Talk:159edo/Notation: Difference between revisions

Line 174:

: BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.

:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are ~~navigational primes~~ (~~for definition~~ of ~~my term "navigational prime" see~~ [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|~~here~~]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval ~~in the sense you noted~~, as 33/32 and 8192/8019 add up to 256/243... However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma. As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]]. This on its face means that there are already multiple types of parachromatic quartertones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)

:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are significant (which, after posting the initial version of this comment, I have confirmed through further investigation and [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|documented my findings on the matter]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval, as 33/32 and 8192/8019 add up to 256/243... However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma. As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]]. This on its face means that there are already multiple types of parachromatic quartertones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)

:: If I take the logic of what I said in the previous comment, that means that a stack of two 33/32 quartertones, plus 8192/8019 plus 729/704 is a full 9/8 whole tone- that means that four quartertones equals a whole tone... If, on the other hand, the rastma is taken from 729/704 and added to 8192/8019, the result is a third 33/32 quartertone plus [[4096/3993]]- another paradiatonic quartertone. This would actually make the addition much more straightforward, as a stack of three 33/32 quartertones plus 4096/3993 is also 9/8. So yes, four quartertones *do* in fact add up to a whole tone. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 15 October 2020 (UTC)

@@ Line 174: / Line 174: @@
 : BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.
-:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are navigational primes (for definition of my term "navigational prime" see [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|here]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval in the sense you noted, as 33/32 and 8192/8019 add up to 256/243...  However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma.  As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]].  This on its face means that there are already multiple types of parachromatic quartertones.  --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)
+:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are significant (which, after posting the initial version of this comment, I have confirmed through further investigation and [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|documented my findings on the matter]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval, as 33/32 and 8192/8019 add up to 256/243...  However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma.  As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]].  This on its face means that there are already multiple types of parachromatic quartertones.  --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)
 :: If I take the logic of what I said in the previous comment, that means that a stack of two 33/32 quartertones, plus 8192/8019 plus 729/704 is a full 9/8 whole tone- that means that four quartertones equals a whole tone...  If, on the other hand, the rastma is taken from 729/704 and added to 8192/8019, the result is a third 33/32 quartertone plus [[4096/3993]]- another paradiatonic quartertone.  This would actually make the addition much more straightforward, as a stack of three 33/32 quartertones plus 4096/3993 is also 9/8.  So yes, four quartertones *do* in fact add up to a whole tone. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 15 October 2020 (UTC)