55edo: Difference between revisions
→Modern renderings: Add Gabriel Fauré's ''Pavane, Op. 50'' (1887) – arranged for harpsichord and rendered by Claudi Meneghin (2026) |
→Theory: Add syntonic comma approximation |
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== Theory == | == Theory == | ||
55edo supports [[meantone]], and is close to [[1/6-comma meantone]]. {{w|Georg Philipp Telemann|Telemann}} suggested it as a theoretical basis for analyzing the [[meantone intervals|intervals of meantone]]. {{w|Leopold Mozart|Leopold}} and {{w|Wolfgang Amadeus Mozart|Wolfgang Mozart}} recommended 55edo or something close to it, with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref> It can also be used for [[mohajira]] and [[liese]] temperaments. It also supports an extremely sharp tuning of [[huygens|huygens/undecimal meantone]] using the 55de [[val]], meaning that primes 7 and 11 are mapped very sharply to their second-best mapping. 55edo is a [[zeta valley edo]], suggesting it does not approximate the harmonic series very well for its size. | 55edo supports [[meantone]], and is close to [[1/6-comma meantone]]. {{w|Georg Philipp Telemann|Telemann}} suggested it as a theoretical basis for analyzing the [[meantone intervals|intervals of meantone]]. {{w|Leopold Mozart|Leopold}} and {{w|Wolfgang Amadeus Mozart|Wolfgang Mozart}} recommended 55edo or something close to it, with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full; part of the reasoning is that 1\55 is extremely close to the size of the syntonic comma [[81/80]].<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref> Indeed, by direct approximation, only [[56edo]] approximates the syntonic comma more closely until reaching much higher edo sizes; the [[patent val]] of 55edo tempers it out, but the 55c val (which supports [[tetracot]]) maps it to 1\55. It can also be used for [[mohajira]] and [[liese]] temperaments. It also supports an extremely sharp tuning of [[huygens|huygens/undecimal meantone]] using the 55de [[val]], meaning that primes 7 and 11 are mapped very sharply to their second-best mapping. 55edo is a [[zeta valley edo]], suggesting it does not approximate the harmonic series very well for its size. | ||
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| 8\55 | | 8\55 | ||
| 174.5 | | 174.5 | ||
| [[10/9]]~[[11/10]] | | [[10/9]]~[[11/10]]<br>[[31/28]] | ||
| [[Tetracot]] (55c) | | [[Tetracot]] (55c)<br>Tricesoprimal tetracot analog (55) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 550: | Line 550: | ||
| 501.8 | | 501.8 | ||
| 4/3 | | 4/3 | ||
| [[Meantone]] (55d) | | [[Meantone]] (55d) / [[Meantone_family#Mildtone|Mildtone]] (55) | ||
|- | |- | ||
| 1 | | 1 | ||