List of 7-prime limit accidentals

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cmloegcmluin
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Re: List of 7-prime limit accidentals

Post by cmloegcmluin »

I thought of that. I think it's a great option in certain contexts, but in big lists of commas that don't unilaterally bypass the creamy nougat center of mid-sized primes, I'm pretty sure this is more difficult to read than if you just wrote out all the zeroes.

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Re: List of 7-prime limit accidentals

Post by cmloegcmluin »

Okay, I don't think I even have to run any sort of script or anything to convince myself that every Sagittal comma is the simplest with its name. This is because the only 3-limit intervals capable of adjusting a pitch within 33.38249264¢ - 11.73000519¢ = 21.65248745¢, which is the largest range among the size categories in Sagittal (that of the "comma"), have 3-exponents large enough that applying it to a Sagittal comma could not possibly result in a reduction of the absolute value of its 3-exponent.

The maximum absolute value of 3-exponents in Sagittal is 14. So theoretically it would be possible to find a 3-limit interval with 3-exponent of up to 27, and it could still reduce the absolute 3-exponent of one of the commas with an absolute 3-exponent of 14 to 13.

But what 3-limit commas exist with 3-exponents less than or equal to 27? The apotome (7), the Pythagorean comma (12), the Pythagorean semitone (5), the Pythagorean large diesis (17), [-30 19⟩, etc. We could go on forever. But what of these are also capable of being applied without changing the size category? None of them. The smallest one is the Pythagorean comma, but it's just too large even for the size category with the largest range, at 23.46001038¢.

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Re: List of 7-prime limit accidentals

Post by cmloegcmluin »

Dave Keenan wrote:(with limma-plus-apotome also called whole-tone).
The name "limma-plus-apotome" looks just like one of the compound size category names, however, "limma" is not one of the base size categories. The Pythgorean limma falls into the "Small-Semitone" size category. Is this to say, then, that an alternative name for "Small-Semitone-plus-Apotome (SS+A)" is "Whole-Tone (W)"?

By the way, on another forum topic I proposed that capitalizing the size category "Comma" might be a solution to distinguish it from the general usage of "comma", but I think that might bind me to capitalizing every size category whose abbreviation is capitalized. Maybe that's okay.

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Re: List of 7-prime limit accidentals

Post by Dave Keenan »

cmloegcmluin wrote:
Tue Jun 23, 2020 11:25 am
Dave Keenan wrote:
Thu Nov 03, 2016 7:06 pm
(with limma-plus-apotome also called whole-tone).
The name "limma-plus-apotome" looks just like one of the compound size category names, however, "limma" is not one of the base size categories. The Pythgorean limma falls into the "Small-Semitone" size category.
It would have been useful if you'd used the quote button to obtain the kind of quote header that contains an up-arrow link to the original post, as I've done above.

In fact "limma" is given in that post as one of the base size categories. But the symbol for limma is given as "MS" (based on the alternative name "medium semitone") because lowercase-L looks too much like a digit 1, and uppercase-L is already used for large-diesis. The Pythagorean limma is 90.225 cents.
Is this to say, then, that an alternative name for "Small-Semitone-plus-Apotome (SS+A)" is "Whole-Tone (W)"?
No. But I'd accept that an alternative name for "Medium-Semitone-plus-Apotome (MS+A)" is "Whole-Tone (W)". :)
By the way, on another forum topic I proposed that capitalizing the size category "Comma" might be a solution to distinguish it from the general usage of "comma", but I think that might bind me to capitalizing every size category whose abbreviation is capitalized. Maybe that's okay.
I don't like it. I note that SI units (i.e. "metric" units) are written all lowercase whether or not their symbol is uppercase.

The only reason the comma size category symbol is uppercase-C is because lowercase-c could be read as "cents".

Imagine that we didn't have that conflict with cents, and so the symbol for comma was "c". Would you still want the size category word to be the one that was capitalised? If so, why? Whatever reason you give, will also be a good reason now, and will be independent of the capitalisation of the symbol. Or if [with lowercase-c as the symbol] you would then want to capitalise the generic term, why not do that now?

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Re: List of 7-prime limit accidentals

Post by cmloegcmluin »

Dave Keenan wrote:
Tue Jun 23, 2020 12:13 pm
It would have been useful if you'd used the quote button to obtain the kind of quote header that contains an up-arrow link to the original post, as I've done above.
Oh man! I'd noticed that sometimes there's that bit of extra stuff (post_id, time, user_id) but I never realized that arrow was clickable. Okay, I'll be more careful to get it from now on. That, along with the anchor bbCode, are quite important and polite tools to use given the amount of information we produce and maintain on this forum.
In fact "limma" is given in that post as one of the base size categories. But the symbol for limma is given as "MS" (based on the alternative name "medium semitone") because lowercase-L looks too much like a digit 1, and uppercase-L is already used for large-diesis. The Pythagorean limma is 90.225 cents.
:sigh: If I had a windowed polymer note for every time I mis-read my table as lower bounds rather than upper bounds... I'd have a melody by now. Sorry about that.

Moreover, I think I've looked at that chart (which I made made my personal table from) a half-dozen times, and I never noticed that medium-semitone was only a parenthetical name and limma was in there as the main name for that size category. Sorry for that too.
I note that SI units (i.e. "metric" units) are written all lowercase whether or not their symbol is uppercase.
And that's a good precedent to follow.

(Weren't you a member of the International Organization for Standardization or something?)
The only reason the comma size category symbol is uppercase-C is because lowercase-c could be read as "cents".
Oh, that makes more sense. I had always just thought that after kleisma y'all decided they were big enough to warrant a capital letter.

I don't think capitalizing the general term was an option, since that's outside our control. And cents is not going anywhere either.

Perhaps "Comma" is not the best solution.

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Re: List of 7-prime limit accidentals

Post by Dave Keenan »

cmloegcmluin wrote:
Tue Jun 23, 2020 2:50 pm
(Weren't you a member of the International Organization for Standardization or something?)
Ha! No. But I can understand why you think so. Because I'm a pedantic bastard who nags other people to get the case right on their SI unit symbols, including your own country's top standards body NIST who briefly had uppercase T for the "metric ton" on their website. Everyone else calls it a "tonne" but I'm not holding that against them.

But hey, I just looked at that page again, and they now have this bizarre table entry "L,1" as the symbol for "liter". Yes, that's a digit 1 not a lowercase L. :o I can feel another email coming on. :) And yes, everyone else calls it a "litre" but I'm not holding that against them.
The only reason the comma size category symbol is uppercase-C is because lowercase-c could be read as "cents".
Oh, that makes more sense. I had always just thought that after kleisma y'all decided they were big enough to warrant a capital letter.
Even the dieses need not have been uppercase, except we had "s" for "schisma" as well as "small-diesis". And once "small-diesis" had an uppercase symbol, it seemed that medium and large dieses had to have uppercase to match. But you're right that from there on, they all had to be uppercase, because big.
Perhaps "Comma" is not the best solution.
I'm still OK with it capitalised, but not all the others. But I'm also OK with not capitalising it, and just disambiguating with extra words when necessary.

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