5L 2s: Difference between revisions

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The near-just part of the region is of interest mainly for those interested in [[Pythagorean tuning]] and large, accurate EDO systems based on close-to-Pythagorean fifths, such as [[41edo|41EDO]] and [[53edo|53EDO]]. This class of tunings is called [[schisma|schismic]] temperament; these tunings can approximate 5-limit harmonies very accurately by [[tempering out]] a small comma called the [[schisma]]. (Technically, 12EDO tempers out the schisma and thus is a schismic tuning, but it is nowhere near as accurate as schismic tunings can be.)

The sharp-of-just part of this range includes so-called "[[neogothic]]" or "parapyth" systems, which tune the diatonic major third slightly sharply of [[81/64]] (around [[14/11]]) and the diatonic minor third slightly flatly of [[32/27]] (around [[13/11]]). Good neogothic EDOs include [[29edo|29EDO]] and [[46edo|46EDO]]. [[17edo|17EDO]] is often considered the sharper end of the neogothic spectrum; its major third at 423 cents is considerably more discordant than in flatter neogothic tunings.

The sharp-of-just part of this range includes so-called "[[neogothic]]" or "parapyth" systems, which tune the diatonic major third slightly sharply of [[81/64]] (around [[14/11]], or slightly flatter, like [[20/17]] or [[33/26]]) and the diatonic minor third slightly flatly of [[32/27]] (around [[13/11]], or slightly flatter, like [[20/17]] or [[33/28]]). Good neogothic EDOs include [[29edo|29EDO]] and [[46edo|46EDO]]. [[17edo|17EDO]] is often considered the sharper end of the neogothic spectrum; its major third at 423 cents is considerably more discordant than in flatter neogothic tunings.

=== Parahard to ultrahard ===

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 The near-just part of the region is of interest mainly for those interested in [[Pythagorean tuning]] and large, accurate EDO systems based on close-to-Pythagorean fifths, such as [[41edo|41EDO]] and [[53edo|53EDO]]. This class of tunings is called [[schisma|schismic]] temperament; these tunings can approximate 5-limit harmonies very accurately by [[tempering out]] a small comma called the [[schisma]]. (Technically, 12EDO tempers out the schisma and thus is a schismic tuning, but it is nowhere near as accurate as schismic tunings can be.)
-The sharp-of-just part of this range includes so-called "[[neogothic]]" or "parapyth" systems, which tune the diatonic major third slightly sharply of [[81/64]] (around [[14/11]]) and the diatonic minor third slightly flatly of [[32/27]] (around [[13/11]]). Good neogothic EDOs include [[29edo|29EDO]] and [[46edo|46EDO]]. [[17edo|17EDO]] is often considered the sharper end of the neogothic spectrum; its major third at 423 cents is considerably more discordant than in flatter neogothic tunings.
+The sharp-of-just part of this range includes so-called "[[neogothic]]" or "parapyth" systems, which tune the diatonic major third slightly sharply of [[81/64]] (around [[14/11]], or slightly flatter, like [[20/17]] or [[33/26]]) and the diatonic minor third slightly flatly of [[32/27]] (around [[13/11]], or slightly flatter, like [[20/17]] or [[33/28]]). Good neogothic EDOs include [[29edo|29EDO]] and [[46edo|46EDO]]. [[17edo|17EDO]] is often considered the sharper end of the neogothic spectrum; its major third at 423 cents is considerably more discordant than in flatter neogothic tunings.
 === Parahard to ultrahard ===