developing a notational comma popularity metric

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cmloegcmluin
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Another stray thought — what do the values look like divided by 10? Still reasonable as ranks?

You couldn’t write that as a plus 2 in the 3 exponent, and it no longer bears any possible explanation with respect to notational concepts, however, it does allow for easier mental calculation in our base-10 reality by shifting over a decimal point. So I thought I’d at least float the suggestion.

Not sure now it’d affect the name though. Either way, maybe we just stick with N2D3 and leave the prime limit bit out of it.
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Re: developing a notational comma popularity metric

Post by Dave Keenan »

cmloegcmluin wrote: Fri Aug 14, 2020 4:37 pm How about `text{ranc}`, for “rank with respect to Ratios Able to be Notated by this Comma”?
Clever, but I don't see how that phrase relates to what we are doing. We are not, in general, feeding it a comma as input. The list of 820 things in the database are not commas.
cmloegcmluin wrote: Sat Aug 15, 2020 12:12 am Are you suggesting that we will eventually also prepare all-encompassing 3-no-pop-rank/com-no-pop-rank metrics too, folding in abs3exp, apotome slope, etc?
Yes. That's the true topic of this thread.
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Dave Keenan wrote: Sat Aug 15, 2020 6:06 am We are not, in general, feeding it a comma as input. The list of 820 things in the database are not commas.
But we would in our tina table have a column for `text{ranc}`, in other words we'd be asking for e.g `text{rank}(5382:5381)`, the first step of which is 5-roughening the comma into something akin to the 820 things in the database, no?

Or in other words, when we take `text{ranc}`(35/11), it is not the case that we care about 35/11, but truly we care about the comma 35:33; we would originally have been asking for the `text{ranc}` of 35:33.

Maybe I still don't get the full picture though.
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Dave Keenan wrote: Sat Aug 15, 2020 6:06 am Yes. That's the true topic of this thread.
Oh okay. Then perhaps we're not ready to start writing up our results yet (and the name of the topic is still good). Until you said this, my assumption had been that I hadn't quite gotten the name of the topic quite right, but that it probably wasn't worth the trouble to go back and rename it to "developing a ratio notational popularity rank".

Isn't developing a "consolidated badness metric" including the 3-exponent stuff going to be its own beast, deserving of its own topic? I don't as of yet have any idea how we're going to combine abs3exp, apotome slope, and N2D3P9 (or whatever) into one metric.
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Re: developing a notational comma popularity metric

Post by Dave Keenan »

cmloegcmluin wrote: Sat Aug 15, 2020 12:26 am Another stray thought — what do the values look like divided by 10? Still reasonable as ranks?

You couldn’t write that as a plus 2 in the 3 exponent, and it no longer bears any possible explanation with respect to notational concepts, however, it does allow for easier mental calculation in our base-10 reality by shifting over a decimal point. So I thought I’d at least float the suggestion.
Yeah. Still reasonable as ranks. But here's what it looks like, with the trendline constrained to pass through (0,0), assuming the database contains all ratios that have N2D3P1 less than 1180 (there was a noticable gap after that).

Image
Not sure now it’d affect the name though. Either way, maybe we just stick with N2D3 and leave the prime limit bit out of it.
I'm already getting used to N2D3P9, pronounced EN-too-dee THREEpee-nine, N2D-3P9, as if, in an alternative Star Wars timeline, Anakin Skywalker could only make one working droid from parts of R2D2, C3P0 and some other droid — maybe N2P9.
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Dave Keenan wrote: Sat Aug 15, 2020 8:20 am here's what it looks like, with the trendline constrained to pass through (0,0), assuming the database contains all ratios that have N2D3P1 less than 1180.
Supercool!
I'm already getting used to N2D3P9, pronounced EN-too-dee THREEpee-nine, N2D-3P9, as if, in an alternative Star Wars timeline, Anakin Skywalker could only make one working droid from parts of R2D2, C3P0 and some other droid — maybe N2P9.
Haha. Yes N2P9 is my second favorite character, after R2D2! I also think "N2D3P9" just has a certain charm, a certain je ne sais quoi. Though I stress it secondary-un-secondary-un-primary-un (w/ the same stress pattern as "counterdemonstration"), not secondary-un-un-primary-un-un (w/ the same stress pattern as "counterintuitive") as you do. Another thing for us to debate! Just kidding.
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Re: developing a notational comma popularity metric

Post by Dave Keenan »

cmloegcmluin wrote: Sat Aug 15, 2020 6:12 am
Dave Keenan wrote: Sat Aug 15, 2020 6:06 am We are not, in general, feeding it a comma as input. The list of 820 things in the database are not commas.
But we would in our tina table have a column for `text{ranc}`, in other words we'd be asking for e.g `text{rank}(5382:5381)`, the first step of which is 5-roughening the comma into something akin to the 820 things in the database, no?
Yes, you could look at it that way. Or you could directly apply the (near-future) metric that will rank commas (taking 3 exponent into account) and you might not not care about its 5-rough sub-metric (N2D3P9).
Or in other words, when we take `text{ranc}`(35/11), it is not the case that we care about 35/11, but truly we care about the comma 35:33; we would originally have been asking for the `text{ranc}` of 35:33.
When we take
\(\text{n}_2\text{d}_3\text{p}_9(35/11)\)
\(\text{n2d3p9}(35/11)\)
\(\text{N2D3P9}(35/11)\)
(which looks best to you?), we might originally have been asking about any one of several 35/11-commas, e.g. 2835/2816.
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Dave Keenan wrote: Sat Aug 15, 2020 9:25 am
cmloegcmluin wrote: Sat Aug 15, 2020 6:12 am But we would in our tina table have a column for `text{ranc}`, in other words we'd be asking for e.g `text{rank}(5382:5381)`, the first step of which is 5-roughening the comma into something akin to the 820 things in the database, no?
Yes, you could look at it that way. Or you could directly apply the (near-future) metric that will rank commas (taking 3 exponent into account) and not care about its 5-rough sub-metric (N2D3P9).
You're right. The idea of a consolidated badness metric would be to insulate those who would dare choose primary commas for Magrathean accents from the problem of weighing its 5-rough-pop-rank against its abs-3-exp and apotome-slope (there may be some familiar faces found over there, sure, but this is a matter of our organizational principles in problem solving). And so, 5-rough-pop-rank is never directly applied to commas; the metric we've developed here will only ever be applied as a submetric of a larger metric which does apply to commas.
Or in other words, when we take `text{ranc}`(35/11), it is not the case that we care about 35/11, but truly we care about the comma 35:33; we would originally have been asking for the `text{ranc}` of 35:33.
When we take `text{n}_2\text{d}_3\text{p}_9(35/11)` or `text{n2d3p9}(35/11)` or `text{N2D3P9}(35/11)` (which looks best to you?), we might originally have been asking about any one of several 35/11-commas, e.g. 2835/2816.
No disagreement here. I could have been clearer that my 35:33 was playing the role of an example, not the only possibility.

I think `text{n}_2\text{d}_3\text{p}_9(35/11)` looks to imply that there may be other quality choices for W, B, and whatever you wanna call that 9. Which there are not. `text{N2D3P9}(35/11)` looks pretty friggin' imposing, yet we see R2D2 and C3PO always capitalized, and I think we should go ahead and take our cues from Mr. Lucas on this one.
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Re: developing a notational comma popularity metric

Post by cmloegcmluin »

Re: my recent question "Isn't developing a "consolidated badness metric" including the 3-exponent stuff going to be its own beast, deserving of its own topic?" I found this:
cmloegcmluin wrote: Thu Jun 25, 2020 1:55 pm I've just had the thought that perhaps we should strike from this topic further discussion of non-2,3-reduced (aka non-5-rough) (aka "full"?) ratios. I believe what we should focus on here are the 5-smooth (aka "notational") ratios.
To which you replied:
Dave Keenan wrote: Thu Jun 25, 2020 3:02 pm I totally agree. In this thread we should stick to the very specific sub-problem of ranking a comma according to the combined popularities of all the pitch ratios it can notate. Hence the removal of the factors of 2 and 3.
Of course a lot has changed since then... but I still think it's the right way to approach things.

(as I said I would, I have begun reviewing the topic from the beginning; I have lots of interesting things to report already, and I'm only on page 2!)
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Re: developing a notational comma popularity metric

Post by Dave Keenan »

OK. I agree to using the capitalisation "N2D3P9" in math expressions too.

Good work finding those earlier agreements re the topic of this thread. I think you'll likely find somewhere where I also agreed to not changing the title at such a late stage, despite it being not quite appropriate, because the forum software doesn't change the title of all the posts. You'd have to do that one post at a time.

But I note that there are two steps to get from a 5-rough-no-pop-rank to a badness metric. The intermediate step is the comma-no-pop-rank [just trying out possible terms here] whose job is to distinguish between commas that notate the same 5-rough pitch ratio (as well as those for different 5-rough pitch ratios). This includes a consideration of abs3exp and/or apotome-slope. This is useful independent of a badness measure, in determining which commas deserve symbols.

So we could choose to make the title of this thread come true by continuing on to that — then start a new thread for the badness, which includes a consideration of the error (in cents or fractions of a tina, or other -ina).

If we start a new thread for comma-no-pop-rank, what should we call it (to distinguish it from this thread)?

The use of the adjective "notational" is messy. Sometimes it refers to the comma and sometimes the popularity. A notational comma is a comma used for notation (i.e. a comma that is used as the value of an accidental or diacritic symbol) as opposed to say a vanishing comma or tempered-out comma. It doesn't make sense (to me) to talk of a notational pitch ratio or notational 5-rough ratio. They aren't used for notation, they need to be notated. They are notated ratios, not notational ratios. But it does make sense to me to talk of the "notational popularity" of such (non-comma) ratios, i.e. how often they turn up needing to be notated, as opposed to say how often they occur as intervals between notes, or how much people like to hear them in chords.

Hence "comma-no-pop-rank" could also be "no-comma-pop-rank", where "no" is short for "notational". But "5-rough-no-pop-rank" could not be "no-5-rough-pop-rank". Hence using the form "comma-no-pop-rank" to make the similarities and differences clear relative to "5-rough-no-pop-rank".

BTW, Can you think of an easy way to generate a list of all the 5-rough ratios with an N2D3P9 of 130 or less? The idea would be to sort them on N2D3P9 and see which ones we have comma-symbols for (in primary roles only). Some would have more than one symbol, but are there any early in the list that have no symbol? And how well do the symbols progress from Spartan to Athenian and on up the precision hierarchy?
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