That is correct. And yes "style" seems like a reasonable term for these. But I note that JI, Trojan and EDO are, in a sense, one style. That's the style where, for fifths in a small range of sizes (2 to 4 cents wide) we define a set of symbols, and capture zones for them, based on the tempered size of the symbols' commas. Although we haven't literally done that (yet) for fifth sizes other than Pythagorean (JI) or 700 cents (Trojan).cmloegcmluin wrote: ↑Tue Mar 31, 2020 3:57 am As far as I can find, this is the only place where such a notation has been proposed or worked with. And it's distinct from the previously existing four Sagittal notation styles* (JI, Trojan, EDO, Prime Factor).
See viewtopic.php?p=843#p843 and viewtopic.php?p=807#p807.
You're welcome.So, first of all, thank you for going to that length to find a Sagittal that worked for my use case!
Agreed.I personally think that this new style is worth keeping and maintaining.
Definitely worth a try.I'm also excited to say that I think I know what I'm doing enough now to hold some opinions, and maybe even suggest modifying your original proposal.
My motivation for this suggestion is that I'd like this notation to support even better accuracy; I want it to compare to Olympian. Your original suggestion capped out at 1.6 cent resolution. But I think with some tweaks we can make a logical notation that is accurate to a half cent.
You need to re-read page 13 of http://sagittal.org/sagittal.pdf from the section heading, and the last paragraph on page 15, and the first paragraph on page 23, and the third paragraph of http://sagittal.org/whatpitch.txt.Here's what I'm thinking: if we're devising a new distinct style, must we bind ourselves to the Trojan capture zones? We're using to represent a 25 cent alteration, while the default value of in JI notation is 16.544 cents. Why not just use the symbols which are a good balance of close to the alteration, and simple? Don't worry about the flag arithmetic or anything like that... this is the notation for dummies!
When the fifths are not pure (Pythagorean), the untempered size of the default comma should be irrelevant. It's the tempered size that matters. The 700c fifth is 1.955c narrower than a pure fifth, so the tempered size in cents, of a comma with a 3-exponent of n differs from its untempered (JI) size by n × 1.955c. For example, the tempered apotome is 113.685 - 7×1.955 = 100 cents. So that's the size of in 700c land.
I did violate this for the diacritics, in my binary 12-relative proposal, because I could see no other way to get fine enough resolution. But this principle should not be violated unless there is a very good reason. But when you are forced to violate it, It makes sense to fall back to the untempered size of symbols or diacritics. For that reason, I find your use of the diacritics preferable to mine, provided we can justify the use of a symbol for 3.125 cents.
I also violated it for my 6.25c symbol, because I thought the standard Trojan for that was visually too big and complicated. I expect George would not have approved of that, unless we could come up with a secondary comma for that symbol whose tempered value was in the right ballpark. In any case, because I've done it for 6.25 cents, I can't complain that you've done it for 3.125 cents.
But I see no reason not to use symbols with approximately the correct tempered size (the standard Trojans), for 100 cents down to 12.5 cents. So it should at worst be:
cents symbol tempered size untempered size 100 100 113.685 50 53.273 25 12.5 6.25 5.758 3.125 3.378 1.5625 1.954 0.78125 0.833 0.390625 0.423
You might fill in the blanks in the above, for homework.
"12R binary" or "binary 12R" is good. But I note that any mixed notation could be considered "polysymbolic" as it may have a sharp or flat and a sagittal.Just because its also 12R doesn't mean we have to call it Trojan either. And maybe since we just renamed Prime Factor Sagittal away from Multi-Sagittal (to avoid potential confusion with multi-shaft symbols) we should question the "Multi-" part too. I'd like the name to encode both its relationship to Trojan and its relationship to Prime Factor, if possible. The best name that occurs to me so far is "12R Binary Notation", which doesn't associate it well with Prime Factor. However, maybe we could make a point of referring to both Prime Factor and 12R Binary notations as "polysymbolic" notations.