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{{Infobox ET}}
{{Infobox ET}}
The '''69 equal divisions of the octave''' ('''69edo'''), or '''69-tone equal temperament''' ('''69tet''', '''69et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 69 [[equal]] parts of about 17.4 [[cent]]s each. Nice.
{{ED intro}}
== Theory ==
69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652{{c}}. Such a fifth is closer to [[2/7-comma meantone]] than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.


== Theory ==
69edo offers two kinds of meantone 12-tone scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium|lithium]] scale, which has a 6:5 step ratio and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.
69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. Such a fifth is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.


69edo offers two kinds of meantone dodecaphonic scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium|lithium]] scale, which has a 6:5 step ratio. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.
In the [[7-limit]] it is a [[mohajira]] system, tempering out [[6144/6125]], but not a septimal meantone system, as [[126/125]] maps to one step. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap|31 & 69}} variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.


In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. It also [[support]]s the 12&69 temperament tempering out 3125/3087 along with [[81/80]]. In the 11-limit it tempers out [[99/98]], and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.
The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is {{nowrap|22 & 69}}, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.


The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is 22 & 69, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.
=== Odd harmonics ===
{{Harmonics in equal|69}}


== Intervals ==
== Intervals ==
{|class="wikitable"
{{Interval table}}
 
=== Proposed names ===
{| class="wikitable mw-collapsible mw-collapsed collapsible center-1 right-3"
|-
|-
!#
! Degree
!Cents
! Carmen's naming system
!Diatonic interval category
! Cents
! Approximate Ratios*
! Error (abs, [[cent|¢]])
|-
|-
|0
| 0
|0.0
| Natural Unison, 1
|perfect unison
| 0.000
| [[1/1]]
| 0.000
|-
|-
|1
| 1
|17.4
| Ptolemy's comma
|superunison
| 17.391
| [[100/99]]
| −0.008
|-
|-
|2
| 2
|34.8
| Jubilisma, lesser septimal sixth tone
|superunison
| 34.783
| [[50/49]], [[101/99]]
| −0.193, 0.157
|-
|-
|3
| 3
|52.2
| lesser septendecimal quartertone, _____
|subminor second
| 52.174
| [[34/33]], [[101/98]]
| 0.491, −0.028
|-
|-
|4
| 4
|69.6
| _____
|subminor second
| 69.565
| [[76/73]]
| −0.158
|-
|-
|5
| 5
|87.0
| Small undevicesimal semitone
|minor second
| 86.957
| [[20/19]]
| −1.844
|-
|-
|6
| 6
|104.3
| Large septendecimal semitone
|minor second
| 104.348
| [[17/16]]
| −0.608
|-
|-
|7
| 7
|121.7
| Septimal diatonic semitone
|supraminor second
| 121.739
| [[15/14]]
| 2.296
|-
|-
|8
| 8
|139.1
| Tridecimal neutral second
|supraminor second
| 139.130
| [[13/12]]
| 0.558
|-
|-
|9
| 9
|156.5
| Vicesimotertial neutral second
|neutral second
| 156.522
| [[23/21]]
| −0.972
|-
|-
|10
| 10
|173.9
| Undevicesimal large neutral second, undevicesimal whole tone
|submajor second
| 173.913
| [[21/19]]
| 0.645
|-
|-
|11
| 11
|191.3
| Quasi-meantone
|major second
| 191.304
| [[19/17]]
| −1.253
|-
|-
|12
| 12
|208.7
| Whole tone
|major second
| 208.696
| [[9/8]]
| 4.786
|-
|-
|13
| 13
|226.1
| Septimal whole tone
|supermajor second
| 226.087
| [[8/7]]
| −5.087
|-
|-
|14
| 14
|243.5
| Vicesimotertial semifourth
|ultramajor second
| 243.478
| [[23/20]]
| 1.518
|-
|-
|15
| 15
|260.9
| Subminor third, undetricesimal subminor third
|subminor third
| 260.870
| [[7/6]], [[29/25]]
| −6.001, 3.920
|-
|-
|16
| 16
|278.3
| Vicesimotertial subminor third
|subminor third
| 278.261
| [[27/23]]
| 0.670
|-
|-
|17
| 17
|295.7
| Pythagorean minor third
|minor third
| 295.652
| [[32/27]]
| 1.517
|-
|-
|18
| 18
|313.0
| Classic minor third
|minor third
| 313.043
| [[6/5]]
| −2.598
|-
|-
|19
| 19
|330.4
| Vicesimotertial supraminor third
|supraminor third
| 330.435
| [[23/19]]
| −0.327
|-
|-
|20
| 20
|347.8
| Undecimal neutral third
|neutral third
| 347.826
| [[11/9]]
| 0.418
|-
|-
|21
| 21
|365.2
| Septendecimal submajor third
|submajor third
| 365.217
| [[21/17]]
| −0.608
|-
|-
|22
| 22
|382.6
| Classic major third
|major third
| 382.609
| [[5/4]]
| −3.705
|-
|-
|23
| 23
|400.0
| Undetricesimal major third, Septendecimal major third
|major third
| 400.000
| [[29/23]], [[34/27]]
| −1.303, 0.910
|-
|-
|24
| 24
|417.4
| Undecimal major third
|major third
| 417.391
| [[14/11]]
| −0.117
|-
|-
|25
| 25
|434.8
| Supermajor third
|supermajor third
| 434.783
| [[9/7]]
| −0.301
|-
|-
|26
| 26
|452.2
| Barbados third
|ultramajor third
| 452.174
| [[13/10]]
| −2.040
|-
|-
|27
| 27
|469.6
| Septimal sub-fourth
|subfourth
| 469.565
| [[21/16]]
| −1.216
|-
|-
|28
| 28
|487.0
| _____
|perfect fourth
| 486.957
| [[53/40]]
| −0.234
|-
|-
|29
| 29
|504.3
| Just perfect fourth
|perfect fourth
| 504.348
| [[4/3]]
| 6.303
|-
|-
|30
| 30
|521.7
| Vicesimotertial acute fourth
|superfourth
| 521.739
| [[23/17]]
| −1.580
|-
|-
|31
| 31
|539.1
| Undecimal augmented fourth
|superfourth
| 539.130
| [[15/11]]
| 2.180
|-
|-
|32
| 32
|556.5
| Undecimal superfourth, undetricesimal superfourth
|superfourth
| 556.522
| [[11/8]], [[29/21]]
| 5.204, −2.275
|-
|-
|33
| 33
|573.9
| Narrow tritone, classic augmented fourth
|low tritone
| 573.913
| [[7/5]], [[25/18]]
| −8.600, 5.196
|-
|-
|34
| 34
|591.3
| _____
|low tritone
| 591.304
| [[31/22]]
| −2.413
|-
|-
|35
| 35
|608.7
| High tritone, undevicesimal tritone
|high tritone
| 608.696
| [[10/7]], [[27/19]]
| −8.792, 0.344
|-
|-
|36
| 36
|626.1
| _____
|high tritone
| 626.087
| [[33/23]]
| 1.088
|-
|-
|37
| 37
|643.5
| Undetricesimal tritone
|subfifth
| 643.478
| [[29/20]]
| 0.215
|-
|-
|38
| 38
|660.9
| Undevicesimal diminished fifth, undecimal diminished fifth
|subfifth
| 660.870
| [[19/13]], [[22/15]]
| 3.884, −2.180
|-
|-
|39
| 39
|678.3
| Vicesimotertial grave fifth, _____
|subfifth
| 678.261
| [[34/23]], [[37/25]]
| 1.580, −0.456
|-
|-
|40
| 40
|695.7
| Just perfect fifth
|perfect fifth
| 695.652
| [[3/2]]
| −6.303
|-
|-
|41
| 41
|713.0
| _____
|perfect fifth
| 713.043
| [[80/53]]
| 0.234
|-
|-
|42
| 42
|730.4
| Super-fifth, undetricesimal super-fifth
|superfifth
| 730.435
| [[32/21]], [[29/19]]
| 1.216, −1.630
|-
|-
|43
| 43
|747.8
| Septendecimal subminor sixth
|ultrafifth
| 747.826
| [[17/11]]
| −5.811
|-
|-
|44
| 44
|765.2
| Subminor sixth
|subminor sixth
| 765.217
| [[14/9]]
| 0.301
|-
|-
|45
| 45
|782.6
| Undecimal minor sixth
|minor sixth
| 782.609
| [[11/7]]
| 0.117
|-
|-
|46
| 46
|800.0
| Septendecimal subminor sixth
|minor sixth
| 800.000
| [[27/17]]
| −0.910
|-
|-
|47
| 47
|817.4
| Classic minor sixth
|minor sixth
| 817.391
| [[8/5]]
| 3.705
|-
|-
|48
| 48
|834.8
| Septendecimal supraminor sixth
|supraminor sixth
| 834.783
| [[34/21]]
| 0.608
|-
|-
|49
| 49
|852.2
| Undecimal neutral sixth
|neutral sixth
| 852.174
| [[18/11]]
| −0.418
|-
|-
|50
| 50
|869.6
| Vicesimotertial submajor sixth
|submajor sixth
| 869.565
| [[38/23]]
| 0.327
|-
|-
|51
| 51
|887.0
| Classic major sixth
|major sixth
| 886.957
| [[5/3]]
| 2.598
|-
|-
|52
| 52
|904.3
| Pythagorean major sixth
|major sixth
| 904.348
| [[27/16]]
| −1.517
|-
|-
|53
| 53
|921.7
| Septendecimal major sixth, undetricesimal major sixth
|supermajor sixth
| 921.739
| [[17/10]], [[29/17]]
| 3.097, −2.883
|-
|-
|54
| 54
|939.1
| Supermajor sixth, undetricesimal supermajor sixth
|supermajor sixth
| 939.130
| [[12/7]], [[50/29]]
| 6.001, −3.920
|-
|-
|55
| 55
|956.5
| Vicesimotertial supermajor sixth
|ultramajor sixth
| 956.522
| [[40/23]]
| −1.518
|-
|-
|56
| 56
|973.9
| Harmonic seventh
|subminor seventh
| 973.913
| [[7/4]]
| 5.087
|-
|-
|57
| 57
|991.3
| Pythagorean minor seventh
|minor seventh
| 991.304
| [[16/9]]
| −4.786
|-
|-
|58
| 58
|1008.7
| Quasi-meantone minor seventh
|minor seventh
| 1008.696
| [[34/19]]
| 1.253
|-
|-
|59
| 59
|1026.1
| Minor neutral undevicesimal seventh
|supraminor seventh
| 1026.087
| [[38/21]]
| −0.645
|-
|-
|60
| 60
|1043.5
| Vicesimotertial neutral seventh
|neutral seventh
| 1043.478
| [[42/23]]
| 0.972
|-
|-
|61
| 61
|1060.9
| Tridecimal neutral seventh
|submajor seventh
| 1060.870
| [[24/13]]
| −0.558
|-
|-
|62
| 62
|1078.3
| Septimal diatonic major seventh
|submajor seventh
| 1078.261
| [[28/15]]
| −2.296
|-
|-
|63
| 63
|1095.7
| Small septendecimal major seventh
|major seventh
| 1095.652
| [[32/17]]
| 0.608
|-
|-
|64
| 64
|1113.0
| Small undevicesimal semitone
|major seventh
| 1113.043
| [[20/19]]
| 1.844
|-
|-
|65
| 65
|1130.4
| _____
|supermajor seventh
| 1130.435
| [[73/38]]
| 0.158
|-
|-
|66
| 66
|1147.8
| Septendecimal supermajor seventh
|ultramajor seventh
| 1147.826
| [[33/17]]
| −0.491
|-
|-
|67
| 67
|1165.2
| _____
|suboctave
| 1165.217
| [[49/25]]
| −0.193
|-
|-
|68
| 68
|1182.6
| _____
|suboctave
| 1182.609
| [[99/50]]
| 0.008
|-
|-
|69
| 69
|1200.0
| Octave, 8
|perfect octave
| 1200.000
| [[2/1]]
| 0.000
|}
|}
=== Odd harmonics ===
<nowiki />* Some simpler ratios listed
{{Harmonics in equal|69}}
 
== Notation ==
=== Ups and downs notation ===
69edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
[[Alternative symbols for ups and downs notation]] uses sharps and flats along with Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals, combined with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[62edo#Sagittal notation|62]] and [[76edo#Sagittal notation|76]].
 
==== Evo flavor ====
<imagemap>
File:69-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 783 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:69-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:69-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 751 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:69-EDO_Revo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:69-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 759 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:69-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning Error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
Line 314: Line 505:
| 2.3
| 2.3
| {{monzo| -109 69 }}
| {{monzo| -109 69 }}
| [{{val| 69 109 }}]
| {{mapping| 69 109 }}
| +1.99
| +1.99
| 1.99
| 1.99
Line 321: Line 512:
| 2.3.5
| 2.3.5
| 81/80, {{monzo| -41 1 17 }}
| 81/80, {{monzo| -41 1 17 }}
| [{{val| 69 109 160 }}]
| {{mapping| 69 109 160 }}
| +1.86
| +1.86
| 1.64
| 1.64
Line 328: Line 519:
| 2.3.5.7
| 2.3.5.7
| 81/80, 126/125, 4117715/3981312
| 81/80, 126/125, 4117715/3981312
| [{{val| 69 109 160 193 }}] (69d)
| {{mapping| 69 109 160 193 }} (69d)
| +2.49
| +2.49
| 1.79
| 1.79
Line 335: Line 526:
| 2.3.5.7
| 2.3.5.7
| 81/80, 3125/3087, 6144/6125
| 81/80, 3125/3087, 6144/6125
| [{{val| 69 109 160 194 }}] (69)
| {{mapping| 69 109 160 194 }} (69)
| +0.94
| +0.94
| 2.13
| 2.13
Line 341: Line 532:
|}
|}


== Table of intervals ==
=== Rank 2 temperaments ===
{| class="wikitable mw-collapsible mw-collapsed collapsible center-1 right-3"
{| class="wikitable center-1 center-2"
|-
|-
! Degree
! Periods<br>per 8ve
! Carmen's naming system
! Generator
! Cents
! Temperaments
! Approximate Ratios*
! Error (abs, [[cent|¢]])
|-
|-
|0
| 1
|Natural Unison, 1
| 2\69
|0.000
| [[Gammy]] (69de)
|[[1/1]]
|0.000
|-
|-
|1
|1
|Ptolemy's comma
|5\69
|17.391
|[[Devichromic chords|Devichromic Octacot]]<ref group="note" name="tempname">Placeholder name, with link to [[Devichromic chords]] article &mdash; no general article currently exists for Devichromic temperament, and this particular incarnation of Devichromic temperament is likely to receive a different permanent name.</ref>
|[[100/99]]
|  -0.008
|-
|2
|Jubilisma, lesser septimal sixth tone
|34.783
|[[50/49]], [[101/99]]
|  -0.193, 0.157
|-
|3
|lesser septendecimal quartertone, _____
|52.174
|[[34/33]], [[101/98]]
| 0.491, -0.028
|-
|4
|_____
|69.565
|[[76/73]]
|  -0.158
|-
|5
|Small undevicesimal semitone
|86.957
|[[20/19]]
|  -1.844
|-
|6
|Large septendecimal semitone
|104.348
|[[17/16]]
|  -0.608
|-
|7
|Septimal diatonic semitone
|121.739
|[[15/14]]
|2.296
|-
|8
|Tridecimal neutral second
|139.130
|[[13/12]]
|0.558
|-
|9
|Vicesimotertial neutral second
|156.522
|[[23/21]]
|  -0.972
|-
|10
| Undevicesimal large neutral second, undevicesimal whole tone
|173.913
|[[21/19]]
|0.645
|-
|11
|Quasi-meantone
|191.304
|[[19/17]]
|  -1.253
|-
|12
|Whole tone
|208.696
|[[9/8]]
|4.786
|-
|13
|Septimal whole tone
|226.087
|[[8/7]]
|  -5.087
|-
|14
|Vicesimotertial semifourth
|243.478
|[[23/20]]
|1.518
|-
|15
|Subminor third, undetricesimal subminor third
|260.870
|[[7/6]], [[29/25]]
|  -6.001, 3.920
|-
|16
| Vicesimotertial subminor third
|278.261
|[[27/23]]
|0.670
|-
|17
|Pythagorean minor third
|295.652
|[[32/27]]
|1.517
|-
|18
|Classic minor third
|313.043
|[[6/5]]
|  -2.598
|-
|19
|Vicesimotertial supraminor third
|330.435
|[[23/19]]
|  -0.327
|-
|20
|Undecimal neutral third
|347.826
|[[11/9]]
|0.418
|-
|21
|Septendecimal submajor third
|365.217
|[[21/17]]
|  -0.608
|-
|22
|Classic major third
|382.609
|[[5/4]]
|  -3.705
|-
|23
| Undetricesimal major third, Septendecimal major third
|400.000
|[[29/23]], [[34/27]]
|  -1.303, 0.910
|-
|24
|Undecimal major third
|417.391
|[[14/11]]
|  -0.117
|-
|25
|Supermajor third
|434.783
|[[9/7]]
|  -0.301
|-
|26
|Barbados third
|452.174
|[[13/10]]
|  -2.040
|-
|27
|Septimal sub-fourth
|469.565
|[[21/16]]
|  -1.216
|-
|-
|28
| 1
|_____
| 19\69
|486.957
| [[Rarity]]
|[[53/40]]
|  -0.234
|-
|-
|29
| 1
|Just perfect fourth
| 20\69
|504.348
| [[Mohaha]] (69e)
|[[4/3]]
|6.303
|-
|-
|30
| 1
|Vicesimotertial acute fourth
| 22\69
|521.739
| [[Caleb]] (69)<br>[[marveltri]] (69)
|[[23/17]]
|  -1.580
|-
|-
|31
| 1
|Undecimal augmented fourth
| 29\69
|539.130
| [[Meantone]] (69d)
|[[15/11]]
|2.180
|-
|-
|32
| 3
|Undecimal superfourth, undetricesimal superfourth
| 5\69
|556.522
| [[Augmented family #Ogene|Ogene]] (69bceef)
|[[11/8]], [[29/21]]
|5.204, -2.275
|-
|-
|33
| 3
|Narrow tritone, classic augmented fourth
| 6\69
|573.913
| [[August]] (7-limit, 69cdd)<br>[[Lithium]] (69)
|[[7/5]], [[25/18]]
|  -8.600, 5.196
|-
|-
|34
| 3
|_____
| 9\69
|591.304
| [[Nessafof]] (69e)
|[[31/22]]
|  -2.413
|-
|35
|High tritone, undevicesimal tritone
|608.696
|[[10/7]], [[27/19]]
|  -8.792, 0.344
|-
|36
|_____
|626.087
|[[33/23]]
|1.088
|-
|37
| Undetricesimal tritone
|643.478
|[[29/20]]
|0.215
|-
|38
| Undevicesimal diminished fifth, undecimal diminished fifth
|660.870
|[[19/13]], [[22/15]]
|3.884, -2.180
|-
|39
|Vicesimotertial grave fifth, _____
|678.261
|[[34/23]], [[37/25]]
|1.580, -0.456
|-
|40
|Just perfect fifth
|695.652
|[[3/2]]
|  -6.303
|-
|41
|_____
|713.043
|[[80/53]]
|0.234
|-
|42
|Super-fifth, undetricesimal super-fifth
|730.435
|[[32/21]], [[29/19]]
|1.216, -1.630
|-
|43
|Septendecimal subminor sixth
|747.826
|[[17/11]]
|  -5.811
|-
|44
|Subminor sixth
|765.217
|[[14/9]]
|0.301
|-
|45
|Undecimal minor sixth
|782.609
|[[11/7]]
|0.117
|-
|46
| Septendecimal subminor sixth
|800.000
|[[27/17]]
|  -0.910
|-
|47
|Classic minor sixth
|817.391
|[[8/5]]
|3.705
|-
|48
|Septendecimal supraminor sixth
|834.783
|[[34/21]]
|0.608
|-
|49
|Undecimal neutral sixth
|852.174
|[[18/11]]
|  -0.418
|-
|50
|Vicesimotertial submajor sixth
|869.565
|[[38/23]]
|0.327
|-
|51
|Classic major sixth
|886.957
|[[5/3]]
|2.598
|-
|52
|Pythagorean major sixth
|904.348
|[[27/16]]
|  -1.517
|-
|53
|Septendecimal major sixth, undetricesimal major sixth
|921.739
|[[17/10]], [[29/17]]
|3.097, -2.883
|-
|54
|Supermajor sixth, undetricesimal supermajor sixth
|939.130
|[[12/7]], [[50/29]]
|6.001, -3.920
|-
|55
|Vicesimotertial supermajor sixth
|956.522
|[[40/23]]
|  -1.518
|-
|56
|Harmonic seventh
|973.913
|[[7/4]]
|5.087
|-
|57
|Pythagorean minor seventh
|991.304
|[[16/9]]
|  -4.786
|-
|58
|Quasi-meantone minor seventh
|1008.696
|[[34/19]]
|1.253
|-
|59
|Minor neutral undevicesimal seventh
|1026.087
|[[38/21]]
|  -0.645
|-
|60
|Vicesimotertial neutral seventh
|1043.478
|[[42/23]]
|0.972
|-
|61
|Tridecimal neutral seventh
|1060.870
|[[24/13]]
|  -0.558
|-
|62
|Septimal diatonic major seventh
|1078.261
|[[28/15]]
|  -2.296
|-
|63
|Small septendecimal major seventh
|1095.652
|[[32/17]]
|0.608
|-
|64
|Small undevicesimal semitone
|1113.043
|[[20/19]]
|1.844
|-
|65
|_____
|1130.435
|[[73/38]]
|0.158
|-
|66
| Septendecimal supermajor seventh
|1147.826
|[[33/17]]
|  -0.491
|-
|67
|_____
|1165.217
|[[49/25]]
|  -0.193
|-
|68
|_____
|1182.609
|[[99/50]]
|0.008
|-
|69
|Octave, 8
|1200.000
|[[2/1]]
|0.000
|}
|}
<nowiki>*</nowiki>some simpler ratios listed
<references group="note" />


== Scales ==
== Scales ==
* Supermajor[11], [[3L 8s]] – 66676667667
* Supermajor[11], [[3L 8s]] – 6 6 6 7 6 6 6 7 6 6 7
* Meantone[7], [[5L 2s]] (gen = 40\69) – 11 11 7 11 11 11 7
* Meantone[7], [[5L 2s]] (gen = 40\69) – 11 11 7 11 11 11 7
* Meantone[12], [[7L 5s]] (gen = 40\69) – 747474774747
* Meantone[12], [[7L 5s]] (gen = 40\69) – 7 4 7 4 7 4 7 7 4 7 4 7
* Baroque[12], 477474747747 (as proposed by Pianoteq plugin)
* Lithium[9], [[3L 6s]] – 11 6 6 11 6 6 11 6 6
* Lithium[9], 11 6 6 11 6 6 11 6 6 - [[3L 6s]]
* Lithium[12], [[9L 3s]] – 5 6 6 6 5 6 6 6 5 6 6 6
* Lithium[12], 566656665666
 
== Instruments ==
 
A [[Lumatone mapping for 69edo]] is available.


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=a4vNlDU6Vkw Hypergiant Sakura] by [[Eliora]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)
* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)
 
; [[Eliora]]
* [https://www.youtube.com/watch?v=a4vNlDU6Vkw ''Hypergiant Sakura''] (2021)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=Z3m4KqpuKPw ''69 hours before''] (2023)


[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Listen]]


{{Todo| review }}
{{Todo| review }}
Retrieved from "https://en.xen.wiki/w/69edo"