24}}
|-
| 25
| 652.2
| [[16/11]]
| {{UDnote|step=25}}
|-
| 26
| 678.3
| [[34/23]], [[40/27]]
| {{UDnote|step=26}}
|-
| 27
| 704.3
| [[3/2]]
| {{UDnote|step=27}}
|-
| 28
| 730.4
| [[26/17]], [[32/21]]
| {{UDnote|step=28}}
|-
| 29
| 756.5
| [[14/9]], [[17/11]], [[20/13]]
| {{UDnote|step=29}}
|-
| 30
| 782.6
| [[11/7]]
| {{UDnote|step=30}}
|-
| 31
| 808.7
| [[8/5]]
| {{UDnote|step=31}}
|-
| 32
| 32
| 4
| 834.8
| 11
| [[13/8]], [[21/13]], [[34/21]]
| 24
| {{UDnote|step=32}}
|-
| 33
| 860.9
| [[18/11]], [[23/14]], [[28/17]]
| {{UDnote|step=33}}
|-
| 34
| 887.0
| [[5/3]]
| {{UDnote|step=34}}
|-
| 35
| 913.0
| [[17/10]], [[22/13]]
| {{UDnote|step=35}}
|-
| 36
| 939.1
| [[12/7]]
| {{UDnote|step=36}}
|-
| 37
| 965.2
| [[7/4]], [[40/23]]
| {{UDnote|step=37}}
|-
| 38
| 991.3
| [[16/9]], [[23/13]]
| {{UDnote|step=38}}
|-
| 39
| 1017.4
| [[9/5]]
| {{UDnote|step=39}}
|-
| 40
| 1043.5
| [[11/6]], [[20/11]], [[42/23]]
| {{UDnote|step=40}}
|-
| 41
| 1069.6
| [[13/7]], [[24/13]], [[28/15]]
| {{UDnote|step=41}}
|-
| 42
| 1095.7
| [[15/8]], [[17/9]], [[32/17]]
| {{UDnote|step=42}}
|-
| 43
| 1121.7
| [[21/11]], [[23/12]], [[40/21]], [[44/23]], [[48/25]]
| {{UDnote|step=43}}
|-
| 44
| 1147.8
| [[27/14]], [[35/18]], [[64/33]]
| {{UDnote|step=44}}
|-
| 45
| 1173.9
| [[63/32]], [[96/49]], [[160/81]]
| {{UDnote|step=45}}
|-
|-
! colspan="2" | [[Fifthspan]]
| 46
| 0
| 1200.0
| +1
| [[2/1]]
| +21
| {{UDnote|step=46}}
| +15
| +11
| +8
| -22
| -3
| +6
|}
|}
<references group="note" />


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 various consequences. [[Rank two temperaments]] it supports include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]] and [[unidec]]. The [[11-limit]] [[Target_tunings|minimax]] tuning for valentine temperament, (11/7)<sup>1/10</sup>, 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]], though others award that distinction to [[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.
=== Proposed interval names and solfèges ===
 
{| class="wikitable center-all right-2 left-2 left-3 left-6 mw-collapsible mw-collapsed"
The fifth of 46 equal is 2.39 cents sharp, 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. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
 
46edo can be treated as two [[23edo]]'s separated by an interval of 26.087 cents.
 
[[Magic22_as_srutis #shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.
 
== Intervals ==
 
{| class="wikitable center-all right-2 left-3 left-4"
|-
|-
! #
! #
! Cents
! Cents
! Approximate Ratios<nowiki>*</nowiki>
! 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" | [[Ups and Downs Notation]]
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! Solfege
! colspan="2" | [[Solfège]]s
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| perfect unison
| perfect unison
| P1
| P1
| D
| D
| Perfect unison
| P1
| D
| da
| do
| do
|-
|-
| 1
| 1
| 26.087
| 26.1
| [[81/80]], [[64/63]], [[49/48]]
| up unison
| up unison
| ^1
| ^1
| ^D
| ^D
| comma-wide unison, <br>super unison
| K1, S1
| KD, SD
| du
| di
| di
|-
|-
| 2
| 2
| 52.174
| 52.2
| [[28/27]], [[36/35]], [[33/32]]
| downminor 2nd
| downminor 2nd
| vm2
| vm2
| vEb
| vEb
| subminor 2nd, uber unison
| sm2, U1
| sEb, UD
| fro
| ro
| ro
|-
|-
| 3
| 3
| 78.261
| 78.3
| [[25/24]], [[21/20]], [[22/21]], [[24/23]], [[23/22]]
| minor 2nd
| minor 2nd
| m2
| m2
| Eb
| Eb
| minor 2nd, <br>classic augmented unison
| m2, kkA1
| Eb, kkD#
| fra
| rih
| rih
|-
|-
| 4
| 4
| 104.348
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| upminor 2nd
| upminor 2nd
| ^m2
| ^m2
| ^Eb
| ^Eb
| classic minor 2nd, <br>comma-narrow aug unison
| Km2, kA1
| KEb, kD#
| fru
| ra
| ra
|-
|-
| 5
| 5
| 130.435
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| dupminor 2nd
| downmid 2nd
| ^^m2
| v~2
| ^^Eb
| ^^Eb
| ru (as in supraminor)
| lesser neutral second, augmented unison
| n2, A1
| UEb, D#
| fri
| ru<ref name="intervals2" group="note">/u/ as in s'''u'''praminor</ref>
|-
|-
| 6
| 6
| 156.522
| 156.5
| [[12/11]], [[11/10]], [[23/21]]
| dudmajor 2nd
| upmid 2nd
| vvM2
| ^~2
| vvE
| vvE
| ruh (as in submajor)
| 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>
|-
|-
| 7
| 7
| 182.609
| 182.6
| [[10/9]]
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
| vE
| vE
| classic/comma-narrow major 2nd
| kM2
| kE
| ro
| reh
| reh
|-
|-
| 8
| 8
| 208.696
| 208.7
| [[9/8]]
| major 2nd
| M2
| E
| major 2nd
| major 2nd
| M2
| M2
| E
| E
| ra
| re
| re
|-
|-
| 9
| 9
| 234.783
| 234.8
| [[8/7]], [[23/20]]
| upmajor 2nd
| upmajor 2nd
| ^M2
| ^M2
| ^E
| ^E
| supermajor 2nd
| SM2
| SE
| ru
| ri
| ri
|-
|-
| 10
| 10
| 260.870
| 260.9
| [[7/6]]
| downminor 3rd
| downminor 3rd
| vm3
| vm3
| vF
| vF
| subminor 3rd
| sm3
| sF
| no
| ma
| ma
|-
|-
| 11
| 11
| 286.957
| 287.0
| [[13/11]], [[20/17]]
| minor 3rd
| m3
| F
| minor 3rd
| minor 3rd
| m3
| m3
| F
| F
| na
| meh
| meh
|-
|-
| 12
| 12
| 313.043
| 313.0
| [[6/5]]
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
| ^F
| ^F
| classic minor 3rd
| Km3
| KF
| nu
| me
| me
|-
|-
| 13
| 13
| 339.130
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| dupminor 3rd
| downmid 3rd
| ^^m3
| v~3
| ^^F
| ^^F
| mu
| lesser neutral 3rd
| n3
| UF
| ni
| mu<ref name="intervals2" group="note" />
|-
|-
| 14
| 14
| 365.217
| 365.2
| [[16/13]], [[26/21]], [[21/17]]
| dudmajor 3rd
| upmid 3rd
| vvM3
| ^~3
| vvF#
| vvF#
| muh
| greater neutral 3rd
| N3
| uF#
| mi
| muh<ref name="intervals3" group="note" />
|-
|-
| 15
| 15
| 391.304
| 391.3
| [[5/4]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
| vF#
| vF#
| classic major 3rd
| kM3
| kF#
| mo
| mi
| mi
|-
|-
| 16
| 16
| 417.391
| 417.4
| [[14/11]], [[23/18]]
| major 3rd
| M3
| F#
| major 3rd
| major 3rd
| M3
| M3
| F#
| F#
| ma
| maa
| maa
|-
|-
| 17
| 17
| 443.478
| 443.5
| [[9/7]], [[13/10]], [[22/17]]
| upmajor 3rd
| upmajor 3rd
| ^M3
| ^M3
| ^F#
| ^F#
| supermajor 3rd
| SM3
| SF#
| mu
| mo
| mo
|-
|-
| 18
| 18
| 469.565
| 469.6
| [[21/16]], [[17/13]]
| down 4th
| down 4th
| v4
| v4
| vG
| vG
| sub 4th
| s4
| sG
| fo
| fe
| fe
|-
|-
| 19
| 19
| 495.652
| 495.7
| [[4/3]]
| perfect 4th
| P4
| G
| perfect 4th
| perfect 4th
| P4
| P4
| G
| G
| fa
| fa
| fa
|-
|-
| 20
| 20
| 521.739
| 521.7
| [[27/20]], [[23/17]]
| up 4th
| up 4th
| ^4
| ^4
| ^G
| ^G
| comma-wide 4th
| K4
| KG
| fu
| fih
| fih
|-
|-
| 21
| 21
| 547.826
| 547.8
| [[11/8]]
| dup 4th
| downmid 4th
| ^^4
| v~4
| ^^G
| ^^G
| uber 4th, sub diminished 5th
| U4, sd5
| UG, sAb
| fi/sho
| fu
| fu
|-
|-
| 22
| 22
| 573.913
| 573.9
| [[7/5]], [[18/13]], [[32/23]]
| dudaug 4th, <br>dim 5th
| upmid 4th, dim 5th
| vvA4, d5
| ^~4, d5
| vvG#, Ab
| vvG#, Ab
| classic augmented 4th, diminished 5th
| kkA4, d5
| kkG#, Ab
| pi/sha
| fi
| fi
|-
|-
| 23
| 23
| 600.000
| 600.0
| [[17/12]], [[24/17]]
| downaug 4th, updim 5th
| downaug 4th, updim 5th
| vA4, ^d5
| vA4, ^d5
| vG#, ^Ab
| vG#, ^Ab
| comma-narrow aug 4th, <br>comma-wide dim 5th
| kA4, Kd5
| kG#, KAb
| po/shu
| seh
| seh
|-
|-
| 24
| 24
| 626.087
| 626.1
| [[10/7]], [[13/9]], [[23/16]]
| aug 4th, dupdim 5th
| aug 4th, downmid 5th
| A4, ^^d5
| A4, v~5
| G#, ^^Ab
| G#, ^^Ab
| augmented 4th, <br>classic diminished 5th
| A4, KKd5
| G#, KKAb
| pa/shi
| se
| se
|-
|-
| 25
| 25
| 652.174
| 652.2
| [[16/11]]
| dud 5th
| double-down 5th
| vv5
| ^~5
| vvA
| vvA
| super augmented 4th, <br>unter 5th
| SA4, u5
| SG#, uA
| pu/si
| su
| su
|-
|-
| 26
| 26
| 678.261
| 678.3
| [[40/27]], [[34/23]]
| down 5th
| down 5th
| v5
| v5
| vA
| vA
| comma-narrow 5th
| k5
| kA
| so
| sih
| sih
|-
|-
| 27
| 27
| 704.348
| 704.3
| [[3/2]]
| perfect 5th
| P5
| A
| perfect 5th
| perfect 5th
| P5
| P5
| A
| A
| sa
| sol
| sol
|-
|-
| 28
| 28
| 730.435
| 730.4
| [[32/21]], [[26/17]]
| up 5th
| up 5th
| ^5
| ^5
| ^A
| ^A
| super 5th
| S5
| SA
| su
| si
| si
|-
|-
| 29
| 29
| 756.522
| 756.5
| [[14/9]], [[20/13]], [[17/11]]
| downminor 6th
| downminor 6th
| vm6
| vm6
| vBb
| vBb
| subminor 6th
| sm6
| sBb
| flo
| lo
| lo
|-
|-
| 30
| 30
| 782.609
| 782.6
| [[11/7]]
| minor 6th
| m6
| Bb
| minor 6th
| minor 6th
| m6
| m6
| Bb
| Bb
| fla
| leh
| leh
|-
|-
| 31
| 31
| 808.696
| 808.7
| [[8/5]]
| upminor 6th
| upminor 6th
| ^m6
| ^m6
| ^Bb
| ^Bb
| classic minor 6th
| Km6
| KBb
| flu
| le
| le
|-
|-
| 32
| 32
| 834.783
| 834.8
| [[13/8]], [[21/13]], [[34/21]]
| dupminor 6th
| downmid 6th
| ^^m6
| v~6
| ^^Bb
| ^^Bb
| lu
| lesser neutral 6th
| n6
| UBb
| fli
| lu<ref name="intervals2" group="note" />
|-
|-
| 33
| 33
| 860.870
| 860.9
| [[18/11]], [[28/17]], [[23/14]]
| dudmajor 6th
| upmid 6th
| vvM6
| ^~6
| vvB
| vvB
| luh
| greater neutral 6th
| N6
| uB
| li
| luh<ref name="intervals3" group="note" />
|-
|-
| 34
| 34
| 886.957
| 887.0
| [[5/3]]
| downmajor 6th
| downmajor 6th
| vM6
| vM6
| vB
| vB
| classic major 6th
| kM6
| kB
| lo
| la
| la
|-
|-
| 35
| 35
| 913.043
| 913.0
| [[22/13]], [[17/10]]
| major 6th
| M6
| B
| major 6th
| major 6th
| M6
| M6
| B
| B
| la
| laa
| laa
|-
|-
| 36
| 36
| 939.130
| 939.1
| [[12/7]]
| upmajor 6th
| upmajor 6th
| ^M6
| ^M6
| ^B
| ^B
| supermajor 6th
| SM6
| SB
| lu
| li
| li
|-
|-
| 37
| 37
| 965.217
| 965.2
| [[7/4]], [[40/23]]
| downminor 7th
| downminor 7th
| vm7
| vm7
| vC
| vC
| subminor 7th
| sm7
| sC
| tho
| ta
| ta
|-
|-
| 38
| 38
| 991.304
| 991.3
| [[16/9]], [[23/13]]
| minor 7th
| m7
| C
| minor 7th
| minor 7th
| m7
| m7
| C
| C
| tha
| teh
| teh
|-
|-
| 39
| 39
| 1017.391
| 1017.4
| [[9/5]]
| upminor 7th
| upminor 7th
| ^m7
| ^m7
| ^C
| ^C
| classic/comma-wide minor 7th
| Km7
| KC
| thu
| te
| te
|-
|-
| 40
| 40
| 1043.478
| 1043.5
| [[11/6]], [[20/11]], [[42/23]]
| dupminor 7th
| downmid 7th
| ^^m7
| v~7
| ^^C
| ^^C
| tu
| lesser neutral 7th, sub diminished 8ve
| n7, sd8
| UC, sDb
| thi
| tu<ref name="intervals2" group="note" />
|-
|-
| 41
| 41
| 1069.565
| 1069.6
| [[24/13]], [[13/7]], [[28/15]]
| dudmajor 7th
| upmid 7th
| vvM7
| ^~7
| vvC#
| vvC#
| tuh
| greater neutral 7th,
diminished 8ve
| N7, d8
| uC#, Db
| ti
| tuh<ref name="intervals3" group="note" />
|-
|-
| 42
| 42
| 1095.652
| 1095.7
| [[15/8]], [[32/17]], [[17/9]]
| downmajor 7th
| downmajor 7th
| vM7
| vM7
| vC#
| vC#
| classic major 7th,
comma-wide dim 8ve
| kM7, Kd8
| kC#, KDb
| to
| ti
| ti
|-
|-
| 43
| 43
| 1121.739
| 1121.7
| [[48/25]], [[40/21]], [[21/11]], [[23/12]], [[44/23]]
| major 7th
| major 7th
| M7
| M7
| C#
| C#
| major 7th, <br>classic diminished 8ve
| M7, KKd8
| C#, KKDb
| ta
| taa
| taa
|-
|-
| 44
| 44
| 1147.826
| 1147.8
| [[27/14]], [[35/18]], [[64/33]]
| upmajor 7th
| upmajor 7th
| ^M7
| ^M7
| ^C#
| ^C#
| supermajor 7th, unter 8ve
| SM7, u8
| SC#, uD
| tu
| to
| to
|-
|-
| 45
| 45
| 1173.913
| 1173.9
| [[160/81]], [[63/32]], [[96/49]]
| down 8ve
| down 8ve
| v8
| v8
| vD
| vD
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| do
| da
| da
|-
|-
| 46
| 46
| 1200.000
| 1200.0
| [[2/1]]
| perfect 8ve
| P8
| D
| perfect 8ve
| perfect 8ve
| P8
| P8
| D
| D
| da
| do
| do
|}
|}
<nowiki>*</nowiki> Based on treating 46-edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46-edo has the 15th harmony poorly approximated in general, because, while both the 3rd and 5th harmonies are sharp by a fair amount and they add up, all the other primes are flat, making the difference even larger, to the extent that it is not [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] (and its inversion [[26/15]]). 9\46edo is closer 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.


Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
=== 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 center-all"
{| class="wikitable center-all"
|-
|-
! quality
! Quality
! color
! Color
! monzo format
! Monzo format
! examples
! Examples
|-
|-
| downminor
| downminor
| zo
| zo
| {a, b, 0, 1}
| {{Monzo| ''a'' ''b'' 0 1 }}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| minor
| minor
| fourthward wa
| fourthward wa
| {a, b}, b &lt; -1
| {{Monzo| ''a'' ''b'' }}, ''b'' < −1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| upminor
| upminor
| gu
| gu
| {a, b, -1}
| {{Monzo| ''a'' ''b'' −1 }}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| downmid
| dupminor
| ilo
| ilo
| {a, b, 0, 0, 1}
| {{Monzo| ''a'' ''b'' 0 0 1 }}
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| upmid
| dudmajor
| lu
| lu
| {a, b, 0, 0, -1}
| {{Monzo| ''a'' ''b'' 0 0 −1 }}
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| downmajor
| downmajor
| yo
| yo
| {a, b, 1}
| {{Monzo| ''a'' ''b'' 1 }}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| major
| major
| fifthward wa
| fifthward wa
| {a, b}, b &gt; 1
| {{Monzo| ''a'' ''b'' }}, ''b'' > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| {a, b, 0, -1}
| {{Monzo| ''a'' ''b'' 0 −1 }}
| 9/7, 12/7
| 9/7, 12/7
|}
|}
All 46edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects 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:
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:


{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! color of the 3rd
! Color of the 3rd
! JI chord
! JI chord
! notes as edosteps
! Notes as edosteps
! notes of C chord
! Notes of C chord
! written name
! Written name
! spoken name
! Spoken name
|-
|-
| zo
| zo
| 6:7:9
| 6:7:9
| 0-10-27
| 0–10–27
| C vEb G
| C vEb G
| Cvm
| Cvm
Line 534: Line 870:
| gu
| gu
| 10:12:15
| 10:12:15
| 0-12-27
| 0–12–27
| C ^Eb G
| C ^Eb G
| C^m
| C^m
Line 541: Line 877:
| ilo
| ilo
| 18:22:27
| 18:22:27
| 0-13-27
| 0–13–27
| C ^^Eb G
| C ^^Eb G
| Cv~
| C^^m
| C downmid
| C dupminor
|-
|-
| lu
| lu
| 22:27:33
| 22:27:33
| 0-14-27
| 0–14–27
| C vvE G
| C vvE G
| C^~
| Cvv
| C upmid
| C dudmajor or C dud
|-
|-
| yo
| yo
| 4:5:6
| 4:5:6
| 0-15-27
| 0–15–27
| C vE G
| C vE G
| Cv
| Cv
Line 562: Line 898:
| ru
| ru
| 14:18:21
| 14:18:21
| 0-17-27
| 0–17–27
| C ^E G
| C ^E G
| C^
| C^
| C upmajor or C up
| C upmajor or C up
|}
|}
For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].
 
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp5-szg}}
 
=== 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}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[39edo #Sagittal notation|39edo]].
 
==== Evo flavor ====
{{Sagittal chart|Evo}}
 
==== Revo flavor ====
{{Sagittal chart}}
 
== Approximation to JI ==
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]


== Just approximation ==
=== 17-odd-limit interval mappings ===
=== Selected just intervals ===
{{Q-odd-limit intervals|46|17}}
The following table shows how [[15-odd-limit intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
 
{| class="wikitable center-all"
=== Consistent circles ===
|+Direct mapping (even if inconsistent)
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]]
|-
| [[10/9]] || 36.1% || Normal || [[Mitonic]] || [[Unidec]], [[hendec]]
|-
| [[31/24]] || 70.2% || Weak || [[Sensible]], [[sensi]] add-31 || [[Bison]] add-31, [[bisensi]] add-31
|}
 
{| 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 || ?
|}
 
For the 23rd-octave temperament that 46edo supports which combines all above 23-note circles, see [[icositritonic]].
 
== 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
|-
|-
! Interval, complement
| 2.3.5.7
! Error (abs, [[Cent|¢]])
| 126/125, 245/243, 1029/1024
| {{mapping| 46 73 107 129 }}
| −0.595
| 1.34
| 5.12
|-
|-
| [[14/11]], [[11/7]]
| 2.3.5.7.11
| 0.117
| 121/120, 126/125, 176/175, 245/243
| {{mapping| 46 73 107 129 159 }}
| −0.274
| 1.36
| 5.20
|-
|-
| [[10/9]], [[9/5]]
| 2.3.5.7.11.13
| 0.205
| 91/90, 121/120, 169/168, 176/175, 245/243
| {{mapping| 46 73 107 129 159 170 }}
| +0.030
| 1.41
| 5.42
|-
|-
| [[14/13]], [[13/7]]
| 2.3.5.7.11.13.17
| 2.137
| 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
|-
|-
| [[13/11]], [[22/13]]
| 2.3.5.7.11.13.17.23
| 2.253
| 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.
 
=== Commas ===
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 }}.
 
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
| '''[[4/3]], [[3/2]]'''
! [[Harmonic limit|Prime<br>limit]]
| '''2.393'''
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
|-
| [[6/5]], [[5/3]]
| 5
| 2.598
| <abbr title="50331648/48828125">(16 digits)</abbr>
| {{monzo| 24 1 -11 }}
| 52.50
| Salegu
| [[Magus comma]]
|-
|-
| '''[[11/8]], [[16/11]]'''
| 5
| '''3.492'''
| <abbr title="1990656/1953125">(14 digits)</abbr>
| {{monzo| 13 5 -9 }}
| 32.95
| Satritrigu
| [[Valentine comma]]
|-
|-
| '''[[8/7]], [[7/4]]'''
| 5
| '''3.609'''
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
|-
| [[9/8]], [[16/9]]
| 5
| 4.786
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
|-
| '''[[5/4]], [[8/5]]'''
| 5
| '''4.991'''
| <abbr title="1600000/1594323">(14 digits)</abbr>
| {{monzo| 9 -13 5 }}
| 6.15
| Saquinyo
| [[Amity comma]]
|-
|-
| '''[[16/13]], [[13/8]]'''
| 7
| '''5.745'''
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
|-
| [[12/11]], [[11/6]]
| 7
| 5.885
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
|-
| [[7/6]], [[12/7]]
| 7
| 6.001
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.80
| Zotrigu
| Starling comma
|-
|-
| [[16/15]], [[15/8]]
| 7
| 7.383
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
|-
| [[13/12]], [[24/13]]
| 7
| 8.138
| [[5120/5103]]
| {{monzo| 10 -6 1 -1 }}
| 5.76
| Saruyo
| Hemifamity comma, aberschisma
|-
|-
| [[11/9]], [[18/11]]
| 7
| 8.278
| <abbr title="2147483648/2144153025">(20 digits)</abbr>
| {{monzo| 31 -6 -2 -6 }}
| 2.69
| Sasa-tribiru-agugu
| [[Pessoalisma]]
|-
|-
| [[9/7]], [[14/9]]
| 7
| 8.394
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
|-
| [[11/10]], [[20/11]]
| 11
| 8.482
| [[121/120]]
| {{monzo|-3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
|-
| [[7/5]], [[10/7]]
| 11
| 8.599
| [[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
|-
|-
| [[18/13]], [[13/9]]
| 13
| 10.531
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|-
| [[13/10]], [[20/13]]
| 13
| 10.736
| [[169/168]]
| {{monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
|-
| [[15/11]], [[22/15]]
| 13
| 10.875
| [[196/195]]
| {{monzo| 2 -1 -1 2 0 -1 }}
| 8.86
| Thuzozogu
| Mynucuma
|-
|-
| [[15/14]], [[28/15]]
| 13
| 10.992
| [[507/500]]
| {{monzo| -2 1 -3 0 0 2 }}
| 24.07
| Thothotrigu
|
|-
|-
| ''[[15/13]], [[26/15]]''
| 13
| ''12.958''
| [[351/350]]
|}
| {{Monzo| -1 3 -2 -1 0 1 }}
 
| 4.94
=== Temperament measures ===
| Thorugugu
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 46et.
| Ratwolfsma
{| class="wikitable center-all"
! colspan="2" |
! 3-limit
! 5-limit
! 7-limit
! 11-limit
! 13-limit
! 17-limit
! 23-limit no-19
|-
|-
! colspan="2" |Octave stretch (¢)
| 13
| -0.755
| [[352/351]]
| -1.219
| {{monzo| 5 -3 0 0 1 -1 }}
| -0.595
| 4.93
| -0.274
| Thulo
| +0.030
| Minor minthma
| +0.047
| +0.101
|-
|-
! rowspan="2" |Error
| 17
! [[TE error|absolute]] (¢)
| [[256/255]]
| 0.75
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| 0.90
| 6.78
| 1.34
| Sugu
| 1.36
| Charisma, septendecimal kleisma
| 1.41
| 1.31
| 1.23
|-
|-
! [[TE simple badness|relative]] (%)
| 17
| 2.89
| [[289/288]]
| 3.45
| {{monzo| -5 -2 0 0 0 0 2 }}
| 5.12
| 6.00
| 5.20
| Soso
| 5.42
| Semitonisma
| 5.02
| 4.72
|}
|}
<references group="note" />


* 46et has a lower relative error than any previous ETs in the 17-, 19-, 23-limit, and others. The next ET that does better in the aforementioned subgroups is 72, 72, 94, respectively.
=== Rank-2 temperaments ===
* 46et is prominent in the no-19 23-limit. The next ET that does better in this subgroup is 140.
{| class="wikitable center-1 center-2 center-3 center-4"
 
== Linear temperaments ==
 
{| class="wikitable"
|-
|-
! Periods <br>per octave
! Periods<br>per 8ve
! Generator
! Generator
! Cents
! Cents
! Temperaments
! Temperaments
! MOS/DE Scales available
! MOS scales
! L:s
! L:s
|-
|-
| 1
| rowspan="11" | 1
| 1\46
| 1\46
| 26.087
| 26.087
|  
| [[Sfourth]]
|  
|  
|  
|  
|-
|-
| 1
| 3\46
| 3\46
| 78.261
| 78.261
| [[Valentine]]
| [[Valentine]]
| 1L 14s (15-tone)
| 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
15L 1s (16-tone)
 
16L 15s (31-tone)
| 4:3 ~ [[Maximal_evenness|quasi-equal]]
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 5\46
| 5\46
| 130.435
| 130.435
| [[Twothirdtonic]]
| [[Twothirdtonic]]
| [[1L_8s|1L 8s]] (9-tone)
| [[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
[[9L_1s|9L 1s]] (10-tone)
 
9L 10s (19-tone)
 
9L 19s (28-tone)
 
9L 28s (37-tone)
| 6:5 ~ QE
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 7\46
| 7\46
| 182.609
| 182.609
| [[Minortone]]
| [[Minortone]] / [[mitonic]]
| [[1L 5s]] (6-tone)
| [[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
[[6L 1s]] (7-tone)
 
7L 6s (13-tone)
 
13L 7s (20-tone)
 
13L 20s (33-tone)
| 11:7
 
7:4
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 9\46
| 9\46
| 234.783
| 234.783
| [[Rodan]]
| [[Rodan]]
| [[1L 4s]] (5-tone)
| [[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
[[1L 5s]] (6-tone)
 
[[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
| 11\46
| 11\46
| 286.957
| 286.957
|  
| [[Amity_family#Gamity|Gamity]]
| [[4L 1s]] (5-tone)
| [[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
[[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
| 13\46
| 13\46
| 339.130
| 339.130
| [[Amity]]/[[hitchcock]]
| [[Amity]] / [[Amity_family#Hitchcock|Hitchcock]]
| [[4L 3s]] (7-tone)
| [[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
[[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
| 15\46
| 15\46
| 391.304
| 391.304
| [[Amigo]]
| [[Magus]] / [[amigo]]
| [[1L 2s]] (3-tone)
| [[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
[[3L 1s]] (4-tone)
 
[[3L 4s]] (7-tone)
 
[[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
| 17\46
| 17\46
| 443.478
| 443.478
| [[Sensi]]
| [[Sensi]]
| [[3L 2s]] (5-tone)
| [[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
[[3L 5s]] (8-tone)
 
[[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
| 19\46
| 19\46
| 495.652
| 495.652
| [[Leapday]]
| [[Leapday]]
| [[2L 3s]] (5-tone)
| [[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
[[5L 2s]] (7-tone)
 
[[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
| 21\46
| 21\46
| 547.826
| 547.826
| [[Heinz]]
| [[Heinz]]
| [[2L 3s]] (5-tone)
| [[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
[[2L 5s]] (7-tone)
 
[[2L 7s]] (9-tone)
 
[[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
| rowspan="11" | 2
| 1\46
| 1\46
| 26.087
| 26.087
Line 1,014: Line 1,299:
|  
|  
|-
|-
| 2
| 2\46
| 2\46
| 52.174
| 52.174
| [[Shrutar]]
| [[Shrutar]]
| 2L 2s (4-tone)
| 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
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[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
 
11:2
 
9:2
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 2
| 3\46
| 3\46
| 78.261
| 78.261
| [[Semivalentine]]
| [[Semivalentine]]
| 2L 2s (4-tone)
| 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
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[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
| 4\46
| 4\46
| 104.348
| 104.348
| [[Srutal]]/[[diaschismic]]
| [[Srutal]] / [[diaschismic]]
| 2L 2s (4-tone)
| 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)
 
| 19:4<br>15:4<br>11:4<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[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
| 5\46
| 5\46
| 130.435
| 130.435
|  
|  
| 2L 2s (4-tone)
| 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)
 
| 18:5<br>13:5<br>8:5 ~ Golden<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[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
| 6\46
| 6\46
| 156.522
| 156.522
| [[Bison]]
| [[Bison]]
| 2L 2s (4-tone)
| 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
 
| 17:6<br>11:6<br>6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[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\46
| 7\46
| 182.609
| 182.609
| [[Unidec]]/[[Hendec|hendec]]
| [[Unidec]] / [[hendec]]
| 2L 2s (4-tone)
| 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)
 
| 16:7<br>9:7<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[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
| 8\46
| 8\46
| 208.696
| 208.696
| [[Abigail]]
| [[Abigail]]
| 2L 2s (4-tone)
| 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)
 
| 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
[[4L 2s]] (6-tone)
 
[[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
| 9\46
| 9\46
| 234.783
| 234.783
| [[Echidnic]]
| [[Echidnic]]
| 2L 2s (4-tone)
| 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)
 
| 14:9<br>9:5<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
[[4L 2s]] (6-tone)
 
[[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
| 10\46
| 10\46
| 260.87
| 260.87
| [[Bamity]]
| [[Bamity]]
| 2L 2s (4-tone)
| 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)
 
| 13:10<br>10:3<br>7:3<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
[[4L 2s]] (6-tone)
 
[[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
| 11\46
| 11\46
| 286.957
| 286.957
| [[Vines]]
| [[Vines]]
| 2L 2s (4-tone)
| 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
|-
| 23
| 1\46
| 26.087
| [[Icositritonic]]
|
|
|}


[[4L 2s]] (6-tone)
== Scales ==
{{Main| List of MOS scales in 46edo }}


[[4L 6s]] (10-tone)
* [[Plum]]
* [[Compdye]]
* [[Smi2s]]


4L 10s (14-tone)
; Sensi
* [[Sensi5]]
* [[Sensi8]]
* [[Sensi11]]
* [[Sensi19]]


4L 14s (18-tone)
; Elfleapday
* [[Elfleapday7]]
* [[Elfleapday8d]]
* [[Elfleapday9]]
* [[Elfleapday10]]
* [[Elfleapday12]]
* [[Elfleapday12f]]


4L 18s (22-tone)
; Elfsensus
* [[Elfsensus7]]
* [[Elfsensus8d]]
* [[Elfsensus9]]
* [[Elfsensus10]]
* [[Elfsensus12]]
* [[Elfsensus12f]]


4L 22s (26-tone)
=== 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}}).


4L 26s (30-tone)
{| class="wikitable center-all"
|-
! Harmonic
! Note (starting from C)
|-
! 1
| style="font-size: 16px;" | C
|-
! 3
| style="font-size: 16px;" | G
|-
! 5
| style="font-size: 16px;" | E{{naturaldown|40}}
|-
! 7
| style="font-size: 16px;" | G&#x1D12A;, B{{flatdown|40}}
|-
! 9
| style="font-size: 16px;" | D
|-
! 11
| style="font-size: 16px;" | E&#x266F;, F{{naturalup2|40}}
|-
! 13
| style="font-size: 16px;" | G&#x266F;, A{{flatup2|40}}
|-
! 15
| style="font-size: 16px;" | B{{naturaldown|40}}
|}


4L 30s (34-tone)
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 46edo]]


4L 34s (38-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 38s (42-tone)
| 12:11 ~ QE


11:1
'''Skip fretting system 46 7 11''' is another skip fretting system for 46edo. The examples on this page are for 7-string [[guitar]].


10:1
; Harmonics
1/1: string 2 open


9:1
2/1: string 3 fret 5


8:1
3/2: not easily accessible


7:1
5/4: string 5 fret 4


6:1
== 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)


5:1
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=_YiCc81ktBI ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)


4:1
; {{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'']


3:1
; {{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])


2:1 ~ QE
; 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)
| 23
| 1\46
| 26.087
|
|
|
|}


== Scales ==
; {{W|Akira Yamaoka}}
*[[plum]]
* [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)
*[[sensi5]]
*[[sensi8]]
*[[sensi11]]
*[[sensi19]]
 
=== Approximation to Mode 8 of the Harmonic Series ===
 
46edo represents [[Overtone 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. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.


* 8\46edo (208.696¢) stands in for frequency ratio [[9/8|9:8]] (203.910¢).
=== 21st century ===
* 7\46edo (182.609¢) stands in for [[10/9|10:9]] (182.404¢).
; [[Bryan Deister]]
* 6\46edo (156.522¢) stands in for [[11/10|11:10]] (165.004¢) and [[12/11|12:11]] (150.637¢).
* [https://www.youtube.com/watch?v=SCpbbov1fSQ ''music box 46edo''] (2025)
* 5\46edo (130.435¢) stands in for [[13/12|13:12]] (138.573¢), [[14/13|14:13]] (128.298¢) and [[15/14|15:14]] (119.443¢).
* [https://www.youtube.com/shorts/K-Gu_YkjYS4 ''46edo improv''] (2025)
* 4\46edo (104.348¢) stands in for [[16/15|16:15]] (111.731¢).
* [https://www.youtube.com/shorts/IWYJPyWE_Ao ''46edo waltz''] (2025)


== Music ==
; [[Jake Freivald]] ([https://soundcloud.com/jdfreivald site])
[http://aaronkristerjohnson.bandcamp.com/track/satiesque Satiesque] by [[Aaron Krister Johnson]].
* [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}}


[http://www.archive.org/details/Chromosounds Chromosounds] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play] by [[Gene Ward Smith]].
; [[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)]


[http://www.archive.org/details/MusicForYourEars Music For Your Ears] [http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] by [[Gene Ward Smith]]. The central portion is in [[27edo]], the rest is in 46edo.
; [[Andrew Heathwaite]]
* [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)


[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] by [[Andrew Heathwaite]].
; [[Aaron Krister Johnson]]
* [https://aaronkristerjohnson.bandcamp.com/track/satiesque ''Satiesque''] (2014)


[http://andrewheathwaite.bandcamp.com/track/tumbledown-stew Tumbledown Stew]  
; [[Claudi Meneghin]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play] by [[Andrew Heathwaite]].
* [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)


[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] by [[Andrew Heathwaite]].
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/light-at-the-end ''Light at the End''] (2020)


[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 Hypnocloudsmack 2]  
; [[Joseph Monzo]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play] by [[Andrew Heathwaite]].
* [https://www.youtube.com/watch?v=gL90m2ri5kw ''I Love the Blackness (unfinished)''] (2008)


[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 Hypnocloudsmack 3]  
; [[Ray Perlner]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play] by [[Andrew Heathwaite]].
* [https://www.youtube.com/watch?v=QDFLKyTXZgs ''Fugue in 46EDO Bohlen-Pierce-Stearns 9 (Sensi Extension) LssLsLsLs "Lambda"'']


[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
; [[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/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 Bach Contrapunctus 4] Claudi Meneghin version
; [[Tristan Bay]]
* [https://www.youtube.com/watch?v=s61YY80E_IA ''Catalyst''] (2025)


[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]
; [[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


[[Category:46edo]]
[[Category:Chromosounds]]
[[Category:chromosounds]]
[[Category:Leapday]]
[[Category:Equal divisions of the octave]]
[[Category:Sensi]]
[[Category:leapday]]
[[Category:Shrutar]]
[[Category:listen]]
[[Category:Valentine]]
[[Category:sensi]]
[[Category:shrutar]]
[[Category:valentine]]
[[Category:Quartismic]]
[[Category:Quartismic]]
[[Category:Listen]]
[[Category:Diaschismic]]
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