Ploidacot/Monocot: Difference between revisions

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In the 7-limit, [[7/4]] can be simply mapped to a subminor seventh (doubly diminished octave, an interval of about 973{{c}} when justly tuned) with lower accuracy compared to helmholtz; this extension is called [[garibaldi]]. In the >11-limit, 11/8 can be found at a hyperfourth (3x-augmented second), and 13/8 at a hyperminor sixth (3x-augmented fourth); this extension is called [[cassandra]].

[[Pontiac]] instead maps it to a more complex triply ~~sub~~ major sixth (pentuply augmented third), but with practically no loss of accuracy compared to schismic. Interpretations to other primes can be found very deep in the monocot chain, as in [[ponta]].

[[Pontiac]] instead maps it to a more complex triply super major sixth (pentuply augmented third), but with practically no loss of accuracy compared to schismic. Interpretations to other primes can be found very deep in the monocot chain, as in [[ponta]].

==== Gary ====

[[Gary]] can be seen as the no-5 restriction of cassandra, keeping the maps of 7/4 and 11/8, so the pythagorean comma is equal to the septimal comma. ~~Unlike schismic, it~~ achieves far greater accuracy compared to cassandra, qualifying as a microtemperament. Additionally, Its major third also maps with incredible accuracy to [[19/15]].

[[Gary]] can be seen as the no-5 restriction of cassandra, keeping the maps of 7/4 and 11/8, so the pythagorean comma is equal to the septimal comma. It achieves far greater accuracy compared to cassandra much like schismic, qualifying as a microtemperament, however, it tunes fifths slightly sharp, not slightly flat of just. Additionally, Its major third also maps with incredible accuracy to [[19/15]].

==== Cotoneum ====

[[Cotoneum]] finds a way to extend gary into the whole >11-limit within monocot with only a slight loss accuracy, though with very high complexity. It finds very complex approximations of 5/4 and 13/8 as -49 and +61 fifths, where the [[41-comma]] now can act as an [[aberschisma]] accidental.

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 In the 7-limit, [[7/4]] can be simply mapped to a subminor seventh (doubly diminished octave, an interval of about 973{{c}} when justly tuned) with lower accuracy compared to helmholtz; this extension is called [[garibaldi]]. In the >11-limit, 11/8 can be found at a hyperfourth (3x-augmented second), and 13/8 at a hyperminor sixth (3x-augmented fourth); this extension is called [[cassandra]].
-[[Pontiac]] instead maps it to a more complex triply sub major sixth (pentuply augmented third), but with practically no loss of accuracy compared to schismic. Interpretations to other primes can be found very deep in the monocot chain, as in [[ponta]].
+[[Pontiac]] instead maps it to a more complex triply super major sixth (pentuply augmented third), but with practically no loss of accuracy compared to schismic. Interpretations to other primes can be found very deep in the monocot chain, as in [[ponta]].
 ==== Gary ====
-[[Gary]] can be seen as the no-5 restriction of cassandra, keeping the maps of 7/4 and 11/8, so the pythagorean comma is equal to the septimal comma. Unlike schismic, it achieves far greater accuracy compared to cassandra, qualifying as a microtemperament. Additionally, Its major third also maps with incredible accuracy to [[19/15]].
+[[Gary]] can be seen as the no-5 restriction of cassandra, keeping the maps of 7/4 and 11/8, so the pythagorean comma is equal to the septimal comma. It achieves far greater accuracy compared to cassandra much like schismic, qualifying as a microtemperament, however, it tunes fifths slightly sharp, not slightly flat of just. Additionally, Its major third also maps with incredible accuracy to [[19/15]].
 ==== Cotoneum ====
 [[Cotoneum]] finds a way to extend gary into the whole >11-limit within monocot with only a slight loss accuracy, though with very high complexity. It finds very complex approximations of 5/4 and 13/8 as -49 and +61 fifths, where the [[41-comma]] now can act as an [[aberschisma]] accidental.