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:::::::::: Ah.  I do know that some of the functions of certain ''rational'' intervals- namely tritones- are determined where they fall in relation to the ''irrational'' half-octave interval.  This is how I separate the Antitonic intervals into "sycophants" and "tyrants".  The fact that I'm one of the relatively few composers who seems to have worked rather extensively with Locrian mode (to where I now have a half-decent idea as to how to use it) has undoubtedly shaped my perceptions of tritones in particular...  From there, I was able to draw on the fact that both 11/8 and 16/11 have relatively small numerators and denominators (as expected of the early members of the harmonic series and subharmonic series), yet, at the same time seem to have high harmonic entropy like most tritones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:10, 25 November 2020 (UTC)
:::::::::: Ah.  I do know that some of the functions of certain ''rational'' intervals- namely tritones- are determined where they fall in relation to the ''irrational'' half-octave interval.  This is how I separate the Antitonic intervals into "sycophants" and "tyrants".  The fact that I'm one of the relatively few composers who seems to have worked rather extensively with Locrian mode (to where I now have a half-decent idea as to how to use it) has undoubtedly shaped my perceptions of tritones in particular...  From there, I was able to draw on the fact that both 11/8 and 16/11 have relatively small numerators and denominators (as expected of the early members of the harmonic series and subharmonic series), yet, at the same time seem to have high harmonic entropy like most tritones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:10, 25 November 2020 (UTC)
::::::::::: Aren't you mixing up something? hopefully just terminology? Tritone is strictly 1/2 of octave, that is, √2, apparently irrational number, not rational even in quotation marks. :-) I think tritone is very fundamental in modern and not-so-modern music, but it is much harder to explain, while rational ratio are apparently fundamental, and their role is on the surface. It's interesting how the concept of "correct" music changed with time. Until a certain time, even the seventh chord widely used these days were considered "disharmonious" and were banned, forget about the tritone... What you are righting looks very interesting though...


:::::::::: Perhaps I should start making more samples to demonstrate more of the kinds of structures where pitches related to the tonic by 11/8 and 16/11 prove to be very important.  If you learn the way you say you do, then I suppose it's only fitting for you to have more of these kinds of samples, as I'm discovering that "Folly of a Drunk" only scratches the surface of what 11/8 and 16/11 are capable of. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:21, 25 November 2020 (UTC)
:::::::::: Perhaps I should start making more samples to demonstrate more of the kinds of structures where pitches related to the tonic by 11/8 and 16/11 prove to be very important.  If you learn the way you say you do, then I suppose it's only fitting for you to have more of these kinds of samples, as I'm discovering that "Folly of a Drunk" only scratches the surface of what 11/8 and 16/11 are capable of. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:21, 25 November 2020 (UTC)
:::::::::::  Would be good. As I understand, one problem is the lack of notation. Recently, we worked with Braining exchanging the sequences produced by my keyboard, as in microtonal EDOs it was the only notation. I devised something roughly similar to MIDI for the exchange. Yes, I've read on some attempts to establish some generalized notation, but I don't think there is something good enough to accept it. Or do you address this problem?
:::::::::::  One other musicologist advised me to write a new section in the notation site (I don't have time now, if you are interested will find out a link), but I answered that I'm not much interested. First of all, this is not very productive work, a big waste of time. More importantly, I'm the one who clearly understands that the modern idea of notation itself is totally wrong, and it is related to the fact that musicians never had enough understanding of the concepts of abstraction, standards, and the like. There is only one layer between the graphically represented musical text and the instrument, and it is beyond any reason. Apparently, some nesting levels of abstraction are needed. Modern notation is usually considered to abstract out concrete instruments, but this is not true — in essence, this is still the same kind of tabs, tied to the piano, and not to abstract tonal system. I know that many musicians find it unbearable to hear such things, but I know it's true.


:::::: For the record, if you're interested in advancing your research on Just Intonation, you might want to check out what I'm doing for [[Alpharabian tuning]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:45, 24 November 2020 (UTC)
:::::: For the record, if you're interested in advancing your research on Just Intonation, you might want to check out what I'm doing for [[Alpharabian tuning]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:45, 24 November 2020 (UTC)