73edo: Difference between revisions

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-'''73-EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[marrakesh]] temperament. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.
+{{Infobox ET}}
+{{ED intro}}
-{| class="wikitable center-all"
+== Theory ==
-|-
+edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tune it better.
-|+ 73-EDO approximation of primary intervals
-|-
-! colspan="2" | Prime number
-! 3
-! 5
-! 7
-! 11
-! 13
-! 17
-! 19
-! 23
-|-
-! rowspan="2" | Error
-! absolute ([[cent|¢]])
-| +4.89
-| +8.21
-| +1.04
-| +7.59
-| -2.17
-| -6.33
-| -1.62
-| -3.62
-|-
-! [[Relative error|relative]] (%)
-| +29.8
-| +49.9
-| +6.3
-| +46.1
-| -13.2
-| -38.5
-| -9.9
-| -22.0
-|-
-! colspan="2" | Degree ([[octave reduction|reduced]])
-| 116 (43)
-| 170 (24)
-| 205 (59)
-| 253 (34)
-| 270 (51)
-| 298 (6)
-| 310 (18)
-| 330 (38)
-|}
-edo fits in mavila scale, by the 9;5 relation in the [[7L_2s|superdiatonic]] scheme.
+edo can be used as a tuning of [[trismegistus]] or [[mavila]], by the 9:5 relation in the [[7L 2s|superdiatonic]] scheme, though neither of these use the most accurate 3/2. It is also notable for supporting the 2.3.5.7.13 version of [[sensi]] entirely by patent val.
-edo is the 21st [[prime edo]].
+=== Prime harmonics ===
+{{Harmonics in equal|73|intervals=prime}}
+=== Subsets and supersets ===
+edo is the 21st [[prime edo]], past [[71edo]] and before [[79edo]].
+== Intervals ==
+{{Interval table}}
+== Notation ==
+=== Sagittal notation ===
+This notation uses the same sagittal sequence as [[80edo#Sagittal notation|80-EDO]].
+==== Evo flavor ====
+<imagemap>
+File:73-EDO_Evo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 719 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 120 106 [[64/63]]
+rect 120 80 220 106 [[81/80]]
+rect 220 80 350 106 [[45/44]]
+rect 350 80 470 106 [[33/32]]
+default [[File:73-EDO_Evo_Sagittal.svg]]
+</imagemap>
+==== Revo flavor ====
+<imagemap>
+File:73-EDO_Revo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 120 106 [[64/63]]
+rect 120 80 220 106 [[81/80]]
+rect 220 80 350 106 [[45/44]]
+rect 350 80 470 106 [[33/32]]
+default [[File:73-EDO_Revo_Sagittal.svg]]
+</imagemap>
+== Scales ==
+* Porky[7]: 10 10 10 13 10 10 10 ((10, 20, 30, 43, 53, 63, 73)\73)
+== Instruments ==
+A [[Lumatone mapping for 73edo]] is available.
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/meZYE1Yj2pY ''microtonal improvisation in 73edo''] (2025)
+* ''Waltz in 73edo'' (2026)
+** [https://www.youtube.com/shorts/sRZEJVBuDl0 ''<nowiki>[short]</nowiki>''] (Lumatone view)
+** [https://www.youtube.com/watch?v=Z-3a5LJlul8 ''<nowiki>[full version]</nowiki>'']
+; [[Claudi Meneghin]]
+* [https://www.youtube.com/watch?v=NuCnLVijULo ''Little Fugue on Happy Birthday''] (2020)
-[[Category:Equal divisions of the octave]]
-[[Category:Prime EDO]]
 [[Category:Marrakesh]]
+[[Category:Listen]]