User talk:SAKryukov: Difference between revisions

Line 353:

::::::: It can be interesting but perhaps later. — [[User:SAKryukov|SA]], ''Tuesday 2020 December 1, 07:35 UTC''

:::::::: Well, since I already typed out my reasoning, I might as well post it, though do feel free to read about it later if need be...

:::::::: The Quartisma, 117440512/117406179, is the difference between 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 best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest two-interval combination 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.

:::::::: the Alpharabian comma, 131769/131072, is the difference between a stack of two 128/121 diatonic semitones and a 9/8 whole tone. The comma gets its name from the association between al-Farabi with the 33/32 quartertone- which is part of the 2-3-11-based tuning. Specifically, it comes through an analogy between the familiar association between Pythagoreas and 3-prime-based tuning on one hand, and the aformementioned association between al-Farabi with the 33/32 quartertone on the other. This analogy is furthered by the fact that 131769/131072 is similar to that of the Pythagorean comma in that it relates diatonic semitones to the 9/8 whole tone.

:::::::: The Betarabian comma, 264627/262144, is the sum of the schisma and the biyatisma (121/120), as well as the sum of the Alpharabian comma and the rastma (243/242). The term "Betarabian" is a derivative of "Alpharabian", and was coined on account of both the rastma being the comma which separates primary and secondary 2-3-11-based intervals and the term "Alpharabian" itself containing the word "Alpha" within it- all that was needed was for "Beta" to be put in place of the "Alpha".

:::::::: I hope this all makes sense now... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:51, 1 December 2020 (UTC)

::: Oh, great! Huygens-Fokker Foundation's list of intervals you referenced in the first paragraph of this section. It can help me to explain to you what is that very characteristic of communication problems I can see in the musicians. In the list, you can see the set of rational-number intervals and some names. Hopefully, all rational numbers in the list are irreducible fractions. What information does this page carry? Next to nothing. The only possible use is this: when you already got some interval from some other source, say, from your own calculation, you can check up: is it one of the well-known intervals or not, and, if it is, what is its well-known name? Even this information has some uncertainty, because, strictly speaking, "well-known" is something uncertain, so the only definitive information you get is this: is my interval on the Huygens-Fokker Foundation's list? :-). And yes, this is exactly what you've checked in this case. You cannot learn anything about any of the concrete commas from this page. For the contrast example, look at any good Wikipedia page. Sometimes you can start from some reference and end up with the study of an entire field of science... — [[User:SAKryukov|SA]], ''Tuesday 2020 December 1, 02:06 UTC''

@@ Line 353: / Line 353: @@
 ::::::: It can be interesting but perhaps later. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Tuesday&nbsp;2020&nbsp;December&nbsp;1,&nbsp;07:35&nbsp;UTC''
+:::::::: Well, since I already typed out my reasoning, I might as well post it, though do feel free to read about it later if need be...
+:::::::: The Quartisma, 117440512/117406179, is the difference between 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 best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest two-interval combination 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.
+:::::::: the Alpharabian comma, 131769/131072, is the difference between a stack of two 128/121 diatonic semitones and a 9/8 whole tone.  The comma gets its name from the association between al-Farabi with the 33/32 quartertone- which is part of the 2-3-11-based tuning.  Specifically, it comes through an analogy between the familiar association between Pythagoreas and 3-prime-based tuning on one hand, and the aformementioned association between al-Farabi with the 33/32 quartertone on the other.  This analogy is furthered by the fact that 131769/131072 is similar to that of the Pythagorean comma in that it relates diatonic semitones to the 9/8 whole tone.
+:::::::: The Betarabian comma, 264627/262144, is the sum of the schisma and the biyatisma (121/120), as well as the sum of the Alpharabian comma and the rastma (243/242).  The term "Betarabian" is a derivative of "Alpharabian", and was coined on account of both the rastma being the comma which separates primary and secondary 2-3-11-based intervals and the term "Alpharabian" itself containing the word "Alpha" within it- all that was needed was for "Beta" to be put in place of the "Alpha".
+:::::::: I hope this all makes sense now... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:51, 1 December 2020 (UTC)
 ::: Oh, great! Huygens-Fokker Foundation's list of intervals you referenced in the first paragraph of this section. It can help me to explain to you what is that very characteristic of communication problems I can see in the musicians. In the list, you can see the set of rational-number intervals and some names. Hopefully, all rational numbers in the list are irreducible fractions. What information does this page carry? Next to nothing. The only possible use is this: when you already got some interval from some other source, say, from your own calculation, you can check up: is it one of the well-known intervals or not, and, if it is, what is its well-known name? Even this information has some uncertainty, because, strictly speaking, "well-known" is something uncertain, so the only definitive information you get is this: is my interval on the Huygens-Fokker Foundation's list? :-). And yes, this is exactly what you've checked in this case. You cannot learn anything about any of the concrete commas from this page. For the contrast example, look at any good Wikipedia page. Sometimes you can start from some reference and end up with the study of an entire field of science... &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Tuesday&nbsp;2020&nbsp;December&nbsp;1,&nbsp;02:06&nbsp;UTC''