JI precision level capture zone boundary defining EDA step names (besides tina)
Posted: Thu May 14, 2020 2:22 am
I'm curious if anyone has ever needed or proposed names for steps of the key EDOs used for defining boundaries of JI precision level capture zones, besides the "tina".
If the 8539-EDO step of the extreme precision level is called a tina, perhaps the other precision levels could take other female given names. The "secor", another irrational interval related to Sagittal by virtue of George, of course, takes its name from a surname (of a specific person who was male), and it's not even an EDO step, so it's certainly not the same, but it's at least another signal that person names may be good for equal divisions of rationals. The only other named big EDO step I can think of is a tredek which is not a person's name... but oh well.
I bring this up because I experienced a brief episode of confusion wherein I conflated the tina, an irrational value, with schisminas, schismas, kleismas, commas, and the like, which are all rational. I'm not sure, but it might actually prevent confusion if we had names for other key irrational pitch intervals, so that "tina" wouldn't be this awkward, barely acknowledged exception, but actually a member of a separate well-recognized category.
I'm not suggesting that we develop a parallel size classification for steps of EDOs, e.g. "anything smaller than 8000-EDO is a tina". That would make some sense, but I'm not sure if its usefulness would be worth the effort of agreeing on the boundary-defining EDOs (akin to the square roots of 3-limit commas used to define boundaries of the rational size classes). I believe it would be better just to focus on names for 2460-EDO etc.
While we're at it, "JI precision level capture zone boundary defining EDO" is quite the mouthful. It might be helpful if we had a pithier of referring to them. I'm looking toward the documentation for Sagittal for this.
Update: I've noticed on the thread about the JI Notation Spreadsheet that @Dave Keenan refers to "the 140th mina" of the extreme JI precision level. It seems like in that case he is using "mina" as equivalent to one step of its capture zone boundary defining EDO. In the case of the extreme precision level, this works out alright, because is 0.423¢ and 1 step of 233-EDA is 0.488¢, so that's close enough. But this breaks down already at the very high precision level, because one schisma (1.954¢) is not close enough to one step of 58-EDA (1.960¢). Well that's what I typed but those numbers are actually even closer, closer still considering them proportionally. But why then does the standard Very High Precision JI Boundaries give 1.3 as the address for ? I guess it's just so it can get squeezed in there between and .
So then I guess actually we may want to take this all the other direction and ensure that we have a rational version of a tina. I know we do from this post as 121:1225n but it's not 3-limit which isn't great (perhaps you could find one by summing together some of the unnoticeable 3-limit commas). And then I guess it's worth pointing out that we use 'mina as an abbreviation for schismina in general, but we also seem to use it specifically to refer to the 455n. Or did I get that wrong and "mina" only refers to the 455n while schismina is the size category? Because if so then maybe we're already onto something, where "mina" refers to either the rational 455n or its step of 233-EDA form, and "tina" refers to either the rational ?t (I guess it would need its own category and to be signified with a little 't')or its step of 809-EDA, and then maybe something like "isma" refers to either the rational 5s or its step of 58-EDA form.
By the way, as I wrote this out, I switched from EDO to EDA, because I'm pretty sure somewhere at some point I saw Dave say something like that they started out defining capture zones by EDOs before they realized eventually it was EDAs that did a better job. But I can't seem to find this. In any case, EDAs are definitely what they're split up into in the JI Notation Sheet, so we'll go with that.
If the 8539-EDO step of the extreme precision level is called a tina, perhaps the other precision levels could take other female given names. The "secor", another irrational interval related to Sagittal by virtue of George, of course, takes its name from a surname (of a specific person who was male), and it's not even an EDO step, so it's certainly not the same, but it's at least another signal that person names may be good for equal divisions of rationals. The only other named big EDO step I can think of is a tredek which is not a person's name... but oh well.
I bring this up because I experienced a brief episode of confusion wherein I conflated the tina, an irrational value, with schisminas, schismas, kleismas, commas, and the like, which are all rational. I'm not sure, but it might actually prevent confusion if we had names for other key irrational pitch intervals, so that "tina" wouldn't be this awkward, barely acknowledged exception, but actually a member of a separate well-recognized category.
I'm not suggesting that we develop a parallel size classification for steps of EDOs, e.g. "anything smaller than 8000-EDO is a tina". That would make some sense, but I'm not sure if its usefulness would be worth the effort of agreeing on the boundary-defining EDOs (akin to the square roots of 3-limit commas used to define boundaries of the rational size classes). I believe it would be better just to focus on names for 2460-EDO etc.
While we're at it, "JI precision level capture zone boundary defining EDO" is quite the mouthful. It might be helpful if we had a pithier of referring to them. I'm looking toward the documentation for Sagittal for this.
Update: I've noticed on the thread about the JI Notation Spreadsheet that @Dave Keenan refers to "the 140th mina" of the extreme JI precision level. It seems like in that case he is using "mina" as equivalent to one step of its capture zone boundary defining EDO. In the case of the extreme precision level, this works out alright, because is 0.423¢ and 1 step of 233-EDA is 0.488¢, so that's close enough. But this breaks down already at the very high precision level, because one schisma (1.954¢) is not close enough to one step of 58-EDA (1.960¢). Well that's what I typed but those numbers are actually even closer, closer still considering them proportionally. But why then does the standard Very High Precision JI Boundaries give 1.3 as the address for ? I guess it's just so it can get squeezed in there between and .
So then I guess actually we may want to take this all the other direction and ensure that we have a rational version of a tina. I know we do from this post as 121:1225n but it's not 3-limit which isn't great (perhaps you could find one by summing together some of the unnoticeable 3-limit commas). And then I guess it's worth pointing out that we use 'mina as an abbreviation for schismina in general, but we also seem to use it specifically to refer to the 455n. Or did I get that wrong and "mina" only refers to the 455n while schismina is the size category? Because if so then maybe we're already onto something, where "mina" refers to either the rational 455n or its step of 233-EDA form, and "tina" refers to either the rational ?t (I guess it would need its own category and to be signified with a little 't')or its step of 809-EDA, and then maybe something like "isma" refers to either the rational 5s or its step of 58-EDA form.
By the way, as I wrote this out, I switched from EDO to EDA, because I'm pretty sure somewhere at some point I saw Dave say something like that they started out defining capture zones by EDOs before they realized eventually it was EDAs that did a better job. But I can't seem to find this. In any case, EDAs are definitely what they're split up into in the JI Notation Sheet, so we'll go with that.