Ploidacot/Monocot: Difference between revisions

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=== Low accuracy ===

=== Mavila ===

==== Mavila ====

[[Mavila]] is an exotemperament that flattens the fifth beyond the diatonic range (to around 670–680{{c}}) so that the "major third" maps flatter than the "minor third", meaning that the "minor third" can be mapped to 5/4 and the "major third" can be mapped to 6/5. This has the effect of "swapping" major and minor intervals from what they are in meantone. This means that the normal chain-of-fifths interval names stop making much sense (but see in [[Mavila#Notation]]).

=== Deeptone ===

==== Deeptone ====

[[Deeptone]] flattens the fifth to around 690{{c}}, so the major third maps to [[16/13]] and the augmented third to [[5/4]], with apotomes mapped so small that they can work as sixth-tones.

=== Trienstonian ===

==== Trienstonian ====

[[Trienstonian]] is an exotemperament where the fifth is tuned so sharp that the major sixth maps to [[7/4]]. This is thus tuned best with tunings around [[5edo]] or sharper, which generate oneirotonic (5L 3s), not diatonic scales.

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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.

@@ Line 93: / Line 93: @@
 === Low accuracy ===
-=== Mavila ===
+==== Mavila ====
 [[Mavila]] is an exotemperament that flattens the fifth beyond the diatonic range (to around 670–680{{c}}) so that the "major third" maps flatter than the "minor third", meaning that the "minor third" can be mapped to 5/4 and the "major third" can be mapped to 6/5. This has the effect of "swapping" major and minor intervals from what they are in meantone. This means that the normal chain-of-fifths interval names stop making much sense (but see in [[Mavila#Notation]]).
-=== Deeptone ===
+==== Deeptone ====
 [[Deeptone]] flattens the fifth to around 690{{c}}, so the major third maps to [[16/13]] and the augmented third to [[5/4]], with apotomes mapped so small that they can work as sixth-tones.
-=== Trienstonian ===
+==== Trienstonian ====
 [[Trienstonian]] is an exotemperament where the fifth is tuned so sharp that the major sixth maps to [[7/4]]. This is thus tuned best with tunings around [[5edo]] or sharper, which generate oneirotonic (5L 3s), not diatonic scales.
@@ Line 119: / Line 119: @@
 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.