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The ''58 equal temperament'', often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[Octave|octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit|17-limit]]s. It is the smallest [[EDO|equal temperament]] which is [[consistent|consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[Tonality_diamond|tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry_Partch_related_scales|Genesis scale]] of [[Harry_Partch|Harry Partch]]. It supports [[Hemififths|hemififths]], [[Myna|myna]], [[Diaschismic|diaschismic]], [[Harry|harry]], [[Hemifamity_temperaments#Mystery|mystery]], [[Hemifamity_temperaments#Buzzard|buzzard]] and [[Starling_temperaments#Thuja|thuja]] [[Regular_Temperaments|temperament]]s, and supplies the [[Optimal_patent_val|optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling_family#Thrush|thrush]], [[Starling_family#Thrush-Bluebird|bluebird]], [[Starling_family#Aplonis|aplonis]] and [[Breed_family#Jove, aka Wonder-Jofur|jofur]].
{{Infobox ET}}
{{Wikipedia|58 equal temperament}}
{{ED intro}}


While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo|29edo]].
== Theory ==
58edo is a strong system in the [[11-limit|11-]], [[13-limit|13-]] and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest distinctly consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-odd-limit [[tonality diamond]] to distinct scale steps), and hence the first which can define a tempered version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]].  


=Scales=
While the [[17/1|17th harmonic]] is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. Since {{nowrap|58 {{=}} 2 × 29}}, 58edo shares the same excellent perfect fifth with [[29edo]]. It is the last edo to have exactly one [[5L 2s|diatonic]] perfect fifth and no [[5edo]] or [[7edo]] fifths.
[[hemif7|hemif7]]


[[hemif10|hemif10]]
The [[19/1|19th]] and [[23/1|23rd]] harmonics are very flat, so it makes sense to use their second-best approximations in the 58hi val. This val is, in fact, one of the first to be [[diamond monotone]] in the 23-odd-limit, past the idiosyncratic 53e val. However, its accuracy is questionable, with primes 19 and 23 being about 13 cents sharp, so one may want to use a larger system like [[62edo]] for the 23-limit instead, which has the added benefit of being meantone.


[[hemif17|hemif17]]
=== Prime harmonics ===
{{Harmonics in equal|58}}


==Intervals==
=== As a tuning of other temperaments ===
As an equal temperament, 58et [[tempering out|tempers out]] [[2048/2025]] in the [[5-limit]]; [[126/125]], [[1728/1715]], and [[5120/5103]] in the [[7-limit]]; [[176/175]], [[243/242]], [[441/440]], [[540/539]], and [[896/891]] in the 11-limit; [[144/143]], [[351/350]], [[364/363]] in the 13-limit. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]], [[thuja]] [[regular temperament|temperament]]s plus a number of [[gravity family]] [[extension]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].


{| class="wikitable"
Of all edos which map the syntonic comma ([[81/80]]) to 1 step by patent val, 58edo is the one with the step size closest to 81/80, with one step of 58edo being less than 1{{cent}} narrower than the just interval.
 
=== Subsets and supersets ===
58edo contains [[2edo]] and [[29edo]] as subsets.
 
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4""
|-
! #
! Cents
! Approximate ratios*
! [[Ups and downs notation]]
|-
|-
| | degree of 58edo
| 0
| | cents value
| 0.0
|pions
| [[1/1]]
|7mus
| {{UDnote|step=0}}
| | ratios
|-
|-
| | 0
| 1
| colspan="3"| 0.00
| 20.7
| | 1/1
| [[56/55]], [[64/63]], [[81/80]], [[91/90]], [[105/104]]
| {{UDnote|step=1}}
|-
|-
| | 1
| 2
| | 20.69
| 41.4
|21.93
| [[36/35]], [[40/39]], [[45/44]], [[49/48]], [[50/49]], [[55/54]]
|26.48 (1A.7C<sub>16</sub>)
| {{UDnote|step=2}}
| | 56/55, 64/63, 81/80, 128/125
|-
|-
| | 2
| 3
| | 41.38
| 62.1
|43.86
| [[26/25]], [[27/26]], [[28/27]], [[33/32]]
|52.97 (34.F7<sub>16</sub>)
| {{UDnote|step=3}}
| | 36/35, 49/48, 50/49, 55/54
|-
|-
| | 3
| 4
| | 62.07
| 82.8
|65.79
| [[21/20]], [[22/21]], ''[[25/24]]''
|79.45 (4F.72<sub>16</sub>)
| {{UDnote|step=4}}
| | 25/24, 26/25, 27/26, 28/27, 33/32
|-
|-
| | 4
| 5
| | 82.76
| 103.4
|87.72
| [[16/15]], [[17/16]], [[18/17]]
|105.93 (69.EE<sub>16</sub>)
| {{UDnote|step=5}}
| | 21/20, 22/21
|-
|-
| | 5
| 6
| | 103.45
| 124.1
|109.655
| [[14/13]], [[15/14]]
|132.41 (84.69<sub>16</sub>)
| {{UDnote|step=6}}
| | 16/15, 17/16, 18/17
|-
|-
| | 6
| 7
| | 124.14
| 144.8
|131.59
| [[12/11]], [[13/12]]
|158.9 (9E.E58<sub>16</sub>)
| {{UDnote|step=7}}
| | 14/13, 15/14, 27/25
|-
|-
| | 7
| 8
| | 144.83
| 165.5
|153.52
| [[11/10]]
|185.38 (B9.61<sub>16</sub>)
| {{UDnote|step=8}}
| | 12/11, 13/12
|-
|-
| | 8
| 9
| | 165.52
| 186.2
|175.45
| [[10/9]]
|211.86 (D3.DD<sub>16</sub>)
| {{UDnote|step=9}}
| | 11/10
|-
|-
| | 9
| 10
| | 186.21
| 206.9
|197.38
| [[9/8]], [[17/15]]
|238.345 (EE.58<sub>16</sub>)
| {{UDnote|step=10}}
| | 10/9
|-
|-
| | 10
| 11
| | 206.9
| 227.6
|219.31
| [[8/7]]
|264.83 (108.D3<sub>16</sub>)
| {{UDnote|step=11}}
| | 9/8, 17/15
|-
|-
| | 11
| 12
| | 227.59
| 248.3
|241.24
| [[15/13]]
|291.31 (123.4F<sub>16</sub>)
| {{UDnote|step=12}}
| | 8/7
|-
|-
| | 12
| 13
| | 248.28
| 269.0
|263.17
| [[7/6]]
|317.79 (13D.CB<sub>16</sub>)
| {{UDnote|step=13}}
| | 15/13
|-
|-
| | 13
| 14
| | 268.97
| 289.7
|285.1
| [[13/11]], [[20/17]]
|344.28 (158.47<sub>16</sub>)
| {{UDnote|step=14}}
| | 7/6
|-
|-
| | 14
| 15
| | 289.655
| 310.3
|307.035
| [[6/5]]
|370.76 (172.C2<sub>16</sub>)
| {{UDnote|step=15}}
| | 13/11, 20/17
|-
|-
| | 15
| 16
| | 310.345
| 331.0
|328.97
| [[17/14]], [[40/33]]
|397.24 (18D.3E<sub>16</sub>)
| {{UDnote|step=16}}
| | 6/5
|-
|-
| | 16
| 17
| | 331.035
| 351.7
|350.9
| [[11/9]], [[16/13]]
|423.72 (1A7.B9<sub>16</sub>)
| {{UDnote|step=17}}
| | 17/14
|-
|-
| | 17
| 18
| | 351.72
| 372.4
|372.83
| [[21/17]], [[26/21]]
|450.21 (1C2.35<sub>16</sub>)
| {{UDnote|step=18}}
| | 11/9, 16/13
|-
|-
| | 18
| 19
| | 372.41
| 393.1
|394.76
| [[5/4]]
|476.69 (1DC.B1<sub>16</sub>)
| {{UDnote|step=19}}
| | 21/17
|-
|-
| | 19
| 20
| | 393.1
| 413.8
|416.69
| [[14/11]]
|503.17 (1F7.2C<sub>16</sub>)
| {{UDnote|step=20}}
| | 5/4
|-
|-
| | 20
| 21
| | 413.79
| 434.5
|438.62
| [[9/7]]
|529.655 (211.A7<sub>16</sub>)
| {{UDnote|step=21}}
| | 14/11
|-
|-
| | 21
| 22
| | 434.48
| 455.2
|460.55
| [[13/10]], [[17/13]], [[22/17]]
|556.14 (22C.23<sub>16</sub>)
| {{UDnote|step=22}}
| | 9/7
|-
|-
| | 22
| 23
| | 455.17
| 475.9
|482.48
| [[21/16]]
|582.62 (246.9F<sub>16</sub>)
| {{UDnote|step=23}}
| | 13/10, 17/13, 22/17
|-
|-
| | 23
| 24
| | 475.86
| 496.6
|504.41
| [[4/3]]
|609.1 (261.1A8<sub>16</sub>)
| {{UDnote|step=24}}
| | 21/16
|-
|-
| | 24
| 25
| | 496.55
| 517.2
|526.345
| [[27/20]]
|635.59 (27B.96<sub>16</sub>)
| {{UDnote|step=25}}
| | 4/3
|-
|-
| | 25
| 26
| | 517.24
| 537.9
|548.28
| [[15/11]]
|662.07 (296.12<sub>16</sub>)
| {{UDnote|step=26}}
| | 27/20
|-
|-
| | 26
| 27
| | 537.93
| 558.6
|570.21
| [[11/8]], [[18/13]]
|688.55 (2B0.5D<sub>16</sub>)
| {{UDnote|step=27}}
| | 15/11
|-
|-
| | 27
| 28
| | 558.62
| 579.3
|592.14
| [[7/5]]
|715.035 (2CB.09<sub>16</sub>)
| {{UDnote|step=28}}
| | 11/8, 18/13
|-
|-
| | 28
| 29
| | 579.31
| 600.0
|614.07
| [[17/12]], [[24/17]]
|741.52 (2F5.84<sub>16</sub>)
| {{UDnote|step=29}}
| | 7/5
|-
|-
| | 29
| 30
| | 600
| 620.7
|636
| [[10/7]]
|768 (300<sub>16</sub>)
| {{UDnote|step=30}}
| | 17/12, 24/17
|-
|-
| | 30
| 31
| | 620.69
| 641.4
|657.93
| [[13/9]], [[16/11]]
|794.48 (31A.7C<sub>16</sub>)
| {{UDnote|step=31}}
| | 10/7
|-
|-
| | 31
| 32
| | 641.38
| 662.1
|679.86
| [[22/15]]
|820.97 (334.F7<sub>16</sub>)
| {{UDnote|step=32}}
| | 13/9, 16/11
|-
|-
| | 32
| 33
| | 662.07
| 682.8
|701.79
| [[40/27]]
|847.45 (34F.72<sub>16</sub>)
| {{UDnote|step=33}}
| | 22/15
|-
|-
| | 33
| 34
| | 682.76
| 703.4
|723.72
| [[3/2]]
|873.93 (369.EE<sub>16</sub>)
| {{UDnote|step=34}}
| | 40/27
|-
|-
| | 34
| 35
| | 703.45
| 724.1
|745.655
| [[32/21]]
|900.41 (384.69<sub>16</sub>)
| {{UDnote|step=35}}
| | 3/2
|-
|-
| | 35
| 36
| | 724.14
| 744.8
|767.59
| [[17/11]], [[20/13]], [[26/17]]
|926.9 (39E.E58<sub>16</sub>)
| {{UDnote|step=36}}
| | 32/21
|-
|-
| | 36
| 37
| | 744.83
| 765.5
|789.52
| [[14/9]]
|953.38 (3B9.61<sub>16</sub>)
| {{UDnote|step=37}}
| | 20/13, 26/17, 17/11
|-
|-
| | 37
| 38
| | 765.52
| 786.2
|811.45
| [[11/7]]
|979.86 (3D3.DD<sub>16</sub>)
| {{UDnote|step=38}}
| | 14/9
|-
|-
| | 38
| 39
| | 786.21
| 806.9
|833.38
| [[8/5]]
|1006.345 (3EE.58<sub>16</sub>)
| {{UDnote|step=39}}
| | 11/7
|-
|-
| | 39
| 40
| | 806.9
| 827.6
|855.31
| [[21/13]], [[34/21]]
|1032.83 (408.D3<sub>16</sub>)
| {{UDnote|step=40}}
| | 8/5
|-
|-
| | 40
| 41
| | 827.59
| 848.3
|877.24
| [[13/8]], [[18/11]]
|1059.31 (423.4F<sub>16</sub>)
| {{UDnote|step=41}}
| | 34/21
|-
|-
| | 41
| 42
| | 848.28
| 869.0
|899.17
| [[28/17]], [[33/20]]
|1085.79 (43D.CB<sub>16</sub>)
| {{UDnote|step=42}}
| | 13/8, 18/11
|-
|-
| | 42
| 43
| | 868.97
| 889.7
|921.1
| [[5/3]]
|1112.28 (458.47<sub>16</sub>)
| {{UDnote|step=43}}
| | 28/17
|-
|-
| | 43
| 44
| | 889.655
| 910.3
|943.035
| [[17/10]], [[22/13]]
|1138.76 (472.C2<sub>16</sub>)
| {{UDnote|step=44}}
| | 5/3
|-
|-
| | 44
| 45
| | 910.345
| 931.0
|964.97
| [[12/7]]
|1165.24 (48D.3E<sub>16</sub>)
| {{UDnote|step=45}}
| | 22/13, 17/10
|-
|-
| | 45
| 46
| | 931.035
| 951.7
|986.9
| [[26/15]]
|1191.72 (4A7.B9<sub>16</sub>)
| {{UDnote|step=46}}
| | 12/7
|-
|-
| | 46
| 47
| | 951.72
| 972.4
|1008.83
| [[7/4]]
|1218.21 (4C2.35<sub>16</sub>)
| {{UDnote|step=47}}
| | 26/15
|-
|-
| | 47
| 48
| | 972.41
| 993.1
|1030.76
| [[16/9]], [[30/17]]
|1244.69 (4DC.B1<sub>16</sub>)
| {{UDnote|step=48}}
| | 7/4
|-
|-
| | 48
| 49
| | 993.1
| 1013.8
|1052.69
| [[9/5]]
|1271.17 (4F7.2C<sub>16</sub>)
| {{UDnote|step=49}}
| | 16/9
|-
|-
| | 49
| 50
| | 1013.79
| 1034.5
|1074.62
| [[20/11]]
|1297.655 (511.A7<sub>16</sub>)
| {{UDnote|step=50}}
| | 9/5
|-
|-
| | 50
| 51
| | 1034.48
| 1055.2
|1096.55
| [[11/6]], [[24/13]]
|1324.14 (52C.23<sub>16</sub>)
| {{UDnote|step=51}}
| | 20/11
|-
|-
| | 51
| 52
| | 1055.17
| 1075.9
|1118.48
| [[13/7]], [[28/15]]
|1350.62 (546.9F<sub>16</sub>)
| {{UDnote|step=52}}
| | 11/6, 24/13
|-
|-
| | 52
| 53
| | 1075.86
| 1096.6
|1140.41
| [[15/8]], [[17/9]], [[32/17]]
|1377.1 (561.1A8<sub>16</sub>)
| {{UDnote|step=53}}
| | 13/7, 28/15
|-
|-
| | 53
| 54
| | 1096.55
| 1117.2
|1162.345
| [[21/11]], [[40/21]], ''[[48/25]]''
|1403.59 (57B.96<sub>16</sub>)
| {{UDnote|step=54}}
| | 15/8, 32/17, 17/9
|-
|-
| | 54
| 55
| | 1117.24
| 1137.9
|1184.28
| [[25/13]], [[27/14]], [[52/27]], [[64/33]]
|1430.07 (596.12<sub>16</sub>)
| {{UDnote|step=55}}
| | 40/21, 21/11
|-
|-
| | 55
| 56
| | 1137.93
| 1158.6
|1206.21
| [[35/18]], [[39/20]], [[49/25]], [[88/45]], [[96/49]], [[108/55]]
|1456.55 (5B0.5D<sub>16</sub>)
| {{UDnote|step=56}}
| |48/25, 25/13, 52/27, 27/14, 64/33
|-
|-
| |56
| 57
| | 1158.62
| 1179.3
|1228.14
| [[55/28]], [[63/32]], [[160/81]], [[180/91]], [[208/105]]
|1483.035 (5CB.09<sub>16</sub>)
| {{UDnote|step=57}}
| |35/18, 96/49, 49/25, 108/55
|-
|-
| |57
| 58
| | 1179.31
| 1200.0
|1250.07
| [[2/1]]
|1509.52 (5F5.84<sub>16</sub>)
| {{UDnote|step=58}}
| |55/28, 63/32, 160/81, 125/64
|}
|}
<nowiki/>* As a 17-limit temperament, inconsistently mapped intervals in ''italic''
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] for 58edo uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp6-szg}}
If double arrows are not desirable, then arrows can be attached to quartertone accidentals:
{{Sharpness-sharp6-qt-szg}}
=== Kite's ups and downs notation ===
58edo 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.
{{Ups and downs sharpness}}
Half-sharps and half-flats can be used to avoid triple arrows:
{{Ups and downs sharpness|58|true}}
=== 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 ===
==== Evo flavor ====
{{Sagittal chart|Evo}}
==== Evo-SZ flavor ====
{{Sagittal chart|Evo-SZ}}


==Rank two temperaments==
==== Revo flavor ====
{{Sagittal chart}}


{| class="wikitable"
=== Hemipyth notation ===
{| class="wikitable center-all right-2 center-3 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Hemipyth notation for 58edo (SW3-style)
|-
! #
! Cents
! Note names<br>on D
|-
| 0
| 0.0
| D
|-
| 2
| 41.4
| α𝄳
|-
| 5
| 103.4
| α
|-
| 7
| 144.8
| E𝄳
|-
| 10
| 206.9
| E
|-
| 12
| 248.3
| β𝄳
|-
| 14
| 289.7
| F
|-
| 15
| 310.3
| β
|-
| 17
| 351.7
| F‡
|-
| 19
| 393.1
| γ
|-
| 22
| 455.2
| γ‡
|-
| 24
| 496.6
| G
|-
| 27
| 558.6
| G‡
|-
| 29
| 600.0
| δ
|-
| 31
| 641.4
| A𝄳
|-
| 34
| 703.4
| A
|-
| 36
| 744.8
| ε𝄳
|-
| 39
| 806.9
| ε
|-
| 41
| 848.3
| B𝄳
|-
| 43
| 889.7
| ζ
|-
| 44
| 910.3
| B
|-
| 46
| 951.7
| ζ‡
|-
|-
! | Period
| 48
! | Generator
| 993.1
! | Name
| C
|-
|-
| | 1\1
| 51
| | 1\58
| 1055.2
| |
| C‡
|-
|-
| |
| 53
| | 3\58
| 1096.6
| |
| η
|-
|-
| |
| 56
| | 5\58
| 1158.6
| |
| η‡
|-
|-
| |  
| 58
| | 7\58
| 1200.0
| |
| D
|}
 
== Approximation to JI ==
=== Interval mappings ===
{{15-odd-limit|58}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
| |  
! rowspan="2" | [[Subgroup]]
| | 9\58
! rowspan="2" | [[Comma list]]
| |
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
| |
! [[TE error|Absolute]] (¢)
| | 11\58
! [[TE simple badness|Relative]] (%)
| | Gorgik
|-
|-
| |  
| 2.3.5
| | 13\58
| 2048/2025, [[1594323/1562500]]
| |  
| {{Mapping| 58 92 135 }}
| −1.29
| 1.22
| 5.89
|-
|-
| |  
| 2.3.5.7
| | 15\58
| 126/125, 1728/1715, 2048/2025
| | Myna
| {{Mapping| 58 92 135 163 }}
| −1.29
| 1.05
| 5.10
|-
|-
| |  
| 2.3.5.7.11
| | 17\58
| 126/125, 176/175, 243/242, 896/891
| | Hemififths
| {{Mapping| 58 92 135 163 201 }}
| −1.45
| 1.00
| 4.83
|-
|-
| |  
| 2.3.5.7.11.13
| | 19\58
| 126/125, 144/143, 176/175, 196/195, 364/363
| |  
| {{Mapping| 58 92 135 163 201 215 }}
| −1.56
| 0.94
| 4.56
|-
|-
| |  
| 2.3.5.7.11.13.17
| | 21\58
| 126/125, 136/135, 144/143, 176/175, 196/195, 364/363
| |  
| {{Mapping| 58 92 135 163 201 215 237 }}
| −1.28
| 1.10
| 5.33
|}
* 58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]].
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
| |
! Periods<br>per 8ve
| | 23\58
! Generator*
| | Buzzard
! Cents*
! Associated<br>ratio*
! Temperament
|-
|-
| |
| 1
| | 25\58
| 3\58
| |  
| 62.1
| 28/27
| [[Unicorn]] / alicorn / qilin
|-
|-
| |
| 1
| | 27\58
| 11\58
| | Thuja
| 227.6
| 8/7
| [[Gorgik]]
|-
|-
| | 1\2
| 1
| | 1\58
| 13\58
| |  
| 269.0
| 7/6
| [[Infraorwell]]
|-
|-
| |
| 1
| | 2\58
| 15\58
| |  
| 310.3
| 6/5
| [[Myna]]
|-
|-
| |
| 1
| | 3\58
| 17\58
| |  
| 351.7
| 49/40
| [[Hemififths]]
|-
|-
| |
| 1
| | 4\58
| 19\58
| | Harry
| 393.1
| 64/51
| [[Emmthird]]
|-
|-
| |
| 1
| | 5\58
| 23\58
| | Srutal/Diaschismic
| 475.9
| 21/16
| [[Buzzard]] / [[subfourth]]
|-
|-
| |
| 1
| | 6\58
| 25\58
| |  
| 517.2
| 27/20
| [[Gravity]] / [[abergravity]] / [[gravid]]
|-
|-
| |
| 1
| | 7\58
| 27\58
| |  
| 558.6
| 11/8
| [[Thuja]]
|-
|-
| |
| 2
| | 8\58
| 3\58
| | Echidna, Supers
| 62.1
| 28/27
| [[Monocerus]]
|-
|-
| |
| 2
| | 9\58
| 1\58
| | Secant
| 20.7
| 81/80
| [[Bicommatic]]
|-
|-
| |  
| 2
| | 10\58
| 9\58
| |
| 186.2
| 10/9
| [[Secant]]
|-
|-
| |  
| 2
| | 11\58
| 17\58<br>(12\58)
| |
| 351.7<br>(248.3)
| 11/9<br>(15/13)
| [[Sruti]]
|-
|-
| |
| 2
| | 12\58
| 21\58<br>(8\58)
| | Sruti
| 434.5<br>(165.5)
| 9/7<br>(11/10)
| [[Echidna]]
|-
|-
| |
| 2
| | 13\58
| 24\58<br>(5\58)
| |  
| 496.6<br>(103.4)
| 4/3<br>(17/16)
| [[Diaschismic]]
|-
|-
| |
| 2
| | 14\58
| 25\58<br>(4\58)
| |  
| 517.2<br>(82.8)
| 27/20<br>(21/20)
| [[Harry]]
|-
|-
| | 1\29
| 29
| | 1\58
| 19\58<br>(1\58)
| | Mystery
| 393.1<br>(20.7)
| 5/4<br>(91/90)
| [[Mystery]]
|}
|}
[[Category:58edo]]
<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
[[Category:buzzard]]
 
[[Category:diaschismic]]
58et can also be detempered to [[semihemi]] ({{nowrap| 58 & 140 }}), [[supers]] ({{nowrap| 58 & 152 }}), [[condor]] ({{nowrap| 58 & 159 }}), and [[eagle]] ({{nowrap| 58 & 212 }}).
[[Category:edo]]
 
[[Category:genesis]]
== Octave stretch or compression ==
[[Category:harry]]
58edo's approximations of harmonics 3, 5, 7, 11, and 13 can all be improved if slightly [[stretched and compressed tuning|compressing the octave]] is acceptable, using tunings such as [[92edt]], [[150ed6]] or [[zpi|289zpi]].
[[Category:hemififths]]
 
[[Category:myna]]
== Scales ==
[[Category:mystery]]
* [[Compdye]]
[[Category:partch]]
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]
* [[Hemif7]]
* [[Hemif10]]
* [[Hemif17]]
 
== Instruments ==
* [[Lumatone mapping for 58edo]]
* [[Skip fretting system 58 2 15|15\58 × 2\58 isomorphic instrument layout]]
* [[Skip fretting system 58 4 15|15\58 × 4\58 isomorphic instrument layout]]
* [[Skip fretting system 58 2 17|17\58 × 2\58 isomorphic instrument layout]]
 
== Music ==
; [[Jeff Brown]]
* [https://www.youtube.com/watch?v=0373hBH87LY ''Fruitbats in Formation''] (2023)
 
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/4J4MNno-4PA ''58edo improv''] (2025)
* [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025)
* [https://www.youtube.com/shorts/H5XG4lrvrP8 ''58edo groove''] (2025)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=XXMjoUxVfLs ''We Wish You A Larry Christmas''] (2024) – in larry, 58edo tuning
 
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=Keclakcqie8 ''58EDO, Mystery temperament and 2 rings of Pythagorean on the Lumatone''] (2021)
 
; [[Xotla]]
* [https://www.youtube.com/watch?v=yTkPhjTEQMw "Wormhole Shmurmhole"], from [https://www.youtube.com/playlist?list=PL4HmfPDldHXueRjmTV-iJN3fsLn_O9jvT ''Just Another Microtonal Music Album''] (2025–2026) – in part, the rest being in 31edo
 
[[Category:Buzzard]]
[[Category:Diaschismic]]
[[Category:Harry]]
[[Category:Hemififths]]
[[Category:Myna]]
[[Category:Mystery]]
[[Category:Harry Partch]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/58edo"