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__FORCETOC__
{{interwiki
=Theory=
| de = 46-EDO
The 46 equal temperament, often abbreviated <b>46-tET</b>, <b>46-EDO</b>, or <b>46-ET</b>, 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]].
| en = 46edo
| es =
| ja =
}}
{{Infobox ET}}
{{ED intro}}


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|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.
== 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 [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], but it is a [[The Riemann zeta function and tuning #Zeta EDO lists|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]].


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.
46edo is also notable for being the smallest equal division to approximate harmonics 3, 5, 7, 11, and 13 with less than 25% [[relative interval error]].


46edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.
[[Rank-2 temperament]]s it [[support]]s include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]], 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 octaves.  


[[Magic22_as_srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian|Indian]] music.
[[Magic22 as srutis #Shrutar.5B22.5D_as_srutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.


=Intervals=
=== Prime harmonics ===
{{Harmonics in equal|46|columns=9}}
{{Harmonics in equal|46|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 46edo (continued)}}


{| class="wikitable"
=== Subsets and supersets ===
46edo can be treated as two circles of [[23edo]] separated by an interval of 26.087 cents.
 
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4 left-7"
|-
! &#35;
! Cents
! Approximate ratios<ref name="interval ratios" group="note">{{sg|limit=2.3.5.7.11.13.17.23&nbsp;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>
! colspan="3" | [[Ups and downs notation]]
([[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" | [[Solfege]]
|-
| 0
| 0.0
| [[1/1]]
| perfect unison
| P1
| D
| Perfect unison
| P1
| D
| da
| do
|-
| 1
| 26.1
| [[81/80]], [[64/63]], [[49/48]]
| up unison
| ^1
| ^D
| comma-wide unison, <br>super unison
| K1, S1
| KD, SD
| du
| di
|-
| 2
| 52.2
| [[28/27]], [[36/35]], [[33/32]]
| downminor 2nd
| vm2
| vEb
| subminor 2nd, uber unison
| sm2, U1
| sEb, UD
| fro
| ro
|-
| 3
| 78.3
| [[25/24]], [[21/20]], [[22/21]], [[24/23]], [[23/22]]
| minor 2nd
| m2
| Eb
| minor 2nd, <br>classic augmented unison
| m2, kkA1
| Eb, kkD#
| fra
| rih
|-
| 4
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| upminor 2nd
| ^m2
| ^Eb
| classic minor 2nd, <br>comma-narrow aug unison
| Km2, kA1
| KEb, kD#
| fru
| ra
|-
| 5
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| 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
| [[12/11]], [[11/10]], [[23/21]]
| 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>
|-
| 7
| 182.6
| [[10/9]]
| downmajor 2nd
| vM2
| vE
| classic/comma-narrow major 2nd
| kM2
| kE
| ro
| reh
|-
|-
! | degree
| 8
! | cents
| 208.7
! | solfege
| [[9/8]]
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]]
| major 2nd
! | approximate ratios
| M2
 
| E
in the [[17-limit|17-limit]]
| major 2nd
| M2
| E
| ra
| re
|-
| 9
| 234.8
| [[8/7]], [[23/20]]
| upmajor 2nd
| ^M2
| ^E
| supermajor 2nd
| SM2
| SE
| ru
| ri
|-
| 10
| 260.9
| [[7/6]]
| downminor 3rd
| vm3
| vF
| subminor 3rd
| sm3
| sF
| no
| ma
|-
| 11
| 287.0
| [[13/11]], [[20/17]]
| minor 3rd
| m3
| F
| minor 3rd
| m3
| F
| na
| meh
|-
| 12
| 313.0
| [[6/5]]
| upminor 3rd
| ^m3
| ^F
| classic minor 3rd
| Km3
| KF
| nu
| me
|-
| 13
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| dupminor 3rd
| ^^m3
| ^^F
| lesser neutral 3rd
| n3
| UF
| ni
| mu<ref name="intervals2" group="note" />
|-
| 14
| 365.2
| [[16/13]], [[26/21]], [[21/17]]
| dudmajor 3rd
| vvM3
| vvF#
| greater neutral 3rd
| N3
| uF#
| mi
| muh<ref name="intervals3" group="note" />
|-
| 15
| 391.3
| [[5/4]]
| downmajor 3rd
| vM3
| vF#
| classic major 3rd
| kM3
| kF#
| mo
| mi
|-
|-
| style="text-align:center;" | 0
| 16
| 0.000
| 417.4
| style="text-align:center;" | do
| [[14/11]], [[23/18]]
| style="text-align:center;" | perfect unison
| major 3rd
| style="text-align:center;" | P1
| M3
| style="text-align:center;" | D
| F#
| | 1/1
| major 3rd
| M3
| F#
| ma
| maa
|-
|-
| style="text-align:center;" | 1
| 17
| | 26.087
| 443.5
| style="text-align:center;" | di
| [[9/7]], [[13/10]], [[22/17]]
| style="text-align:center;" | up unison
| upmajor 3rd
| style="text-align:center;" | ^1
| ^M3
| style="text-align:center;" | ^D
| ^F#
| |
| supermajor 3rd
| SM3
| SF#
| mu
| mo
|-
|-
| style="text-align:center;" | 2
| 18
| | 52.174
| 469.6
| style="text-align:center;" | ro
| [[21/16]], [[17/13]]
| style="text-align:center;" | downminor 2nd
| down 4th
| style="text-align:center;" | vm2
| v4
| style="text-align:center;" | vEb
| vG
| |
| sub 4th
| s4
| sG
| fo
| fe
|-
|-
| style="text-align:center;" | 3
| 19
| | 78.261
| 495.7
| style="text-align:center;" | rih
| [[4/3]]
| style="text-align:center;" | minor 2nd
| perfect 4th
| style="text-align:center;" | m2
| P4
| style="text-align:center;" | Eb
| G
| |
| perfect 4th
| P4
| G
| fa
| fa
|-
|-
| style="text-align:center;" | 4
| 20
| | 104.348
| 521.7
| style="text-align:center;" | ra
| [[27/20]], [[23/17]]
| style="text-align:center;" | upminor 2nd
| up 4th
| style="text-align:center;" | ^m2
| ^4
| style="text-align:center;" | ^Eb
| ^G
| | 16/15, 17/16, 18/17
| comma-wide 4th
| K4
| KG
| fu
| fih
|-
|-
| style="text-align:center;" | 5
| 21
| | 130.435
| 547.8
| style="text-align:center;" | ru (as in supraminor)
| [[11/8]]
| style="text-align:center;" | downmid 2nd
| dup 4th
| style="text-align:center;" | v~2
| ^^4
| style="text-align:center;" | ^^Eb
| ^^G
| | 13/12, 14/13, 15/14
| uber 4th, sub diminished 5th
| U4, sd5
| UG, sAb
| fi/sho
| fu
|-
|-
| style="text-align:center;" | 6
| 22
| | 156.522
| 573.9
| style="text-align:center;" | ruh (as in submajor)
| [[7/5]], [[18/13]], [[32/23]]
| style="text-align:center;" | upmid 2nd
| dudaug 4th, <br>dim 5th
| style="text-align:center;" | ^~2
| vvA4, d5
| style="text-align:center;" | vvE
| vvG#, Ab
| | 12/11, 11/10
| classic augmented 4th, diminished 5th
| kkA4, d5
| kkG#, Ab
| pi/sha
| fi
|-
|-
| style="text-align:center;" | 7
| 23
| | 182.609
| 600.0
| style="text-align:center;" | reh
| [[17/12]], [[24/17]]
| style="text-align:center;" | downmajor 2nd
| downaug 4th, updim 5th
| style="text-align:center;" | vM2
| vA4, ^d5
| style="text-align:center;" | vE
| vG#, ^Ab
| | 10/9
| comma-narrow aug 4th, <br>comma-wide dim 5th
| kA4, Kd5
| kG#, KAb
| po/shu
| seh
|-
|-
| style="text-align:center;" | 8
| 24
| | 208.696
| 626.1
| style="text-align:center;" | re
| [[10/7]], [[13/9]], [[23/16]]
| style="text-align:center;" | major 2nd
| aug 4th, dupdim 5th
| style="text-align:center;" | M2
| A4, ^^d5
| style="text-align:center;" | E
| G#, ^^Ab
| | 9/8, 17/15
| augmented 4th, <br>classic diminished 5th
| A4, KKd5
| G#, KKAb
| pa/shi
| se
|-
|-
| style="text-align:center;" | 9
| 25
| | 234.783
| 652.2
| style="text-align:center;" | ri
| [[16/11]]
| style="text-align:center;" | upmajor 2nd
| dud 5th
| style="text-align:center;" | ^M2
| vv5
| style="text-align:center;" | ^E
| vvA
| | 8/7, 15/13*
| super augmented 4th, <br>unter 5th
| SA4, u5
| SG#, uA
| pu/si
| su
|-
|-
| style="text-align:center;" | 10
| 26
| | 260.87
| 678.3
| style="text-align:center;" | ma
| [[40/27]], [[34/23]]
| style="text-align:center;" | downminor 3rd
| down 5th
| style="text-align:center;" | vm3
| v5
| style="text-align:center;" | vF
| vA
| | 7/6, 15/13*
| comma-narrow 5th
| k5
| kA
| so
| sih
|-
|-
| style="text-align:center;" | 11
| 27
| | 286.957
| 704.3
| style="text-align:center;" | meh
| [[3/2]]
| style="text-align:center;" | minor 3rd
| perfect 5th
| style="text-align:center;" | m3
| P5
| style="text-align:center;" | F
| A
| | 13/11, 20/17
| perfect 5th
| P5
| A
| sa
| sol
|-
|-
| style="text-align:center;" | 12
| 28
| | 313.043
| 730.4
| style="text-align:center;" | me
| [[32/21]], [[26/17]]
| style="text-align:center;" | upminor 3rd
| up 5th
| style="text-align:center;" | ^m3
| ^5
| style="text-align:center;" | ^F
| ^A
| | 6/5
| super 5th
| S5
| SA
| su
| si
|-
|-
| style="text-align:center;" | 13
| 29
| | 339.13
| 756.5
| style="text-align:center;" | mu
| [[14/9]], [[20/13]], [[17/11]]
| style="text-align:center;" | downmid 3rd
| downminor 6th
| style="text-align:center;" | v~3
| vm6
| style="text-align:center;" | ^^F
| vBb
| | 11/9, 17/14
| subminor 6th
| sm6
| sBb
| flo
| lo
|-
|-
| style="text-align:center;" | 14
| 30
| | 365.217
| 782.6
| style="text-align:center;" | muh
| [[11/7]]
| style="text-align:center;" | upmid 3rd
| minor 6th
| style="text-align:center;" | ^~3
| m6
| style="text-align:center;" | vvF#
| Bb
| | 16/13
| minor 6th
| m6
| Bb
| fla
| leh
|-
|-
| style="text-align:center;" | 15
| 31
| | 391.304
| 808.7
| style="text-align:center;" | mi
| [[8/5]]
| style="text-align:center;" | downmajor 3rd
| upminor 6th
| style="text-align:center;" | vM3
| ^m6
| style="text-align:center;" | vF#
| ^Bb
| | 5/4
| classic minor 6th
| Km6
| KBb
| flu
| le
|-
|-
| style="text-align:center;" | 16
| 32
| | 417.391
| 834.8
| style="text-align:center;" | maa
| [[13/8]], [[21/13]], [[34/21]]
| style="text-align:center;" | major 3rd
| dupminor 6th
| style="text-align:center;" | M3
| ^^m6
| style="text-align:center;" | F#
| ^^Bb
| | 14/11
| lesser neutral 6th
| n6
| UBb
| fli
| lu<ref name="intervals2" group="note" />
|-
|-
| style="text-align:center;" | 17
| 33
| | 443.478
| 860.9
| style="text-align:center;" | mo
| [[18/11]], [[28/17]], [[23/14]]
| style="text-align:center;" | upmajor 3rd
| dudmajor 6th
| style="text-align:center;" | ^M3
| vvM6
| style="text-align:center;" | ^F#
| vvB
| | 9/7, 13/10, 22/17
| greater neutral 6th
| N6
| uB
| li
| luh<ref name="intervals3" group="note" />
|-
|-
| style="text-align:center;" | 18
| 34
| | 469.565
| 887.0
| style="text-align:center;" | fe
| [[5/3]]
| style="text-align:center;" | down 4th
| downmajor 6th
| style="text-align:center;" | v4
| vM6
| style="text-align:center;" | vG
| vB
| | 17/13
| classic major 6th
| kM6
| kB
| lo
| la
|-
|-
| style="text-align:center;" | 19
| 35
| | 495.652
| 913.0
| style="text-align:center;" | fa
| [[22/13]], [[17/10]]
| style="text-align:center;" | perfect 4th
| major 6th
| style="text-align:center;" | P4
| M6
| style="text-align:center;" | G
| B
| | 4/3
| major 6th
| M6
| B
| la
| laa
|-
|-
| style="text-align:center;" | 20
| 36
| | 521.739
| 939.1
| style="text-align:center;" | fih
| [[12/7]]
| style="text-align:center;" | up 4th
| upmajor 6th
| style="text-align:center;" | ^4
| ^M6
| style="text-align:center;" | ^G
| ^B
| |
| supermajor 6th
| SM6
| SB
| lu
| li
|-
|-
| style="text-align:center;" | 21
| 37
| | 547.826
| 965.2
| style="text-align:center;" | fu
| [[7/4]], [[40/23]]
| style="text-align:center;" | downmid 4th
| downminor 7th
| style="text-align:center;" | v~4
| vm7
| style="text-align:center;" | ^^G
| vC
| | 11/8, 15/11
| subminor 7th
| sm7
| sC
| tho
| ta
|-
|-
| style="text-align:center;" | 22
| 38
| | 573.913
| 991.3
| style="text-align:center;" | fi
| [[16/9]], [[23/13]]
| style="text-align:center;" | upmid 4th, dim 5th
| minor 7th
| style="text-align:center;" | ^~4, d5
| m7
| style="text-align:center;" | vvG#, Ab
| C
| | 7/5, 18/13
| minor 7th
| m7
| C
| tha
| teh
|-
|-
| style="text-align:center;" | 23
| 39
| | 600
| 1017.4
| style="text-align:center;" | seh
| [[9/5]]
| style="text-align:center;" | downaug 4th, updim 5th
| upminor 7th
| style="text-align:center;" | vA4, ^d5
| ^m7
| style="text-align:center;" | vG#, ^Ab
| ^C
| | 17/12, 24/17
| classic/comma-wide minor 7th
| Km7
| KC
| thu
| te
|-
|-
| style="text-align:center;" | 24
| 40
| | 626.087
| 1043.5
| style="text-align:center;" | se
| [[11/6]], [[20/11]], [[42/23]]
| style="text-align:center;" | aug 4th, downmid 5th
| dupminor 7th
| style="text-align:center;" | A4, v~5
| ^^m7
| style="text-align:center;" | G#, ^^Ab
| ^^C
| | 10/7, 13/9
| lesser neutral 7th, sub diminished 8ve
| n7, sd8
| UC, sDb
| thi
| tu<ref name="intervals2" group="note" />
|-
|-
| style="text-align:center;" | 25
| 41
| | 652.174
| 1069.6
| style="text-align:center;" | su
| [[24/13]], [[13/7]], [[28/15]]
| style="text-align:center;" | double-down 5th
| dudmajor 7th
| style="text-align:center;" | ^~5
| vvM7
| style="text-align:center;" | vvA
| vvC#
| | 16/11, 22/15
| greater neutral 7th,
diminished 8ve
| N7, d8
| uC#, Db
| ti
| tuh<ref name="intervals3" group="note" />
|-
|-
| style="text-align:center;" | 26
| 42
| | 678.261
| 1095.7
| style="text-align:center;" | sih
| [[15/8]], [[32/17]], [[17/9]]
| style="text-align:center;" | down 5th
| downmajor 7th
| style="text-align:center;" | v5
| vM7
| style="text-align:center;" | vA
| vC#
| |
| classic major 7th,
comma-wide dim 8ve
| kM7, Kd8
| kC#, KDb
| to
| ti
|-
|-
| style="text-align:center;" | 27
| 43
| | 704.348
| 1121.7
| style="text-align:center;" | sol
| [[48/25]], [[40/21]], [[21/11]], [[23/12]], [[44/23]]
| style="text-align:center;" | perfect 5th
| major 7th
| style="text-align:center;" | P5
| M7
| style="text-align:center;" | A
| C#
| | 3/2
| major 7th, <br>classic diminished 8ve
| M7, KKd8
| C#, KKDb
| ta
| taa
|-
|-
| style="text-align:center;" | 28
| 44
| | 730.435
| 1147.8
| style="text-align:center;" | si
| [[27/14]], [[35/18]], [[64/33]]
| style="text-align:center;" | up 5th
| upmajor 7th
| style="text-align:center;" | ^5
| ^M7
| style="text-align:center;" | ^A
| ^C#
| | 26/17
| supermajor 7th, unter 8ve
| SM7, u8
| SC#, uD
| tu
| to
|-
|-
| style="text-align:center;" | 29
| 45
| | 756.522
| 1173.9
| style="text-align:center;" | lo
| [[160/81]], [[63/32]], [[96/49]]
| style="text-align:center;" | downminor 6th
| down 8ve
| style="text-align:center;" | vm6
| v8
| style="text-align:center;" | vBb
| vD
| | 14/9, 20/13, 17/11
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| do
| da
|-
|-
| style="text-align:center;" | 30
| 46
| | 782.609
| 1200.0
| style="text-align:center;" | leh
| [[2/1]]
| style="text-align:center;" | minor 6th
| perfect 8ve
| style="text-align:center;" | m6
| P8
| style="text-align:center;" | Bb
| D
| | 11/7
| perfect 8ve
| P8
| D
| da
| do
|}
 
=== 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"
|-
|-
| style="text-align:center;" | 31
! Quality
| | 808.696
! Color
| style="text-align:center;" | le
! Monzo Format
| style="text-align:center;" | upminor 6th
! Examples
| style="text-align:center;" | ^m6
| style="text-align:center;" | ^Bb
| | 8/5
|-
|-
| style="text-align:center;" | 32
| downminor
| | 834.783
| zo
| style="text-align:center;" | lu
| [a, b, 0, 1>
| style="text-align:center;" | downmid 6th
| 7/6, 7/4
| style="text-align:center;" | v~6
| style="text-align:center;" | ^^Bb
| | 13/8
|-
|-
| style="text-align:center;" | 33
| minor
| | 860.87
| fourthward wa
| style="text-align:center;" | luh
| [a, b>, b &lt; −1
| style="text-align:center;" | upmid 6th
| 32/27, 16/9
| style="text-align:center;" | ^~6
| style="text-align:center;" | vvB
| | 18/11, 28/17
|-
|-
| style="text-align:center;" | 34
| upminor
| | 886.957
| gu
| style="text-align:center;" | la
| [a, b, −1>
| style="text-align:center;" | downmajor 6th
| 6/5, 9/5
| style="text-align:center;" | vM6
| style="text-align:center;" | vB
| | 5/3
|-
|-
| style="text-align:center;" | 35
| dupminor
| | 913.043
| ilo
| style="text-align:center;" | laa
| [a, b, 0, 0, 1>
| style="text-align:center;" | major 6th
| 11/9, 11/6
| style="text-align:center;" | M6
| style="text-align:center;" | B
| | 22/13, 17/10
|-
|-
| style="text-align:center;" | 36
| dudmajor
| | 939.13
| lu
| style="text-align:center;" | li
| [a, b, 0, 0, −1>
| style="text-align:center;" | upmajor 6th
| 12/11, 18/11
| style="text-align:center;" | ^M6
| style="text-align:center;" | ^B
| | 12/7, 26/15*
|-
|-
| style="text-align:center;" | 37
| downmajor
| | 965.217
| yo
| style="text-align:center;" | ta
| [a, b, 1>
| style="text-align:center;" | downminor 7th
| 5/4, 5/3
| style="text-align:center;" | vm7
| style="text-align:center;" | vC
| | 7/4, 26/15*
|-
|-
| style="text-align:center;" | 38
| major
| | 991.304
| fifthward wa
| style="text-align:center;" | teh
| [a, b>, b &gt; 1
| style="text-align:center;" | minor 7th
| 9/8, 27/16
| style="text-align:center;" | m7
| style="text-align:center;" | C
| | 16/9, 30/17
|-
|-
| style="text-align:center;" | 39
| upmajor
| | 1017.391
| ru
| style="text-align:center;" | te
| [a, b, 0, −1>
| style="text-align:center;" | upminor 7th
| 9/7, 12/7
| style="text-align:center;" | ^m7
|}
| style="text-align:center;" | ^C
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:
| | 9/5
 
{| class="wikitable center-all"
|-
|-
| style="text-align:center;" | 40
! Color of the 3rd
| | 1043.478
! JI Chord
| style="text-align:center;" | tu
! Notes as Edosteps
| style="text-align:center;" | downmid 7th
! Notes of C Chord
| style="text-align:center;" | v~7
! Written Name
| style="text-align:center;" | ^^C
! Spoken Name
| | 11/6, 20/11
|-
|-
| style="text-align:center;" | 41
| zo
| | 1069.565
| 6:7:9
| style="text-align:center;" | tuh
| 0–10–27
| style="text-align:center;" | upmid 7th
| C vEb G
| style="text-align:center;" | ^~7
| Cvm
| style="text-align:center;" | vvC#
| C downminor
| | 24/13, 13/7, 28/15
|-
|-
| style="text-align:center;" | 42
| gu
| | 1095.652
| 10:12:15
| style="text-align:center;" | ti
| 0–12–27
| style="text-align:center;" | downmajor 7th
| C ^Eb G
| style="text-align:center;" | vM7
| C^m
| style="text-align:center;" | vC#
| C upminor
| | 15/8, 32/17, 17/9
|-
|-
| style="text-align:center;" | 43
| ilo
| | 1121.739
| 18:22:27
| style="text-align:center;" | taa
| 0–13–27
| style="text-align:center;" | major 7th
| C ^^Eb G
| style="text-align:center;" | M7
| C^^m
| style="text-align:center;" | C#
| C dupminor
| |
|-
|-
| style="text-align:center;" | 44
| lu
| | 1147.826
| 22:27:33
| style="text-align:center;" | to
| 0–14–27
| style="text-align:center;" | upmajor 7th
| C vvE G
| style="text-align:center;" | ^M7
| Cvv
| style="text-align:center;" | ^C#
| C dudmajor or C dud
| |  
|-
|-
| style="text-align:center;" | 45
| yo
| | 1173.913
| 4:5:6
| style="text-align:center;" | da
| 0–15–27
| style="text-align:center;" | down 8ve
| C vE G
| style="text-align:center;" | v8
| Cv
| style="text-align:center;" | vD
| C downmajor or C down
| |
|-
|-
| style="text-align:center;" | 46
| ru
| | 1200.000
| 14:18:21
| style="text-align:center;" | do
| 0–17–27
| style="text-align:center;" | perfect 8ve
| C ^E G
| style="text-align:center;" | P8
| C^
| style="text-align:center;" | D
| C upmajor or C up
| | 2/1
|}
|}
*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]].
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].
 
== Notation ==
=== Ups and downs notation ===
46edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
{{Sharpness-sharp5a}}
Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp5}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[39edo #Sagittal notation|39edo]].
 
==== Evo flavor ====
<imagemap>
File:46-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 511 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:46-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:46-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 557 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:46-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]


Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
=== 17-odd-limit interval mappings ===
{{Q-odd-limit intervals|46|17}}


{| class="wikitable"
=== 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
|-
|-
! | quality
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! 1\1 !! 1\2
! | color
! | monzo format
! | examples
|-
|-
| style="text-align:center;" | downminor
| [[68/65]] || 25.9% || Normal || [[Valentine]] || [[Semivalentine]]
| style="text-align:center;" | zo
| style="text-align:center;" | {a, b, 0, 1}
| style="text-align:center;" | 7/6, 7/4
|-
|-
| style="text-align:center;" | minor
| [[10/9]] || 36.1% || Normal || [[Mitonic]] || [[Unidec]], [[hendec]]
| style="text-align:center;" | fourthward wa
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | 32/27, 16/9
|-
|-
| style="text-align:center;" | upminor
| [[31/24]] || 70.2% || Weak || [[Sensible]], [[sensi]] add-31 || [[Bison]] add-31, [[bisensi]] add-31
| style="text-align:center;" | gu
|}
| style="text-align:center;" | {a, b, -1}
 
| style="text-align:center;" | 6/5, 9/5
{| class="wikitable center-all left-4"
|+ style="font-size: 105%;" | 23-note circles by gen. with related half-octave temperaments
|-
|-
| style="text-align:center;" | downmid
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! Temperaments
| style="text-align:center;" | ilo
| style="text-align:center;" | {a, b, 0, 0, 1}
| style="text-align:center;" | 11/9, 11/6
|-
|-
| style="text-align:center;" | upmid
| [[17/16]] || 53.5% || Weak || [[Diaschismic]]
| style="text-align:center;" | lu
| style="text-align:center;" | {a, b, 0, 0, -1}
| style="text-align:center;" | 12/11, 18/11
|-
|-
| style="text-align:center;" | downmajor
| [[23/21]] || 85.7% || Weak || [[Bison]]
| style="text-align:center;" | yo
| style="text-align:center;" | {a, b, 1}
| style="text-align:center;" | 5/4, 5/3
|-
|-
| style="text-align:center;" | major
| [[44/39]] || 12.3% || Super-strong || [[Abigail]]
| style="text-align:center;" | fifthward wa
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | 9/8, 27/16
|-
|-
| style="text-align:center;" | upmajor
| [[21/17]] || 53.6% || Weak || ?
| style="text-align:center;" | ru
|-
| style="text-align:center;" | {a, b, 0, -1}
| [[14/11]] || 10.2% || Super-strong || ?
| style="text-align:center;" | 9/7, 12/7
|-
| [[21/16]] || 107% || Sub-weak || ?
|}
|}
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:


{| class="wikitable"
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]] (%)
|-
|-
! | color of the 3rd
| 2.3
! | JI chord
| {{monzo| 73 -46 }}
! | notes as edosteps
| {{mapping| 46 73 }}
! | notes of C chord
| −0.755
! | written name
| 0.75
! | spoken name
| 2.89
|-
|-
| style="text-align:center;" | zo
| 2.3.5
| style="text-align:center;" | 6:7:9
| 2048/2025, 78732/78125
| style="text-align:center;" | 0-10-27
| {{mapping| 46 73 107 }}
| style="text-align:center;" | C vEbv G
| −1.219
| style="text-align:center;" | Cvm
| 0.90
| style="text-align:center;" | C downminor
| 3.45
|-
|-
| style="text-align:center;" | gu
| 2.3.5.7
| style="text-align:center;" | 10:12:15
| 126/125, 245/243, 1029/1024
| style="text-align:center;" | 0-12-27
| {{mapping| 46 73 107 129 }}
| style="text-align:center;" | C ^Eb G
| −0.595
| style="text-align:center;" | C^m
| 1.34
| style="text-align:center;" | C upminor
| 5.12
|-
|-
| style="text-align:center;" | ilo
| 2.3.5.7.11
| style="text-align:center;" | 18:22:27
| 121/120, 126/125, 176/175, 245/243
| style="text-align:center;" | 0-13-27
| {{mapping| 46 73 107 129 159 }}
| style="text-align:center;" | C ^^Eb G
| −0.274
| style="text-align:center;" | Cv~
| 1.36
| style="text-align:center;" | C downmid
| 5.20
|-
|-
| style="text-align:center;" |lu
| 2.3.5.7.11.13
| style="text-align:center;" |22:27:33
| 91/90, 121/120, 169/168, 176/175, 245/243
| style="text-align:center;" |0-14-27
| {{mapping| 46 73 107 129 159 170 }}
| style="text-align:center;" |C vvE G
| +0.030
| style="text-align:center;" |C^~
| 1.41
| style="text-align:center;" |C upmid
| 5.42
|-
|-
| style="text-align:center;" | yo
| 2.3.5.7.11.13.17
| style="text-align:center;" | 4:5:6
| 91/90, 121/120, 154/153, 169/168, 176/175, 245/243
| style="text-align:center;" | 0-15-27
| {{mapping| 46 73 107 129 159 170 188 }}
| style="text-align:center;" | C vE G
| +0.047
| style="text-align:center;" | Cv
| 1.31
| style="text-align:center;" | C downmajor or C down
| 5.02
|-
|-
| style="text-align:center;" | ru
| 2.3.5.7.11.13.17.23
| style="text-align:center;" | 14:18:21
| 91/90, 121/120, 154/153, 169/168, 176/175, 208/207, 231/230
| style="text-align:center;" | 0-17-27
| {{mapping| 46 73 107 129 159 170 188 208 }}
| style="text-align:center;" | C ^E G
| +0.101
| style="text-align:center;" | C^
| 1.23
| style="text-align:center;" | C upmajor or C up
| 4.72
|}
|}
For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
* 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.


==Selected just intervals by error==
=== Commas ===
The following table shows how [[Just-24|some prominent just intervals]] are represented in 46edo (ordered by absolute error).
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="wikitable"
{| 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)
|-
|-
! | Interval, complement
| 5
! | Error (abs., in [[cent|cents]])
| <abbr title="50331648/48828125">(16 digits)</abbr>
| {{monzo| 24 1 -11 }}
| 52.50
| Salegu
| [[Magus comma]]
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| 5
| style="text-align:center;" | 0.117
| <abbr title="1990656/1953125">(14 digits)</abbr>
| {{monzo| 13 5 -9 }}
| 32.95
| Satritrigu
| [[Valentine comma]]
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| 5
| style="text-align:center;" | 0.205
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| 5
| style="text-align:center;" | 2.137
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| 5
| style="text-align:center;" | 2.253
| <abbr title="1600000/1594323">(14 digits)</abbr>
| {{monzo| 9 -13 5 }}
| 6.15
| Saquinyo
| [[Amity comma]]
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| 7
| style="text-align:center;" | '''2.393'''
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| 7
| style="text-align:center;" | 2.598
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| 7
| style="text-align:center;" | 3.492
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.80
| Zotrigu
| Starling comma
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| 7
| style="text-align:center;" | '''3.609'''
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| 7
| style="text-align:center;" | 4.786
| [[5120/5103]]
| {{monzo| 10 -6 1 -1 }}
| 5.76
| Saruyo
| Hemifamity comma, aberschisma
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| 7
| style="text-align:center;" | '''4.991'''
| <abbr title="2147483648/2144153025">(20 digits)</abbr>
| {{monzo| 31 -6 -2 -6 }}
| 2.69
| Sasa-tribiru-agugu
| [[Pessoalisma]]
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| 7
| style="text-align:center;" | '''5.745'''
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| 11
| style="text-align:center;" | 5.885
| [[121/120]]
| {{monzo|-3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| 11
| style="text-align:center;" | 6.001
| [[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
| 9.86
| Lorugugu
| Valinorsma
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| 11
| style="text-align:center;" | 7.383
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| 11
| style="text-align:center;" | 8.138
| [[385/384]]
| {{monzo|-7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| 11
| style="text-align:center;" | 8.278
| [[441/440]]
| {{monzo| -3 2 -1 2 -1 }}
| 3.93
| Luzozogu
| Werckisma
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| 13
| style="text-align:center;" | 8.394
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| 13
| style="text-align:center;" | 8.482
| [[169/168]]
| {{monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| 13
| style="text-align:center;" | 8.599
| [[196/195]]
| {{monzo| 2 -1 -1 2 0 -1 }}
| 8.86
| Thuzozogu
| Mynucuma
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| 13
| style="text-align:center;" | 10.531
| [[507/500]]
| {{monzo| -2 1 -3 0 0 2 }}
| 24.07
| Thothotrigu
|
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| 13
| style="text-align:center;" | 10.736
| [[351/350]]
| {{Monzo| -1 3 -2 -1 0 1 }}
| 4.94
| Thorugugu
| Ratwolfsma
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| 13
| style="text-align:center;" | 10.875
| [[352/351]]
| {{monzo| 5 -3 0 0 1 -1 }}
| 4.93
| Thulo
| Minor minthma
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| 17
| style="text-align:center;" | 10.992
| [[256/255]]
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| 6.78
| Sugu
| Charisma, septendecimal kleisma
|-
|-
| style="text-align:center;" | 15/13, 26/15
| 17
| style="text-align:center;" | 12.958
| [[289/288]]
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| Soso
| Semitonisma
|}
|}


=Linear temperaments=
=== Rank-2 temperaments ===
 
{| class="wikitable center-1 center-2 center-3 center-4"
{| class="wikitable"
|-
! Periods<br>per 8ve
! 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]] / [[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
|-
|-
! | Periods
| 19\46
 
| 495.652
per octave
| [[Leapday]]
! | Generator
| [[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)
! | Cents
| 11:8<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
! | Temperaments
! | MOS/DE Scales available
! | L:s
|-
|-
| | 1
| 21\46
| | 1\46
| 547.826
| | 26.087
| [[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
| |
|-
|-
| | 1
| rowspan="11" | 2
| | 3\46
| 1\46
| | 78.261
| 26.087
| | [[Valentine|Valentine]]
| [[Ketchup]]
| | 1L 14s (15-tone)
|  
 
|  
15L 1s (16-tone)
 
16L 15s (31-tone)
| | 4:3 ~ [[Maximal_evenness|quasi-equal]]
 
3:1
 
2:1 ~ QE
|-
|-
| | 1
| 2\46
| | 5\46
| 52.174
| | 130.435
| [[Shrutar]]
| | [[Twothirdtonic|Twothirdtonic]]
| 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)
| | [[1L_8s|1L 8s]] (9-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
 
[[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
| 3\46
| | 7\46
| 78.261
| | 182.609
| [[Semivalentine]]
| | [[Minortone|Minortone]]
| 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)
| | [[1L_5s|1L 5s]] (6-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
 
[[6L_1s|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
| 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
| | 339.130
| [[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
== Scales ==
{{Main| List of MOS scales in 46edo }}


17:2
* [[Plum]]
* [[Compdye]]
* [[Smi2s]]


15:2
; Sensi
* [[Sensi5]]
* [[Sensi8]]
* [[Sensi11]]
* [[Sensi19]]


13:2
; Elfleapday
* [[Elfleapday7]]
* [[Elfleapday8d]]
* [[Elfleapday9]]
* [[Elfleapday10]]
* [[Elfleapday12]]
* [[Elfleapday12f]]


11:2
; Elfsensus
* [[Elfsensus7]]
* [[Elfsensus8d]]
* [[Elfsensus9]]
* [[Elfsensus10]]
* [[Elfsensus12]]
* [[Elfsensus12f]]


9:2
=== 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}}).


7:2
{| class="wikitable center-all"
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| | 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)
 
4L 26s (30-tone)
 
4L 30s (34-tone)
 
4L 34s (38-tone)
 
4L 38s (42-tone)
| | 12:11 ~ QE
 
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
| |
| |
| |
|}


=Scales=
2/1: string 3 fret 5
*[[plum|plum]]
*[[sensi5|sensi5]]
*[[sensi8|sensi8]]
*[[sensi11|sensi11]]
*[[sensi19|sensi19]]


==Approximation to Mode 8 of the Harmonic Series==
3/2: not easily accessible


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.
5/4: string 5 fret 4


8\46edo (208.696¢) stands in for frequency ratio [[9/8|9:8]] (203.910¢).
== Music ==
=== Modern renditions ===
; {{W|Johann Sebastian Bach}}
* [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)
* [https://www.youtube.com/watch?v=4yetEubmIk0 "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)


7\46edo (182.609¢) stands in for [[10/9|10:9]] (182.404¢).
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=_YiCc81ktBI ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)


6\46edo (156.522¢) stands in for [[11/10|11:10]] (165.004¢) and [[12/11|12:11]] (150.637¢).
; {{W|Scott Joplin}}
* [https://www.youtube.com/watch?v=GXIoWsvFMzI ''Maple Leaf Rag''] (1899) – with syntonic comma adjustment, arranged for harpsichord and rendered by Claudi Meneghin (2024)


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¢).
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=SCpbbov1fSQ ''music box 46edo''] (2025)  


4\46edo (104.348¢) stands in for [[16/15|16:15]] (111.731¢).
; [[Jake Freivald]] ([https://soundcloud.com/jdfreivald site])
* [https://soundcloud.com/jdfreivald/a-seed-planted-yet-another ''A Seed Planted - (Yet another version: 46 EDO)''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3 play]{{dead link}}


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


[http://www.archive.org/details/MusicForYourEars Music For Your Ears] [http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith.]] The central portion is in [[27edo|27edo]], the rest is in 46edo.
; [[Claudi Meneghin]]
* [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
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 Bach Contrapunctus 4] Claudi Meneghin version
* [https://www.youtube.com/watch?v=-6ORgyqom5M ''Chaconne et Fugue à 5 "Les Regrets"'']
* [https://www.youtube.com/watch?v=1r55c2nppe8 ''El Rossinyol'']
* [https://www.youtube.com/watch?v=JwjoT6ceU20 ''Arietta with 5 Variations'', for Organ]
* [https://www.youtube.com/watch?v=rmgWC_jruSg ''Fugue in 46edo (as Sensi)'', for two organs] (2024)


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


[http://andrewheathwaite.bandcamp.com/track/tumbledown-stew Tumbledown Stew]  
; [[Joseph Monzo]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]].
* [https://www.youtube.com/watch?v=gL90m2ri5kw ''I Love the Blackness (unfinished)''] (2008)


[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|Andrew Heathwaite]].
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=QDFLKyTXZgs ''Fugue in 46EDO Bohlen-Pierce-Stearns 9 (Sensi Extension) LssLsLsLs "Lambda"'']


[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 Hypnocloudsmack 2]  
; [[Gene Ward Smith]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]].  
* [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://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 Hypnocloudsmack 3]  
; [[Tristan Bay]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]].
* [https://www.youtube.com/watch?v=s61YY80E_IA ''Catalyst''] (2025)


[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
; vivi mouse
* [https://soundcloud.com/vivi-mouse-emoji/valentines-day ''valentine's day''] (2025)


[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 Bach Contrapunctus 4] Claudi Meneghin version
== Notes ==
<references group="note" />


[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:Chromosounds]]
[[Category:46edo]]
[[Category:Leapday]]
[[Category:chromosounds]]
[[Category:Sensi]]
[[Category:edo]]
[[Category:Shrutar]]
[[Category:leapday]]
[[Category:Valentine]]
[[Category:listen]]
[[Category:Quartismic]]
[[Category:sensi]]
[[Category:Listen]]
[[Category:shrutar]]
[[Category:Diaschismic]]
[[Category:valentine]]
Retrieved from "https://en.xen.wiki/w/46edo"