Fifth-chroma temperaments: Difference between revisions

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Absurdity was extended to the 29-limit; the mapping for prime 29 is obvious via 1\7 = 32/29 being accurate. The mapping for prime 23 is via 23/20 being equated with 8/7, which isn't ideal, but both edo tunings (77edo and 84edo) have resources to make various elements of 29-limit harmony possible.

==== Novamajor ====

This temperament, originally found independently in the form of a peculiar high-badness 5-limit temperament called "Isnes" ("Sensi" backwards, and can be understood as tempering [[19791209299968/19073486328125|(128/125)<sup>5</sup> / (25/24)<sup>2</sup>]]), is a full 29-limit temperament that is better understood not in terms of generators (where it is very complex and doesn't make much musical sense) but instead as making the following intervals equidistant (which can be seen as a guarantee of a certain kind of metaphorical colour palette with certain properties):

* inframinor third: ~15/13

* subminor third: ~7/6

* neominor third: ~20/17 (note the absence of ~13/11, which here is ambiguous in mapping between novaminor third (77edo) and neominor third (80edo))

* novaminor third: ~19/16 (note the absence of ~25/21, which here is ambiguous in mapping between minor third (77edo) and novaminor third (80edo))

* minor third: ~6/5

* supraminor third: ~35/29~29/24~23/19 (note the absence of ~17/14~40/33, which here is ambiguous in mapping between supraminor third (77edo) and subneutral third (80edo))

* subneutral third: ~39/32~50/41~11/9

* superneutral third: ~27/22~16/13

* submajor third: ~36/29~56/45 (note the absence of ~26/21, which here is ambiguous in mapping between submajor third (77edo) and superneutral third (80edo))

* major third: ~5/4

* novamajor third: ~24/19~43/34~19/15

* neomajor third: ~14/11~37/29~23/18

* supermajor third: ~9/7

* ultramajor third: ~13/10

Therefore, the reason for the name "novamajor" is that the structure that the aforementioned "guarantee of a certain kind of metaphorical colour palette with certain properties" via making those intervals equidistant relates it directly to [[User:Godtone#Intervals|the interval colour names devised by User:Godtone]], with the most idiosyncratic term (that has seen least adoption by others) being "novamajor" and "novaminor", and as the novamajor third is the generator of this temperament, it seemed a fitting name. (The associated 5-limit temperament was discovered independently by User:Godtone with this high-limit application in mind, but isnes wasn't found at the time for various reasons including the ratio not being shown.)

@@ Line 65: / Line 65: @@
 {{ See also | Absurdity }}
 Absurdity was extended to the 29-limit; the mapping for prime 29 is obvious via 1\7 = 32/29 being accurate. The mapping for prime 23 is via 23/20 being equated with 8/7, which isn't ideal, but both edo tunings (77edo and 84edo) have resources to make various elements of 29-limit harmony possible.
+==== Novamajor ====
+{{ See also | Augmented–chromatic equivalence continuum }}
+This temperament, originally found independently in the form of a peculiar high-badness 5-limit temperament called "Isnes" ("Sensi" backwards, and can be understood as tempering [[19791209299968/19073486328125|(128/125)<sup>5</sup> / (25/24)<sup>2</sup>]]), is a full 29-limit temperament that is better understood not in terms of generators (where it is very complex and doesn't make much musical sense) but instead as making the following intervals equidistant (which can be seen as a guarantee of a certain kind of metaphorical colour palette with certain properties):
+* inframinor third: ~15/13
+* subminor third: ~7/6
+* neominor third: ~20/17 (note the absence of ~13/11, which here is ambiguous in mapping between novaminor third (77edo) and neominor third (80edo))
+* novaminor third: ~19/16 (note the absence of ~25/21, which here is ambiguous in mapping between minor third (77edo) and novaminor third (80edo))
+* minor third: ~6/5
+* supraminor third: ~35/29~29/24~23/19 (note the absence of ~17/14~40/33, which here is ambiguous in mapping between supraminor third (77edo) and subneutral third (80edo))
+* subneutral third: ~39/32~50/41~11/9
+* superneutral third: ~27/22~16/13
+* submajor third: ~36/29~56/45 (note the absence of ~26/21, which here is ambiguous in mapping between submajor third (77edo) and superneutral third (80edo))
+* major third: ~5/4
+* novamajor third: ~24/19~43/34~19/15
+* neomajor third: ~14/11~37/29~23/18
+* supermajor third: ~9/7
+* ultramajor third: ~13/10
+Therefore, the reason for the name "novamajor" is that the structure that the aforementioned "guarantee of a certain kind of metaphorical colour palette with certain properties" via making those intervals equidistant relates it directly to [[User:Godtone#Intervals|the interval colour names devised by User:Godtone]], with the most idiosyncratic term (that has seen least adoption by others) being "novamajor" and "novaminor", and as the novamajor third is the generator of this temperament, it seemed a fitting name. (The associated 5-limit temperament was discovered independently by User:Godtone with this high-limit application in mind, but isnes wasn't found at the time for various reasons including the ratio not being shown.)

Fifth-chroma temperaments: Difference between revisions

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