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== Theory ==
== Theory ==
72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is [[consistent]] in the [[17-odd-limit]] and is the ninth [[zeta integral edo]]. It is the second edo (after [[58edo|58]]) to be [[consistency|distinctly consistent]] in the [[11-odd-limit]], the first edo to be [[consistency|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% relative error (about 4 cents), and the first edo to be consistent in the 12- and 13-[[odd prime sum limit|odd-prime-sum-limit]].  
72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is the second edo (after [[58edo|58]]) to be [[consistent]] in the [[17-odd-limit]], and the second edo (also after 58) to be [[consistency|distinctly consistent]] in the [[11-odd-limit]], but it is the first edo to be [[consistency|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% [[relative interval error|relative error]] (about 4 cents). It also has pretty good accuracy for the [[19-limit]], being almost consistent to the entire [[21-odd-limit]] with the only inconsistency occurring at [[19/13]] and its [[octave complement]]. It is the ninth [[zeta integral edo]].


The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.
The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.


72et is the only 11-limit regular temperament which treats harmonics 24 to 28 as being equidistant in pitch, splits [[25/24]] into two equal [[49/48]][[~]][[50/49]]'s, and splits [[28/27]] into two equal [[55/54]]~[[56/55]]'s (144edo is enfactored in the 11-limit with 72edo, so it is already covered here). It is also an excellent tuning for [[miracle]] temperament, especially the 11-limit version, and the related rank-3 temperament [[prodigy]], and is a good tuning for other temperaments and scales, including [[wizard]], [[harry]], [[catakleismic]], [[compton]], [[unidec]] and [[tritikleismic]].
The [[octave reduction|octave reduced]] [[13/1|13th harmonic]] is mapped on 50\72, an interval inherited from [[36edo]] (25\36) that is a very close approximation to [[acoustic phi]], and the [[17/1|17th]] and [[19/1|19th harmonics]] come from 12edo.  
 
The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 72edo could be treated as a 2.3.5.7.11.ϕ.17 temperament.


72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].
72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].
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{{Harmonics in equal|72|columns=11}}
{{Harmonics in equal|72|columns=11}}
{{Harmonics in equal|72|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 72edo (continued)}}
{{Harmonics in equal|72|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 72edo (continued)}}
=== As a tuning of other temperaments ===
72et is the only 11-limit regular temperament which treats harmonics 24 to 28 as being equidistant in pitch, splits [[25/24]] into two equal [[49/48]][[~]][[50/49]]'s, and splits [[28/27]] into two equal [[55/54]]~[[56/55]]'s (144edo is enfactored in the 11-limit with 72edo, so it is already covered here). It is also an excellent tuning for [[miracle]] temperament, especially the 11-limit version, and the related rank-3 temperament [[prodigy]], and is a good tuning for other temperaments and scales, including [[wizard]], [[harry]], [[catakleismic]], [[compton]], [[unidec]] and [[tritikleismic]].


=== Subsets and supersets ===
=== Subsets and supersets ===
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== Intervals ==
== Intervals ==
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|limit=19-limit}} For lower limits see [[Table of 72edo intervals]].</ref>
! Approximate ratios<ref group="note">As a 19-limit temperament, inconsistent intervals in ''italic''. For a table of intervals by prime limit, see [[Table of 72edo intervals]].</ref>
! colspan="3" | [[Ups and downs notation]]
! [[Kite's ups and downs notation|Ups and downs notation]]
! colspan="3" | [[SKULO interval names|SKULO interval names and notation]]
! (K, S, U)
|-
|-
| 0
| 0
| 0.0
| 0.0
| 1/1
| [[1/1]]
| P1
| {{UDnote|step=0}}
| perfect unison
| D
| P1
| perfect unison
| D
| D
|-
|-
| 1
| 1
| 16.7
| 16.7
| 81/80, 91/90, 99/98, 100/99, 105/104
| [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]]
| ^1
| {{UDnote|step=1}}
| up unison
| ^D
| K1, L1
| comma-wide unison, large unison
| KD, LD
| KD
|-
|-
| 2
| 2
| 33.3
| 33.3
| 45/44, 49/48, 50/49, 55/54, 64/63
| [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]]
| ^^
| {{UDnote|step=2}}
| dup unison
| ^^D
| S1, O1
| super unison, on unison
| SD, OD
| SD
|-
|-
| 3
| 3
| 50.0
| 50.0
| 33/32, 36/35, 40/39
| [[33/32]], [[36/35]], [[40/39]]
| ^<sup>3</sup>1, v<sup>3</sup>m2
| {{UDnote|step=3}}
| trup unison, trudminor 2nd
|-
| ^<sup>3</sup>D, v<sup>3</sup>Eb
| U1, H1, hm2
| uber unison, hyper unison, hypominor 2nd
| UD, HD, uEb
| UD, uEb
|-
| 4
| 4
| 66.7
| 66.7
| 25/24, 26/25, 27/26, 28/27
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| vvm2
| {{UDnote|step=4}}
| dudminor 2nd
| vvEb
| kkA1, sm2
| classic aug unison, subminor 2nd
| kkD#, sEb
| sD#, (kkD#), sEb
|-
|-
| 5
| 5
| 83.3
| 83.3
| 20/19, 21/20, 22/21
| [[20/19]], [[21/20]], [[22/21]]
| vm2
| {{UDnote|step=5}}
| downminor 2nd
| vEb
| kA1, lm2
| comma-narrow aug unison, little minor 2nd
| kD#, lEb
| kD#, kEb
|-
|-
| 6
| 6
| 100.0
| 100.0
| 17/16, 18/17, 19/18
| [[17/16]], [[18/17]], [[19/18]]
| m2
| {{UDnote|step=6}}
| minor 2nd
| Eb
| m2
| minor 2nd
| Eb
| Eb
|-
|-
| 7
| 7
| 116.7
| 116.7
| 15/14, 16/15
| [[15/14]], [[16/15]]
| ^m2
| {{UDnote|step=7}}
| upminor 2nd
| ^Eb
| Km2
| classic minor 2nd
| KEb
| KEb
|-
|-
| 8
| 8
| 133.3
| 133.3
| 13/12, 14/13, 27/25
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2, v~2
| {{UDnote|step=8}}
| dupminor 2nd, downmid 2nd
| ^^Eb
| Om2
| on minor 2nd
| OEb
| SEb
|-
|-
| 9
| 9
| 150.0
| 150.0
| 12/11
| [[12/11]]
| ~2
| {{UDnote|step=9}}
| mid 2nd
| v<sup>3</sup>E
| N2
| neutral 2nd
| UEb/uE
| UEb/uE
|-
|-
| 10
| 10
| 166.7
| 166.7
| 11/10
| [[11/10]], [[21/19]]
| ^~2, vvM2
| {{UDnote|step=10}}
| upmid 2nd, dudmajor 2nd
| vvE
| oM2
| off major 2nd
| oE
| sE
|-
|-
| 11
| 11
| 183.3
| 183.3
| 10/9
| [[10/9]]
| vM2
| {{UDnote|step=11}}
| downmajor 2nd
| vE
| kM2
| classic/comma-narrow major 2nd
| kE
| kE
|-
|-
| 12
| 12
| 200.0
| 200.0
| 9/8, 19/17
| [[9/8]], [[19/17]]
| M2
| {{UDnote|step=12}}
| major 2nd
| E
| M2
| major 2nd
| E
| E
|-
|-
| 13
| 13
| 216.7
| 216.7
| 17/15, 25/22
| [[17/15]], [[25/22]]
| ^M2
| {{UDnote|step=13}}
| upmajor 2nd
| ^E
| LM2
| large major 2nd
| LE
| KE
|-
|-
| 14
| 14
| 233.3
| 233.3
| 8/7
| [[8/7]]
| ^^M2
| {{UDnote|step=14}}
| dupmajor 2nd
|-
| ^^E
| 15
| SM2
| 250.0
| supermajor 2nd
| [[15/13]], [[22/19]]
| SE
| {{UDnote|step=15}}
| SE
|-
| 15
| 250.0
| 15/13, 22/19
| ^<sup>3</sup>M2, <br>v<sup>3</sup>m3
| trupmajor 2nd,<br>trudminor 3rd
| ^<sup>3</sup>E, <br>v<sup>3</sup>F
| HM2, hm3
| hypermajor 2nd, hypominor 3rd
| HE, hF
| UE, uF
|-
|-
| 16
| 16
| 266.7
| 266.7
| 7/6
| [[7/6]]
| vvm3
| {{UDnote|step=16}}
| dudminor 3rd
| vvF
| sm3
| subminor 3rd
| sF
| sF
|-
|-
| 17
| 17
| 283.3
| 283.3
| 13/11, 20/17
| [[13/11]], [[20/17]]
| vm3
| {{UDnote|step=17}}
| downminor 3rd
| vF
| lm3
| little minor 3rd
| lF
| kF
|-
|-
| 18
| 18
| 300.0
| 300.0
| 19/16, 25/21, 32/27
| [[19/16]], [[25/21]], [[32/27]]
| m3
| {{UDnote|step=18}}
| minor 3rd
| F
| m3
| minor 3rd
| F
| F
|-
|-
| 19
| 19
| 316.7
| 316.7
| 6/5
| [[6/5]]
| ^m3
| {{UDnote|step=19}}
| upminor 3rd
| ^F
| Km3
| classic minor 3rd
| KF
| KF
|-
|-
| 20
| 20
| 333.3
| 333.3
| 17/14, 39/32, 40/33
| [[17/14]], ''[[39/32]]'', [[40/33]]
| ^^m3, v~3
| {{UDnote|step=20}}
| dupminor 3rd, downmid 3rd
| ^^F
| Om3
| on minor third
| OF
| SF
|-
|-
| 21
| 21
| 350.0
| 350.0
| 11/9, 27/22
| [[11/9]], [[27/22]]
| ~3
| {{UDnote|step=21}}
| mid 3rd
|-
| ^<sup>3</sup>F
| 22
| N3
| 366.7
| neutral 3rd
| [[16/13]], [[21/17]], [[26/21]]
| UF/uF#
| {{UDnote|step=22}}
| UF/uF#
|-
| 22
| 366.7
| 16/13, 21/17, 26/21
| ^~3, vvM3
| upmid 3rd, dudmajor 3rd
| vvF#
| oM3
| off major 3rd
| oF#
| sF#
|-
|-
| 23
| 23
| 383.3
| 383.3
| 5/4
| [[5/4]]
| vM3
| {{UDnote|step=23}}
| downmajor 3rd
| vF#
| kM3
| classic major 3rd
| kF#
| kF#
|-
|-
| 24
| 24
| 400.0
| 400.0
| 24/19
| [[24/19]]
| M3
| {{UDnote|step=24}}
| major 3rd
|-
| F#
| 25
| M3
| 416.7
| major 3rd
| [[14/11]], [[19/15]]
| F#
| {{UDnote|step=25}}
| F#
|-
| 25
| 416.7
| 14/11, 19/15
| ^M3
| upmajor 3rd
| ^F#
| LM3
| large major 3rd
| LF#
| KF#
|-
|-
| 26
| 26
| 433.3
| 433.3
| 9/7
| [[9/7]]
| ^^M3
| {{UDnote|step=26}}
| dupmajor 3rd
| ^^F#
| SM3
| supermajor 3rd
| SF#
| SF#
|-
|-
| 27
| 27
| 450.0
| 450.0
| 13/10, 22/17
| [[13/10]], [[22/17]]
| ^<sup>3</sup>M3, v<sup>3</sup>4
| {{UDnote|step=27}}
| trupmajor 3rd, trud 4th
| ^<sup>3</sup>F#, v<sup>3</sup>G
| HM3, h4
| hypermajor 3rd, hypo 4th
| HF#, hG
| UF#, uG
|-
|-
| 28
| 28
| 466.7
| 466.7
| 17/13, 21/16
| [[17/13]], [[21/16]]
| vv4
| {{UDnote|step=28}}
| dud 4th
| vvG
| s4
| sub 4th
| sG
| sG
|-
|-
| 29
| 29
| 483.3
| 483.3
| 33/25
| [[33/25]]
| v4
| {{UDnote|step=29}}
| down 4th
| vG
| l4
| little 4th
| lG
| kG
|-
|-
| 30
| 30
| 500.0
| 500.0
| 4/3
| [[4/3]]
| P4
| {{UDnote|step=30}}
| perfect 4th
| G
| P4
| perfect 4th
| G
| G
|-
|-
| 31
| 31
| 516.7
| 516.7
| 27/20
| [[27/20]]
| ^4
| {{UDnote|step=31}}
| up 4th
|-
| ^G
| 32
| K4
| 533.3
| comma-wide 4th
| [[15/11]], [[19/14]], ''[[26/19]]''
| KG
| {{UDnote|step=32}}
| KG
|-
|-
| 32
| 533.3
| 15/11, 19/14, ''26/19''
| ^^4, v~4
| dup 4th, downmid 4th
| ^^G
| O4
| on 4th
| OG
| SG
|-
| 33
| 33
| 550.0
| 550.0
| 11/8
| [[11/8]]
| ~4
| {{UDnote|step=33}}
| mid 4th
| ^<sup>3</sup>G
| U4/N4
| uber 4th / neutral 4th
| UG
| UG
|-
|-
| 34
| 34
| 566.7
| 566.7
| 18/13, 25/18
| [[18/13]], [[25/18]]
| ^~4, vvA4
| {{UDnote|step=34}}
| upmid 4th, dudaug 4th
|-
| vvG#
| 35
| kkA4, sd5
| classic aug 4th, sub dim 5th
| kkG#, sAb
| SG#, (kkG#), sAb
|-
| 35
| 583.3
| 583.3
| 7/5
| [[7/5]]
| vA4, vd5
| {{UDnote|step=35}}
| downaug 4th, <br>downdim 5th
| vG#, vAb
| kA4, ld5
| comma-narrow aug 4th, little dim 5th
| kG#, lAb
| kG#, kAb
|-
|-
| 36
| 36
| 600.0
| 600.0
| 17/12, 24/17
| [[17/12]], [[24/17]]
| A4, d5
| {{UDnote|step=36}}
| aug 4th, dim 5th
| G#, Ab
| A4, d5
| aug 4th, dim 5th
| G#, Ab
| G#, Ab
|-
|-
| 37
| 37
| 616.7
| 616.7
| 10/7
| [[10/7]]
| ^A4, ^d5
| {{UDnote|step=37}}
| upaug 4th, updim 5th
|-
| ^G#, ^Ab
| 38
| LA4, Kd5
| 633.3
| large aug 4th, comma-wide dim 5th
| [[13/9]], [[36/25]]
| LG#, KAb
| {{UDnote|step=38}}
| KG#, KAb
|-
| 38
| 633.3
| 13/9, 36/25
| v~5, ^^d5
| downmid 5th, <br>dupdim 5th
| ^^Ab
| SA4, KKd5
| super aug 4th, classic dim 5th
| SG#, KKAb
| SG#, SAb, (KKAb)
|-
|-
| 39
| 39
| 650.0
| 650.0
| 16/11
| [[16/11]]
| ~5
| {{UDnote|step=39}}
| mid 5th
| v<sup>3</sup>A
| u5/N5
| unter 5th / neutral 5th
| uA
| uA
|-
|-
| 40
| 40
| 666.7
| 666.7
| ''19/13'', 22/15, 28/19
| ''[[19/13]]'', [[22/15]], [[28/19]]
| vv5, ^~5
| {{UDnote|step=40}}
| dud 5th, upmid 5th
| vvA
| o5
| off 5th
| oA
| sA
|-
|-
| 41
| 41
| 683.3
| 683.3
| 40/27
| [[40/27]]
| v5
| {{UDnote|step=41}}
| down 5th
| vA
| k5
| comma-narrow 5th
| kA
| kA
|-
|-
| 42
| 42
| 700.0
| 700.0
| 3/2
| [[3/2]]
| P5
| {{UDnote|step=42}}
| perfect 5th
| A
| P5
| perfect 5th
| A
| A
|-
|-
| 43
| 43
| 716.7
| 716.7
| 50/33
| [[50/33]]
| ^5
| {{UDnote|step=43}}
| up 5th
| ^A
| L5
| large fifth
| LA
| KA
|-
|-
| 44
| 44
| 733.3
| 733.3
| 26/17, 32/21
| [[26/17]], [[32/21]]
| ^^5
| {{UDnote|step=44}}
| dup 5th
|-
| ^^A
| 45
| S5
| 750.0
| super fifth
| [[17/11]], [[20/13]]
| SA
| {{UDnote|step=45}}
| SA
|-
| 45
| 750.0
| 17/11, 20/13
| ^<sup>3</sup>5, v<sup>3</sup>m6
| trup 5th, trudminor 6th
| ^<sup>3</sup>A, v<sup>3</sup>Bb
| H5, hm6
| hyper fifth, hypominor 6th
| HA, hBb
| UA, uBb
|-
|-
| 46
| 46
| 766.7
| 766.7
| 14/9
| [[14/9]]
| vvm6
| {{UDnote|step=46}}
| dudminor 6th
| vvBb
| sm6
| superminor 6th
| sBb
| sBb
|-
|-
| 47
| 47
| 783.3
| 783.3
| 11/7, 30/19
| [[11/7]], [[30/19]]
| vm6
| {{UDnote|step=47}}
| downminor 6th
| vBb
| lm6
| little minor 6th
| lBb
| kBb
|-
|-
| 48
| 48
| 800.0
| 800.0
| 19/12
| [[19/12]]
| m6
| {{UDnote|step=48}}
| minor 6th
| Bb
| m6
| minor 6th
| Bb
| Bb
|-
|-
| 49
| 49
| 816.7
| 816.7
| 8/5
| [[8/5]]
| ^m6
| {{UDnote|step=49}}
| upminor 6th
| ^Bb
| Km6
| classic minor 6th
| kBb
| kBb
|-
|-
| 50
| 50
| 833.3
| 833.3
| 13/8, 21/13, 34/21
| [[13/8]], [[21/13]], [[34/21]]
| ^^m6, v~6
| {{UDnote|step=50}}
| dupminor 6th, downmid 6th
| ^^Bb
| Om6
| on minor 6th
| oBb
| sBb
|-
|-
| 51
| 51
| 850.0
| 850.0
| 18/11, 44/27
| [[18/11]], [[44/27]]
| ~6
| {{UDnote|step=51}}
| mid 6th
| v<sup>3</sup>B
| N6
| neutral 6th
| UBb, uB
| UBb, uB
|-
|-
| 52
| 52
| 866.7
| 866.7
| 28/17, 33/20, 64/39
| [[28/17]], [[33/20]], ''[[64/39]]''
| ^~6, vvM6
| {{UDnote|step=52}}
| upmid 6th, dudmajor 6th
| vvB
| oM6
| off major 6th
| oB
| sB
|-
|-
| 53
| 53
| 883.3
| 883.3
| 5/3
| [[5/3]]
| vM6
| {{UDnote|step=53}}
| downmajor 6th
| vB
| kM6
| classic major 6th
| kB
| kB
|-
|-
| 54
| 54
| 900.0
| 900.0
| 27/16, 32/19, 42/25
| [[27/16]], [[32/19]], [[42/25]]
| M6
| {{UDnote|step=54}}
| major 6th
| B
| M6
| major 6th
| B
| B
|-
|-
| 55
| 55
| 916.7
| 916.7
| 17/10, 22/13
| [[17/10]], [[22/13]]
| ^M6
| {{UDnote|step=55}}
| upmajor 6th
| ^B
| LM6
| large major 6th
| LB
| KB
|-
|-
| 56
| 56
| 933.3
| 933.3
| 12/7
| [[12/7]]
| ^^M6
| {{UDnote|step=56}}
| dupmajor 6th
| ^^B
| SM6
| supermajor 6th
| SB
| SB
|-
|-
| 57
| 57
| 950.0
| 950.0
| 19/11, 26/15
| [[19/11]], [[26/15]]
| ^<sup>3</sup>M6, <br>v<sup>3</sup>m7
| {{UDnote|step=57}}
| trupmajor 6th,<br>trudminor 7th
| ^<sup>3</sup>B, <br>v<sup>3</sup>C
| HM6, hm7
| hypermajor 6th, hypominor 7th
| HB, hC
| UB, uC
|-
|-
| 58
| 58
| 966.7
| 966.7
| 7/4
| [[7/4]]
| vvm7
| {{UDnote|step=58}}
| dudminor 7th
| vvC
| sm7
| subminor 7th
| sC
| sC
|-
|-
| 59
| 59
| 983.3
| 983.3
| 30/17, 44/25
| [[30/17]], [[44/25]]
| vm7
| {{UDnote|step=59}}
| downminor 7th
|-
| vC
| 60
| lm7
| 1000.0
| little minor 7th
| [[16/9]], [[34/19]]
| lC
| {{UDnote|step=60}}
| kC
|-
| 60
| 1000.0
| 16/9, 34/19
| m7
| minor 7th
| C
| m7
| minor 7th
| C
| C
|-
|-
| 61
| 61
| 1016.7
| 1016.7
| 9/5
| [[9/5]]
| ^m7
| {{UDnote|step=61}}
| upminor 7th
| ^C
| Km7
| classic/comma-wide minor 7th
| KC
| KC
|-
|-
| 62
| 62
| 1033.3
| 1033.3
| 20/11
| [[20/11]], [[38/21]]
| ^^m7, v~7
| {{UDnote|step=62}}
| dupminor 7th, downmid 7th
| ^^C
| Om7
| on minor 7th
| OC
| SC
|-
|-
| 63
| 63
| 1050.0
| 1050.0
| 11/6
| [[11/6]]
| ~7
| {{UDnote|step=63}}
| mid 7th
| ^<sup>3</sup>C
| N7, hd8
| neutral 7th, hypo dim 8ve
| UC/uC#, hDb
| UC/uC#, uDb
|-
|-
| 64
| 64
| 1066.7
| 1066.7
| 13/7, 24/13, 50/27
| [[13/7]], [[24/13]], [[50/27]]
| ^~7, vvM7
| {{UDnote|step=64}}
| upmid 7th, dudmajor 7th
| vvC#
| oM7, sd8
| off major 7th, sub dim 8ve
| oC#, sDb
| sC#, sDb
|-
|-
| 65
| 65
| 1083.3
| 1083.3
| 15/8, 28/15
| [[15/8]], [[28/15]]
| vM7
| {{UDnote|step=65}}
| downmajor 7th
| vC#
| kM7, ld8
| classic major 7th, little dim 8ve
| kC#, lDb
| kC#, kDb
|-
|-
| 66
| 66
| 1100.0
| 1100.0
| 17/9, 32/17, 36/19
| [[17/9]], [[32/17]], [[36/19]]
| M7
| {{UDnote|step=66}}
| major 7th
| C#
| M7, d8
| major 7th, dim 8ve
| C#, Db
| C#, Db
|-
|-
| 67
| 67
| 1116.7
| 1116.7
| 19/10, 21/11, 40/21
| [[19/10]], [[21/11]], [[40/21]]
| ^M7
| {{UDnote|step=67}}
| upmajor 7th
| ^C#
| LM7, Kd8
| large major 7th, comma-wide dim 8ve
| LC#, KDb
| KC#, KDb
|-
|-
| 68
| 68
| 1133.3
| 1133.3
| 25/13, 27/14, 48/25, 52/27
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| ^^M7
| {{UDnote|step=68}}
| dupmajor 7th
| ^^C#
| SM7, KKd8
| supermajor 7th, classic dim 8ve
| SC#, KKDb
| SC#, SDb, (KKDb)
|-
|-
| 69
| 69
| 1150.0
| 1150.0
| 35/18, 39/20, 64/33
| [[35/18]], [[39/20]], [[64/33]]
| ^<sup>3</sup>M7, v<sup>3</sup>8
| {{UDnote|step=69}}
| trupmajor 7th, trud octave
| ^<sup>3</sup>C#, v<sup>3</sup>D
| HM7, u8, h8
| hypermajor 7th, unter 8ve, hypo 8ve
| HC#, uD, hD
| UC#, uDb, uD
|-
|-
| 70
| 70
| 1166.7
| 1166.7
| 49/25, 55/28, 63/32, 88/45, 96/49
| [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]]
| vv8
| {{UDnote|step=70}}
| dud octave
| vvD
| s8, o8
| sub 8ve, off 8ve
| sD, oD
| sD
|-
|-
| 71
| 71
| 1183.3
| 1183.3
| 99/50, 160/81, 180/91, 196/99, 208/105
| [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]]
| v8
| {{UDnote|step=71}}
| down octave
| vD
| k8, l8
| comma-narrow 8ve, little 8ve
| kD, lD
| kD
|-
|-
| 72
| 72
| 1200.0
| 1200.0
| 2/1
| [[2/1]]
| P8
| {{UDnote|step=72}}
| perfect octave
| D
| P8
| perfect octave
| D
| D
|}
|}
<references group="note" />
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Proposed interval names and solfèges ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
 
|+ style="font-size: 105%; white-space: nowrap;" | Table of proposed interval names and solfèges
{| class="wikitable center-all"
|-
|-
! Quality
! #
! [[Color notation|Color]]
! Cents
! Monzo format
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]
! Examples
! colspan="3" | [[SKULO interval names|SKULO interval names and notation]]
! (K, S, U)
|-
| 0
| 0.0
| P1
| perfect unison
| D
| P1
| perfect unison
| D
| D
|-
| 1
| 16.7
| ^1
| up unison
| ^D
| K1, L1
| comma-wide unison, large unison
| KD, LD
| KD
|-
| 2
| 33.3
| ^^
| dup unison
| ^^D
| S1, O1
| super unison, on unison
| SD, OD
| SD
|-
| 3
| 50.0
| ^<sup>3</sup>1, v<sup>3</sup>m2
| trup unison, trudminor 2nd
| ^<sup>3</sup>D, v<sup>3</sup>Eb
| U1, H1, hm2
| uber unison, hyper unison, hypominor 2nd
| UD, HD, uEb
| UD, uEb
|-
| 4
| 66.7
| vvm2
| dudminor 2nd
| vvEb
| kkA1, sm2
| classic aug unison, subminor 2nd
| kkD#, sEb
| sD#, (kkD#), sEb
|-
| 5
| 83.3
| vm2
| downminor 2nd
| vEb
| kA1, lm2
| comma-narrow aug unison, little minor 2nd
| kD#, lEb
| kD#, kEb
|-
| 6
| 100.0
| m2
| minor 2nd
| Eb
| m2
| minor 2nd
| Eb
| Eb
|-
| 7
| 116.7
| ^m2
| upminor 2nd
| ^Eb
| Km2
| classic minor 2nd
| KEb
| KEb
|-
| 8
| 133.3
| ^^m2, v~2
| dupminor 2nd, downmid 2nd
| ^^Eb
| Om2
| on minor 2nd
| OEb
| SEb
|-
| 9
| 150.0
| ~2
| mid 2nd
| v<sup>3</sup>E
| N2
| neutral 2nd
| UEb/uE
| UEb/uE
|-
| 10
| 166.7
| ^~2, vvM2
| upmid 2nd, dudmajor 2nd
| vvE
| oM2
| off major 2nd
| oE
| sE
|-
| 11
| 183.3
| vM2
| downmajor 2nd
| vE
| kM2
| classic/comma-narrow major 2nd
| kE
| kE
|-
| 12
| 200.0
| M2
| major 2nd
| E
| M2
| major 2nd
| E
| E
|-
| 13
| 216.7
| ^M2
| upmajor 2nd
| ^E
| LM2
| large major 2nd
| LE
| KE
|-
| 14
| 233.3
| ^^M2
| dupmajor 2nd
| ^^E
| SM2
| supermajor 2nd
| SE
| SE
|-
| 15
| 250.0
| ^<sup>3</sup>M2, <br>v<sup>3</sup>m3
| trupmajor 2nd,<br>trudminor 3rd
| ^<sup>3</sup>E, <br>v<sup>3</sup>F
| HM2, hm3
| hypermajor 2nd, hypominor 3rd
| HE, hF
| UE, uF
|-
| 16
| 266.7
| vvm3
| dudminor 3rd
| vvF
| sm3
| subminor 3rd
| sF
| sF
|-
| 17
| 283.3
| vm3
| downminor 3rd
| vF
| lm3
| little minor 3rd
| lF
| kF
|-
| 18
| 300.0
| m3
| minor 3rd
| F
| m3
| minor 3rd
| F
| F
|-
| 19
| 316.7
| ^m3
| upminor 3rd
| ^F
| Km3
| classic minor 3rd
| KF
| KF
|-
| 20
| 333.3
| ^^m3, v~3
| dupminor 3rd, downmid 3rd
| ^^F
| Om3
| on minor third
| OF
| SF
|-
| 21
| 350.0
| ~3
| mid 3rd
| ^<sup>3</sup>F
| N3
| neutral 3rd
| UF/uF#
| UF/uF#
|-
| 22
| 366.7
| ^~3, vvM3
| upmid 3rd, dudmajor 3rd
| vvF#
| oM3
| off major 3rd
| oF#
| sF#
|-
| 23
| 383.3
| vM3
| downmajor 3rd
| vF#
| kM3
| classic major 3rd
| kF#
| kF#
|-
| 24
| 400.0
| M3
| major 3rd
| F#
| M3
| major 3rd
| F#
| F#
|-
| 25
| 416.7
| ^M3
| upmajor 3rd
| ^F#
| LM3
| large major 3rd
| LF#
| KF#
|-
| 26
| 433.3
| ^^M3
| dupmajor 3rd
| ^^F#
| SM3
| supermajor 3rd
| SF#
| SF#
|-
| 27
| 450.0
| ^<sup>3</sup>M3, v<sup>3</sup>4
| trupmajor 3rd, trud 4th
| ^<sup>3</sup>F#, v<sup>3</sup>G
| HM3, h4
| hypermajor 3rd, hypo 4th
| HF#, hG
| UF#, uG
|-
| 28
| 466.7
| vv4
| dud 4th
| vvG
| s4
| sub 4th
| sG
| sG
|-
| 29
| 483.3
| v4
| down 4th
| vG
| l4
| little 4th
| lG
| kG
|-
| 30
| 500.0
| P4
| perfect 4th
| G
| P4
| perfect 4th
| G
| G
|-
| 31
| 516.7
| ^4
| up 4th
| ^G
| K4
| comma-wide 4th
| KG
| KG
|-
| 32
| 533.3
| ^^4, v~4
| dup 4th, downmid 4th
| ^^G
| O4
| on 4th
| OG
| SG
|-
| 33
| 550.0
| ~4
| mid 4th
| ^<sup>3</sup>G
| U4/N4
| uber 4th / neutral 4th
| UG
| UG
|-
| 34
| 566.7
| ^~4, vvA4
| upmid 4th, dudaug 4th
| vvG#
| kkA4, sd5
| classic aug 4th, sub dim 5th
| kkG#, sAb
| SG#, (kkG#), sAb
|-
| 35
| 583.3
| vA4, vd5
| downaug 4th, <br>downdim 5th
| vG#, vAb
| kA4, ld5
| comma-narrow aug 4th, little dim 5th
| kG#, lAb
| kG#, kAb
|-
| 36
| 600.0
| A4, d5
| aug 4th, dim 5th
| G#, Ab
| A4, d5
| aug 4th, dim 5th
| G#, Ab
| G#, Ab
|-
| 37
| 616.7
| ^A4, ^d5
| upaug 4th, updim 5th
| ^G#, ^Ab
| LA4, Kd5
| large aug 4th, comma-wide dim 5th
| LG#, KAb
| KG#, KAb
|-
| 38
| 633.3
| v~5, ^^d5
| downmid 5th, <br>dupdim 5th
| ^^Ab
| SA4, KKd5
| super aug 4th, classic dim 5th
| SG#, KKAb
| SG#, SAb, (KKAb)
|-
| 39
| 650.0
| ~5
| mid 5th
| v<sup>3</sup>A
| u5/N5
| unter 5th / neutral 5th
| uA
| uA
|-
| 40
| 666.7
| vv5, ^~5
| dud 5th, upmid 5th
| vvA
| o5
| off 5th
| oA
| sA
|-
| 41
| 683.3
| v5
| down 5th
| vA
| k5
| comma-narrow 5th
| kA
| kA
|-
| 42
| 700.0
| P5
| perfect 5th
| A
| P5
| perfect 5th
| A
| A
|-
| 43
| 716.7
| ^5
| up 5th
| ^A
| L5
| large fifth
| LA
| KA
|-
| 44
| 733.3
| ^^5
| dup 5th
| ^^A
| S5
| super fifth
| SA
| SA
|-
| 45
| 750.0
| ^<sup>3</sup>5, v<sup>3</sup>m6
| trup 5th, trudminor 6th
| ^<sup>3</sup>A, v<sup>3</sup>Bb
| H5, hm6
| hyper fifth, hypominor 6th
| HA, hBb
| UA, uBb
|-
| 46
| 766.7
| vvm6
| dudminor 6th
| vvBb
| sm6
| superminor 6th
| sBb
| sBb
|-
| 47
| 783.3
| vm6
| downminor 6th
| vBb
| lm6
| little minor 6th
| lBb
| kBb
|-
| 48
| 800.0
| m6
| minor 6th
| Bb
| m6
| minor 6th
| Bb
| Bb
|-
| 49
| 816.7
| ^m6
| upminor 6th
| ^Bb
| Km6
| classic minor 6th
| kBb
| kBb
|-
| 50
| 833.3
| ^^m6, v~6
| dupminor 6th, downmid 6th
| ^^Bb
| Om6
| on minor 6th
| oBb
| sBb
|-
| 51
| 850.0
| ~6
| mid 6th
| v<sup>3</sup>B
| N6
| neutral 6th
| UBb, uB
| UBb, uB
|-
| 52
| 866.7
| ^~6, vvM6
| upmid 6th, dudmajor 6th
| vvB
| oM6
| off major 6th
| oB
| sB
|-
| 53
| 883.3
| vM6
| downmajor 6th
| vB
| kM6
| classic major 6th
| kB
| kB
|-
| 54
| 900.0
| M6
| major 6th
| B
| M6
| major 6th
| B
| B
|-
| 55
| 916.7
| ^M6
| upmajor 6th
| ^B
| LM6
| large major 6th
| LB
| KB
|-
| 56
| 933.3
| ^^M6
| dupmajor 6th
| ^^B
| SM6
| supermajor 6th
| SB
| SB
|-
| 57
| 950.0
| ^<sup>3</sup>M6, <br>v<sup>3</sup>m7
| trupmajor 6th,<br>trudminor 7th
| ^<sup>3</sup>B, <br>v<sup>3</sup>C
| HM6, hm7
| hypermajor 6th, hypominor 7th
| HB, hC
| UB, uC
|-
| 58
| 966.7
| vvm7
| dudminor 7th
| vvC
| sm7
| subminor 7th
| sC
| sC
|-
| 59
| 983.3
| vm7
| downminor 7th
| vC
| lm7
| little minor 7th
| lC
| kC
|-
| 60
| 1000.0
| m7
| minor 7th
| C
| m7
| minor 7th
| C
| C
|-
| 61
| 1016.7
| ^m7
| upminor 7th
| ^C
| Km7
| classic/comma-wide minor 7th
| KC
| KC
|-
| 62
| 1033.3
| ^^m7, v~7
| dupminor 7th, downmid 7th
| ^^C
| Om7
| on minor 7th
| OC
| SC
|-
| 63
| 1050.0
| ~7
| mid 7th
| ^<sup>3</sup>C
| N7, hd8
| neutral 7th, hypo dim 8ve
| UC/uC#, hDb
| UC/uC#, uDb
|-
| 64
| 1066.7
| ^~7, vvM7
| upmid 7th, dudmajor 7th
| vvC#
| oM7, sd8
| off major 7th, sub dim 8ve
| oC#, sDb
| sC#, sDb
|-
| 65
| 1083.3
| vM7
| downmajor 7th
| vC#
| kM7, ld8
| classic major 7th, little dim 8ve
| kC#, lDb
| kC#, kDb
|-
| 66
| 1100.0
| M7
| major 7th
| C#
| M7, d8
| major 7th, dim 8ve
| C#, Db
| C#, Db
|-
| 67
| 1116.7
| ^M7
| upmajor 7th
| ^C#
| LM7, Kd8
| large major 7th, comma-wide dim 8ve
| LC#, KDb
| KC#, KDb
|-
| 68
| 1133.3
| ^^M7
| dupmajor 7th
| ^^C#
| SM7, KKd8
| supermajor 7th, classic dim 8ve
| SC#, KKDb
| SC#, SDb, (KKDb)
|-
| 69
| 1150.0
| ^<sup>3</sup>M7, v<sup>3</sup>8
| trupmajor 7th, trud octave
| ^<sup>3</sup>C#, v<sup>3</sup>D
| HM7, u8, h8
| hypermajor 7th, unter 8ve, hypo 8ve
| HC#, uD, hD
| UC#, uDb, uD
|-
| 70
| 1166.7
| vv8
| dud octave
| vvD
| s8, o8
| sub 8ve, off 8ve
| sD, oD
| sD
|-
| 71
| 1183.3
| v8
| down octave
| vD
| k8, l8
| comma-narrow 8ve, little 8ve
| kD, lD
| kD
|-
| 72
| 1200.0
| P8
| perfect octave
| D
| P8
| perfect octave
| D
| D
|}
 
=== 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"
|-
! Quality
! [[Color notation|Color]]
! Monzo format
! Examples
|-
| dudminor
| zo
| (a b 0 1)
| [[7/6]], [[7/4]]
|-
| minor
| fourthward wa
| (a b), b < -1
| [[32/27]], [[16/9]]
|-
| upminor
| gu
| (a b -1)
| [[6/5]], [[9/5]]
|-
| rowspan="2" | dupminor, <br>downmid
| luyo
| (a b 1 0 -1)
| [[15/11]]
|-
| tho
| (a b 0 0 0 1)
| [[13/8]], [[13/9]]
|-
| rowspan="2" | mid
| ilo
| (a b 0 0 1)
| [[11/9]], [[11/6]]
|-
| lu
| (a b 0 0 -1)
| [[12/11]], [[18/11]]
|-
| rowspan="2" | upmid, <br>dudmajor
| logu
| (a b -1 0 1)
| [[11/10]]
|-
| thu
| (a b 0 0 0 -1)
| [[16/13]], [[18/13]]
|-
| downmajor
| yo
| (a b 1)
| [[5/4]], [[5/3]]
|-
| major
| fifthward wa
| (a b), b > 1
| [[9/8]], [[27/16]]
|-
| dupmajor
| ru
| (a b 0 -1)
| [[9/7]], [[12/7]]
|-
| rowspan="2" | trupmajor, <br>trudminor
| thogu
| (a b -1 0 0 1)
| [[13/10]]
|-
| thuyo
| (a b 1 0 0 -1)
| [[15/13]]
|}
All 72edo chords can be named using ups and downs. An up, down or mid 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). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:
 
{| class="wikitable center-all"
|-
! [[Color notation|Color of the 3rd]]
! JI chord
! Notes as edosteps
! Notes of C chord
! Written name
! Spoken name
|-
|-
| dudminor
| zo
| zo
| (a b 0 1)
| 6:7:9
| 7/6, 7/4
| 0-16-42
| C vvEb G
| Cvvm
| C dudminor
|-
|-
| minor
| fourthward wa
| (a b), b < -1
| 32/27, 16/9
|-
| upminor
| gu
| gu
| (a b -1)
| 10:12:15
| 6/5, 9/5
| 0-19-42
| C ^Eb G
| C^m
| C upminor
|-
|-
| rowspan="2" | dupminor, <br>downmid
| ilo
| luyo
| 18:22:27
| (a b 1 0 -1)
| 0-21-42
| 15/11
| C v<span style="font-size: 90%; vertical-align: super;">3</span>E G
| C~
| C mid
|-
|-
| tho
| yo
| (a b 0 0 0 1)
| 4:5:6
| 13/8, 13/9
| 0-23-42
| C vE G
| Cv
| C downmajor or C down
|-
|-
| rowspan="2" | mid
| ru
| ilo
| 14:18:27
| (a b 0 0 1)
| 0-26-42
| 11/9, 11/6
| C ^^E G
|-
| C^^
| lu
| C dupmajor or C dup
| (a b 0 0 -1)
| 12/11, 18/11
|-
| rowspan="2" | upmid, <br>dudmajor
| logu
| (a b -1 0 1)
| 11/10
|-
| thu
| (a b 0 0 0 -1)
| 16/13, 18/13
|-
| downmajor
| yo
| (a b 1)
| 5/4, 5/3
|-
| major
| fifthward wa
| (a b), b > 1
| 9/8, 27/16
|-
| dupmajor
| ru
| (a b 0 -1)
| 9/7, 12/7
|-
| rowspan="2" | trupmajor, <br>trudminor
| thogu
| (a b -1 0 0 1)
| 13/10
|-
| thuyo
| (a b 1 0 0 -1)
| 15/13
|}
|}
All 72edo chords can be named using ups and downs. An up, down or mid 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). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:
For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].  


{| class="wikitable center-all"
=== Relationship between primes and rings ===
|-
In 72tet, there are 6 [[ring number|rings]]. 12edo is the plain ring; thus every 6 degrees is the 3-limit.
! [[Color notation|Color of the 3rd]]
 
! JI chord
Then, after each subsequent degree in reverse, a new prime limit is unveiled from it:
! Notes as edosteps
* −1 degree (the down ring) corrects [[81/64]] to [[5/4]] via descending [[81/80]]
! Notes of C chord
* −2 degrees (the dud ring) corrects [[16/9]] to [[7/4]] via descending [[64/63]]
! Written name
* +3 degrees  (the trup ring) corrects [[4/3]] to [[11/8]] via [[33/32]]
! Spoken name
* +2 degrees (the dup ring) corrects [[128/81]] to [[13/8]] via [[1053/1024]]
|-
* 0 degrees (the plain ring) corrects [[256/243]] to [[17/16]] via [[4131/4096]]
| zo
* 0 degrees (the plain ring) corrects [[32/27]] to [[19/16]] via [[513/512]]
| 6:7:9
Thus the product of a ratio's monzo with {{map| 0 0 -1 -2 3 2 0 0 }}, modulo 6, specifies which ring the ratio lies on.
| 0-16-42
 
| C vvEb G
== Notation ==
| Cvvm
=== Stein–Zimmermann–Gould notation ===
| C dudminor
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
|-
{{Sharpness-sharp6-szg}}
| gu
 
| 10:12:15
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
| 0-19-42
{{Sharpness-sharp6-qt-szg}}
| C ^Eb G
| C^m
| C upminor
|-
| ilo
| 18:22:27
| 0-21-42
| C v<span style="font-size: 90%; vertical-align: super;">3</span>E G
| C~
| C mid
|-
| yo
| 4:5:6
| 0-23-42
| C vE G
| Cv
| C downmajor or C down
|-
| ru
| 14:18:27
| 0-26-42
| C ^^E G
| C^^
| C dupmajor or C dup
|}
For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].
 
=== Relationship between primes and rings ===
In 72tet, there are 6 [[ring number|rings]]. 12edo is the plain ring; thus every 6 degrees is the 3-limit.
 
Then, after each subsequent degree in reverse, a new prime limit is unveiled from it:
* −1 degree (the down ring) corrects 81/64 to 5/4 via 80/81
* −2 degrees (the dud ring) corrects 16/9 to 7/4 via 63/64
* +3 degrees  (the trup ring) corrects 4/3 to 11/8 via 33/32
* +2 degrees (the dup ring) corrects 128/81 to 13/8 via 1053/1024
* 0 degrees (the plain ring) corrects 256/243 to 17/16 via 4131/4096
* 0 degrees (the plain ring) corrects 32/27 to 19/16 via 513/512
Thus the product of a ratio's monzo with {{map| 0 0 -1 -2 3 2 0 0 }}, modulo 6, specifies which ring the ratio lies on.


== Notation ==
=== Kite's ups and downs notation ===
=== Ups and downs notation ===
72edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
72edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Ups and downs sharpness}}
{{Ups and downs sharpness}}


Half-sharps and half-flats can be used to avoid triple arrows:
Half-sharps and half-flats can be used to avoid triple arrows:
{{Ups and downs sharpness|72|true}}
{{Ups and downs sharpness|72|true}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with 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}}


=== Sagittal notation ===
=== Sagittal notation ===
Line 1,010: Line 1,313:
From the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 72edo in the Revo flavor of Sagittal:  
From the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 72edo in the Revo flavor of Sagittal:  


[[File:72edo Sagittal.png|frame|none]]
<div class="noresize">
[[File:72edo Sagittal.png]]
</div>


=== Ivan Wyschnegradsky's notation ===
=== Ivan Wyschnegradsky's notation ===
Line 1,158: Line 1,463:
| 7.32
| 7.32
| Cataharry comma
| Cataharry comma
|-
|7
|[[33075/32768]]
|[-15 3 2 2⟩
|16.14
|Mirwomo comma
|-
|-
| 7
| 7
Line 1,206: Line 1,505:
| 3.78
| 3.78
| Moctdel comma
| Moctdel comma
|-
|11
|[[2835/2816]]
|[-8 4 1 1 -1⟩
|11.64
|Fwiwisma
|-
|-
| 11
| 11
Line 1,224: Line 1,517:
| 3.03
| 3.03
| Wizardharry comma
| Wizardharry comma
|-
|11
|[[4125/4096]]
|[-12 1 3 0 1⟩
|12.21
|
|-
|11
|[[4375/4356]]
|[-2 -2 4 1 -2⟩
|7.53
|
|-
|-
| 11
| 11
Line 1,242: Line 1,523:
| 3.60
| 3.60
| Liganellus comma
| Liganellus comma
|-
|11
|[[8019/8000]]
|[-6 6 -3 0 1⟩
|4.11
|Trimitone comma
|-
|11
|[[9375/9317]]
|[0 1 5 -1 -3⟩
|10.74
|
|-
|-
| 11
| 11
Line 1,260: Line 1,529:
| 0.18
| 0.18
| Kalisma
| Kalisma
|-
|11
|[[12005/11979]]
|[0 -2 1 4 -3⟩
|3.75
|Unisquarisma
|-
|11
|[[14700/14641]]
|[2 1 2 2 -4⟩
|6.96
|
|-
|11
|[[15625/15488]]
|[-7 0 6 0 -2⟩
|15.25
|
|-
|-
| 11
| 11
Line 1,326: Line 1,577:
| 2.38
| 2.38
| Squbema
| Squbema
|-
|13
|[[975/968]]
|[-3 1 2 0 -2 1⟩
|12.47
|
|-
|-
| 13
| 13
Line 1,338: Line 1,583:
| 1.73
| 1.73
| Sinbadma
| Sinbadma
|-
|13
|[[1287/1280]]
|[-8 2 -1 0 1 1⟩
|9.44
|Catadictma
|-
|13
|[[1573/1568]]
|[-5 0 0 -2 2 1⟩
|5.51
|Lambeth comma
|-
|-
| 13
| 13
Line 1,356: Line 1,589:
| 2.20
| 2.20
| Nicola
| Nicola
|-
|13
|[[1625/1617]]
|[0 -1 3 -2 -1 1⟩
|8.54
|Sopreisma
|-
|-
| 13
| 13
Line 1,374: Line 1,601:
| 0.83
| 0.83
| Ibnsinma
| Ibnsinma
|-
|13
|[[2197/2178]]
|[-1 -2 0 0 -2 3⟩
|15.04
|
|-
|-
| 13
| 13
| [[2197/2187]]
| [[6656/6655]]
| [0 -7 0 0 0 3⟩
| {{Monzo| 9 0 -1 0 -3 1 }}
| 7.90
| 0.26012
|Threedie
| Jacobin comma
|-
|13
|[[2704/2695]]
|[4 0 -1 -2 -1 2⟩
|5.77
|
|-
|13
|[[3042/3025]]
|[1 2 -2 0 -2 2⟩
|9.70
|Diagassormisma
|-
|13
|[[3159/3136]]
|[-6 5 0 -2 0 1⟩
|12.65
|
|-
|13
|[[3185/3168]]
|[-5 -2 1 2 -1 1⟩
|9.27
|
|-
|13
|[[3549/3520]]
|[-6 1 -1 1 -1 2⟩
|14.20
|
|-
|13
|[[4394/4375]]
|[1 0 -4 -1 0 3⟩
|7.50
|Hebrewsma
|-
|13
|[[4459/4455]]
|[0 -4 -1 3 -1 1⟩
|1.55
|Tristanisma
|-
|13
|[[6656/6655]]
|[9 0 -1 0 -3 1⟩
|0.26
|Jacobin comma
|-
|13
|[[7605/7546]]
|[-1 2 1 -3 -1 2⟩
|13.48
|
|-
|13
|[[8125/8064]]
|[-7 -2 4 -1 0 1⟩
|13.05
|
|-
|13
|[[8281/8192]]
|[-13 0 0 2 0 2⟩
|18.71
|Diahuntmisma
|-
|13
|[[8281/8250]]
|[-1 -1 -3 2 -1 2⟩
|6.49
|
|-
|13
|[[9295/9216]]
|[-10 -2 1 0 1 2⟩
|14.78
|
|-
|13
|[[9295/9261]]
|[0 -3 1 -3 1 2⟩
|6.34
|
|-
|13
|[[9360/9317]]
|[4 2 1 -1 -3 1⟩
|7.97
|
|}
|}
<references group="note" />
<references group="note" />
Line 1,539: Line 1,670:
| 516.7
| 516.7
| 27/20
| 27/20
| [[Marvo]] / [[zarvo]]
| [[Gravity]] / [[marvo]] / [[zarvo]]
|-
|-
| 1
| 1
Line 1,611: Line 1,742:
| 316.7<br>(50.0)
| 316.7<br>(50.0)
| 6/5<br>(36/35)
| 6/5<br>(36/35)
| [[Ennealimmal]] / ennealimnic
| [[Ennealimmal]] / ennealimnic / ennealiminal
|-
|-
| 9
| 9
Line 1,643: Line 1,774:
| [[Gamelstearn]]
| [[Gamelstearn]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


== Octave stretch or compression ==
== Octave stretch or compression ==
Line 1,671: Line 1,802:
* [[JuneGloom]]
* [[JuneGloom]]
* [[Keenanmarvel]]
* [[Keenanmarvel]]
* [[Prodigy]][19]: 5 2 5 4 5 2 5 2 5 2 5 4 5 2 5 2 5 5 2


=== Harmonic scale ===
=== Harmonic scale ===
Line 1,867: Line 1,999:


; [[Jake Freivald]]
; [[Jake Freivald]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday'']{{dead link}} in the [[lazysunday]] scale
* [https://web.archive.org/web/20201127014336/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday''] in the [[lazysunday]] scale


{{Wikipedia|In vain (Haas)}}
{{Wikipedia|In vain (Haas)}}
Line 1,878: Line 2,010:


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']{{dead link}}
* [https://web.archive.org/web/20201127015744/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
Line 1,884: Line 2,016:


; [[Prent Rodgers]]
; [[Prent Rodgers]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']{{dead link}}
* [https://web.archive.org/web/20201127012907/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']


; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
Retrieved from "https://en.xen.wiki/w/72edo"