Talk:159edo/Notation: Difference between revisions

Line 175:

:: 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_Key_Signatures|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)

:: 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 [[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)

Revision as of 14:17, 15 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary ← Older edit		Revision as of 15:45, 15 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary Newer edit →
Line 175:		Line 175:

	:: 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_Key_Signatures\|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 navigational primes (for definition of my term "navigational prime" see [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_Key_Signatures\|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)

			:: 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 [[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)