Extending Trojan notation to finer resolution

cmloegcmluin
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Re: Extending Trojan notation to finer resolution

Dave Keenan wrote: Fri May 29, 2020 12:37 pm Oh, wot? You thought you'd won the argument? Ha!
It's the journey that counts, not the destination!
And in the character map, use "12 Relative (Trojan)" and uncapitalise "monzo". You can uncapitalise all but the first word of all the titles if you want. Making the above "12 relative (Trojan)". Of course leave things that are normally capitalised, like the initialisms EDO and IPA.
Ah! I had promised the Monz I would uncapitalize monzo for him. I see that I did it in the source document (in Google Sheets) but failed to propagate it to the hosted file on sagittal.org yet.

I think we should keep names of notations capitalized as we previously discussed, though. And I think the hyphen is better (lest anyone, even for half a moment, think it's a "Relative Notation" with aspect of "12" rather than a "Notation" with aspect of "12-Relative").

Dave Keenan
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Re: Extending Trojan notation to finer resolution

cmloegcmluin wrote: Fri May 29, 2020 12:52 pm I think we should keep names of notations capitalized as we previously discussed, though. And I think the hyphen is better (lest anyone, even for half a moment, think it's a "Relative Notation" with aspect of "12" rather than a "Notation" with aspect of "12-Relative").
Agreed.

cmloegcmluin
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Re: Extending Trojan notation to finer resolution

I'm still in suspense about my symbol choices for the actual Trinary 12-Relative notation, @Dave Keenan.

And I realized that I've just done the thing I bothered you about the other day: link from a public thread to one of our private ones (private because I have volunteered to do a bunch of work on Sagittal resources and I often need to ask embarrassing questions, not because we're trying to leave anyone out of something they'd be interested in). Here's the relevant info from the link, about capitalization:
cmloegcmluin wrote: Thu May 14, 2020 1:59 am But what about the different notations Sagittal offers? Should they all be capitalized? My vote is yes, as it calls attention to them as specific things to learn, differentiate, and be mindful of, rather than generic things which may or may not exist in other systems and for which we might expect prior external knowledge to have significant importance. But similar to how I thought for symbol sets, I don't think the word "notation" should be capitalized. So among our standard notations we would have Prime Factor notation, 108EDO notation, Extreme Precision JI notation, etc.
Dave Keenan wrote: Fri May 15, 2020 2:07 am I agree with all your capitalisation preferences.

Dave Keenan
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Re: Extending Trojan notation to finer resolution

I like your suggestion of as its secondary comma 7:25k (224:225), instead of  , for 1°324 (using a 700 ¢ notational fifth), to eliminate a symbol size reversal. I confirm that it is a valid choice and has the tempered size you claim.

And I accept that we have no choice but to use the untempered sizes for the accents.

I don't see the need to use the secondary 3125C for  . Doesn't the primary 7C work just fine for that here? But apart from that, I think your trinary 12-relative notation is perfect. So that's a wrap. Well done.

cmloegcmluin
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Re: Extending Trojan notation to finer resolution

Dave Keenan wrote: Mon Jun 15, 2020 7:32 pm I don't see the need to use the secondary 3125C for  . Doesn't the primary 7C work just fine for that here?
The 7C does work just fine, yes.

I suppose I only suggested the 3125C because it was slightly closer to the 33.333 target in its tempered size (and its untempered size, for whatever that's worth).

Had I done this work today, I may not have suggested the 3125C at all. My intuition now says that the commas in this context are for justification purposes, and that a secondary comma would only ever be something to resort to when the primary comma did not suffice.

And I suppose if we wanted to be objective about what "sufficing" entailed we'd want the tempered value of the comma to be closer to 33.333 than the next value in the trinary notation — in terms of the equation c = 100×3⁻ⁿ — so, given that the 7C's value of ≈31.174¢ is well above 100*3⁻¹⋅⁵ ≈ 19.245¢, I should definitely have stuck with that.

Perhaps I was just excited at the time, having just learned about using secondary commas to expand possibilities when designing notations, and I overcompensated.

Later version:
• Re: the 3125C, I think I may have just overcompensated upon learned that we could use secondary commas. It seems clear to me now that we'd only want to do that as a last resort, when the tempered version of the primary comma didn't work at all. And since 100×3-1.5 ≈ 19.245¢, which would be the midway point of sorts between 33.333 and 11.111, and the tempered 1/7C at 31.174 is well on the correct side of that bound, it should certainly win the day.

Here's the final chart then (now with directed comma names! and I guess "apotome" should be the "1A"):

cents		symbols	tempered size	untempered size	EDO step	comma	primary?
±100		 	100.000		113.685 	12		1A	yes
±33.33333333	 	31.174		27.264		36		1/7C	yes
±11.11111111	 	11.199		24.884		108		19/5C	yes
±3.703703704	 	3.802		7.712		324		25/7k	no
±1.234567901	 	-13.686		1.954		972		5s	yes
±0.4115226337	 	4.333		0.423		2916		1/455n	yes

But apart from that, I think your trinary 12-relative notation is perfect. So that's a wrap. Well done.
Thanks for indulging my curiosity! It may not be destined to be the most popular Sagittal notation, but I can certainly see it being the right notation for something I would write one day.

And of course thank you for your guidance in making it happen!

[Note from Dave: I accidentally hit the edit icon on this post instead of the quote icon — a hazard of having moderator powers. I have now restored it from my browser cache. The short post that I intended as a response is quoted in full in Cmloegcmluin's following post.]

cmloegcmluin
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Re: Extending Trojan notation to finer resolution

If we put a nickel in a jar every time one of us edited each other's post instead of quoting it, we'd be... well, we'd probably have about a 7C by now.

Maybe the worst part is that I don't even get notified when it happens! I just came back here to grab my final table for the docs, when I noticed it was gone.

I forget — do you have a better way of getting my previous post back besides using ChromeCacheView or the like?
Dave Keenan wrote:I think the apotome should be called "3A". If is 1A, what is  ?
My first reaction was "ah, yes, great point... 1's reciprocal is itself, so we can't effectively indicate what its inversion would be; the 1/1A is the same thing, but 1/3A is different from the 3A."

But then I realized: wait, wouldn't just be a 1A down? Just as is a 1/5C up and is a 1/5C down?

Dave Keenan