Talk:IFDO: Difference between revisions

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:::::::: One thing I'm confused about is that I thought recently on Discord you said you preferred OD and UD over EFD and ELD, though it was on the condition that they be able to apply to divisions of irrational intervals and therefore be non-JI (which I noted was an unacceptable condition). I only find it slightly less unacceptable to use EFD where OD is possible, because of the implication that an EFD must be non-JI. But maybe I'm just a bit lost because there have been so many subtleties to this discussion, and it has been fragmented in so many places, and it's taken place relatively slowly over the course of many years, so it's hard for me to keep everything straight. I have probably accidentally said inconsistent things here or there, so I sincerely apologize if you find that I wasted your time or confused you due to something like that.

:::::::: Oh, but I did figure out what you meant by a "sequence division" in the discussion above. I think my confusion arose because we're using "sequence" in two different ways. The system I designed with Paul and Billy uses sequence as opposed to a division, i.e. open-ended as opposed to periodic. But you're using sequence as in arithmetic sequence, geometric sequence, harmonic sequence, etc. (which are closely related to arithmetic mean, geometric mean, harmonic mean, etc.) Sorry I didn't understand that immediately. So, I propose that since in your context, we can use "progression" as an exact synonym, we stick to using "progression" for that context, to avoid further miscommunication. Hopefully that works for you, too. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:55, 31 March 2023 (UTC)

::::::::: Hmmm, here's another way to speak of ''odo'''s lack of orthogonality: it contains redundant information, as both ''otonal'' and ''octave'' imply rationality and not becuz it has to be designed this way. An orthogonal system will have these kind of redundancies minimized, like that orthogonality in linear algebra, you know. In this case ado or efdo is sufficient to uniquely identify the object with rationality conveyed thru the divided interval itself, so it's advantageous. Using ''otonal'' will introduce a kind of perplexity in which we can find "grammatically" possible but "semantically" invalid combinations such as *''odφ''.

::::::::: I can see how ''sequence'' means two different things. What I was calling the ''sequence'' was also known as "linspace" in some programming libraries, if that makes any sense to you. For the open-ended sequence, let's say ''progression'' from now on.

::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:54, 1 April 2023 (UTC)

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 :::::::: One thing I'm confused about is that I thought recently on Discord you said you preferred OD and UD over EFD and ELD, though it was on the condition that they be able to apply to divisions of irrational intervals and therefore be non-JI (which I noted was an unacceptable condition). I only find it slightly less unacceptable to use EFD where OD is possible, because of the implication that an EFD must be non-JI. But maybe I'm just a bit lost because there have been so many subtleties to this discussion, and it has been fragmented in so many places, and it's taken place relatively slowly over the course of many years, so it's hard for me to keep everything straight. I have probably accidentally said inconsistent things here or there, so I sincerely apologize if you find that I wasted your time or confused you due to something like that.
 :::::::: Oh, but I did figure out what you meant by a "sequence division" in the discussion above. I think my confusion arose because we're using "sequence" in two different ways. The system I designed with Paul and Billy uses sequence as opposed to a division, i.e. open-ended as opposed to periodic. But you're using sequence as in arithmetic sequence, geometric sequence, harmonic sequence, etc. (which are closely related to arithmetic mean, geometric mean, harmonic mean, etc.) Sorry I didn't understand that immediately. So, I propose that since in your context, we can use "progression" as an exact synonym, we stick to using "progression" for that context, to avoid further miscommunication. Hopefully that works for you, too. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:55, 31 March 2023 (UTC)
+::::::::: Hmmm, here's another way to speak of ''odo'''s lack of orthogonality: it contains redundant information, as both ''otonal'' and ''octave'' imply rationality and not becuz it has to be designed this way. An orthogonal system will have these kind of redundancies minimized, like that orthogonality in linear algebra, you know. In this case ado or efdo is sufficient to uniquely identify the object with rationality conveyed thru the divided interval itself, so it's advantageous. Using ''otonal'' will introduce a kind of perplexity in which we can find "grammatically" possible but "semantically" invalid combinations such as *''odφ''.
+::::::::: I can see how ''sequence'' means two different things. What I was calling the ''sequence'' was also known as "linspace" in some programming libraries, if that makes any sense to you. For the open-ended sequence, let's say ''progression'' from now on.
+::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:54, 1 April 2023 (UTC)