Talk:159edo/Notation: Difference between revisions

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: 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_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)

Revision as of 07:21, 15 October 2020 view source TallKite (talk \| contribs) autopatrolled, Sysops 3,990 edits →My Second Idea for a Notation System ← Older edit		Revision as of 14:17, 15 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary Newer edit →
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	: 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.		: 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_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)