73edo: Difference between revisions

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 {{Infobox ET}}
-'''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. 73 EDO has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.
+{{ED intro}}
-{{Primes in edo|73|columns=9}}
+== 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.
-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 ==
-* [https://www.youtube.com/watch?v=NuCnLVijULo Little Fugue on Happy Birthday] by [[Claudi Meneghin]]
+; [[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|##]] <!-- 2-digit number -->
-[[Category:Prime EDO]]
 [[Category:Marrakesh]]
+[[Category:Listen]]