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__FORCETOC__
__FORCETOC__
-----
=Theory=
 
=46 tone equal temperament=
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]].
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]].


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


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.
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.
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46edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.
46edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.


=46edo srutis=
[[Magic22_as_srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian|Indian]] music.
[[Magic22_as_srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian|Indian]] music.


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{| class="wikitable"
{| class="wikitable"
|-
|-
! | degrees of 46edo
! | degree
! | cents
! | solfege
! | solfege
! | cents value
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]]
! | approximate ratios
! | approximate ratios


in the [[17-limit|17-limit]]
in the [[17-limit|17-limit]]
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]]
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| 0.000
| style="text-align:center;" | do
| style="text-align:center;" | do
| 0.000
| | 1/1
| style="text-align:center;" | perfect unison
| style="text-align:center;" | perfect unison
| style="text-align:center;" | P1
| style="text-align:center;" | P1
| style="text-align:center;" | D
| style="text-align:center;" | D
| | 1/1
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| | 26.087
| style="text-align:center;" | di
| style="text-align:center;" | di
| | 26.087
| |
| style="text-align:center;" | up unison
| style="text-align:center;" | up unison
| style="text-align:center;" | ^1
| style="text-align:center;" | ^1
| style="text-align:center;" | D^
| style="text-align:center;" | ^D
| |
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| | 52.174
| style="text-align:center;" | ro
| style="text-align:center;" | ro
| | 52.174
| |
| style="text-align:center;" | downminor 2nd
| style="text-align:center;" | downminor 2nd
| style="text-align:center;" | vm2
| style="text-align:center;" | vm2
| style="text-align:center;" | Ebv
| style="text-align:center;" | vEb
| |
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| | 78.261
| style="text-align:center;" | rih
| style="text-align:center;" | rih
| | 78.261
| |
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | m2
| style="text-align:center;" | m2
| style="text-align:center;" | Eb
| style="text-align:center;" | Eb
| |
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| | 104.348
| style="text-align:center;" | ra
| style="text-align:center;" | ra
| | 104.348
| | 16/15, 17/16, 18/17
| style="text-align:center;" | upminor 2nd
| style="text-align:center;" | upminor 2nd
| style="text-align:center;" | ^m2
| style="text-align:center;" | ^m2
| style="text-align:center;" | Eb^
| style="text-align:center;" | ^Eb
| | 16/15, 17/16, 18/17
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| | 130.435
| style="text-align:center;" | ru (as in supraminor)
| style="text-align:center;" | ru (as in supraminor)
| | 130.435
| | 13/12, 14/13, 15/14
| style="text-align:center;" | downmid 2nd
| style="text-align:center;" | downmid 2nd
| style="text-align:center;" | v~2
| style="text-align:center;" | v~2
| style="text-align:center;" | Eb^^
| style="text-align:center;" | ^^Eb
| | 13/12, 14/13, 15/14
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| | 156.522
| style="text-align:center;" | ruh (as in submajor)
| style="text-align:center;" | ruh (as in submajor)
| | 156.522
| | 12/11, 11/10
| style="text-align:center;" | upmid 2nd
| style="text-align:center;" | upmid 2nd
| style="text-align:center;" | ^~2
| style="text-align:center;" | ^~2
| style="text-align:center;" | Evv
| style="text-align:center;" | vvE
| | 12/11, 11/10
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| | 182.609
| style="text-align:center;" | reh
| style="text-align:center;" | reh
| | 182.609
| | 10/9
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | vM2
| style="text-align:center;" | vM2
| style="text-align:center;" | Ev
| style="text-align:center;" | vE
| | 10/9
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| | 208.696
| style="text-align:center;" | re
| style="text-align:center;" | re
| | 208.696
| | 9/8, 17/15
| style="text-align:center;" | major 2nd
| style="text-align:center;" | major 2nd
| style="text-align:center;" | M2
| style="text-align:center;" | M2
| style="text-align:center;" | E
| style="text-align:center;" | E
| | 9/8, 17/15
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| | 234.783
| style="text-align:center;" | ri
| style="text-align:center;" | ri
| | 234.783
| | 8/7, 15/13*
| style="text-align:center;" | upmajor 2nd
| style="text-align:center;" | upmajor 2nd
| style="text-align:center;" | ^M2
| style="text-align:center;" | ^M2
| style="text-align:center;" | E^
| style="text-align:center;" | ^E
| | 8/7, 15/13*
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| | 260.87
| style="text-align:center;" | ma
| style="text-align:center;" | ma
| | 260.87
| | 7/6, 15/13*
| style="text-align:center;" | downminor 3rd
| style="text-align:center;" | downminor 3rd
| style="text-align:center;" | vm3
| style="text-align:center;" | vm3
| style="text-align:center;" | Fv
| style="text-align:center;" | vF
| | 7/6, 15/13*
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| | 286.957
| style="text-align:center;" | meh
| style="text-align:center;" | meh
| | 286.957
| | 13/11, 20/17
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | m3
| style="text-align:center;" | m3
| style="text-align:center;" | F
| style="text-align:center;" | F
| | 13/11, 20/17
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| | 313.043
| style="text-align:center;" | me
| style="text-align:center;" | me
| | 313.043
| | 6/5
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | ^m3
| style="text-align:center;" | ^m3
| style="text-align:center;" | F^
| style="text-align:center;" | ^F
| | 6/5
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| | 339.13
| style="text-align:center;" | mu
| style="text-align:center;" | mu
| | 339.13
| | 11/9, 17/14
| style="text-align:center;" | downmid 3rd
| style="text-align:center;" | downmid 3rd
| style="text-align:center;" | v~3
| style="text-align:center;" | v~3
| style="text-align:center;" | F^^
| style="text-align:center;" | ^^F
| | 11/9, 17/14
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| | 365.217
| style="text-align:center;" | muh
| style="text-align:center;" | muh
| | 365.217
| | 16/13
| style="text-align:center;" | upmid 3rd
| style="text-align:center;" | upmid 3rd
| style="text-align:center;" | ^~3
| style="text-align:center;" | ^~3
| style="text-align:center;" | F#vv
| style="text-align:center;" | vvF#
| | 16/13
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| | 391.304
| style="text-align:center;" | mi
| style="text-align:center;" | mi
| | 391.304
| | 5/4
| style="text-align:center;" | downmajor 3rd
| style="text-align:center;" | downmajor 3rd
| style="text-align:center;" | vM3
| style="text-align:center;" | vM3
| style="text-align:center;" | F#v
| style="text-align:center;" | vF#
| | 5/4
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| | 417.391
| style="text-align:center;" | maa
| style="text-align:center;" | maa
| | 417.391
| | 14/11
| style="text-align:center;" | major 3rd
| style="text-align:center;" | major 3rd
| style="text-align:center;" | M3
| style="text-align:center;" | M3
| style="text-align:center;" | F#
| style="text-align:center;" | F#
| | 14/11
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| | 443.478
| style="text-align:center;" | mo
| style="text-align:center;" | mo
| | 443.478
| | 9/7, 13/10, 22/17
| style="text-align:center;" | upmajor 3rd
| style="text-align:center;" | upmajor 3rd
| style="text-align:center;" | ^M3
| style="text-align:center;" | ^M3
| style="text-align:center;" | F#^
| style="text-align:center;" | ^F#
| | 9/7, 13/10, 22/17
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| | 469.565
| style="text-align:center;" | fe
| style="text-align:center;" | fe
| | 469.565
| | 17/13
| style="text-align:center;" | down 4th
| style="text-align:center;" | down 4th
| style="text-align:center;" | v4
| style="text-align:center;" | v4
| style="text-align:center;" | Gv
| style="text-align:center;" | vG
| | 17/13
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| | 495.652
| style="text-align:center;" | fa
| style="text-align:center;" | fa
| | 495.652
| | 4/3
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | P4
| style="text-align:center;" | P4
| style="text-align:center;" | G
| style="text-align:center;" | G
| | 4/3
|-
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| | 521.739
| style="text-align:center;" | fih
| style="text-align:center;" | fih
| | 521.739
| |
| style="text-align:center;" | up 4th
| style="text-align:center;" | up 4th
| style="text-align:center;" | ^4
| style="text-align:center;" | ^4
| style="text-align:center;" | G^
| style="text-align:center;" | ^G
| |
|-
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| | 547.826
| style="text-align:center;" | fu
| style="text-align:center;" | fu
| | 547.826
| style="text-align:center;" | downmid 4th
| style="text-align:center;" | v~4
| style="text-align:center;" | ^^G
| | 11/8, 15/11
| | 11/8, 15/11
| style="text-align:center;" | double-up 4th
| style="text-align:center;" | ^^4
| style="text-align:center;" | G^^
|-
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| | 573.913
| style="text-align:center;" | fi
| style="text-align:center;" | fi
| | 573.913
| style="text-align:center;" | upmid 4th, dim 5th
| style="text-align:center;" | ^~4, d5
| style="text-align:center;" | vvG#, Ab
| | 7/5, 18/13
| | 7/5, 18/13
| style="text-align:center;" | double-down aug 4th,
dim 5th
| style="text-align:center;" | vvA4, d5
| style="text-align:center;" | G#vv, Ab
|-
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| | 600
| style="text-align:center;" | seh
| style="text-align:center;" | seh
| | 600
| | 17/12, 24/17
| style="text-align:center;" | downaug 4th, updim 5th
| style="text-align:center;" | downaug 4th, updim 5th
| style="text-align:center;" | vA4, ^d5
| style="text-align:center;" | vA4, ^d5
| style="text-align:center;" | G#v, Ab^
| style="text-align:center;" | vG#, ^Ab
| | 17/12, 24/17
|-
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| | 626.087
| style="text-align:center;" | se
| style="text-align:center;" | se
| | 626.087
| style="text-align:center;" | aug 4th, downmid 5th
| style="text-align:center;" | A4, v~5
| style="text-align:center;" | G#, ^^Ab
| | 10/7, 13/9
| | 10/7, 13/9
| style="text-align:center;" | aug 4th, double-up dim 5th
| style="text-align:center;" | A4, ^^d5
| style="text-align:center;" | G#, Ab^^
|-
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| | 652.174
| style="text-align:center;" | su
| style="text-align:center;" | su
| | 652.174
| style="text-align:center;" | double-down 5th
| style="text-align:center;" | ^~5
| style="text-align:center;" | vvA
| | 16/11, 22/15
| | 16/11, 22/15
| style="text-align:center;" | double-down 5th
| style="text-align:center;" | vv5
| style="text-align:center;" | Avv
|-
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| | 678.261
| style="text-align:center;" | sih
| style="text-align:center;" | sih
| | 678.261
| |
| style="text-align:center;" | down 5th
| style="text-align:center;" | down 5th
| style="text-align:center;" | v5
| style="text-align:center;" | v5
| style="text-align:center;" | Av
| style="text-align:center;" | vA
| |
|-
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| | 704.348
| style="text-align:center;" | sol
| style="text-align:center;" | sol
| | 704.348
| | 3/2
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | P5
| style="text-align:center;" | P5
| style="text-align:center;" | A
| style="text-align:center;" | A
| | 3/2
|-
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| | 730.435
| style="text-align:center;" | si
| style="text-align:center;" | si
| | 730.435
| | 26/17
| style="text-align:center;" | up 5th
| style="text-align:center;" | up 5th
| style="text-align:center;" | ^5
| style="text-align:center;" | ^5
| style="text-align:center;" | A^
| style="text-align:center;" | ^A
| | 26/17
|-
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 29
| | 756.522
| style="text-align:center;" | lo
| style="text-align:center;" | lo
| | 756.522
| | 14/9, 20/13, 17/11
| style="text-align:center;" | downminor 6th
| style="text-align:center;" | downminor 6th
| style="text-align:center;" | vm6
| style="text-align:center;" | vm6
| style="text-align:center;" | Bbv
| style="text-align:center;" | vBb
| | 14/9, 20/13, 17/11
|-
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 30
| | 782.609
| style="text-align:center;" | leh
| style="text-align:center;" | leh
| | 782.609
| | 11/7
| style="text-align:center;" | minor 6th
| style="text-align:center;" | minor 6th
| style="text-align:center;" | m6
| style="text-align:center;" | m6
| style="text-align:center;" | Bb
| style="text-align:center;" | Bb
| | 11/7
|-
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 31
| | 808.696
| style="text-align:center;" | le
| style="text-align:center;" | le
| | 808.696
| | 8/5
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | ^m6
| style="text-align:center;" | ^m6
| style="text-align:center;" | Bb^
| style="text-align:center;" | ^Bb
| | 8/5
|-
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 32
| | 834.783
| style="text-align:center;" | lu
| style="text-align:center;" | lu
| | 834.783
| | 13/8
| style="text-align:center;" | downmid 6th
| style="text-align:center;" | downmid 6th
| style="text-align:center;" | v~6
| style="text-align:center;" | v~6
| style="text-align:center;" | Bb^^
| style="text-align:center;" | ^^Bb
| | 13/8
|-
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 33
| | 860.87
| style="text-align:center;" | luh
| style="text-align:center;" | luh
| | 860.87
| | 18/11, 28/17
| style="text-align:center;" | upmid 6th
| style="text-align:center;" | upmid 6th
| style="text-align:center;" | ^~6
| style="text-align:center;" | ^~6
| style="text-align:center;" | Bvv
| style="text-align:center;" | vvB
| | 18/11, 28/17
|-
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 34
| | 886.957
| style="text-align:center;" | la
| style="text-align:center;" | la
| | 886.957
| | 5/3
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | vM6
| style="text-align:center;" | vM6
| style="text-align:center;" | Bv
| style="text-align:center;" | vB
| | 5/3
|-
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 35
| | 913.043
| style="text-align:center;" | laa
| style="text-align:center;" | laa
| | 913.043
| | 22/13, 17/10
| style="text-align:center;" | major 6th
| style="text-align:center;" | major 6th
| style="text-align:center;" | M6
| style="text-align:center;" | M6
| style="text-align:center;" | B
| style="text-align:center;" | B
| | 22/13, 17/10
|-
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 36
| | 939.13
| style="text-align:center;" | li
| style="text-align:center;" | li
| | 939.13
| | 12/7, 26/15*
| style="text-align:center;" | upmajor 6th
| style="text-align:center;" | upmajor 6th
| style="text-align:center;" | ^M6
| style="text-align:center;" | ^M6
| style="text-align:center;" | B^
| style="text-align:center;" | ^B
| | 12/7, 26/15*
|-
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 37
| | 965.217
| style="text-align:center;" | ta
| style="text-align:center;" | ta
| | 965.217
| | 7/4, 26/15*
| style="text-align:center;" | downminor 7th
| style="text-align:center;" | downminor 7th
| style="text-align:center;" | vm7
| style="text-align:center;" | vm7
| style="text-align:center;" | Cv
| style="text-align:center;" | vC
| | 7/4, 26/15*
|-
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 38
| | 991.304
| style="text-align:center;" | teh
| style="text-align:center;" | teh
| | 991.304
| | 16/9, 30/17
| style="text-align:center;" | minor 7th
| style="text-align:center;" | minor 7th
| style="text-align:center;" | m7
| style="text-align:center;" | m7
| style="text-align:center;" | C
| style="text-align:center;" | C
| | 16/9, 30/17
|-
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 39
| | 1017.391
| style="text-align:center;" | te
| style="text-align:center;" | te
| | 1017.391
| | 9/5
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | ^m7
| style="text-align:center;" | ^m7
| style="text-align:center;" | C^
| style="text-align:center;" | ^C
| | 9/5
|-
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 40
| | 1043.478
| style="text-align:center;" | tu
| style="text-align:center;" | tu
| | 1043.478
| | 11/6, 20/11
| style="text-align:center;" | downmid 7th
| style="text-align:center;" | downmid 7th
| style="text-align:center;" | v~7
| style="text-align:center;" | v~7
| style="text-align:center;" | C^^
| style="text-align:center;" | ^^C
| | 11/6, 20/11
|-
|-
| style="text-align:center;" | 41
| style="text-align:center;" | 41
| | 1069.565
| style="text-align:center;" | tuh
| style="text-align:center;" | tuh
| | 1069.565
| | 24/13, 13/7, 28/15
| style="text-align:center;" | upmid 7th
| style="text-align:center;" | upmid 7th
| style="text-align:center;" | ^~7
| style="text-align:center;" | ^~7
| style="text-align:center;" | C#vv
| style="text-align:center;" | vvC#
| | 24/13, 13/7, 28/15
|-
|-
| style="text-align:center;" | 42
| style="text-align:center;" | 42
| | 1095.652
| style="text-align:center;" | ti
| style="text-align:center;" | ti
| | 1095.652
| | 15/8, 32/17, 17/9
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | vM7
| style="text-align:center;" | vM7
| style="text-align:center;" | C#v
| style="text-align:center;" | vC#
| | 15/8, 32/17, 17/9
|-
|-
| style="text-align:center;" | 43
| style="text-align:center;" | 43
| | 1121.739
| style="text-align:center;" | taa
| style="text-align:center;" | taa
| | 1121.739
| |
| style="text-align:center;" | major 7th
| style="text-align:center;" | major 7th
| style="text-align:center;" | M7
| style="text-align:center;" | M7
| style="text-align:center;" | C#
| style="text-align:center;" | C#
| |
|-
|-
| style="text-align:center;" | 44
| style="text-align:center;" | 44
| | 1147.826
| style="text-align:center;" | to
| style="text-align:center;" | to
| | 1147.826
| |
| style="text-align:center;" | upmajor 7th
| style="text-align:center;" | upmajor 7th
| style="text-align:center;" | ^M7
| style="text-align:center;" | ^M7
| style="text-align:center;" | C#^
| style="text-align:center;" | ^C#
| |
|-
|-
| style="text-align:center;" | 45
| style="text-align:center;" | 45
| | 1173.913
| style="text-align:center;" | da
| style="text-align:center;" | da
| | 1173.913
| |
| style="text-align:center;" | down 8ve
| style="text-align:center;" | down 8ve
| style="text-align:center;" | v8
| style="text-align:center;" | v8
| style="text-align:center;" | Dv
| style="text-align:center;" | vD
| |
|-
|-
| style="text-align:center;" | 46
| style="text-align:center;" | 46
| | 1200.000
| style="text-align:center;" | do
| style="text-align:center;" | do
| | 1200.000
| | 2/1
| style="text-align:center;" | perfect 8ve
| style="text-align:center;" | perfect 8ve
| style="text-align:center;" | P8
| style="text-align:center;" | P8
| style="text-align:center;" | D
| style="text-align:center;" | D
| | 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]].
*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]].
Line 455: Line 450:
| style="text-align:center;" | 9/7, 12/7
| style="text-align:center;" | 9/7, 12/7
|}
|}
All 46edo chords can be named using ups and downs. Here are the zo, gu, ilo, yo and ru triads:
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"
{| class="wikitable"
Line 469: Line 464:
| style="text-align:center;" | 6:7:9
| style="text-align:center;" | 6:7:9
| style="text-align:center;" | 0-10-27
| style="text-align:center;" | 0-10-27
| style="text-align:center;" | C Ebv G
| style="text-align:center;" | C vEbv G
| style="text-align:center;" | C.vm
| style="text-align:center;" | Cvm
| style="text-align:center;" | C downminor
| style="text-align:center;" | C downminor
|-
|-
Line 476: Line 471:
| style="text-align:center;" | 10:12:15
| style="text-align:center;" | 10:12:15
| style="text-align:center;" | 0-12-27
| style="text-align:center;" | 0-12-27
| style="text-align:center;" | C Eb^ G
| style="text-align:center;" | C ^Eb G
| style="text-align:center;" | C.^m
| style="text-align:center;" | C^m
| style="text-align:center;" | C upminor
| style="text-align:center;" | C upminor
|-
|-
Line 483: Line 478:
| style="text-align:center;" | 18:22:27
| style="text-align:center;" | 18:22:27
| style="text-align:center;" | 0-13-27
| style="text-align:center;" | 0-13-27
| style="text-align:center;" | C Eb^^ G
| style="text-align:center;" | C ^^Eb G
| style="text-align:center;" | C.v~
| style="text-align:center;" | Cv~
| style="text-align:center;" | C downmid
| style="text-align:center;" | C downmid
|-
| style="text-align:center;" |lu
| style="text-align:center;" |22:27:33
| style="text-align:center;" |0-43-27
| style="text-align:center;" |C vvE G
| style="text-align:center;" |C^~
| style="text-align:center;" |C upmid
|-
|-
| style="text-align:center;" | yo
| style="text-align:center;" | yo
| style="text-align:center;" | 4:5:6
| style="text-align:center;" | 4:5:6
| style="text-align:center;" | 0-15-27
| style="text-align:center;" | 0-15-27
| style="text-align:center;" | C Ev G
| style="text-align:center;" | C vE G
| style="text-align:center;" | C.v
| style="text-align:center;" | Cv
| style="text-align:center;" | C downmajor or C dot down
| style="text-align:center;" | C downmajor or C down
|-
|-
| style="text-align:center;" | ru
| style="text-align:center;" | ru
| style="text-align:center;" | 14:18:27
| style="text-align:center;" | 14:18:27
| style="text-align:center;" | 0-17-27
| style="text-align:center;" | 0-17-27
| style="text-align:center;" | C E^ G
| style="text-align:center;" | C ^E G
| style="text-align:center;" | C.^
| style="text-align:center;" | C^
| style="text-align:center;" | C upmajor or C dot up
| style="text-align:center;" | C upmajor or C up
|}
|}
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].


==Selected just intervals by error==
==Selected just intervals by error==
Line 524: Line 526:
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | 2.393
| style="text-align:center;" | '''2.393'''
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
Line 533: Line 535:
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | 3.609
| style="text-align:center;" | '''3.609'''
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
Line 539: Line 541:
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | 4.991
| style="text-align:center;" | '''4.991'''
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | 5.745
| style="text-align:center;" | '''5.745'''
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
Line 580: Line 582:
| style="text-align:center;" | 10.992
| style="text-align:center;" | 10.992
|-
|-
| style="text-align:center;" | ''[[15/13|15/13]], [[26/15|26/15]]''
| style="text-align:center;" | 15/13, 26/15
| style="text-align:center;" | ''12.958''
| style="text-align:center;" | 12.958
|}
|}


Line 1,251: Line 1,253:
|}
|}


=Approximation to Mode 8 of the Harmonic Series=
=Scales=
*[[plum|plum]]
*[[sensi5|sensi5]]
*[[sensi8|sensi8]]
*[[sensi11|sensi11]]
*[[sensi19|sensi19]]
 
==Approximation to Mode 8 of the Harmonic Series==


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.
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.
Line 1,264: Line 1,273:


4\46edo (104.348¢) stands in for [[16/15|16:15]] (111.731¢).
4\46edo (104.348¢) stands in for [[16/15|16:15]] (111.731¢).
=Scales=
*[[plum|plum]]
*[[sensi5|sensi5]]
*[[sensi8|sensi8]]
*[[sensi11|sensi11]]
*[[sensi19|sensi19]]


=Music=
=Music=
Retrieved from "https://en.xen.wiki/w/46edo"