2100edo: Difference between revisions

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The ~~2100 equal division divides the octave into 2100 parts of precisely 4/7 cents (0.5714 cents) each. The~~ patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit ~~schismatic aka~~ [[~~Schismatic_family~~|helmholtz]] temperament, and the 7-limit [[~~Schismatic_family#Sesquiquartififths|~~sesquiquartififths ~~temperament~~]]. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but ~~<~~2100 ~~3319 4876 5890|~~ is notable for being ~~nearly identical~~ to [[~~Quarter-comma_meantone|~~quarter-comma meantone]].

The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to [[quarter-comma meantone]].

=== Odd harmonics ===

=== Subsets and supersets ===

Since 2100 factors into {{factorization|2100}}, 2100edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050 }}.

[[Category:Meantone]]

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-The 2100 equal division divides the octave into 2100 parts of precisely 4/7 cents (0.5714 cents) each. The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka [[Schismatic_family|helmholtz]] temperament, and the 7-limit [[Schismatic_family#Sesquiquartififths|sesquiquartififths temperament]]. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but &lt;2100 3319 4876 5890| is notable for being nearly identical to [[Quarter-comma_meantone|quarter-comma meantone]].
+{{Infobox ET}}
+{{ED intro}}
+The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to [[quarter-comma meantone]].
+=== Odd harmonics ===
+{{Harmonics in equal|2100}}
+=== Subsets and supersets ===
+Since 2100 factors into {{factorization|2100}}, 2100edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050 }}.
+[[Category:Meantone]]