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{{Infobox ET}}
{{Infobox ET}}
{{Wikipedia| 53 equal temperament }}
{{Wikipedia| 53 equal temperament }}
{{EDO intro|53}}
{{ED intro}}


== Theory ==
== Theory ==
53edo is notable as an excellent [[5-limit]] system, a fact apparently first noted by {{w|Isaac Newton}}<ref>[https://emusicology.org/index.php/EMR/article/view/7647/6030 Muzzulini, Daniel. 2021. "Isaac Newton's Microtonal Approach to Just Intonation". ''Empirical Musicology Review'' 15 (3-4):223-48. https://doi.org/10.18061/emr.v15i3-4.7647.]</ref>, notably tempering out [[Mercator's comma]] (3<sup>53</sup>/2<sup>84</sup>), the [[schisma|schisma (32805/32768)]], [[15625/15552|kleisma (15625/15552)]], and [[amity comma|amity comma (1600000/1594323)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], [[3125/3087|gariboh comma (3125/3087)]], and [[4375/4374|ragisma (4375/4374)]]. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[Marvel family #Athene|athene]] temperament. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit.  
53edo is notable as an excellent [[5-limit]] system, a fact apparently first noted by {{w|Isaac Newton}}<ref>[https://emusicology.org/index.php/EMR/article/view/7647/6030 Muzzulini, Daniel. 2021. "Isaac Newton's Microtonal Approach to Just Intonation". ''Empirical Musicology Review'' 15 (3–4):223–48. https://doi.org/10.18061/emr.v15i3-4.7647.]</ref>. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. In the opinion of some, 53edo is the first equal division to deal adequately with the [[13-limit]], while others award that distinction to [[41edo]] or [[46edo]]. Like 41 and 46, 53 is distinctly [[consistent]] in the [[9-odd-limit]] (and if we exclude the most damaged interval pair, 7/5 and 10/7, is [[consistent to distance]] 2), but among them, 53 is the first that finds the [[interseptimal interval]]s [[15/13]] and [[13/10]] distinctly from adjacent [[7-limit|septimal]] intervals [[8/7]] and [[7/6]], and [[9/7]] and [[21/16]], respectively, which is essential to its 13-limit credibility. It also avoids equating [[11/9]] with [[16/13]], so that the former is tuned very flat to equate it with a slightly flat [[~]][[39/32]] – a feature shared by 46edo. It is almost consistent to the entire [[15-odd-limit]], with the only inconsistency occurring at [[14/11]] (and its octave complement), which is mapped inconsistently sharp and equated with [[9/7]], but it has the benefit of doing very well in larger prime/subgroup-limited odd-limits. It can be treated as a no-11's, no-17's tuning, on which it is consistent all the way up to the [[27-odd-limit]].
 
As an equal temperament, it notably [[tempering out|tempers out]] [[Mercator's comma]] (3<sup>53</sup>/2<sup>84</sup>), the [[schisma|schisma (32805/32768)]], [[15625/15552|kleisma (15625/15552)]], and [[amity comma|amity comma (1600000/1594323)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]] for which it is a [[Marvel#Tunings|relatively efficient tuning]], [[1728/1715|orwellisma (1728/1715)]], [[3125/3087|gariboh comma (3125/3087)]], and [[4375/4374|ragisma (4375/4374)]]. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[marvel family #Athene|athene]] temperament.  


53edo has also found a certain dissemination as an edo tuning for [[Arabic, Turkish, Persian|Arabic, Turkish, and Persian music]]. It can also be used as an extended [[3-limit|Pythagorean tuning]], since its fifths are almost indistinguishable from just.
53edo has also found a certain dissemination as an edo tuning for [[Arabic, Turkish, Persian|Arabic, Turkish, and Persian music]]. It can also be used as an extended [[3-limit|Pythagorean tuning]], since its fifths are almost indistinguishable from just.
Line 17: Line 19:


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|53|columns=13}}
{{Harmonics in equal|53|columns=9}}
53edo also has reasonably good approximations to a number of higher primes such as 71, 73, 79 and 83. See [[#Approximation to JI]].  
{{Harmonics in equal|53|columns=10|start=10|collapsed=true|title=Approximation of prime harmonics in 53edo (continued)}}
 
See [[#Approximation to JI]] for details and a more in-depth discussion.


=== Subsets and supersets ===
=== Subsets and supersets ===
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{| class="wikitable center-all right-2 left-3 left-5"
{| class="wikitable center-all right-2 left-3 left-5"
|-
|-
! &#35;
! #
! Cents
! Cents
! Approximate Ratios<ref group="note">{{sg|limit=no-17's [[19-limit]]}} ''Italics'' represent inconsistent intervals which are mapped by the 19-limit [[patent val]] to their second-closest (as opposed to closest) approximation in 53edo. </ref>
! Approximate ratios<ref group="note">{{sg|limit=no-17's [[19-limit]]}} ''Italics'' represent inconsistent intervals which are mapped by the 19-limit [[patent val]] to their second-closest (as opposed to closest) approximation in 53edo. </ref>
! colspan="3" | [[Ups and downs notation|Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]] ([[enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^d2)
! colspan="2" | [[Solfege]]s
! colspan="2" | [[Solfege]]s
|-
|-
| 0
| 0
| 0.00
| 0.0
| [[1/1]]
| [[1/1]]
| P1
| P1
Line 44: Line 48:
|-
|-
| 1
| 1
| 22.64
| 22.6
| [[81/80]], [[64/63]], [[50/49]]
| ''[[50/49]]'', [[64/63]], [[81/80]]
| ^1
| ^1
| up unison
| up unison
Line 53: Line 57:
|-
|-
| 2
| 2
| 45.28
| 45.3
| [[49/48]], [[36/35]], [[33/32]], [[128/125]]
| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| ^^1, vvm2
| ^^1, vvm2
| dup unison, dudminor 2nd
| dup unison, dudminor 2nd
Line 62: Line 66:
|-
|-
| 3
| 3
| 67.92
| 67.9
| [[25/24]], [[28/27]], [[22/21]], [[27/26]], [[26/25]]
| ''[[22/21]]'', [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| vvA1, vm2
| vvA1, vm2
| dudaug 1sn, downminor 2nd
| dudaug 1sn, downminor 2nd
Line 71: Line 75:
|-
|-
| 4
| 4
| 90.57
| 90.6
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| vA1, m2
| vA1, m2
Line 80: Line 84:
|-
|-
| 5
| 5
| 113.21
| 113.2
| [[16/15]], [[15/14]]
| [[15/14]], [[16/15]]
| A1, ^m2
| A1, ^m2
| aug 1sn, upminor 2nd
| aug 1sn, upminor 2nd
Line 89: Line 93:
|-
|-
| 6
| 6
| 135.85
| 135.8
| [[14/13]], [[13/12]], [[27/25]]
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
Line 98: Line 102:
|-
|-
| 7
| 7
| 158.49
| 158.5
| [[35/32]], [[12/11]], [[11/10]], [[57/52]], [[800/729]]
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
Line 107: Line 111:
|-
|-
| 8
| 8
| 181.13
| 181.1
| [[10/9]]
| [[10/9]]
| vM2
| vM2
Line 116: Line 120:
|-
|-
| 9
| 9
| 203.77
| 203.8
| [[9/8]]
| [[9/8]]
| M2
| M2
Line 125: Line 129:
|-
|-
| 10
| 10
| 226.42
| 226.4
| [[8/7]], [[256/225]]
| [[8/7]], [[256/225]]
| ^M2
| ^M2
Line 134: Line 138:
|-
|-
| 11
| 11
| 249.06
| 249.1
| [[15/13]], [[144/125]], [[125/108]]
| [[15/13]], [[22/19]], [[125/108]], [[144/125]]
| ^^M2, vvm3
| ^^M2, vvm3
| dupmajor 2nd, dudminor 3rd
| dupmajor 2nd, dudminor 3rd
Line 143: Line 147:
|-
|-
| 12
| 12
| 271.70
| 271.7
| [[7/6]], [[75/64]]
| [[7/6]], [[75/64]]
| vm3
| vm3
Line 152: Line 156:
|-
|-
| 13
| 13
| 294.34
| 294.3
| [[13/11]], [[19/16]], [[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
| m3
| m3
Line 161: Line 165:
|-
|-
| 14
| 14
| 316.98
| 317.0
| [[6/5]]
| [[6/5]]
| ^m3
| ^m3
Line 170: Line 174:
|-
|-
| 15
| 15
| 339.62
| 339.6
| [[11/9]], [[243/200]]
| [[11/9]], [[243/200]]
| ^^m3
| ^^m3
Line 179: Line 183:
|-
|-
| 16
| 16
| 362.26
| 362.3
| [[16/13]], [[100/81]]
| [[16/13]], [[100/81]]
| vvM3
| vvM3
Line 188: Line 192:
|-
|-
| 17
| 17
| 384.91
| 384.9
| [[5/4]]
| [[5/4]]
| vM3
| vM3
Line 197: Line 201:
|-
|-
| 18
| 18
| 407.55
| 407.5
| [[19/15]], [[24/19]], [[81/64]]
| [[19/15]], [[24/19]], [[81/64]]
| M3
| M3
Line 206: Line 210:
|-
|-
| 19
| 19
| 430.19
| 430.2
| [[9/7]], ''[[14/11]]''
| [[9/7]], ''[[14/11]]''
| ^M3
| ^M3
Line 215: Line 219:
|-
|-
| 20
| 20
| 452.83
| 452.8
| [[13/10]], [[125/96]], [[162/125]]
| [[13/10]], [[125/96]], [[162/125]]
| ^^M3, vv4
| ^^M3, vv4
Line 224: Line 228:
|-
|-
| 21
| 21
| 475.47
| 475.5
| [[21/16]], [[25/19]], [[675/512]], [[320/243]]
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| v4
| v4
| down 4th
| down 4th
Line 233: Line 237:
|-
|-
| 22
| 22
| 498.11
| 498.1
| [[4/3]]
| [[4/3]]
| P4
| P4
Line 242: Line 246:
|-
|-
| 23
| 23
| 520.75
| 520.8
| [[27/20]]
| [[19/14]], [[27/20]]
| ^4
| ^4
| up 4th
| up 4th
Line 251: Line 255:
|-
|-
| 24
| 24
| 543.40
| 543.4
| [[11/8]], [[15/11]], [[26/19]]
| [[11/8]], [[15/11]], [[26/19]]
| ^^4
| ^^4
Line 260: Line 264:
|-
|-
| 25
| 25
| 566.04
| 566.0
| [[18/13]]
| [[18/13]]
| vvA4, vd5
| vvA4, vd5
Line 269: Line 273:
|-
|-
| 26
| 26
| 588.68
| 588.7
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
| vA4, d5
| vA4, d5
Line 278: Line 282:
|-
|-
| 27
| 27
| 611.32
| 611.3
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| A4, ^d5
| A4, ^d5
Line 287: Line 291:
|-
|-
| 28
| 28
| 633.96
| 634.0
| [[13/9]]
| [[13/9]]
| ^A4, ^^d5
| ^A4, ^^d5
Line 296: Line 300:
|-
|-
| 29
| 29
| 656.60
| 656.6
| [[16/11]], [[19/13]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]]
| vv5
| vv5
Line 305: Line 309:
|-
|-
| 30
| 30
| 679.25
| 679.2
| [[40/27]]
| [[28/19]], [[40/27]]
| v5
| v5
| down 5th
| down 5th
Line 314: Line 318:
|-
|-
| 31
| 31
| 701.89
| 701.9
| [[3/2]]
| [[3/2]]
| P5
| P5
Line 323: Line 327:
|-
|-
| 32
| 32
| 724.53
| 724.5
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| ^5
| ^5
Line 332: Line 336:
|-
|-
| 33
| 33
| 747.17
| 747.2
| [[20/13]], [[192/125]], [[125/81]]
| [[20/13]], [[125/81]], [[192/125]]
| ^^5, vvm6
| ^^5, vvm6
| dup 5th, dudminor 6th
| dup 5th, dudminor 6th
Line 341: Line 345:
|-
|-
| 34
| 34
| 769.81
| 769.8
| [[14/9]], [[25/16]], ''[[11/7]]''
| ''[[11/7]]'', [[14/9]], [[25/16]]
| vm6
| vm6
| downminor 6th
| downminor 6th
Line 350: Line 354:
|-
|-
| 35
| 35
| 792.45
| 792.5
| [[19/12]], [[30/19]], [[128/81]]
| [[19/12]], [[30/19]], [[128/81]]
| m6
| m6
Line 359: Line 363:
|-
|-
| 36
| 36
| 815.09
| 815.1
| [[8/5]]
| [[8/5]]
| ^m6
| ^m6
Line 368: Line 372:
|-
|-
| 37
| 37
| 837.74
| 837.7
| [[13/8]], [[81/50]]
| [[13/8]], [[81/50]]
| ^^m6
| ^^m6
Line 377: Line 381:
|-
|-
| 38
| 38
| 860.38
| 860.4
| [[18/11]], [[400/243]]
| [[18/11]], [[400/243]]
| vvM6
| vvM6
Line 386: Line 390:
|-
|-
| 39
| 39
| 883.02
| 883.0
| [[5/3]]
| [[5/3]]
| vM6
| vM6
Line 395: Line 399:
|-
|-
| 40
| 40
| 905.66
| 905.7
| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
| M6
| M6
Line 404: Line 408:
|-
|-
| 41
| 41
| 928.30
| 928.3
| [[12/7]]
| [[12/7]]
| ^M6
| ^M6
Line 413: Line 417:
|-
|-
| 42
| 42
| 950.94
| 950.9
| [[26/15]], [[125/72]], [[216/125]]
| [[19/11]], [[26/15]], [[125/72]], [[216/125]]
| ^^M6, vvm7
| ^^M6, vvm7
| dupmajor 6th, dudminor 7th
| dupmajor 6th, dudminor 7th
Line 422: Line 426:
|-
|-
| 43
| 43
| 973.58
| 973.6
| [[7/4]]
| [[7/4]]
| vm7
| vm7
Line 431: Line 435:
|-
|-
| 44
| 44
| 996.23
| 996.2
| [[16/9]]
| [[16/9]]
| m7
| m7
Line 440: Line 444:
|-
|-
| 45
| 45
| 1018.87
| 1018.9
| [[9/5]]
| [[9/5]]
| ^m7
| ^m7
Line 449: Line 453:
|-
|-
| 46
| 46
| 1041.51
| 1041.5
| [[64/35]], [[11/6]], [[20/11]], [[729/400]]
| [[11/6]], [[20/11]], [[64/35]], [[729/400]]
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
Line 458: Line 462:
|-
|-
| 47
| 47
| 1064.15
| 1064.2
| [[13/7]], [[24/13]], [[50/27]]
| [[13/7]], [[24/13]], [[50/27]]
| vvM7
| vvM7
Line 467: Line 471:
|-
|-
| 48
| 48
| 1086.79
| 1086.8
| [[15/8]]
| [[15/8]]
| vM7
| vM7
Line 476: Line 480:
|-
|-
| 49
| 49
| 1109.43
| 1109.4
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| M7
| M7
Line 485: Line 489:
|-
|-
| 50
| 50
| 1132.08
| 1132.1
| [[48/25]], [[27/14]], [[21/11]], [[52/27]], [[25/13]]
| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]]
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
Line 494: Line 498:
|-
|-
| 51
| 51
| 1154.72
| 1154.7
| [[96/49]], [[35/18]], [[64/33]], [[125/64]]
| [[35/18]], [[64/33]], [[96/49]], [[125/64]]
| ^^M7, vv8
| ^^M7, vv8
| dupmajor 7th, dud 8ve
| dupmajor 7th, dud 8ve
Line 503: Line 507:
|-
|-
| 52
| 52
| 1177.36
| 1177.4
| [[160/81]], [[63/32]], [[49/25]]
| ''[[49/25]]'', [[63/32]], [[160/81]]
| v8
| v8
| down 8ve
| down 8ve
Line 512: Line 516:
|-
|-
| 53
| 53
| 1200.00
| 1200.0
| [[2/1]]
| [[2/1]]
| P8
| P8
Line 528: Line 532:
! Quality
! Quality
! [[Kite's color notation|Color]]
! [[Kite's color notation|Color]]
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
| downminor
| downminor
| zo
| zo
| (a, b, 0, 1)
| {{nowrap|(a, b, 0, 1)}}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| minor
| minor
| fourthward wa
| fourthward wa
| (a, b) with b &lt; -1
| {{nowrap|(a, b)}} with {{nowrap|b &lt; −1}}
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| upminor
| upminor
| gu
| gu
| (a, b, -1)
| {{nowrap|(a, b, −1)}}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| dupminor
| dupminor
| ilo
| ilo
| (a, b, 0, 0, 1)
| {{nowrap|(a, b, 0, 0, 1)}}
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| dudmajor
| dudmajor
| lu
| lu
| (a, b, 0, 0, -1)
| {{nowrap|(a, b, 0, 0, −1)}}
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| downmajor
| downmajor
| yo
| yo
| (a, b, 1)
| {{nowrap|(a, b, 1)}}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| major
| major
| fifthward wa
| fifthward wa
| (a, b) with b &gt; 1
| {{nowrap|(a, b)}} with {{nowrap|b &gt; 1}}
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| (a, b, 0, -1)
| {{nowrap|(a, b, 0, −1)}}
| 9/7, 12/7
| 9/7, 12/7
|}
|}
All 53edo 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.
All 53edo 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 {{nowrap|{{dash|6, 1, 3, 5, 7, 9, 11, 13}}}}). Alterations are always enclosed in parentheses, additions never are.


Here are the zo, gu, ilo, lu, yo and ru triads:
Here are the zo, gu, ilo, lu, yo and ru triads:
Line 577: Line 581:
|-
|-
! [[Kite's color notation|Color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI Chord
! JI chord
! Notes as Edosteps
! Notes as edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo
| zo
| 6:7:9
| 6:7:9
| 0-12-31
| 0–12–31
| C vEb G
| C vEb G
| Cvm
| Cvm
Line 592: Line 596:
| gu
| gu
| 10:12:15
| 10:12:15
| 0-14-31
| 0–14–31
| C ^Eb G
| C ^Eb G
| C^m
| C^m
Line 599: Line 603:
| ilo
| ilo
| 18:22:27
| 18:22:27
| 0-15-31
| 0–15–31
| C ^^Eb G
| C ^^Eb G
| C^^m
| C^^m
Line 606: Line 610:
| lu
| lu
| 22:27:33
| 22:27:33
| 0-16-31
| 0–16–31
| C vvE G
| C vvE G
| Cvv
| Cvv
Line 613: Line 617:
| yo
| yo
| 4:5:6
| 4:5:6
| 0-17-31
| 0–17–31
| C vE G
| C vE G
| Cv
| Cv
Line 620: Line 624:
| ru
| ru
| 14:18:21
| 14:18:21
| 0-19-31
| 0–19–31
| C ^E G
| C ^E G
| C^
| C^
| C upmajor or C up
| C upmajor or C up
|}
|}
For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
Using [[Helmholtz-Ellis notation|Helmholtz&ndash;Ellis]] accidentals, 53edo can be notated using [[ups and downs notation]]:
53edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
{{Sharpness-sharp5a}}
Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp5}}
{{Sharpness-sharp5}}
Here, a sharp raises by five steps (commas), and a flat lowers by five steps, so single and double arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with triple arrows.


=== Sagittal ===
=== Sagittal notation ===
The following table shows [[sagittal notation]] accidentals in one apotome for 53edo.  
==== Evo flavor ====
<imagemap>
File:53-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 567 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 270 106 [[6561/6400]]
rect 270 80 370 106 [[40/39]]
default [[File:53-EDO_Evo_Sagittal.svg]]
</imagemap>


{| class="wikitable center-all"
==== Revo flavor ====
! Steps
<imagemap>
| 0
File:53-EDO_Revo_Sagittal.svg
| 1
desc none
| 2
rect 80 0 300 50 [[Sagittal_notation]]
| 3
rect 300 0 543 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
| 4
rect 20 80 120 106 [[81/80]]
| 5
rect 120 80 270 106 [[6561/6400]]
|-
rect 270 80 370 106 [[40/39]]
! Symbol
default [[File:53-EDO_Revo_Sagittal.svg]]
| [[File:Sagittal natural.png]]
</imagemap>
| [[File:Sagittal pai.png]]
 
| [[File:Sagittal phai.png]]
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.
| [[File:Sagittal sharp phao.png]]
| [[File:Sagittal sharp pao.png]]
| [[File:Sagittal sharp.png]]
|}


== Relationship to 12edo ==
== Relationship to 12edo ==
Whereas 12edo has a circle of twelve 5ths, 53edo has a spiral of twelve 5ths (since 31\53 is on the 7\12 kite in the scale tree). This shows 53edo in a 12edo-friendly format. Excellent for introducing 53edo to musicians unfamiliar with microtonal music. The two innermost and two outermost intervals on the spiral are duplicates.
53edo's [[circle of fifths|circle of 53 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This makes sense to do because going up by 12 fifths results in the Pythagorean comma (by definition), which is mapped to one edostep and is thus also the syntonic and septimal comma, introducing a simple second accidental in the form of the arrow to reach useful intervals from the basic 12-chromatic scale. The one-edostep comma is a requirement in Kite's theory, and implies that 31\53 is on the 7\12 kite in the [[scale tree]].  
 
This "spiral of fifths" can be a useful construct for introducing 53edo to musicians unfamiliar with microtonal music. It may help composers and musicians to make visual sense of the notation, and to understand what size of a jump is likely to land them where compared to 12edo.
 
The two innermost and two outermost intervals on the spiral are duplicates, reflecting the fact that it is a repeating circle at heart and the spiral shape is only a helpful illusion.


[[File:53-edo spiral.png|588x588px]]
[[File:53-edo spiral.png|588x588px]]


== Approximation to JI ==
== Approximation to JI ==
[[File:53ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 7-limit intervals approximated in 53edo]]
53edo provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy–Zarlino "just major" scale.
 
53edo provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 707: Line 720:


=== Higher-limit JI ===
=== Higher-limit JI ===
There is also a cluster of usable higher primes starting at 71; even 89 (4.84{{cent}} flat), 97 (4.63{{cent}} sharp) and 101 (2.6{{cent}} sharp) are usable if placed in just the right context.
53edo has only 5 pairs of inconsistent intervals in the full 27-odd-limit: {11/7,&nbsp;14/11}, {[[17/11]],&nbsp;[[22/17]]}, {[[19/17]],&nbsp;[[34/19]]}, {[[21/11]],&nbsp;[[22/21]]}, and {[[23/22]],&nbsp;[[44/23]]}. This is perhaps remarkable compared to 9 pairs in 46edo and 11 pairs in 41edo, because the smallest edo after 53edo to get 5 or less inconsistencies in the 27-odd-limit is [[99edo]] (using the 99[[wart|ef]] [[val]]), followed by [[111edo]] ([[patent val]]), [[130edo]] (patent val) and [[159edo]] (also patent); all of these get 5 inconsistencies as well except 159edo which gets 1 and which is itself a superset of 53edo. However, most interpret the approximation of prime 17 in 53edo as too off for all but the most opportunistic harmonies, and some question the 23 and possibly also 11, so the practical significance of this is debatable.
{{Harmonics in equal|53|columns=4|start=20}}
 
As shown below, there is also a cluster of usable higher primes starting at 71; even 89 (4.84{{c}} flat), 97 (4.63{{c}} sharp) and 101 (2.6{{c}} sharp) are usable if placed in just the right context. (Note that prime 67 is almost perfectly off.)
{{Harmonics in equal|53|columns=4|start=20|title=Approximation of large prime harmonics in 53edo}}


This make 53edo excellent (for its size) in the 2.3.5.7.11.13.19.23.37.41.71.73.79.83 subgroup, although some higher error primes like 11 and 23 require the right context to be convincing.
This makes 53edo excellent (for its size) in the 2.3.5.7.11.13.19.23.37.41.71.73(.79.83.101) subgroup, although some higher error primes like 11 and 23 require the right context to be convincing.


Note that the high primes, in [[rooted]] (/2<sup>''n''</sup>) position, essentially act as alternate interpretations of [[LCJI]] intervals, if you want to force a rooted interpretation; namely: [[71/64]] as ~[[10/9]], [[73/64]] as ~[[8/7]], [[79/64]] as ~[[16/13]], and perhaps most questionably in the context of 53edo, [[83/64]] as ~[[13/10]].
Note that the high primes, in [[rooted]] (/2<sup>''n''</sup>) position, essentially act as alternate interpretations of [[LCJI]] intervals, if you want to force a rooted interpretation; namely: [[71/64]] as ~[[10/9]], [[73/64]] as ~[[8/7]], [[79/64]] as ~[[16/13]], and perhaps most questionably in the context of 53edo, [[83/64]] as ~[[13/10]].
Line 716: Line 731:
== 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" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[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 726: Line 742:
|-
|-
| 2.3
| 2.3
| {{monzo| -84 53 }}
| {{Monzo| -84 53 }}
| {{mapping| 53 84 }}
| {{Mapping| 53 84 }}
| +0.022
| +0.022
| 0.022
| 0.022
Line 734: Line 750:
| 2.3.5
| 2.3.5
| 15625/15552, 32805/32768
| 15625/15552, 32805/32768
| {{mapping| 53 84 123 }}
| {{Mapping| 53 84 123 }}
| +0.216
| +0.216
| 0.276
| 0.276
Line 741: Line 757:
| 2.3.5.7
| 2.3.5.7
| 225/224, 1728/1715, 3125/3087
| 225/224, 1728/1715, 3125/3087
| {{mapping| 53 84 123 149 }}
| {{Mapping| 53 84 123 149 }}
| &minus;0.262
| −0.262
| 0.861
| 0.861
| 3.81
| 3.81
Line 748: Line 764:
| 2.3.5.7.11
| 2.3.5.7.11
| 99/98, 121/120, 176/175, 2200/2187
| 99/98, 121/120, 176/175, 2200/2187
| {{mapping| 53 84 123 149 183 }}
| {{Mapping| 53 84 123 149 183 }}
| +0.248
| +0.248
| 1.279
| 1.279
Line 755: Line 771:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 99/98, 121/120, 169/168, 176/175, 275/273
| 99/98, 121/120, 169/168, 176/175, 275/273
| {{mapping| 53 84 123 149 183 196 }}
| {{Mapping| 53 84 123 149 183 196 }}
| +0.332
| +0.332
| 1.183
| 1.183
Line 762: Line 778:
| 2.3.5.7.11.13.19
| 2.3.5.7.11.13.19
| 99/98, 121/120, 169/168, 176/175, 209/208, 275/273
| 99/98, 121/120, 169/168, 176/175, 209/208, 275/273
| {{mapping| 53 84 123 149 183 196 225 }}
| {{Mapping| 53 84 123 149 183 196 225 }}
| +0.391
| +0.391
| 1.105
| 1.105
Line 774: Line 790:
{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
Line 783: Line 799:
| 3
| 3
| <abbr title="19383245667680019896796723/19342813113834066795298816">(52 digits)</abbr>
| <abbr title="19383245667680019896796723/19342813113834066795298816">(52 digits)</abbr>
| {{monzo| -84 53 }}
| {{Monzo| -84 53 }}
| 3.62
| 3.62
| Tribilawa
| Tribilawa
Line 790: Line 806:
| 5
| 5
| [[2109375/2097152|(14 digits)]]
| [[2109375/2097152|(14 digits)]]
| {{monzo| -21 3 7 }}
| {{Monzo| -21 3 7 }}
| 10.06
| 10.06
| Lasepyo
| Lasepyo
Line 797: Line 813:
| 5
| 5
| [[15625/15552]]
| [[15625/15552]]
| {{monzo| -6 -5 6 }}
| {{Monzo| -6 -5 6 }}
| 8.11
| 8.11
| Tribiyo
| Tribiyo
Line 804: Line 820:
| 5
| 5
| <abbr title="1600000/1594323">(14 digits)</abbr>
| <abbr title="1600000/1594323">(14 digits)</abbr>
| {{monzo| 9 -13 5 }}
| {{Monzo| 9 -13 5 }}
| 6.15
| 6.15
| Saquinyo
| Saquinyo
Line 811: Line 827:
| 5
| 5
| <abbr title="10485760000/10460353203">(22 digits)</abbr>
| <abbr title="10485760000/10460353203">(22 digits)</abbr>
| {{monzo| 24 -21 4 }}
| {{Monzo| 24 -21 4 }}
| 4.20
| 4.20
| Sasaquadyo
| Sasaquadyo
Line 818: Line 834:
| 5
| 5
| [[32805/32768]]
| [[32805/32768]]
| {{monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
| 1.95
| 1.95
| Layo
| Layo
Line 825: Line 841:
| 7
| 7
| [[3125/3087]]
| [[3125/3087]]
| {{monzo| 0 -2 5 -3 }}
| {{Monzo| 0 -2 5 -3 }}
| 21.18
| 21.18
| Triru-aquinyo
| Triru-aquinyo
Line 832: Line 848:
| 7
| 7
| [[1728/1715]]
| [[1728/1715]]
| {{monzo| 6 3 -1 -3 }}
| {{Monzo| 6 3 -1 -3 }}
| 13.07
| 13.07
| Triru-agu
| Triru-agu
Line 839: Line 855:
| 7
| 7
| [[225/224]]
| [[225/224]]
| {{monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| 7.71
| 7.71
| Ruyoyo
| Ruyoyo
Line 846: Line 862:
| 7
| 7
| [[4375/4374]]
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| {{Monzo| -1 -7 4 1 }}
| 0.40
| 0.40
| Zoquadyo
| Zoquadyo
Line 853: Line 869:
| 11
| 11
| [[99/98]]
| [[99/98]]
| {{monzo| -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| 17.58
| 17.58
| Loruru
| Loruru
Line 860: Line 876:
| 11
| 11
| [[121/120]]
| [[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
| {{Monzo| -3 -1 -1 0 2 }}
| 14.37
| 14.37
| Lologu
| Lologu
Line 867: Line 883:
| 11
| 11
| [[176/175]]
| [[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
| {{Monzo| 4 0 -2 -1 1 }}
| 9.86
| 9.86
| Lorugugu
| Lorugugu
Line 874: Line 890:
| 11
| 11
| <abbr title="94489280512/94143178827">(22 digits)</abbr>
| <abbr title="94489280512/94143178827">(22 digits)</abbr>
| {{monzo| 33 -23 0 0 1 }}
| {{Monzo| 33 -23 0 0 1 }}
| 6.35
| 6.35
| Trisalo
| Trisalo
Line 881: Line 897:
| 11
| 11
| [[385/384]]
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| 4.50
| 4.50
| Lozoyo
| Lozoyo
Line 888: Line 904:
| 11
| 11
| [[540/539]]
| [[540/539]]
| {{monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
| 3.21
| 3.21
| Lururuyo
| Lururuyo
Line 895: Line 911:
| 13
| 13
| [[275/273]]
| [[275/273]]
| {{monzo| 0 -1 2 -1 1 -1 }}
| {{Monzo| 0 -1 2 -1 1 -1 }}
| 12.64
| 12.64
| Thuloruyoyo
| Thuloruyoyo
Line 902: Line 918:
| 13
| 13
| [[169/168]]
| [[169/168]]
| {{monzo| -3 -1 0 -1 0 2 }}
| {{Monzo| -3 -1 0 -1 0 2 }}
| 10.27
| 10.27
| Thothoru
| Thothoru
Line 909: Line 925:
| 13
| 13
| [[625/624]]
| [[625/624]]
| {{monzo| -4 -1 4 0 0 -1 }}
| {{Monzo| -4 -1 4 0 0 -1 }}
| 2.77
| 2.77
| Thuquadyo
| Thuquadyo
Line 916: Line 932:
| 13
| 13
| [[676/675]]
| [[676/675]]
| {{monzo| 2 -3 -2 0 0 2 }}
| {{Monzo| 2 -3 -2 0 0 2 }}
| 2.56
| 2.56
| Bithogu
| Bithogu
Line 923: Line 939:
| 13
| 13
| [[1001/1000]]
| [[1001/1000]]
| {{monzo| -3 0 -3 1 1 1 }}
| {{Monzo| -3 0 -3 1 1 1 }}
| 1.73
| 1.73
| Tholozotrigu
| Tholozotrigu
Line 930: Line 946:
| 13
| 13
| [[2080/2079]]
| [[2080/2079]]
| {{monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| 0.83
| 0.83
| Tholuruyo
| Tholuruyo
Line 937: Line 953:
| 13
| 13
| [[4096/4095]]
| [[4096/4095]]
| {{monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| 0.42
| 0.42
| Sathurugu
| Sathurugu
Line 945: Line 961:
=== Linear temperaments ===
=== Linear temperaments ===
* [[List of edo-distinct 53et rank two temperaments]]
* [[List of edo-distinct 53et rank two temperaments]]
* [[Schismic-Mercator equivalence continuum]]
* [[Schismic–Mercator equivalence continuum]]


{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+ Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator
! Generator*
! Cents
! Cents*
! Associated<br>Ratio
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
| 1
| 1
| 2\53
| 2\53
| 45.28
| 45.3
| 36/35
| 36/35
| [[Quartonic]]
| [[Quartonic]]
Line 964: Line 980:
| 1
| 1
| 5\53
| 5\53
| 113.21
| 113.2
| 16/15
| 16/15
| [[Misneb]]
| [[Misneb]]
|-
| 1
| 6\53
| 135.8
| [[13/12]]~[[14/13]]
| [[Doublethink]]
|-
|-
| 1
| 1
| 7\53
| 7\53
| 158.49
| 158.5
| 11/10
| 11/10
| [[Hemikleismic]]
| [[Hemikleismic]]
Line 976: Line 998:
| 1
| 1
| 9\53
| 9\53
| 203.77
| 203.8
| 9/8
| 9/8
| [[Baldy]]
| [[Baldy]]
Line 982: Line 1,004:
| 1
| 1
| 10\53
| 10\53
| 226.42
| 226.4
| 8/7
| 8/7
| [[Semaja]]
| [[Semaja]]
Line 988: Line 1,010:
| 1
| 1
| 11\53
| 11\53
| 249.06
| 249.1
| 15/13
| 15/13
| [[Hemischis]] / [[hemigari]]
| [[Hemischis]] / [[hemigari]]
Line 994: Line 1,016:
| 1
| 1
| 12\53
| 12\53
| 271.70
| 271.7
| 7/6
| 7/6
| [[Orwell]]
| [[Orwell]]
Line 1,000: Line 1,022:
| 1
| 1
| 13\53
| 13\53
| 294.34
| 294.3
| 25/21
| 25/21
| [[Kleiboh]]
| [[Kleiboh]]
Line 1,006: Line 1,028:
| 1
| 1
| 14\53
| 14\53
| 316.98
| 317.0
| 6/5
| 6/5
| [[Hanson]] / [[catakleismic]] / [[countercata]]
| [[Hanson]] / [[catakleismic]] / [[countercata]]
Line 1,012: Line 1,034:
| 1
| 1
| 15\53
| 15\53
| 339.62
| 339.6
| 11/9
| 11/9
| [[Amity]] / [[houborizic]]
| [[Amity]] / [[houborizic]]
Line 1,018: Line 1,040:
| 1
| 1
| 16\53
| 16\53
| 362.26
| 362.3
| 16/13
| 16/13
| [[Submajor]]
| [[Submajor]]
Line 1,024: Line 1,046:
| 1
| 1
| 18\53
| 18\53
| 407.55
| 407.5
| 1225/972
| 1225/972
| [[Ditonic]] / [[coditone]]
| [[Ditonic]] / [[coditone]]
Line 1,030: Line 1,052:
| 1
| 1
| 19\53
| 19\53
| 430.19
| 430.2
| 9/7
| 9/7
| [[Hamity]]
| [[Hamity]]
|-
| 1
| 20\53
| 452.8
| 13/10
| [[Maja]]
|-
|-
| 1
| 1
| 21\53
| 21\53
| 475.47
| 475.5
| 21/16
| 21/16
| [[Vulture]] / [[buzzard]]
| [[Vulture]] / [[buzzard]]
Line 1,042: Line 1,070:
| 1
| 1
| 22\53
| 22\53
| 498.11
| 498.1
| 4/3
| 4/3
| [[Garibaldi]] / [[pontiac]]
| [[Garibaldi]] / [[pontiac]]
Line 1,048: Line 1,076:
| 1
| 1
| 23\53
| 23\53
| 520.75
| 520.8
| 4/3
| 4/3
| [[Mavila]] (53bbcc)
| [[Mavila]] (53bbcc)
Line 1,054: Line 1,082:
| 1
| 1
| 25\53
| 25\53
| 566.04
| 566.0
| 18/13
| 18/13
| [[Tricot]]
| [[Alphatrimot]]
|-
|-
| 1
| 1
| 26\53
| 26\53
| 588.68
| 588.7
| 45/32
| 45/32
| [[Untriton]] / [[aufo]]
| [[Untriton]] / [[aufo]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave


== Scales ==
== Scales ==
 
=== Mos scales ===
=== MOS scales ===
While there is only one possible generator for the [[5L 2s|diatonic]] [[mos scale]] supported by this edo, there are a greater number of generators for other mosses such as the [[2L 5s|antidiatonic]] scale.
While there is only one possible generator for the [[5L 2s|diatonic]] [[mos scale]] supported by this edo, there are a greater number of generators for other mosses such as the [[2L 5s|antidiatonic]] scale.
* [[List of MOS scales in 53edo]]
* [[List of MOS scales in 53edo]]
Line 1,074: Line 1,102:
=== Scales approximated from JI ===
=== Scales approximated from JI ===
* The [[eagle 53]] scale described by [[John O'Sullivan]]
* The [[eagle 53]] scale described by [[John O'Sullivan]]
* Ptolmey&mdash;Zarlino justly-intonated major: 9 8 5 9 8 9 5
* Ptolmey–Zarlino justly-intonated major: 9 8 5 9 8 9 5
* Ptolmey&mdash;Zarlino justly-intonated minor: 9 5 8 9 5 9 8
* Ptolmey–Zarlino justly-intonated minor: 9 5 8 9 5 9 8
 
; From [[AFDO]]s
{{Idiosyncratic terms}}
* Composite Cliffedge (approximated from [[60afdo]]): 12 10 9 19 3
* Composite Cliffedge (approximated from [[60afdo]]): 12 10 9 19 3
* Composite Deja Vu (approximated from [[101afdo]]): 14 17 5 9 8
* Composite Deja Vu (approximated from [[101afdo]]): 14 17 5 9 8
Line 1,092: Line 1,123:


=== Other scales ===
=== Other scales ===
* [[Sequar5m]]: 6 3 6 2 3 6 2 3 6 3 2 6 3 2
* [[cthon5m]]: 6 3 6 2 3 6 2 3 6 3 2 6 3 2
* Palace (approximated from [[Porky]] in [[29edo]]): 7 7 8 9 7 7 8
* Palace{{idio}} (approximated from [[Porky]] in [[29edo]]): 7 7 8 9 7 7 8
 
== Instruments ==
* [[Lumatone mapping for 53edo]]
* [[Skip fretting system 53 3 14]]
* [[Skip fretting system 53 3 17]]


== Music ==
== Music ==
Line 1,103: Line 1,139:
* ''Prelude and Fugue in C Major, No. 1'', BWV 846, from ''The Well-Tempered Clavier'', Book I (1722) – rendered by [[Mykhaylo Khramov]]
* ''Prelude and Fugue in C Major, No. 1'', BWV 846, from ''The Well-Tempered Clavier'', Book I (1722) – rendered by [[Mykhaylo Khramov]]
** [https://web.archive.org/web/20201127013408/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Prelude] · [https://web.archive.org/web/20201127012701/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Fugue]
** [https://web.archive.org/web/20201127013408/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Prelude] · [https://web.archive.org/web/20201127012701/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Fugue]
* [https://www.youtube.com/watch?v=WyLDjrLa94Y "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=GK9YwSphw5Y "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2025)
* [https://www.youtube.com/watch?v=daWx5-iegW0 "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – with syntonic-comma adjustment, rendered by Claudi Meneghin (2025)
* [https://www.youtube.com/watch?v=dZyrIOMEmzo "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=dZyrIOMEmzo "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=vcinR7nUthA "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=vcinR7nUthA "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
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=== 21st century ===
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/r-Tzq33OGM4 ''microtonal improvisation in 53edo''] (2025)
; [[Francium]]
; [[Francium]]
* [https://www.youtube.com/watch?v=GLQ1gD4bshY ''Space Race''] (2022)
* [https://www.youtube.com/watch?v=GLQ1gD4bshY ''Space Race''] (2022)
* "strange worlds" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/6mjYGHlW7lSoez8NsDz021 Spotify] | [https://francium223.bandcamp.com/track/strange-worlds Bandcamp] | [https://www.youtube.com/watch?v=tPwRWVjeKA8 YouTube] – Hanson[11] in 53edo
* "strange worlds" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/6mjYGHlW7lSoez8NsDz021 Spotify] | [https://francium223.bandcamp.com/track/strange-worlds Bandcamp] | [https://www.youtube.com/watch?v=tPwRWVjeKA8 YouTube] – in Hanson[11], 53edo tuning
* [https://www.youtube.com/watch?v=kwELa9kP8YU ''Blasphemous Rumors''] (2024) – Blackdye in 53edo
* "Blasphemous Rumors" from ''TOTMC September to December 2024'' (2024) – [https://open.spotify.com/track/7nOrawE5wLqllqMAApHadh Spotify] | [https://francium223.bandcamp.com/track/blasphemous-rumours Bandcamp] | [https://www.youtube.com/watch?v=kwELa9kP8YU YouTube] – in Blackdye, 53edo tuning
* "It's a Good Idea to Have a Good Time." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/3rYiNMcOQ5Oxz7F6mQZsfw Spotify] | [https://francium223.bandcamp.com/track/its-a-good-idea-to-have-a-good-time Bandcamp] | [https://www.youtube.com/watch?v=D-i-4Sv-vqE YouTube]
* "Decearing Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/2KfOutrIDfbk4S9kxYi8sL Spotify] | [https://francium223.bandcamp.com/track/decearing-egg Bandcamp] | [https://www.youtube.com/watch?v=_CJ5MgIRKnM YouTube]
* "Husband Head Void" from ''Void'' (2025) – [https://open.spotify.com/track/4yvyDZv8dBjOiurzoTjpBj Spotify] | [https://francium223.bandcamp.com/track/husband-head-void Bandcamp] | [https://www.youtube.com/watch?v=HMnklwjEdF0 YouTube]
* "Lasagna Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/6sJil69QOqxNWrWrkgm3rl Spotify] | [https://francium223.bandcamp.com/track/lasagna-cat Bandcamp] | [https://www.youtube.com/watch?v=Ay2zhVnTlxw YouTube]


; [[Andrew Heathwaite]]
; [[Andrew Heathwaite]]
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; [[MortisTheneRd]]
; [[MortisTheneRd]]
* [https://www.youtube.com/watch?v=TWVN8ui48ew ''Psychedelic Inventions in 53edo''] (2024)
* [https://www.youtube.com/watch?v=TWVN8ui48ew ''Psychedelic Inventions in 53edo''] (2024)
; [[Mundoworld]]
* from ''No Fun House'' (2025)
** "No Explanations" – [https://open.spotify.com/track/4IM4RoS9BrkgsFXEbAOenQ Spotify] | [https://mundoworld.bandcamp.com/track/no-explanations Bandcamp] | [https://www.youtube.com/watch?v=WPlxi22rf0I YouTube] – in Gorgo[11], 53edo tuning
** "Liminal" – [https://open.spotify.com/track/6ouYOGwv6Vm1hbEC9QxFMc Spotify] | [https://mundoworld.bandcamp.com/track/liminal Bandcamp] | [https://www.youtube.com/watch?v=yKKZ_x8sIjg YouTube] – in Gorgo[11], 53edo tuning


; [[Prent Rodgers]]
; [[Prent Rodgers]]
* ''Whisper Song'' (2007) – [https://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html blog] | [https://web.archive.org/web/20201127013644/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3 play] | [https://soundcloud.com/prent-rodgers/whisper-song-in-53-edo SoundCloud]
* ''Whisper Song'' (2007) – [https://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html blog] | [https://web.archive.org/web/20201127013644/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3 play] | [https://soundcloud.com/prent-rodgers/whisper-song-in-53-edo SoundCloud]
; [[Sevish]]
* "[[Droplet]]", from ''[[Rhythm and Xen]]'' (2015) – [https://sevish.bandcamp.com/track/droplet Bandcamp] | [https://soundcloud.com/sevish/droplet?in=sevish/sets/rhythm-and-xen SoundCloud] | [https://www.youtube.com/watch?v=xVZy9GUeMqY YouTube] – drum and bass in Orwell[9], 53edo tuning


; [[Subhraag Singh]]
; [[Subhraag Singh]]
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; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
* ''Trio in Orwell'' (archived 2010) – [https://www.archive.org/details/TrioInOrwell detail] | [https://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] – Orwell[9] in 53edo
* ''Trio in Orwell'' (archived 2010) – [https://www.archive.org/details/TrioInOrwell detail] | [https://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] – in Orwell[9], 53edo tuning


; [[Nick Stephens]]
; [[Nick Stephens]]
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; [[Cam Taylor]]
; [[Cam Taylor]]
* [https://soundcloud.com/cam-taylor-2-1/mothers ''mothers''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/mothers ''mothers''] (2014)
* [https://www.youtube.com/watch?v=xIy8I0XfUDI ''Schumann: The Poet Speaks in 53-equal (5-limit) on the Lumatone''] (2022)
* [https://www.youtube.com/watch?v=vpgbnACq1rA ''53-equal: lydian/aeolian pentatonic''] (2023)
* [https://www.youtube.com/watch?v=LyWW3w7PhlE ''53-equal Luma MKI: around a drone on middle C''] (2023)
* [https://www.youtube.com/watch?v=l9Y8NEqIkug ''22 shrutis as Schismatic[22] in A446Hz (53-equal)''] (2024)
* [https://www.youtube.com/watch?v=IdiMNP4MSx8&t=2s&pp=0gcJCbIJAYcqIYzv ''A meander around 53-equal on the Lumatone''] (2025) (this is actually a keyboard mapping guide)


; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* ''The Fallen of Kleismic15'' (2013) – [http://chrisvaisvil.com/the-fallen-of-kleismic15/ blog] | [http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] – Kleismic[15] in 53edo
* ''The Fallen of Kleismic15'' (2013) – [http://chrisvaisvil.com/the-fallen-of-kleismic15/ blog] | [http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] – in Kleismic[15], 53edo tuning


; [[Valeriana of the Night]]
; [[Valeriana of the Night]]
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* "Taking Flight" from ''Nano Particular'' (2019) – [https://open.spotify.com/track/2zp6oM57m6BvQgyOZ5kmuZ Spotify] | [https://xotla.bandcamp.com/track/taking-flight-53edo Bandcamp] | [https://www.youtube.com/watch?v=sIsfYQATouc YouTube]
* "Taking Flight" from ''Nano Particular'' (2019) – [https://open.spotify.com/track/2zp6oM57m6BvQgyOZ5kmuZ Spotify] | [https://xotla.bandcamp.com/track/taking-flight-53edo Bandcamp] | [https://www.youtube.com/watch?v=sIsfYQATouc YouTube]
* "Detective Duckweed" from ''Jazzbeetle'' (2023) – [https://open.spotify.com/track/77iDGy7hRx8az3ODrDm5Kl Spotify] | [https://xotla.bandcamp.com/track/detective-duckweed-53edo Bandcamp] | [https://youtu.be/FNXEPB4Gm54 YouTube] – jazzy big band electronic hybrid
* "Detective Duckweed" from ''Jazzbeetle'' (2023) – [https://open.spotify.com/track/77iDGy7hRx8az3ODrDm5Kl Spotify] | [https://xotla.bandcamp.com/track/detective-duckweed-53edo Bandcamp] | [https://youtu.be/FNXEPB4Gm54 YouTube] – jazzy big band electronic hybrid
== Instruments ==
* [[Lumatone mapping for 53edo]]
* [[Skip fretting system 53 3 14]]


== Notes ==
== Notes ==
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== References ==
== References ==
<references />
<references/>


[[Category:3-limit record edos|##]] <!-- 2-digit number -->
[[Category:Amity]]
[[Category:Amity]]
[[Category:Hanson]]
[[Category:Kleismic]]
[[Category:Kleismic]]
[[Category:Island]]
[[Category:Island]]
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[[Category:Orwell]]
[[Category:Orwell]]
[[Category:Schismic]]
[[Category:Schismic]]
[[Category:3-limit]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/53edo"