53edo: Difference between revisions
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{{interwiki | |||
| de = 53-EDO | |||
| en = 53edo | |||
| es = | |||
| ja = | |||
}} | |||
{{Infobox ET}} | |||
{{Wikipedia| 53 equal temperament }} | |||
{{ED intro}} | |||
== 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>. 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's step is sometimes called the "Holdrian comma", despite the 53rd root of 2 being an irrational number; the step's role as a "comma" comes from it being an approximation of the Pythagorean comma and syntonic comma. | |||
53edo | |||
=== Prime harmonics === | |||
{{Harmonics in equal|53|columns=9}} | |||
{{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 === | ||
53edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | |||
Many of its multiples such as [[159edo]], [[212edo]], [[742edo]], [[901edo]] and [[954edo]] have good consistency limits and are each of their own interest. The [[mercator family]] comprises rank-2 temperaments with 1/53-octave periods. | |||
= | == Intervals == | ||
[[ | {| class="wikitable center-all right-2 left-3 left-5" | ||
[[ | |- | ||
[[ | ! # | ||
[[ | ! 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> | ||
[[ | ! 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 | |||
|- | |||
| 0 | |||
| 0.0 | |||
| [[1/1]] | |||
| P1 | |||
| unison | |||
| D | |||
| Da | |||
| Do | |||
|- | |||
| 1 | |||
| 22.6 | |||
| ''[[50/49]]'', [[64/63]], [[81/80]] | |||
| ^1 | |||
| up unison | |||
| ^D | |||
| Du | |||
| Di | |||
|- | |||
| 2 | |||
| 45.3 | |||
| [[33/32]], [[36/35]], [[49/48]], [[128/125]] | |||
| ^^1, vvm2 | |||
| dup unison, dudminor 2nd | |||
| ^^D, vvEb | |||
| Di / Fre | |||
| Daw | |||
|- | |||
| 3 | |||
| 67.9 | |||
| ''[[22/21]]'', [[25/24]], [[26/25]], [[27/26]], [[28/27]] | |||
| vvA1, vm2 | |||
| dudaug 1sn, downminor 2nd | |||
| vvD#, vEb | |||
| Fro | |||
| Ro | |||
|- | |||
| 4 | |||
| 90.6 | |||
| [[19/18]], [[20/19]], [[21/20]], [[256/243]] | |||
| vA1, m2 | |||
| downaug 1sn, minor 2nd | |||
| vD#, Eb | |||
| Fra | |||
| Rih | |||
|- | |||
| 5 | |||
| 113.2 | |||
| [[15/14]], [[16/15]] | |||
| A1, ^m2 | |||
| aug 1sn, upminor 2nd | |||
| D#, ^Eb | |||
| Fru | |||
| Ra | |||
|- | |||
| 6 | |||
| 135.8 | |||
| [[13/12]], [[14/13]], [[27/25]] | |||
| ^^m2 | |||
| dupminor 2nd | |||
| ^^Eb | |||
| Fri | |||
| Ru | |||
|- | |||
| 7 | |||
| 158.5 | |||
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]] | |||
| vvM2 | |||
| dudmajor 2nd | |||
| vvE | |||
| Re | |||
| Ruh | |||
|- | |||
| 8 | |||
| 181.1 | |||
| [[10/9]] | |||
| vM2 | |||
| downmajor 2nd | |||
| vE | |||
| Ro | |||
| Reh | |||
|- | |||
| 9 | |||
| 203.8 | |||
| [[9/8]] | |||
| M2 | |||
| major 2nd | |||
| E | |||
| Ra | |||
| Re | |||
|- | |||
| 10 | |||
| 226.4 | |||
| [[8/7]], [[256/225]] | |||
| ^M2 | |||
| upmajor 2nd | |||
| ^E | |||
| Ru | |||
| Ri | |||
|- | |||
| 11 | |||
| 249.1 | |||
| [[15/13]], [[22/19]], [[125/108]], [[144/125]] | |||
| ^^M2, vvm3 | |||
| dupmajor 2nd, dudminor 3rd | |||
| ^^E, vvF | |||
| Ri / Ne | |||
| Raw | |||
|- | |||
| 12 | |||
| 271.7 | |||
| [[7/6]], [[75/64]] | |||
| vm3 | |||
| downminor 3rd | |||
| vF | |||
| No | |||
| Ma | |||
|- | |||
| 13 | |||
| 294.3 | |||
| [[13/11]], [[19/16]], [[32/27]] | |||
| m3 | |||
| minor 3rd | |||
| F | |||
| Na | |||
| Meh | |||
|- | |||
| 14 | |||
| 317.0 | |||
| [[6/5]] | |||
| ^m3 | |||
| upminor 3rd | |||
| ^F | |||
| Nu | |||
| Me | |||
|- | |||
| 15 | |||
| 339.6 | |||
| [[11/9]], [[243/200]] | |||
| ^^m3 | |||
| dupminor 3rd | |||
| ^^F | |||
| Ni | |||
| Mu | |||
|- | |||
| 16 | |||
| 362.3 | |||
| [[16/13]], [[100/81]] | |||
| vvM3 | |||
| dudmajor 3rd | |||
| vvF# | |||
| Me | |||
| Muh | |||
|- | |||
| 17 | |||
| 384.9 | |||
| [[5/4]] | |||
| vM3 | |||
| downmajor 3rd | |||
| vF# | |||
| Mo | |||
| Mi | |||
|- | |||
| 18 | |||
| 407.5 | |||
| [[19/15]], [[24/19]], [[81/64]] | |||
| M3 | |||
| major 3rd | |||
| F# | |||
| Ma | |||
| Maa | |||
|- | |||
| 19 | |||
| 430.2 | |||
| [[9/7]], ''[[14/11]]'' | |||
| ^M3 | |||
| upmajor 3rd | |||
| ^F# | |||
| Mu | |||
| Mo | |||
|- | |||
| 20 | |||
| 452.8 | |||
| [[13/10]], [[125/96]], [[162/125]] | |||
| ^^M3, vv4 | |||
| dupmajor 3rd, dud 4th | |||
| ^^F#, vvG | |||
| Mi / Fe | |||
| Maw | |||
|- | |||
| 21 | |||
| 475.5 | |||
| [[21/16]], [[25/19]], [[320/243]], [[675/512]] | |||
| v4 | |||
| down 4th | |||
| vG | |||
| Fo | |||
| Fe | |||
|- | |||
| 22 | |||
| 498.1 | |||
| [[4/3]] | |||
| P4 | |||
| perfect 4th | |||
| G | |||
| Fa | |||
| Fa | |||
|- | |||
| 23 | |||
| 520.8 | |||
| [[19/14]], [[27/20]] | |||
| ^4 | |||
| up 4th | |||
| ^G | |||
| Fu | |||
| Fih | |||
|- | |||
| 24 | |||
| 543.4 | |||
| [[11/8]], [[15/11]], [[26/19]] | |||
| ^^4 | |||
| dup 4th | |||
| ^^G | |||
| Fi / She | |||
| Fu | |||
|- | |||
| 25 | |||
| 566.0 | |||
| [[18/13]] | |||
| vvA4, vd5 | |||
| dudaug 4th, downdim 5th | |||
| vvG#, vAb | |||
| Pe / Sho | |||
| Fuh | |||
|- | |||
| 26 | |||
| 588.7 | |||
| [[7/5]], [[45/32]] | |||
| vA4, d5 | |||
| downaug 4th, dim 5th | |||
| vG#, Ab | |||
| Po / Sha | |||
| Fi | |||
|- | |||
| 27 | |||
| 611.3 | |||
| [[10/7]], [[64/45]] | |||
| A4, ^d5 | |||
| aug 4th, updim 5th | |||
| G#, ^Ab | |||
| Pa / Shu | |||
| Se | |||
|- | |||
| 28 | |||
| 634.0 | |||
| [[13/9]] | |||
| ^A4, ^^d5 | |||
| upaug 4th, dupdim 5th | |||
| ^G#, ^^Ab | |||
| Pu / Shi | |||
| Suh | |||
|- | |||
| 29 | |||
| 656.6 | |||
| [[16/11]], [[19/13]], [[22/15]] | |||
| vv5 | |||
| dud 5th | |||
| vvA | |||
| Pi / Se | |||
| Su | |||
|- | |||
| 30 | |||
| 679.2 | |||
| [[28/19]], [[40/27]] | |||
| v5 | |||
| down 5th | |||
| vA | |||
| So | |||
| Sih | |||
|- | |||
| 31 | |||
| 701.9 | |||
| [[3/2]] | |||
| P5 | |||
| perfect 5th | |||
| A | |||
| Sa | |||
| Sol | |||
|- | |||
| 32 | |||
| 724.5 | |||
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]] | |||
| ^5 | |||
| up 5th | |||
| ^A | |||
| Su | |||
| Si | |||
|- | |||
| 33 | |||
| 747.2 | |||
| [[20/13]], [[125/81]], [[192/125]] | |||
| ^^5, vvm6 | |||
| dup 5th, dudminor 6th | |||
| ^^A, vvBb | |||
| Si / Fle | |||
| Saw | |||
|- | |||
| 34 | |||
| 769.8 | |||
| ''[[11/7]]'', [[14/9]], [[25/16]] | |||
| vm6 | |||
| downminor 6th | |||
| vBb | |||
| Flo | |||
| Lo | |||
|- | |||
| 35 | |||
| 792.5 | |||
| [[19/12]], [[30/19]], [[128/81]] | |||
| m6 | |||
| minor 6th | |||
| Bb | |||
| Fla | |||
| Leh | |||
|- | |||
| 36 | |||
| 815.1 | |||
| [[8/5]] | |||
| ^m6 | |||
| upminor 6th | |||
| ^Bb | |||
| Flu | |||
| Le | |||
|- | |||
| 37 | |||
| 837.7 | |||
| [[13/8]], [[81/50]] | |||
| ^^m6 | |||
| dupminor 6th | |||
| ^^Bb | |||
| Fli | |||
| Lu | |||
|- | |||
| 38 | |||
| 860.4 | |||
| [[18/11]], [[400/243]] | |||
| vvM6 | |||
| dudmajor 6th | |||
| vvB | |||
| Le | |||
| Luh | |||
|- | |||
| 39 | |||
| 883.0 | |||
| [[5/3]] | |||
| vM6 | |||
| downmajor 6th | |||
| vB | |||
| Lo | |||
| La | |||
|- | |||
| 40 | |||
| 905.7 | |||
| [[22/13]], [[27/16]], [[32/19]] | |||
| M6 | |||
| major 6th | |||
| B | |||
| La | |||
| Laa | |||
|- | |||
| 41 | |||
| 928.3 | |||
| [[12/7]] | |||
| ^M6 | |||
| upmajor 6th | |||
| ^B | |||
| Lu | |||
| Li | |||
|- | |||
| 42 | |||
| 950.9 | |||
| [[19/11]], [[26/15]], [[125/72]], [[216/125]] | |||
| ^^M6, vvm7 | |||
| dupmajor 6th, dudminor 7th | |||
| ^^B, vvC | |||
| Li / The | |||
| Law | |||
|- | |||
| 43 | |||
| 973.6 | |||
| [[7/4]] | |||
| vm7 | |||
| downminor 7th | |||
| vC | |||
| Tho | |||
| Ta | |||
|- | |||
| 44 | |||
| 996.2 | |||
| [[16/9]] | |||
| m7 | |||
| minor 7th | |||
| C | |||
| Tha | |||
| Teh | |||
|- | |||
| 45 | |||
| 1018.9 | |||
| [[9/5]] | |||
| ^m7 | |||
| upminor 7th | |||
| ^C | |||
| Thu | |||
| Te | |||
|- | |||
| 46 | |||
| 1041.5 | |||
| [[11/6]], [[20/11]], [[64/35]], [[729/400]] | |||
| ^^m7 | |||
| dupminor 7th | |||
| ^^C | |||
| Thi | |||
| Tu | |||
|- | |||
| 47 | |||
| 1064.2 | |||
| [[13/7]], [[24/13]], [[50/27]] | |||
| vvM7 | |||
| dudmajor 7th | |||
| vvC# | |||
| Te | |||
| Tuh | |||
|- | |||
| 48 | |||
| 1086.8 | |||
| [[15/8]] | |||
| vM7 | |||
| downmajor 7th | |||
| vC# | |||
| To | |||
| Ti | |||
|- | |||
| 49 | |||
| 1109.4 | |||
| [[19/10]], [[36/19]], [[40/21]], [[243/128]] | |||
| M7 | |||
| major 7th | |||
| C# | |||
| Ta | |||
| Tih | |||
|- | |||
| 50 | |||
| 1132.1 | |||
| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]] | |||
| ^M7 | |||
| upmajor 7th | |||
| ^C# | |||
| Tu | |||
| To | |||
|- | |||
| 51 | |||
| 1154.7 | |||
| [[35/18]], [[64/33]], [[96/49]], [[125/64]] | |||
| ^^M7, vv8 | |||
| dupmajor 7th, dud 8ve | |||
| ^^C#, vvD | |||
| Ti / De | |||
| Taw | |||
|- | |||
| 52 | |||
| 1177.4 | |||
| ''[[49/25]]'', [[63/32]], [[160/81]] | |||
| v8 | |||
| down 8ve | |||
| vD | |||
| Do | |||
| Da | |||
|- | |||
| 53 | |||
| 1200.0 | |||
| [[2/1]] | |||
| P8 | |||
| perfect 8ve | |||
| D | |||
| Da | |||
| Do | |||
|} | |||
=== 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 | |||
! [[Kite's color notation|Color]] | |||
! Monzo format | |||
! Examples | |||
|- | |||
| downminor | |||
| zo | |||
| {{nowrap|(a, b, 0, 1)}} | |||
| 7/6, 7/4 | |||
|- | |||
| minor | |||
| fourthward wa | |||
| {{nowrap|(a, b)}} with {{nowrap|b < −1}} | |||
< | | 32/27, 16/9 | ||
|- | |||
| upminor | |||
| gu | |||
| {{nowrap|(a, b, −1)}} | |||
| 6/5, 9/5 | |||
|- | |||
| dupminor | |||
| ilo | |||
| {{nowrap|(a, b, 0, 0, 1)}} | |||
| 11/9, 11/6 | |||
|- | |||
| dudmajor | |||
| lu | |||
| {{nowrap|(a, b, 0, 0, −1)}} | |||
| 12/11, 18/11 | |||
|- | |||
| downmajor | |||
| yo | |||
| {{nowrap|(a, b, 1)}} | |||
| 5/4, 5/3 | |||
|- | |||
| major | |||
| fifthward wa | |||
| {{nowrap|(a, b)}} with {{nowrap|b > 1}} | |||
| 9/8, 27/16 | |||
|- | |||
| upmajor | |||
| ru | |||
| {{nowrap|(a, b, 0, −1)}} | |||
| 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 {{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: | |||
{| class="wikitable center-all" | |||
|- | |||
! [[Kite's color notation|Color of the 3rd]] | |||
! JI chord | |||
! Notes as edosteps | |||
! Notes of C chord | |||
! Written name | |||
! Spoken name | |||
|- | |||
| zo | |||
| 6:7:9 | |||
| 0–12–31 | |||
| C vEb G | |||
| Cvm | |||
| C downminor | |||
|- | |||
| gu | |||
| 10:12:15 | |||
| 0–14–31 | |||
| C ^Eb G | |||
| C^m | |||
| C upminor | |||
|- | |||
| ilo | |||
| 18:22:27 | |||
| 0–15–31 | |||
| C ^^Eb G | |||
| C^^m | |||
| C dupminor | |||
|- | |||
| lu | |||
| 22:27:33 | |||
| 0–16–31 | |||
| C vvE G | |||
| Cvv | |||
| C dudmajor or C dud | |||
|- | |||
| yo | |||
| 4:5:6 | |||
| 0–17–31 | |||
| C vE G | |||
| Cv | |||
| C downmajor or C down | |||
|- | |||
| ru | |||
| 14:18:21 | |||
| 0–19–31 | |||
| C ^E G | |||
| C^ | |||
| C upmajor or C up | |||
|} | |||
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]]. | |||
== Notation == | |||
=== 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}} | |||
=== Sagittal notation === | |||
==== 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> | |||
==== Revo flavor ==== | |||
<imagemap> | |||
File:53-EDO_Revo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 543 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_Revo_Sagittal.svg]] | |||
</imagemap> | |||
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | |||
== Relationship to 12edo == | |||
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]] | |||
== Approximation to JI == | |||
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" | |||
|- | |||
! Interval | |||
! Ratio | |||
! Size | |||
! Difference | |||
|- | |||
| Perfect fifth | |||
| 3/2 | |||
| 31 | |||
| −0.07 cents | |||
|- | |||
| Major third | |||
| 5/4 | |||
| 17 | |||
| −1.40 cents | |||
|- | |||
| Minor third | |||
| 6/5 | |||
| 14 | |||
| +1.34 cents | |||
|- | |||
| rowspan="2" | Major second | |||
| 9/8 | |||
| 9 | |||
| −0.14 cents | |||
|- | |||
| 10/9 | |||
| 8 | |||
| −1.27 cents | |||
|- | |||
| Minor second | |||
| 16/15 | |||
| 5 | |||
| +1.48 cents | |||
|} | |||
Because the 5th is so accurate, 53edo also offers good approximations for Pythagorean thirds. In addition, the 43\53 interval is only 4.8 cents wider than 7/4, so 53edo can also be used for 7-limit harmony, in which it tempers out the [[septimal kleisma]], 225/224. | |||
=== 15-odd-limit interval mappings === | |||
{{Q-odd-limit intervals|53}} | |||
=== Higher-limit JI === | |||
53edo has only 5 pairs of inconsistent intervals in the full 27-odd-limit: {11/7, 14/11}, {[[17/11]], [[22/17]]}, {[[19/17]], [[34/19]]}, {[[21/11]], [[22/21]]}, and {[[23/22]], [[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. | |||
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 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]]. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{Monzo| -84 53 }} | |||
| {{Mapping| 53 84 }} | |||
| +0.022 | |||
| 0.022 | |||
| 0.10 | |||
|- | |||
| 2.3.5 | |||
| 15625/15552, 32805/32768 | |||
| {{Mapping| 53 84 123 }} | |||
| +0.216 | |||
| 0.276 | |||
| 1.22 | |||
|- | |||
| 2.3.5.7 | |||
| 225/224, 1728/1715, 3125/3087 | |||
| {{Mapping| 53 84 123 149 }} | |||
| −0.262 | |||
| 0.861 | |||
| 3.81 | |||
|- | |||
| 2.3.5.7.11 | |||
| 99/98, 121/120, 176/175, 2200/2187 | |||
| {{Mapping| 53 84 123 149 183 }} | |||
| +0.248 | |||
| 1.279 | |||
| 5.64 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 99/98, 121/120, 169/168, 176/175, 275/273 | |||
| {{Mapping| 53 84 123 149 183 196 }} | |||
| +0.332 | |||
| 1.183 | |||
| 5.22 | |||
|- | |||
| 2.3.5.7.11.13.19 | |||
| 99/98, 121/120, 169/168, 176/175, 209/208, 275/273 | |||
| {{Mapping| 53 84 123 149 183 196 225 }} | |||
| +0.391 | |||
| 1.105 | |||
| 4.88 | |||
|} | |||
* 53et is lower in relative error than any previous equal temperaments in the 3-, 5-, and 13-limit. The next equal temperaments doing better in these subgroups are 306, 118, and 58, respectively. It is even more prominent in the 2.3.5.7.13.19 and 2.3.5.7.13.19.23 subgroups, and the next equal temperament doing better in either subgroup is 130. | |||
=== Commas === | |||
Commas that 53edo tempers out using its patent val, {{val| 53 84 123 149 183 196 225 }}, include: | |||
{| class="commatable wikitable center-1 center-2 right-4 center-5" | |||
|- | |||
! [[Harmonic limit|Prime<br>limit]] | |||
! [[Ratio]]<ref group="note">{{rd}}</ref> | |||
! [[Monzo]] | |||
! [[Cent]]s | |||
! [[Color name]] | |||
! Name(s) | |||
|- | |||
| 3 | |||
| <abbr title="19383245667680019896796723/19342813113834066795298816">(52 digits)</abbr> | |||
| {{Monzo| -84 53 }} | |||
| 3.62 | |||
| Tribilawa | |||
| 53-comma, [[Mercator's comma]] | |||
|- | |||
| 5 | |||
| [[2109375/2097152|(14 digits)]] | |||
| {{Monzo| -21 3 7 }} | |||
| 10.06 | |||
| Lasepyo | |||
| [[Semicomma]] | |||
|- | |||
| 5 | |||
| [[15625/15552]] | |||
| {{Monzo| -6 -5 6 }} | |||
| 8.11 | |||
| Tribiyo | |||
| Kleisma | |||
|- | |||
| 5 | |||
| <abbr title="1600000/1594323">(14 digits)</abbr> | |||
| {{Monzo| 9 -13 5 }} | |||
| 6.15 | |||
| Saquinyo | |||
| [[Amity comma]] | |||
|- | |||
| 5 | |||
| <abbr title="10485760000/10460353203">(22 digits)</abbr> | |||
| {{Monzo| 24 -21 4 }} | |||
| 4.20 | |||
| Sasaquadyo | |||
| [[Vulture comma]] | |||
|- | |||
| 5 | |||
| [[32805/32768]] | |||
| {{Monzo| -15 8 1 }} | |||
| 1.95 | |||
| Layo | |||
| Schisma | |||
|- | |||
| 7 | |||
| [[3125/3087]] | |||
| {{Monzo| 0 -2 5 -3 }} | |||
| 21.18 | |||
| Triru-aquinyo | |||
| Gariboh comma | |||
|- | |||
| 7 | |||
| [[1728/1715]] | |||
| {{Monzo| 6 3 -1 -3 }} | |||
| 13.07 | |||
| Triru-agu | |||
| Orwellisma | |||
|- | |||
| 7 | |||
| [[225/224]] | |||
| {{Monzo| -5 2 2 -1 }} | |||
| 7.71 | |||
| Ruyoyo | |||
| Marvel comma, septimal kleisma | |||
|- | |||
| 7 | |||
| [[4375/4374]] | |||
| {{Monzo| -1 -7 4 1 }} | |||
| 0.40 | |||
| Zoquadyo | |||
| Ragisma | |||
|- | |||
| 11 | |||
| [[99/98]] | |||
| {{Monzo| -1 2 0 -2 1 }} | |||
| 17.58 | |||
| Loruru | |||
| Mothwellsma | |||
|- | |||
| 11 | |||
| [[121/120]] | |||
| {{Monzo| -3 -1 -1 0 2 }} | |||
| 14.37 | |||
| Lologu | |||
| Biyatisma | |||
|- | |||
| 11 | |||
| [[176/175]] | |||
| {{Monzo| 4 0 -2 -1 1 }} | |||
| 9.86 | |||
| Lorugugu | |||
| Valinorsma | |||
|- | |||
| 11 | |||
| <abbr title="94489280512/94143178827">(22 digits)</abbr> | |||
| {{Monzo| 33 -23 0 0 1 }} | |||
| 6.35 | |||
| Trisalo | |||
| [[Pythrabian comma]] | |||
|- | |||
| 11 | |||
| [[385/384]] | |||
| {{Monzo| -7 -1 1 1 1 }} | |||
| 4.50 | |||
| Lozoyo | |||
| Keenanisma | |||
|- | |||
| 11 | |||
| [[540/539]] | |||
| {{Monzo| 2 3 1 -2 -1 }} | |||
| 3.21 | |||
| Lururuyo | |||
| Swetisma | |||
|- | |||
| 13 | |||
| [[275/273]] | |||
| {{Monzo| 0 -1 2 -1 1 -1 }} | |||
| 12.64 | |||
| Thuloruyoyo | |||
| Gassorma | |||
|- | |||
| 13 | |||
| [[169/168]] | |||
| {{Monzo| -3 -1 0 -1 0 2 }} | |||
| 10.27 | |||
| Thothoru | |||
| Buzurgisma, dhanvantarisma | |||
|- | |||
| 13 | |||
| [[625/624]] | |||
| {{Monzo| -4 -1 4 0 0 -1 }} | |||
| 2.77 | |||
| Thuquadyo | |||
| Tunbarsma | |||
|- | |||
| 13 | |||
| [[676/675]] | |||
| {{Monzo| 2 -3 -2 0 0 2 }} | |||
| 2.56 | |||
| Bithogu | |||
| Island comma, parizeksma | |||
|- | |||
| 13 | |||
| [[1001/1000]] | |||
| {{Monzo| -3 0 -3 1 1 1 }} | |||
| 1.73 | |||
| Tholozotrigu | |||
| Fairytale comma, sinbadma | |||
|- | |||
| 13 | |||
| [[2080/2079]] | |||
| {{Monzo| 5 -3 1 -1 -1 1 }} | |||
| 0.83 | |||
| Tholuruyo | |||
| Ibnsinma, sinaisma | |||
|- | |||
| 13 | |||
| [[4096/4095]] | |||
| {{Monzo| 12 -2 -1 -1 0 -1 }} | |||
| 0.42 | |||
| Sathurugu | |||
| Schismina | |||
|} | |||
=== Linear temperaments === | |||
* [[List of edo-distinct 53et rank two temperaments]] | |||
* [[Schismic–Mercator equivalence continuum]] | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperament | |||
|- | |||
| 1 | |||
| 2\53 | |||
| 45.3 | |||
| 36/35 | |||
| [[Quartonic]] | |||
|- | |||
| 1 | |||
| 5\53 | |||
| 113.2 | |||
| 16/15 | |||
| [[Misneb]] | |||
|- | |||
| 1 | |||
| 6\53 | |||
| 135.8 | |||
| [[13/12]]~[[14/13]] | |||
| [[Doublethink]] | |||
|- | |||
| 1 | |||
| 7\53 | |||
| 158.5 | |||
| 11/10 | |||
| [[Hemikleismic]] | |||
|- | |||
| 1 | |||
| 9\53 | |||
| 203.8 | |||
| 9/8 | |||
| [[Baldy]] | |||
|- | |||
| 1 | |||
| 10\53 | |||
| 226.4 | |||
| 8/7 | |||
| [[Semaja]] | |||
|- | |||
| 1 | |||
| 11\53 | |||
| 249.1 | |||
| 15/13 | |||
| [[Hemischis]] / [[hemigari]] | |||
|- | |||
| 1 | |||
| 12\53 | |||
| 271.7 | |||
| 7/6 | |||
| [[Orwell]] | |||
|- | |||
| 1 | |||
| 13\53 | |||
| 294.3 | |||
| 25/21 | |||
| [[Kleiboh]] | |||
|- | |||
| 1 | |||
| 14\53 | |||
| 317.0 | |||
| 6/5 | |||
| [[Hanson]] / [[catakleismic]] / [[countercata]] | |||
|- | |||
| 1 | |||
| 15\53 | |||
| 339.6 | |||
| 11/9 | |||
| [[Amity]] / [[houborizic]] | |||
|- | |||
| 1 | |||
| 16\53 | |||
| 362.3 | |||
| 16/13 | |||
| [[Submajor]] | |||
|- | |||
| 1 | |||
| 18\53 | |||
| 407.5 | |||
| 1225/972 | |||
| [[Ditonic]] / [[coditone]] | |||
|- | |||
| 1 | |||
| 19\53 | |||
| 430.2 | |||
| 9/7 | |||
| [[Hamity]] | |||
|- | |||
| 1 | |||
| 20\53 | |||
| 452.8 | |||
| 13/10 | |||
| [[Maja]] | |||
|- | |||
| 1 | |||
| 21\53 | |||
| 475.5 | |||
| 21/16 | |||
| [[Vulture]] / [[buzzard]] | |||
|- | |||
| 1 | |||
| 22\53 | |||
| 498.1 | |||
| 4/3 | |||
| [[Garibaldi]] / [[pontiac]] | |||
|- | |||
| 1 | |||
| 23\53 | |||
| 520.8 | |||
| 4/3 | |||
| [[Mavila]] (53bbcc) | |||
|- | |||
| 1 | |||
| 25\53 | |||
| 566.0 | |||
| 18/13 | |||
| [[Alphatrimot]] | |||
|- | |||
| 1 | |||
| 26\53 | |||
| 588.7 | |||
| 45/32 | |||
| [[Untriton]] / [[aufo]] | |||
|} | |||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave | |||
== 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. | |||
* [[List of MOS scales in 53edo]] | |||
* [[1953 scale]] | |||
=== Scales approximated from JI === | |||
* The [[eagle 53]] scale described by [[John O'Sullivan]] | |||
* Ptolmey–Zarlino justly-intonated major: 9 8 5 9 8 9 5 | |||
* 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 Deja Vu (approximated from [[101afdo]]): 14 17 5 9 8 | |||
* Composite Dungeon (approximated from [[30afdo]]): 17 5 9 4 18 | |||
* Composite Freeway (approximated from [[6afdo]]): 12 10 9 8 7 7 | |||
* Composite Geode (approximated from [[6afdo]]): 12 10 9 15 7 | |||
* Composite Labyrinth (approximated from [[30afdo]]): 7 7 17 5 17 | |||
* Composite Mushroom (approximated from [[30afdo]]): 12 10 9 3 19 | |||
* Composite Underpass (approximated from [[10afdo]]): 14 17 10 4 8 | |||
* Spectral Arcade (approximated from [[32afdo]]): 17 4 10 12 10 | |||
* Spectral Mechanical (approximated from [[16afdo]]): 13 4 14 12 10 | |||
* Spectral Moonbeam (approximated from [[16afdo]]): 9 4 18 17 5 | |||
* Spectral Springwater (approximated from [[8afdo]]): 9 8 14 12 10 | |||
* Spectral Starship (approximated from [[68ifdo]]): 4 13 4 10 12 10 | |||
* Spectral Volcanic (approximated from [[16afdo]]): 5 12 14 12 10 | |||
=== Other scales === | |||
* [[cthon5m]]: 6 3 6 2 3 6 2 3 6 3 2 6 3 2 | |||
* 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 == | |||
{{Catrel| 53edo tracks }} | |||
=== Modern renderings === | |||
; {{W|Johann Sebastian Bach}} | |||
* [https://www.youtube.com/watch?v=ax43zKpDq9o "Jesus bleibet meine Freude" from ''Herz und Mund und Tat und Leben'', BWV 147] (1723) – tuned in 53edo, rendered by [[Claudi Meneghin]] (2021) | |||
* ''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://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=vcinR7nUthA "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024) | |||
; {{W|Nicolaus Bruhns}} | |||
* [https://www.youtube.com/watch?v=aprEqsCAP6Q ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023) | |||
* [https://www.youtube.com/watch?v=r6R4SsaT8ig ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024) | |||
; {{W|George Frideric Handel}} | |||
* [https://www.youtube.com/watch?v=7I7mD-DzfIo ''Suite in D minor HWV 428 for Harpsichord - Allemande''] (1720) – rendered by Claudi Meneghin (2024) | |||
; {{W|Scott Joplin}} | |||
* [https://www.youtube.com/watch?v=AKXMuhB3uHQ ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024) | |||
* [https://www.youtube.com/watch?v=t-pRqKGX0oo ''Maple Leaf Rag''] (1899) – with syntonic comma adjustment, arranged for harpsichord and rendered by Claudi Meneghin (2024) | |||
; {{W|Shirō Sagisu}} | |||
* [https://www.youtube.com/watch?v=DiPB__AOXdk ''Qui veut faire l'ange fait la bete''] – rendered by [[MortisTheneRd]] (2024) | |||
* [https://www.youtube.com/watch?v=DCENVnxH6bI ''Bande-announce''] – rendered by MortisTheneRd (2024) | |||
=== 21st century === | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/r-Tzq33OGM4 ''microtonal improvisation in 53edo''] (2025) | |||
; [[Francium]] | |||
* [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] – in Hanson[11], 53edo tuning | |||
* "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]] | |||
* [https://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho ''Elf Dine on Ho Ho''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3 play]{{dead link}} | |||
* [https://andrewheathwaite.bandcamp.com/track/spun ''Spun''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play]{{dead link}} | |||
; [[Hideya]] | |||
* [https://www.youtube.com/watch?v=QpeCMz9kJ-s ''Like Uminari''] (2021) | |||
; [[Nathan Ho]] | |||
* [https://www.youtube.com/watch?v=lGfV9LB-01U ''53edo microtonal algorithmic IDM in SuperCollider''] (2023) | |||
; [[Aaron Krister Johnson]] ([http://www.akjmusic.com site]{{dead link}}) | |||
* [http://www.akjmusic.com/audio/desert_prayer.mp3 ''Desert Prayer'']{{dead link}} | |||
; [[MortisTheneRd]] | |||
* [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]] | |||
* ''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]] | |||
* [https://soundcloud.com/user-215518655-72150190/stranges-53edo-inspired-by ''"Stranges"''] (2021) | |||
; [[Gene Ward Smith]] | |||
* ''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]] | |||
* "Initialising", from ''Microwave'' (2019) – [https://microwave64.bandcamp.com/track/initialising Bandcamp] | [https://soundcloud.com/nick-stephens-8/initialising SoundCloud] | |||
; [[Cam Taylor]] | |||
* [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]] | |||
* ''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]] | |||
* [https://www.youtube.com/watch?v=eMPQDRTHGhg ''Hero''] (2023) | |||
; [[Randy Wells]] | |||
* [https://www.youtube.com/watch?v=c6i3CsVHKhU ''Ficta''] (2021) | |||
; [[Xotla]] | |||
* "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 | |||
== Notes == | |||
<references group="note" /> | |||
== References == | |||
<references/> | |||
[[Category:3-limit record edos|##]] <!-- 2-digit number --> | |||
[[Category:Amity]] | |||
[[Category:Kleismic]] | |||
[[Category:Island]] | |||
[[Category:Marvel]] | |||
[[Category:Orson]] | |||
[[Category:Orwell]] | |||
[[Category:Schismic]] | |||
[[Category:Listen]] | |||