50edo: Difference between revisions
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→Modern renderings: Add J. S. Bach's "Ricercar a 6" from ''The Musical Offering'', BWV 1079 (1747) – rendered by Claudi Meneghin (2026) |
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== Theory == | == Theory == | ||
As an equal temperament, 50et [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a [[meantone]] system, and in that capacity has historically drawn some notice; it is a somewhat sharp approximation of [[2/7-comma meantone]] (and is almost exactly 5/18-comma meantone). In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts – 50edo, in one word. Later, {{w|W. S. B. Woolhouse}} noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher-limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is also the highest edo | As an equal temperament, 50et [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a [[meantone]] system, and in that capacity has historically drawn some notice; it is a somewhat sharp approximation of [[2/7-comma meantone]] (and is almost exactly 5/18-comma meantone). In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts – 50edo, in one word. Later, {{w|W. S. B. Woolhouse}} noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher-limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is also the highest edo for which the mapping of [[9/8]] and [[10/9]] to the same interval is [[consistent]], with two stacked fifths falling almost exactly 3/7-syntonic-comma sharp of 10/9 and 4/7-comma flat of 9/8. It is also almost consistent to the no-21s [[25-odd-limit]], only barely missing consistent mappings of [[11/9]] and [[18/11]]. | ||
50edo is also quite strong in the realm of tertian harmony for a meantone system, as the errors on [[7/6]], [[6/5]], [[5/4]], and [[9/7]] are all balanced to be roughly half as flat as the fifth, meaning that this set of thirds taken as a whole is minimally out-of-tune given the damage induced by meantone. Though it fails to approximate [[11/9]] well by virtue of not having a perfect hemififth, it inherits the excellent [[16/13]] from [[10edo]] and additionally has a 1.2{{c}} flat [[13/11]], providing even more qualities of roughly just thirds alongside their more complex [[fifth complement]]s. | 50edo is also quite strong in the realm of tertian harmony for a meantone system, as the errors on [[7/6]], [[6/5]], [[5/4]], and [[9/7]] are all balanced to be roughly half as flat as the fifth, meaning that this set of thirds taken as a whole is minimally out-of-tune given the damage induced by meantone. Though it fails to approximate [[11/9]] well by virtue of not having a perfect hemififth, it inherits the excellent [[16/13]] from [[10edo]] and additionally has a 1.2{{c}} flat [[13/11]], providing even more qualities of roughly just thirds alongside their more complex [[fifth complement]]s. | ||
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=== Modern renderings === | === Modern renderings === | ||
; {{W|Johann Sebastian Bach}} | ; {{W|Johann Sebastian Bach}} | ||
* [https://www.youtube.com/watch?v=RnYqc0NKMLM "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024) | * [https://www.youtube.com/watch?v=RnYqc0NKMLM "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by [[Claudi Meneghin]] (2024) | ||
* [https://www.youtube.com/watch?v=e6fMO-sue4Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) | * [https://www.youtube.com/watch?v=e6fMO-sue4Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) — rendered by Claudi Meneghin (2024) | ||
* | * "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080 (1742–1749) | ||
* [https://www.youtube.com/watch?v=qjb9DDM32Ic " | ** [https://www.youtube.com/watch?v=M3wQu4UF1pg organ version] — rendered by Claudi Meneghin (2024) | ||
** [https://www.youtube.com/watch?v=qjb9DDM32Ic harpsichord version] — rendered by Claudi Meneghin (2025) | |||
* [https://www.youtube.com/watch?v=n3KMEufstaY "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2026) | |||
; {{W|David Belasco}} | ; {{W|David Belasco}} | ||
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; {{W|Gabriel Fauré}} | ; {{W|Gabriel Fauré}} | ||
* | * ''Pavane'', op. 50 (1887) — arranged for harpsichord and rendered by Claudi Meneghin ([https://www.youtube.com/watch?v=7djfrUlw2ck 2020]; [https://www.youtube.com/watch?v=TyfwFJL9yE0 2026]) | ||
; {{W|Toby Fox}} | ; {{W|Toby Fox}} | ||