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

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

Post by cmloegmcluin »

Good point!

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

Post by FloraC »

"Athena" sounds so refreshing. One glimpse and I was exactly like
cmloegcmluin wrote: Sat Jun 13, 2020 3:49 ambut... c'mon, "athena"!
Moreover, it's a real word. So no need to create something like "medina", which is sheer artificial. Also I prefer "highna" to "highina", must I choose one.

This thread draws my interest cuz I'm exploring "kleisma-sized" edo recently.

I found a specific rank-2 temperament that tempers out most schisminas and is useful for finding "kleisma-sized" solutions. It's 224 & 270, called abigail, defined as tempering out 1716/1715, 2080/2079, 3025/3024 and 4096/4095. So all "kleisma-sized" intervals including (from large to small) 5120/5103, 325/324, 351/350, 352/351, 364/363, 385/384, 441/440 and 847/845 are tempered to one step.

The difference between 224et and 270et consists in how you classify 225/224~243/242 and 540/539. In 224et, 225/224~243/242 is treated as a "kleisma" and 540/539 is treated as a schism(in)a (therefore tempered out), so the avg size of a "kleisma" is larger. In 270et, 540/539 is treated as a "kleisma" and 225/224~243/242 equals two kleismas, so the avg size of "kleisma" is smaller.

There's a fact worth noting that the 5/7-kleisma factors into a 5-schisma (32805/32768) and a 7-schisma (33554432/33480783, 3.80 cents). So another difference is that 224et tempers out the 5-schisma whereas 270et tempers out the 7-schisma.

Ofc, 441/440 and 847/845 aren't in the region of kleisma by definition, let alone 540/539. That probably explains why 21eda is more natural as a "kleisma-sized" solution than 26eda (~270edo).

Nonetheless, I can't resist 20eda (198et and 212et in particular). It's so tempting to have a true neutral third.

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

Post by cmloegmcluin »

FloraC wrote: Sun Nov 15, 2020 9:01 pm "Athena" sounds so refreshing. One glimpse and I was exactly like
cmloegcmluin wrote: Sat Jun 13, 2020 3:49 ambut... c'mon, "athena"!
Moreover, it's a real word. So no need to create something like "medina", which is sheer artificial. Also I prefer "highna" to "highina", must I choose one.
Very interesting ideas in the rest of your post, @FloraC, but I do want to address this bit which is most directly related to the topic title. Dave and I have been working with ultrina, highina, and medina in the months since this discussion. If you use "athena", I'm sure people will know what you're talking about. And I am fond for it myself (it was my suggestion, after all)! But I know think that the advantages of the names unmistakably matching their corresponding JI precision level notation outweigh other considerations. Except mina, which of course kicked off the whole "ina" thing in the first place, and "tina", whose hysteresis (thanks again for that word, @Dave Keenan) we should not try to overcome. So we'll be using ultrina, highina, and medina in the official Sagittal materials and recommend you use them too. But it's not certainly something I'd want to quibble about.

Actually, though, we may not have actually considered "highna", or "hina". I think either of those still satisfy the condition of matching the corresponding JI precision level notation. So it's fine with me if we tweak that one. Let me know if anyone else has other thoughts on it.

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

Post by FloraC »

I understand this thread has been half a year old and what I say here may not matter. Keep on the great work. I'd love to see new official materials!

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

Post by cmloegmcluin »

FloraC wrote: Mon Nov 16, 2020 11:13 am I understand this thread has been half a year old and what I say here may not matter. Keep on the great work. I'd love to see new official materials!
Oh gosh! I really didn't mean to come across like your suggestions didn't matter. Sorry about that. In fact I do want to consider your suggestion of "highna".

I hope you'll find that decisions about fringe Sagittal concepts like this don't get made merely on the basis of opinion, or who shouts the loudest. Certainly I'm in no position to say what's what or not. I just showed up earlier this year myself. I suppose Dave has some "veto" power, being a co-creator and all, but he's not one to use it. We definitely value airing ideas and pros and cons and weighing everything in the balance. And some hysteresis can be overcome. Heck, I suggested we rename an entire notation of Sagittal, I made a case, and it came to pass ("Prime Factor" used to be "Multi-Sagittal"). So the last thing I want to do is discourage your creativity with improving Sagittal. Hope that clears things up.

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

Post by FloraC »

Clear.

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

Post by cmloegmcluin »

FYI, Dave and I were discussing elsewhere recently performing an experiment, where for each EDA, we'd find the least bad comma in the vicinity of each degree, and then average the badness of these commas. We'd then produce a chart showing how, as the EDA increases, the average badness goes down, but more importantly, we'd expect to find some local minima on its erratic way down, and we'd hope to find these minima at the EDA's which Sagittal's JI precision level notations organize themselves around. We kind of expect they'll be related to zeta peaks, but who knows.

Maybe I'm misunderstanding, but it sounds like you're looking at different EDAs to use directly as scales or tunings. Did I get that right? If so, it's certainly different than how Sagittal is using them in this context, but probably more related than I can easily imagine. This is pretty heady stuff for me still.

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

Post by FloraC »

Well, I don't use edas as tunings. I just find some important implications in edas, e.g. odd edas have no true neutral thirds, and vice versa.

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

Post by volleo6144 »

cmloegcmluin wrote: Mon Nov 16, 2020 2:11 pm Maybe I'm misunderstanding, but it sounds like you're looking at different EDAs to use directly as scales or tunings. Did I get that right? If so, it's certainly different than how Sagittal is using them in this context, but probably more related than I can easily imagine. This is pretty heady stuff for me still.
I'm not sure what's really beneficial about the EDA usage here either, outside of making it so that if we ever do decide to notate 17078edo then we don't run into notes that are precisely on the line between two symbols' capture zones. After all, 809eda = 8539.3847edo is actually much farther from Riemann's 8539.0083edo than actual 8539edo is (and 233eda = 2459.4272edo is literally closer to 2459 than 2460)...

Also note that the L/SS boundary just before the 488th tina differs by only a tiny amount based on which definition of the tina you're using (it's 487.9725 of 809eda and 487.9505 of 8539edo), so there aren't many commas that will fall in different tinas depending on our choice. (There will still be some, which is why I would have probably suggested that the boundaries be set with respect to 17078edo and not to 1618eda... had I been here to discuss at the time1.)

However, extending 809eda to a full tuning feels more ... theoretical and impractical, as it's not even 3-limit2 consistent (1:2 + 2:3 = 1:3, but 8539 + 4995 ≠ 13535)!

1 Seeing as we're already using a similar proposition (233eda instead of 2460edo) for the Extreme-precision notation, I'm feeling like we can't exactly change it anymore. Well, I mean... at least it's not objectively a mistake in quite as hilariously obvious a way as Unicode's U+FE18 ︘ Presentation Form for Vertical Right White Lenticular Brakcet...

2 by which I mean integer limit, because odd limit doesn't really make sense for a non-octave tuning
A random guy who sometimes doodles about Sagittal and microtonal music in general in his free time.

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

Post by Dave Keenan »

FloraC wrote: Sun Nov 15, 2020 9:01 pm "Athena" sounds so refreshing. One glimpse and I was exactly like
cmloegcmluin wrote: Sat Jun 13, 2020 3:49 ambut... c'mon, "athena"!
Moreover, it's a real word. So no need to create something like "medina", which is sheer artificial. Also I prefer "highna" to "highina", must I choose one.
Yes. For the medium-precision-level unit I prefer "athena", but spelled as "athina" (to fit the pattern of the others and avoid confusion with the goddess), because "Medina" happens to be the name of an ancient city (the second-holiest city in Islam) which could suggest that it couldn't possibly be related to the athenian set because that is named after the ancient city of Athens.
cmloegcmluin wrote: Mon Nov 16, 2020 9:16 am Actually, though, we may not have actually considered "highna", or "hina". I think either of those still satisfy the condition of matching the corresponding JI precision level notation. So it's fine with me if we tweak that one. Let me know if anyone else has other thoughts on it.
Yes. I prefer "hina" (pronounced "heena") to either "highna" or "highina".

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