User talk:SAKryukov: Difference between revisions

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:::::::: The Quartisma, 117440512/117406179, is the difference between a stack of five 33/32 quartertones and one 7/6 subminor third, and since 33/32 is a quartertone, while the comma itself is unnoticeable, I came up with the name "quartisma" based on "quartertone" and "schisma".

:::::::: The Nexus comma, 1771561/1769472, is the difference between a stack of three 128/121 Alpharabian diatonic semitones and a 32/27 minor third. The 128/121 semitone is an example of pure 11 prime interval, while the 32/27 minor third is an example of pure 3 prime interval, and both the 11 prime and the 3 prime are significant in their own ways. Specifically, while the 3 prime has its connections to the diatonic scale, and the perfect intervals 3/2 and 4/3, the 11 prime can be mathematically calculated to be the virtually the best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest known combination of two rational quartertone intervals that can be added together to make a 9/8 whole tone. Since tempering out 1771561/1769472 joins the 3 prime chain and the 11 prime chain together, it makes sense to call it the "nexus comma".

:::::::: The Nexus comma, 1771561/1769472, is the difference between a stack of three 128/121 Alpharabian diatonic semitones and a 32/27 minor third. The 128/121 semitone is an example of pure 11 prime interval, while the 32/27 minor third is an example of pure 3 prime interval, and both the 11 prime and the 3 prime are significant in their own ways. Specifically, while the 3 prime has its connections to the diatonic scale, and the perfect intervals 3/2 and 4/3, the 11 prime can be mathematically calculated to be the virtually the best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest known combination of two distinct, rational quartertone intervals that can be added together to make a 9/8 whole tone. Since tempering out 1771561/1769472 joins the 3 prime chain and the 11 prime chain together, it makes sense to call it the "nexus comma".

:::::::: The Symbiotic comma is the difference between 77/72 and 2187/2048, and the sum of the quartisma and the nexus comma. It gets its name both from the fact that it is tempered out in such notable temperaments as vishnu, newt, kwai, supers, guiron and amity, and, from the fact that it also makes a good extension to a number of other temperaments such as canou.

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 :::::::: The Quartisma, 117440512/117406179, is the difference between a stack of five 33/32 quartertones and one 7/6 subminor third, and since 33/32 is a quartertone, while the comma itself is unnoticeable, I came up with the name "quartisma" based on "quartertone" and "schisma".
-:::::::: The Nexus comma, 1771561/1769472, is the difference between a stack of three 128/121 Alpharabian diatonic semitones and a 32/27 minor third.  The 128/121 semitone is an example of pure 11 prime interval, while the 32/27 minor third is an example of pure 3 prime interval, and both the 11 prime and the 3 prime are significant in their own ways.  Specifically, while the 3 prime has its connections to the diatonic scale, and the perfect intervals 3/2 and 4/3, the 11 prime can be mathematically calculated to be the virtually the best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest known combination of two rational quartertone intervals that can be added together to make a 9/8 whole tone.  Since tempering out 1771561/1769472 joins the 3 prime chain and the 11 prime chain together, it makes sense to call it the "nexus comma".
+:::::::: The Nexus comma, 1771561/1769472, is the difference between a stack of three 128/121 Alpharabian diatonic semitones and a 32/27 minor third.  The 128/121 semitone is an example of pure 11 prime interval, while the 32/27 minor third is an example of pure 3 prime interval, and both the 11 prime and the 3 prime are significant in their own ways.  Specifically, while the 3 prime has its connections to the diatonic scale, and the perfect intervals 3/2 and 4/3, the 11 prime can be mathematically calculated to be the virtually the best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest known combination of two distinct, rational quartertone intervals that can be added together to make a 9/8 whole tone.  Since tempering out 1771561/1769472 joins the 3 prime chain and the 11 prime chain together, it makes sense to call it the "nexus comma".
 :::::::: The Symbiotic comma is the difference between 77/72 and 2187/2048, and the sum of the quartisma and the nexus comma.  It gets its name both from the fact that it is tempered out in such notable temperaments as vishnu, newt, kwai, supers, guiron and amity, and, from the fact that it also makes a good extension to a number of other temperaments such as canou.