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=65 tone equal temperament=
{{Infobox ET}}
{{ED intro}}


'''65edo''' divides the [[Octave|octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma|schisma]], 32805/32768, the [[sensipent_comma|sensipent comma]], 78732/78125, and the [[Wuerschmidt_comma|wuerschmidt comma]]. In the [[7-limit|7-limit]], there are two different maps; the first is <65 103 151 182|, [[tempering_out|tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit|5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt_temperament|wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.
== Theory ==
65et can be characterized as the temperament which [[tempering out|tempers out]] 32805/32768 ([[schisma]]), 78732/78125 ([[sensipent comma]]), 393216/390625 ([[würschmidt comma]]), and {{monzo| -13 17 -6 }} ([[graviton]]). In the [[7-limit]], there are two different maps; the first is {{val| 65 103 151 '''182''' }} (65), tempering out [[126/125]], [[245/243]] and [[686/675]], so that it [[support]]s [[sensi]], and the second is {{val| 65 103 151 '''183''' }} (65d), tempering out [[225/224]], [[3125/3087]], [[4000/3969]] and [[5120/5103]], so that it supports [[garibaldi]]. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[würschmidt]] temperament (wurschmidt and worschmidt) these two mappings provide.


65edo approximates the intervals [[3/2|3/2]], [[5/4|5/4]], [[11/8|11/8]] and [[19/16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just_intonation_subgroup|just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit|19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N_subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo|130edo]].
65edo approximates the intervals [[3/2]], [[5/4]], [[11/8]], [[19/16]], [[23/16]], [[31/16]] and [[47/32]] well, so that it does a good job representing the 2.3.5.11.19.23.31.47 [[just intonation subgroup]]. To this one may want to add [[17/16]], [[29/16]] and [[43/32]], giving the [[47-limit]] no-7's no-13's no-37's no-41's subgroup 2.3.5.11.17.19.23.29.31.43.47. In this sense it is a tuning of [[schismic]]/[[nestoria]] that focuses on the very primes that [[53edo]] neglects (which instead elegantly connects primes 7, 13, 37, and 41 to nestoria). Also of interest is the [[19-limit]] [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as the [[zeta]] edo [[130edo]].


65edo contains [[13edo|13edo]] as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded Rubble: a Xenuke Unfolded].
=== Prime harmonics ===
{{Harmonics in equal|65|intervals=prime|columns=15}}


=Intervals=
=== Subsets and supersets ===
65edo contains [[5edo]] and [[13edo]] as subsets. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [[Andrew Heathwaite]]'s composition [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded ''Rubble: a Xenuke Unfolded''].


{| class="wikitable"
[[130edo]], which doubles its, corrects its approximation to harmonics 7 and 13.
 
== Intervals ==
{| class="wikitable center-all right-2 left-3"
|-
! #
! [[Cent]]s
! Approximate ratios<ref group="note">{{sg|limit=2.3.5.11.13/7.17.19.23.29.31.47 subgroup}}</ref>
! colspan="2" | [[Ups and downs notation]]
|-
| 0
| 0.00
| 1/1
| P1
| D
|-
| 1
| 18.46
| 81/80, 88/87, 93/92, 94/93, 95/94, 96/95, 100/99, 121/120, 115/114, 116/115, 125/124
| ^1
| ^D
|-
| 2
| 36.92
| 45/44, 46/45, 47/46, 48/47, 55/54, 128/125
| ^^1
| ^^D
|-
| 3
| 55.38
| 30/29, 31/30, 32/31, 33/32, 34/33
| vvm2
| vvEb
|-
| 4
| 73.85
| 23/22, 24/23, 25/24, 47/45
| vm2
| vEb
|-
| 5
| 92.31
| 18/17, 19/18, 20/19, 58/55, 135/128, 256/243
| m2
| Eb
|-
| 6
| 110.77
| 16/15, 17/16, 33/31
| A1/^m2
| D#/^Eb
|-
| 7
| 129.23
| 14/13, 27/25, 55/51
| v~2
| ^^Eb
|-
| 8
| 147.69
| 12/11, 25/23
| ~2
| vvvE
|-
| 9
| 166.15
| 11/10, 32/29
| ^~2
| vvE
|-
| 10
| 184.62
| 10/9, 19/17
| vM2
| vE
|-
| 11
| 203.08
| 9/8, 64/57
| M2
| E
|-
| 12
| 221.54
| 17/15, 25/22, 33/29, 58/51
| ^M2
| ^E
|-
| 13
| 240.00
| 23/20, 31/27, 38/33, 54/47, 55/48
| ^^M2
| ^^E
|-
| 14
| 258.46
| 22/19, 29/25, 36/31, 64/55
| vvm3
| vvF
|-
|-
!  rowspan="2"| [[Degree|Degree]]
| 15
!  colspan="3"| Size
| 276.92
| 20/17, 27/23, 34/29, 75/64
| vm3
| vF
|-
|-
![[cent|Cents]]
| 16
!pions
| 295.38
!7mus
| 19/16, 32/27
| m3
| F
|-
|-
| colspan="4" style="text-align:center;" | 0
| 17
| 313.85
| 6/5, 55/46
| ^m3
| ^F
|-
|-
| style="text-align:center;" | 1
| 18
| style="text-align:right;" | 18.4615
| 332.31
|19.5692
| 23/19, 40/33
|23.6308 (17.A17A<sub>16</sub>)
| v~3
| ^^F
|-
|-
| style="text-align:center;" | 2
| 19
| style="text-align:right;" | 36.9231
| 350.77
|39.1385
| 11/9, 27/22, 38/31
|47.2615 (2F.42F4<sub>16</sub>)
| ~3
| ^^^F
|-
|-
| style="text-align:center;" | 3
| 20
| style="text-align:right;" | 55.3846
| 369.23
|58.7077
| 26/21, 47/38, 68/55
|70.8923 (46.E46E<sub>16</sub>)
| ^~3
| vvF#
|-
|-
| style="text-align:center;" | 4
| 21
| style="text-align:right;" | 73.84615
| 387.69
|78.2769
| 5/4, 64/51
|94.5231 (5E.85E8<sub>16</sub>)
| vM3
| vF#
|-
|-
| style="text-align:center;" | 5
| 22
| style="text-align:right;" | 92.3077
| 406.15
|97.84615
| 19/15, 24/19, 29/23, 34/27, 81/64
|118.15385 (76.2762<sub>16</sub>)
| M3
| F#
|-
|-
| style="text-align:center;" | 6
| 23
| style="text-align:right;" | 110.7692
| 424.62
|117.4154
| 23/18, 32/25
|141.7846 (8D.C8DD<sub>16</sub>)
| ^M3
| ^F#
|-
|-
| style="text-align:center;" | 7
| 24
| style="text-align:right;" | 129.2308
| 443.08
|136.9846
| 22/17, 31/24, 40/31, 128/99
|165.4154 (A5.6A57<sub>16</sub>)
| ^^M3
| ^^F#
|-
|-
| style="text-align:center;" | 8
| 25
| style="text-align:right;" | 147.6923
| 461.54
|156.55385
| 30/23, 47/36, 72/55
|189.04615 (BD.0BD1<sub>16</sub>)
| vv4
| vvG
|-
|-
| style="text-align:center;" | 9
| 26
| style="text-align:right;" | 166.15385
| 480.00
|176.1231
| 29/22, 33/25, 62/47
|212.6769 (D4.AD4B<sub>16</sub>
| v4
| vG
|-
|-
| style="text-align:center;" | 10
| 27
| style="text-align:right;" | 184.6154
| 498.46
|195.6923
| 4/3
|236.3077 (EC.4EC5<sub>16</sub>)
| P4
| G
|-
|-
| style="text-align:center;" | 11
| 28
| style="text-align:right;" | 203.0769
| 516.92
|215.2615
| 23/17, 27/20, 31/23
|259.9385 (103.F03F<sub>16</sub>)
| ^4
| ^G
|-
|-
| style="text-align:center;" | 12
| 29
| style="text-align:right;" | 221.5385
| 535.38
|234.8308
| 15/11, 34/25, 64/47
|283.5692 (11B.91B9<sub>16</sub>)
| v~4
| ^^G
|-
|-
| style="text-align:center;" | 13
| 30
| style="text-align:right;" | 240
| 553.85
|254.4
| 11/8, 40/29, 62/45
|307.2 (133.3333<sub>16</sub>)
| ~4
| ^^^G
|-
|-
| style="text-align:center;" | 14
| 31
| style="text-align:right;" | 258.4615
| 572.31
|273.9692
| 25/18, 32/23
|330.8308 (14A.D4AD<sub>16</sub>)
| ^~4/vd5
| vvG#/vAb
|-
|-
| style="text-align:center;" | 15
| 32
| style="text-align:right;" | 276.9231
| 590.77
|293.5385
| 24/17, 31/22, 38/27, 45/32
|354.4615 (162.7627<sub>16</sub>)
| vA4/d5
| vG#/Ab
|-
|-
| style="text-align:center;" | 16
| 33
| style="text-align:right;" | 295.3846
| 609.23
|313.1077
| 17/12, 27/19, 44/31, 64/45
|378.0923 (17A.17A18<sub>16</sub>)
| A4/^d5
| G#/^Ab
|-
|-
| style="text-align:center;" | 17
| 34
| style="text-align:right;" | 313.84615
| 627.69
|332.6769
| 36/25, 23/16
|401.7231 (191.B91C<sub>16</sub>)
| ^A4/v~5
| ^G#/^^Ab
|-
|-
| style="text-align:center;" | 18
| 35
| style="text-align:right;" | 332.3077
| 646.15
|352.24615
| 16/11, 29/20, 45/31
|425.35385 (1A9.5A96<sub>16</sub>)
| ~5
| vvvA
|-
|-
| style="text-align:center;" | 19
| 36
| style="text-align:right;" | 350.7692
| 664.62
|371.8154
| 22/15, 25/17, 47/32
|448.9846 (1C0.FC1<sub>16</sub>)
| ^~5
| vvA
|-
|-
| style="text-align:center;" | 20
| 37
| style="text-align:right;" | 369.2308
| 683.08
|391.3846
| 34/23, 40/27, 46/31
|472.6154 (1D8.9D8A<sub>16</sub>)
| v5
| vA
|-
|-
| style="text-align:center;" | 21
| 38
| style="text-align:right;" | 387.6923
| 701.54
|410.95385
| 3/2
|496.24615 (1F0.3F04<sub>16</sub>)
| P5
| A
|-
|-
| style="text-align:center;" | 22
| 39
| style="text-align:right;" | 406.15385
| 720.00
|430.5231
| 44/29, 50/33, 47/31
|519.8769 (207.E07E<sub>16</sub>)
| ^5
| ^A
|-
|-
| style="text-align:center;" | 23
| 40
| style="text-align:right;" | 424.6154
| 738.46
|450.0923
| 23/15, 55/36, 72/47
|543.5077 (21F.81F8<sub>16</sub>)
| ^^5
| ^^A
|-
|-
| style="text-align:center;" | 24
| 41
| style="text-align:right;" | 443.0769
| 756.92
|469.6615
| 17/11, 48/31, 31/20, 99/64
|567.1385 (237.2372<sub>16</sub>)
| vvm6
| vvBb
|-
|-
| style="text-align:center;" | 25
| 42
| style="text-align:right;" | 461.5385
| 775.38
|489.2308
| 25/16, 36/23
|590.7692 (24E.C4ED<sub>16</sub>)
| vm6
| vBb
|-
|-
| style="text-align:center;" | 26
| 43
| style="text-align:right;" | 480
| 793.85
|508.8
| 19/12, 27/17, 30/19, 46/29, 128/81
|614.4 (266.6666<sub>16</sub>)
| m6
| Bb
|-
|-
| style="text-align:center;" | 27
| 44
| style="text-align:right;" | 498.4615
| 812.31
|528.3692
| 8/5, 51/32
|638.0308 (27E07E08<sub>16</sub>)
| ^m6
| ^Bb
|-
|-
| style="text-align:center;" | 28
| 45
| style="text-align:right;" | 516.9231
| 830.77
|547.9385
| 21/13, 55/34, 76/47
|661.6615 (295.A95B<sub>16</sub>)
| v~6
| ^^Bb
|-
|-
| style="text-align:center;" | 29
| 46
| style="text-align:right;" | 535.3846
| 849.23
|567.5077
| 18/11, 31/19, 44/27
|685.2923 (2AD.4AD4<sub>16</sub>)
| ~6
| vvvB
|-
|-
| style="text-align:center;" | 30
| 47
| style="text-align:right;" | 553.84615
| 867.69
|587.0769
| 33/20, 38/23
|708.9231 (2C4.EC4F<sub>16</sub>)
| ^~6
| vvB
|-
|-
| style="text-align:center;" | 31
| 48
| style="text-align:right;" | 572.3077
| 886.15
|606.64615
| 5/3, 92/55
|732.55385 (2DC.8DC9<sub>16</sub>)
| vM6
| vB
|-
|-
| style="text-align:center;" | 32
| 49
| style="text-align:right;" | 590.7692
| 904.62
|626.2154
| 27/16, 32/19
|756.1846 (2F4.2F42<sub>16</sub>)
| M6
| B
|-
|-
| style="text-align:center;" | 33
| 50
| style="text-align:right;" | 609.2308
| 923.08
|645.7846
| 17/10, 29/17, 46/27, 128/75
|779.8154 (30B.D0BD<sub>16</sub>)
| ^M6
| ^B
|-
|-
| style="text-align:center;" | 34
| 51
| style="text-align:right;" | 627.6923
| 941.54
|665.35385
| 19/11, 31/18, 50/29, 55/32
|803.44615 (323.7237<sub>16</sub>)
| ^^M6
| ^^B
|-
|-
| style="text-align:center;" | 35
| 52
| style="text-align:right;" | 646.1538
| 960.00
|684.9231
| 33/19, 40/23, 47/27, 54/31, 96/55
|827.0769 (33B.13B1<sub>16</sub>)
| vvm7
| vvC
|-
|-
| style="text-align:center;" | 36
| 53
| style="text-align:right;" | 664.6154
| 978.46
|704.4923
| 30/17, 44/25, 51/29, 58/33
|850.7077 (352.B52B<sub>16</sub>)
| vm7
| vC
|-
|-
| style="text-align:center;" | 37
| 54
| style="text-align:right;" | 683.0769
| 996.92
|724.0615
| 16/9, 57/32
|874.3385 (36A.56A5<sub>16</sub>)
| m7
| C
|-
|-
| style="text-align:center;" | 38
| 55
| style="text-align:right;" | 701.5385
| 1015.38
|743.6308
| 9/5, 34/19
|897.9692 (381.F81F8<sub>16</sub>)
| ^m7
| ^C
|-
|-
| style="text-align:center;" | 39
| 56
| style="text-align:right;" | 720
| 1033.85
|763.2
| 20/11, 29/16
|921.6 (399.999A<sub>16</sub>)
| v~7
| ^^C
|-
|-
| style="text-align:center;" | 40
| 57
| style="text-align:right;" | 738.4615
| 1052.31
|782.7692
| 11/6, 46/25
|945.2308 (3B1.3B13<sub>16</sub>)
| ~7
| ^^^C
|-
|-
| style="text-align:center;" | 41
| 58
| style="text-align:right;" | 756.9231
| 1070.77
|802.3385
| 13/7, 50/27, 102/55
|968.8615 (3C8.DC8E<sub>16</sub>)
| ^~7
| vvC#
|-
|-
| style="text-align:center;" | 42
| 59
| style="text-align:right;" | 775.3846
| 1089.23
|821.9077
| 15/8, 32/17, 62/33
|992.4923 (3E0.7E08<sub>16</sub>)
| vM7
| vC#
|-
|-
| style="text-align:center;" | 43
| 60
| style="text-align:right;" | 793.84615
| 1107.69
|841.4769
| 17/9, 19/10, 36/19, 55/29, 243/128, 256/135
|1016.1231 (3F8.1F82<sub>16</sub>)
| M7
| C#
|-
|-
| style="text-align:center;" | 44
| 61
| style="text-align:right;" | 812.3077
| 1126.15
|861.04615
| 23/12, 44/23, 48/25, 90/47
|1039.75385 (40F.C0FC<sub>16</sub>)
| ^M7
| ^C#
|-
|-
| style="text-align:center;" | 45
| 62
| style="text-align:right;" | 830.7692
| 1144.62
|880.6154
| 29/15, 31/16, 33/17, 60/31, 64/33
|1063.3846 (427.6276<sub>16</sub>)
| ^^M7
| ^^C#
|-
|-
| style="text-align:center;" | 46
| 63
| style="text-align:right;" | 849.2308
| 1163.08
|900.1846
| 45/23, 47/24, 88/45, 92/47, 108/55, 125/64
|1087.0154 (43F.03F<sub>16</sub>)
| vv8
| vvD
|-
|-
| style="text-align:center;" | 47
| 64
| style="text-align:right;" | 867.6923
| 1181.54
|919.75385
| 87/55, 93/47, 95/48, 99/50, 115/58, 160/81, 184/93, 188/95, 228/115, 240/121, 248/125
|1110.64615 (456.A56A<sub>16</sub>)
| v8
| vD
|-
|-
| style="text-align:center;" | 48
| 65
| style="text-align:right;" | 886.15385
| 1200.00
|939.3231
| 2/1
|1134.2769 (46E.46E4<sub>16</sub>)
| P8
| D
|}
<references group="note" />
 
== Notation ==
=== Ups and downs notation ===
65edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Sharpness-sharp6a}}
 
Half-sharps and half-flats can be used to avoid triple arrows:
{{Sharpness-sharp6b}}
 
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
 
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}
 
=== Ivan Wyschnegradsky's notation ===
Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used:
 
{{sharpness-sharp6-iw}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[72edo#Sagittal notation|72]] and [[79edo#Sagittal notation|79]].
 
==== Evo flavor ====
<imagemap>
File:65-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 220 106 [[64/63]]
rect 220 80 340 106 [[33/32]]
default [[File:65-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:65-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 650 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 220 106 [[64/63]]
rect 220 80 340 106 [[33/32]]
default [[File:65-EDO_Revo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:65-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 639 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 220 106 [[64/63]]
rect 220 80 340 106 [[33/32]]
default [[File:65-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 334
| steps = 65.0158450885860
| step size = 18.4570391781413
| tempered height = 7.813349
| pure height = 7.642373
| integral = 1.269821
| gap = 16.514861
| octave = 1199.70754657919
| consistent = 6
| distinct = 6
}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
| style="text-align:center;" | 49
! rowspan="2" | [[Subgroup]]
| style="text-align:right;" | 904.6154
! rowspan="2" | [[Comma list]]
|958.8923
! rowspan="2" | [[Mapping]]
|1157.9077 (485.E85E8<sub>16</sub>)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
| style="text-align:center;" | 50
! [[TE error|Absolute]] (¢)
| style="text-align:right;" | 923.0769
! [[TE simple badness|Relative]] (%)
|978.4615
|1181.53845 (49D.89D9<sub>16</sub>)
|-
|-
| style="text-align:center;" | 51
| 2.3
| style="text-align:right;" | 941.5385
| {{monzo| -103 65 }}
|998.0308
| {{mapping| 65 103 }}
|1205.1692 (4B5.2B53<sub>16</sub>)
| +0.131
| 0.131
| 0.71
|-
|-
| style="text-align:center;" | 52
| 2.3.5
| style="text-align:right;" | 960
| 32805/32768, 78732/78125
|1017.6
| {{mapping| 65 103 151 }}
|1228.8 (4CC.CCCD<sub>16</sub>)
| −0.110
| 0.358
| 1.94
|-
|-
| style="text-align:center;" | 53
| 2.3.5.11
| style="text-align:right;" | 978.4615
| 243/242, 4000/3993, 5632/5625
|1037.1692
| {{mapping| 65 103 151 225 }}
|1252.4308 (4E4.6E47<sub>16</sub>)
| −0.266
| 0.410
| 2.22
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
| style="text-align:center;" | 54
! Periods<br>per 8ve
| style="text-align:right;" | 996.9231
! Generator*
|1056.7385
! Cents*
|1276.0615 (4FC.0FC1<sub>16</sub>)
! Associated<br>ratio*
! Temperament
|-
|-
| style="text-align:center;" | 55
| 1
| style="text-align:right;" | 1015.3846
| 3\65
|1076.3077
| 55.38
|1299.6923 (513.B13B<sub>16</sub>)
| 33/32
| [[Escapade]]
|-
|-
| style="text-align:center;" | 56
| 1
| style="text-align:right;" | 1033.84615
| 9\65
|1095.8769
| 166.15
|1323.3231 (52B.52B5<sub>16</sub>)
| 11/10
| [[Squirrel]] etc.
|-
|-
| style="text-align:center;" | 57
| 1
| style="text-align:right;" | 1052.3077
| 12\65
|1115.44615
| 221.54
|1346.95385 (542,F42F<sub>16</sub>)
| 25/22
| [[Hemisensi]]
|-
|-
| style="text-align:center;" | 58
| 1
| style="text-align:right;" | 1070.7692
| 19\65
|1135.0154
| 350.77
|1370.5846 (55A.95A9<sub>16</sub>)
| 11/9
| [[Karadeniz]]
|-
|-
| style="text-align:center;" | 59
| 1
| style="text-align:right;" | 1089.2308
| 21\65
|1154.5846
| 387.69
|1394.2154 (572.3723<sub>16</sub>)
| 5/4
| [[Würschmidt]]
|-
|-
| style="text-align:center;" | 60
| 1
| style="text-align:right;" | 1107.6923
| 24\65
|1174.1535
| 443.08
|1417.84615 (589.D89E<sub>16</sub>)
| 162/125
| [[Sensipent]]
|-
|-
| style="text-align:center;" | 61
| 1
| style="text-align:right;" | 1126.15385
| 27\65
|1193.7231
| 498.46
|1441.4769 (5A1.7A18<sub>16</sub>)
| 4/3
| [[Helmholtz (temperament)|Helmholtz]] / [[nestoria]] / [[photia]]
|-
|-
| style="text-align:center;" | 62
| 1
| style="text-align:right;" | 1144.6154
| 28\65
|1213.2923
| 516.92
|1465.1077 (5B9.1B92<sub>16</sub>)
| 27/20
| [[Larry]]
|-
|-
| style="text-align:center;" | 63
| 5
| style="text-align:right;" | 1163.0769
| 20\65<br>(6\65)
|1232.8615
| 369.23<br>(110.77)
|1488.7385 (5D0.BD0C<sub>16</sub>)
| 99/80<br>(16/15)
| [[Quintosec]]
|-
|-
| style="text-align:center;" | 64
| 5
| style="text-align:right;" | 1181.5385
| 27\65<br>(1\65)
|1252.4308
| 498.46<br>(18.46)
|1512.3692 (5E8.5E86<sub>16</sub>)
| 4/3<br>(81/80)
| [[Quintile]]
|-
|-
| style="text-align:center;" | 65
| 5
| style="text-align:right;" | 1200
| 30\65<br>(4\65)
|1272
| 553.85<br>(73.85)
|1536 (600<sub>16</sub>)
| 11/8<br>(25/24)
| [[Countdown]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Scales ==
* Amulet{{idiosyncratic}}, (approximated from [[25edo]], subset of [[würschmidt]]): 5 3 5 5 3 5 12 5 5 3 5 12 5
* [[Photia7]]
* [[Photia12]]
* [[Skateboard7]]
== Instruments ==
[[Lumatone mapping for 65edo]]


=Scales=
== Music ==
[[photia7|photia7]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025).


[[photia12|photia12]]     
[[Category:Listen]]
[[Category:11/8]]
[[Category:Schismic]]
[[Category:13/8]]
[[Category:Sensipent]]
[[Category:17/16]]
[[Category:Subgroup temperaments]]
[[Category:19/16]]
[[Category:Würschmidt]]
[[Category:3/2]]
[[Category:5/4]]
[[Category:65edo]]
[[Category:edo]]
[[Category:intervals]]
[[Category:listen]]
[[Category:schismic]]
[[Category:sensipent]]
[[Category:subgroup]]
[[Category:theory]]
[[Category:wuerschmidt]]
[[Category:wurschmidt]]
Retrieved from "https://en.xen.wiki/w/65edo"