JI precision level capture zone boundary defining EDA step names (besides tina)

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JI precision level capture zone boundary defining EDA step names (besides tina)

Post by cmloegcmluin »

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.

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Re: JI precision level capture zone boundary defining EDA step names (besides tina)

Post by Dave Keenan »

Post by cmloegcmluin » Mon May 25, 2020 8:37 am

So is it the case that one step of 58-EDA can also be, without disclaimer, referred to as a "schisma"?

And one step of 47-EDA is actually pretty close to a schisma plus a (schis)mina, so could it be called a "mamina"?

And one step of 21-EDA is not super far from :|(: ... when we use the word "kleisma" outside of a specific kleisma, could it refer to a step of 21-EDA?

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Re: JI precision level capture zone boundary defining EDA step names (besides tina)

Post by Dave Keenan »

Post by Dave Keenan » Mon May 25, 2020 6:43 pm

Yes, in the context of discussing the EDAs that correspond to the JI precision levels, it's fine to use tina for 1 step of 809-EDA, mina for one step of 233-EDA and schisma for one step of 58-EDA. I can claim that neither tina nor mina is the name of a size category, although "mina" was derived by abbreviating "schismina". That requires that we not refer to say 5:19n (1216/1215) as the 5:19-mina, but only as the 5:19-schismina.

As you kind of pointed out, "schisma" only works as both a size category and a step of 58-EDA because historically "THE schisma" is the rational interval we call the 5-schisma, which is extremely close in size to the irrational 1/58th of an apotome.

This doesn't work with "kleisma" and 21-EDA because historically "THE kleisma" is the 5⁶-kleisma which is about 8.1 cents. You can however refer to 1 step of 21-EDA as a "quarter-comma" as in "quarter-comma meantone", being 1/4 of the 5-comma.

I'm unaware of any such name for 1/47-EDA. For "mamina" to make sense, we'd have to already be calling the 1/58th-apotome schisma a "ma". But this seems too easily confused with the "mi" and "mo" syllables for a mina.

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Re: JI precision level capture zone boundary defining EDA step names (besides tina)

Post by cmloegcmluin »

Dave Keenan wrote: ↑
Mon May 25, 2020 1:43 am
Yes, in the context of discussing the EDAs that correspond to the JI precision levels, it's fine to use tina for 1 step of 809-EDA, mina for one step of 233-EDA and schisma for one step of 58-EDA. I can claim that neither tina nor mina is the name of a size category, although "mina" was derived by abbreviating "schismina". That requires that we not refer to say 5:19n (1216/1215) as the 5:19-mina, but only as the 5:19-schismina.
Got it.

So when I said
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?
I was closer the second time: "schismina" is the size category, and is the one used in comma names such as the 455-schismina (where "mina" cannot be used), and "mina" only refers to a step of 233-EDA.
As you kind of pointed out, "schisma" only works as both a size category and a step of 58-EDA because historically "THE schisma" is the rational interval we call the 5-schisma, which is extremely close in size to the irrational 1/58th of an apotome.
Emphasis on the "kind of" ;)

So "tina" and "mina" are unambiguous, referring to nothing other than irrational EDA steps. "Schisma" is ambiguous though. If we really needed to, maybe we could distinguish them as the "just schisma" and the "EDA-schisma". But the necessity should be rare.
This doesn't work with "kleisma" and 21-EDA because historically "THE kleisma" is the 5⁶-kleisma which is about 8.1 cents.
I see. I didn't get the picture quite right from reading viewtopic.php?p=582#p582. I see now that an internet search turns up no other hits for "complex Pythagorean kleisma", "complex kleisma", or "Pythagorean kleisma" besides that post. So our size-category-defining 3-limit kleisma [ 317 -200 ⟩ is not THE kleisma by a long stretch. It'd have to beat out both the 5⁶-kleisma (which is not represented by a symbol in Sagittal) and the septimal kleisma (see here, here, and here) (what we call the 25/7k in Sagittal and represent with a :'::|(: ).
You can however refer to 1 step of 21-EDA as a "quarter-comma" as in "quarter-comma meantone", being 1/4 of the 5-comma.
Good observation.

If we ever wanted a single two-syllable word for it akin to tina and mina, then, could we call it a "quacom"? Meant to invoke quantom. Not QualComm. I'm not going to force the issue, though as I said in the OP, I do think that having names for all of these important EDA steps could help forestall conflation of the tina with the others.
I'm unaware of any such name for 1/47-EDA. For "mamina" to make sense, we'd have to already be calling the 1/58th-apotome schisma a "ma". But this seems too easily confused with the "mi" and "mo" syllables for a mina.
Ma mamina!

Yeah yeah yeah, I agree...

Well, 1°47-EDA is close to a ninth of the same comma. So that one could be a "nincom", as in "ninth-comma", and "you're a nincompoop if you're using the High precision level". :lol:

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