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::::::::::: 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...
::::::::::: 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...
:::::::::::: No.  There are multiple ''rational'' intervals that are called [[tritone|tritones]]- see [[45/32]] and [[64/45]] for just two examples, or at least that's the case in English (I assume Russian has different names for intervals).  That said, the specific √2/1 tritone- the half-octave, as I'm referring to it here- is definitely a special kind of tritione and is indeed very fundamental in both modern and not-so-modern music. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:30, 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)
:::::::::: 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?
:::::::::::  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.
 
:::::::::::: So far, I'm assuming that the first task is to create a set of proper interval names- yes, we do need to build on the historical note names for purposes of making our concepts understandable, and for that, I'm taking inspiration from [[SHEFKHED interval names]], and you can see some my work in dealing with quartertones on the [[Alpharabian tuning]] page. I would also recommend attempting to build off of conventional notation for the same reasons, and I do have [[Talk:159edo_notation #My Second Idea for a Notation System|ideas in the works for 159edo notation]].  Yes, judging from what I hear you saying, there's bound to be problems, but since the diatonic scale is fundamental on account of its close ties to the 3 prime, problems related to this are on some level unavoidable. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:30, 25 November 2020 (UTC)
 
::::::::::: 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.
 
:::::::::::: On one level, you are right, but if you trace the origin of the piano system far enough back, you see that the idea for the default group of seven notes goes back to the Romans, who misunderstood the direction of construction and the arrangement of note names when they tried to borrow it from the Ancient Greeks before them.  Also, there's a reason that 3-prime-based just intonation is called "Pythagorean tuning" in English after all. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:30, 25 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)
:::::: 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)