Naming commas and other intervals: a compilation of various sources

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Re: Naming commas and other intervals: a compilation of various sources

Post by Dave Keenan »

cmloegcmluin wrote: Tue Dec 08, 2020 4:54 pm Okay, time for more questions. Well, let me phrase things in the form of a minimal table of examples with my assumptions:
To be able to answer, I had to check which of these gave positive cents upward) and which negative (downward). I see they are all upward.
comma name inputresulting commareasoning
1/5C[-4 4,-1 ⟩
5C[-4 4 -1 ⟩directed form is preferred, but undirected form is valid (and historical)
Are you saying that if you want the downward [4 -4 1 ⟩ you need to write "5/1C"? Hmm. I never wanted that.
c1/5C(error)c1/5C cannot be interpreted as "short for" the c5C
I don't understand why this wouldn't be [34 -20 -1⟩.
c5C[-34 20 1⟩
1/5k(error)do not assume you mean the c1/5k if you don't ask for complexity
I don't understand why this wouldn't be [99 -61 -1⟩.
5k[-99 61 1⟩
c1/5k[-153 98 -1⟩
c5k[-153 98 -1 ⟩
c5k has no history, so why wouldn't it be [153 -98 1 ⟩.
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Re: Naming commas and other intervals: a compilation of various sources

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Dave Keenan wrote: Tue Jun 16, 2020 10:38 am That's another reason to use directed ratios instead of undirected, in the comma names, as @cmloegcmluin suggests. I note that we use a slash instead of a colon, to indicate a directed ratio. But for something as complex as that, we'd just use the monzos (for the positive cents). And of course, such monzos are inherently directed.

I find it annoying to have to write 1/5-comma and 1/7-comma instead of 5-comma and 7-comma, but I'll get used to it. It does give the user useful extra information about how to use the symbols.
Dave Keenan wrote: Tue Nov 10, 2020 2:23 pm But why would we use undirected comma names at all in future? I'm tempted to replace them all with directed names in the XH article and everywhere they appear on the forum, to avoid confusing new readers with the two types of name.
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Re: Naming commas and other intervals: a compilation of various sources

Post by Dave Keenan »

I direct:-) you to this thread:
viewtopic.php?f=12&t=492
Dave Keenan wrote: Tue Jun 23, 2020 10:06 am If we have both colons and slashes, then how does the reader know if "5C" is intended to be directed or not? I'd prefer not to have to write 5/1C.
In short, if there is no colon, treat it as directed, i.e. nC is the same as n/1C. e.g. "5C" is the same as "5/1C" (both are downward). [Edit: It turns out you can treat it as directed or undirected, with the same result. Explained later in this post.]

But should 5:7k and 7:5k both be the same as 7/5k (because 7/5 is greater than 1, although the comma happens to be downward)? Or should they both be the same as 5/7k (because the comma is upward)? i.e. should the undirected name give the comma whose simplest notated ratio is greater than 1? Or should it give the comma that is greater than 1?

Back when we only used undirected comma names, we had to put the word "up" or "down" after it to give it a direction, although when giving the symbol for a comma, we would often default to the upward symbol as representative of the pair.

So we can consider the parsing of undirected (i.e. colon-containing) comma names without an up or down as something new, and as such we can ensure that it makes no difference whether "5C" is interpreted as undirected or directed, i.e. as equivalent to 1:5C or 5/1C.

That requires that an undirected name should give the comma whose simplest notated ratio is greater than 1. i.e. m:nC = max(m,n)/min(m,n)C. e.g. 5:7k and 7:5k are both the same as 7/5k (which happens to be downward)

So I'm saying "history is irrelevant" since history required "up" or "down". Of course, you might choose to also parse names containing "up" or "down", in which case "up" gives the undirected value of the comma, and "down" gives the reciprocal of the undirected value of the comma. So "5:7k up" and "7:5k up" are both the same as 5/7k because it is upward. And "5-comma up" is 81/80 while "5-comma" is 80/81.

You might even allow the slightly perverse "1/5C up" (which would be the same as "5C up"), and "1/5C down" (which would be the same as "5C down"). i.e. You might treat "down" and "up" like postfix unary operators (that first take the undirected value of their argument, then respectively invert it or not).

So, your table should be:

comma name inputresulting commareasoning
1/5C[-4 4,-1 ⟩
5C[4 -4 1 ⟩ can equally be read as directed 5/1 or undirected 1:5 or 5:1
5C up[-4 4,-1 ⟩the above forms are preferred, but this form is valid (and historical)
5C down[4 -4 1 ⟩the above forms are preferred, but this form is valid (and historical)
c1/5C[34 -20 -1⟩
c5C[-34 20 1⟩
1/5k[99 -61 -1⟩
5k[-99 61 1⟩
c1/5k[-153 98 -1⟩
c5k[153 -98 1 ⟩
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Re: Naming commas and other intervals: a compilation of various sources

Post by cmloegcmluin »

Dave Keenan wrote: Tue Dec 08, 2020 5:16 pm To be able to answer, I had to check which of these gave positive cents upward) and which negative (downward). I see they are all upward.
Wow. I'm really sorry. I wrote this post in haste while brushing my teeth before bed, hoping I'd get the answers I needed by morning when I'd sit down to hammer this bit out. I didn't foresee it'd trigger so much work on your end.

A huge assumption I realize I didn't impart on you is that currently there's only one place where we currently parse comma names: in the CLI tool for analyzing JI pitches and finding commas. In this context, downward pitches are supported, but don't really bring much to the table. They have the same 2,3-class, so all that info is the same. And they have the same notating commas, so all that info is the same. Literally the only difference is that the cents and apotome slope have opposite signs. So, up and down versions of the same comma didn't even occur to me for consideration.

Of course, one day, this same code should be plugged into inputs on the web for the Sagittal notation calculator, and there someone may well be notating a score with some subharmonic pitches, and want to input such a pitch in comma name form. At the present moment, however, my pitch parsing code — without ever needing to have made any special concessions for these — can receive downward pitches as quotients (1/2), cents (-1200¢), monzos ([-1⟩), and decimals (0.5), but it can't receive downward pitches as comma names yet.

I'm not sure now is the time to add this functionality, however. A big difference between the comma name input format and that of the other four input formats (quotient, cents, monzo, decimal) is that comma names can only be used to describe comma-sized pitches, i.e. up to a double apotome of ≈227.37¢. They're mostly useful when deployed as alterations to something else, likely a Pythagorean nominal (A,B,C,D,E,F,G). This all makes perfect sense in the context of a web tool for notating a pitch set, where you pick which nominal is your 1/1, etc. etc. but for a tool for analyzing a JI pitch or finding commas, it hardly makes sense to configure stuff like that. I mean, I guess I could imagine someone would want to, but it's certainly not MVP before I'd share it out. The main thrust of the JI pitch scripts are agnostic to a chain of fifths.

That said, if we know that we're eventually going to want to let users type something like "G 5C down" and get the right notation for it, I should not write code now that I'll have to throw away when I get there. So we do have to address this up/down to some extent now.

Another aspect of this situation which I think contributed to me not considering up or downs here was that counterexample volleo6144 found of two commas with the same size category (MS+A), same undirected comma name quotient (5^146 = 1121038771459853656738983666631932905024209553501212617405654627111832866148688481189310550689697265625; one of them that, and the other 1/that), and same ATE (2):

[336 2 -146>
[-342 2 146>

So in other words, treating the opposite direction quotient as a synonym for flipping "up or down", rather than a potentially completely different comma, then that's fine in general, but this counterexample shows how that could be ambiguous. Because if someone input "1/112...625MS+A", it wouldn't be clear whether they meant the 112...625MS+A down, or the actual 1/112...625MS+A which also exists.

Right after volleo6144 shared the counterexample you said of it:
Dave Keenan wrote: Tue Jun 16, 2020 10:38 am That's another reason to use directed ratios instead of undirected, in the comma names, as @cmloegcmluin suggests.
Which I understood as agreement with that ambiguity. And more recently you said:
Dave Keenan wrote: Sat Nov 07, 2020 10:03 am it was noted that such directed comma names would also serve to distinguish the two commas of the counterexample. But I note that, even if their names could not be distinguished in that way, it would not have any practical consequences as the counterexample commas were of no musical relevance.
Again agreeing with the ambiguity conceptually, but questioning its importance.

So I can see an argument for this counterexample being so wildly unmusical that we shouldn't let it block our decision to use flipping the quotients as synonymous with flipping up/down. @volleo6144, when you found that counterexample, did you mean to imply that it was the simplest possible counterexample? Or is it still an open question whether there are many much simpler counterexamples?

But I still personally think it's a bad idea to smoosh the up/down direction of the comma in with its name. I think it's very much preferable to keep it separate. I think we covered this already on this thread: viewtopic.php?p=1799#p1799
comma name inputresulting commareasoning
1/5C[-4 4 -1 ⟩
5C[-4 4 -1 ⟩directed form is preferred, but undirected form is valid (and historical)
Are you saying that if you want the downward [4 -4 1 ⟩ you need to write "5/1C"? Hmm. I never wanted that.
So, no. That never occurred to me. "1/5C down" would be what I'd go with myself.
c1/5C(error)c1/5C cannot be interpreted as "short for" the c5C
I don't understand why this wouldn't be [34 -20 -1⟩.
Again, as explained above, I never considered downward comma names in the code yet. But now that I am considering it, again as stated above, I still think it's preferable for the up/down direction to be a separate piece of information, and not smooshed in with the name of the comma. [34 -20 -1⟩, in my opinion, should be requested in comma name form as "c5c down".
c5C[-34 20 1⟩
1/5k(error)do not assume you mean the c1/5k if you don't ask for complexity
I don't understand why this wouldn't be [99 -61 -1⟩.
Same reason again. [99 -61 -1⟩ is the 5k down, not the 1/5k.
5k[-99 61 1⟩
c1/5k[-153 98 -1⟩
c5k[-153 98 -1 ⟩
c5k has no history, so why wouldn't it be [153 -98 1 ⟩.
I'm not about to build in a table of which comma names have history and which don't. That'd be work to implement and maintain, overcomplicate the code, and also be unpredictable to users, or they may well disagree with our choices.

Again, [153 -98 1 ⟩ should be "c1/5k down", or "c5k down". Or if you don't like the idea of treating "n" as "1/n" when unambiguous, I could just have those error; but then you wouldn't be able to use "5C", and I don't think you'd want that. I think we should have it everywhere or nowhere.
Dave Keenan wrote: Tue Dec 08, 2020 5:42 pm
Dave Keenan wrote: Tue Jun 16, 2020 10:38 am That's another reason to use directed ratios instead of undirected, in the comma names, as @cmloegcmluin suggests.
Heh... I just realized I quoted the same snippet as you did. But you just posted the quotes without any new information about the quotes, so I'm not sure exactly why you reposted them.
Dave Keenan wrote: Tue Dec 08, 2020 6:44 pm I direct:-) you to this thread:
viewtopic.php?f=12&t=492
The smiley looks great here by the way... because you have the fine control of font size, it seems.

I'll admit I'm having a really hard time following your thoughts in your last post here. Perhaps it might be easier to communicate through examples. Here's my latest table then. It expands upon my original table and disagrees with yours:

comma name inputresulting comma
5C (up)[-4 4 -1 ⟩
5/1C (up)(error)
1/5C (up)[-4 4 -1 ⟩
5:1C (up)[-4 4 -1 ⟩
1:5C (up)[-4 4 -1 ⟩
5C down[4 -4 1 ⟩
5/1C down(error)
1/5C down[4 -4 1 ⟩
5:1C down[4 -4 1 ⟩
1:5C down[4 -4 1 ⟩
c5C (up)[-34 20 1⟩
c5/1C (up)[-34 20 1⟩
c1/5C (up)(error)
c5:1C (up)[-34 20 1⟩
c1:5C (up)[-34 20 1⟩
c5C down[34 -20 -1⟩
c5/1C down[34 -20 -1⟩
c1/5C down(error)
c5:1C down[34 -20 -1⟩
c1:5C down[34 -20 -1⟩
5k (up)[-99 61 1⟩
5/1k (up)[-99 61 1⟩
1/5k (up)(error)
5:1k (up)[-99 61 1⟩
1:5k (up)[-99 61 1⟩
5k down[99 -61 -1⟩
5/1k down[99 -61 -1⟩
1/5k down(error)
5:1k down[99 -61 -1⟩
1:5k down[99 -61 -1⟩
c5k (up)[-153 98 -1⟩
c5/1k (up)(error)
c1/5k (up)[-153 98 -1⟩
c5:1k (up)[-153 98 -1⟩
c1:5k (up)[-153 98 -1⟩
c5k down[153 -98 1 ⟩
c5/1k down(error)
c1/5k down[153 -98 1 ⟩
c5:1k down[153 -98 1 ⟩
c1:5k down[153 -98 1 ⟩
112...625MS+A (up)[-342 2 146>
112...625/1MS+A (up)[-342 2 146>
1/112...625MS+A (up)[336 2 -146>
112...625:1MS+A (up)(error)
1:112...625MS+A (up)(error)
112...625MS+A down[342 -2 -146>
112...625/1MS+A down[342 -2 -146>
1/112...625MS+A down[-336 -2 146>
112...625:1MS+A down(error)
1:112...625MS+A down(error)
5/7k (up)[10 -6 1 -1⟩
7/5k (up)(error)
5:7k (up)[10 -6 1 -1⟩
7:5k (up)[10 -6 1 -1⟩
5/7k down[-10 6 -1 1⟩
7/5k down(error)
5:7k down[-10 6 -1 1⟩
7:5k down[-10 6 -1 1⟩
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Re: Naming commas and other intervals: a compilation of various sources

Post by Dave Keenan »

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Re: Naming commas and other intervals: a compilation of various sources

Post by cmloegcmluin »

:lol:

So I take it you 100% agree with my table then...

JK. It's alright. We don't actually have to sort this out now. I'm happy leaving it as a to-do. I thought I really wanted to knock out all the stuff related to comma names, but you're right, parsing them is whole nuther can. I can come back to this whenever.
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Re: Naming commas and other intervals: a compilation of various sources

Post by Dave Keenan »

I'm happy to thrash it out now-ish. Clearly I was confused — thinking I could have my cake and eat it too. But now that I realise I can't, I'm willing to live with the terrible ambiguity of which is the true 1121038771459853656738983666631932905024209553501212617405654627111832866148688481189310550689697265625-comma.

Remember that I want to be able to write:

When you add the 5-comma symbol :\!: to the 11-diesis symbol :/|\: you get the 55-comma symbol :|\: because the downward and upward left barbs cancel each other out.

So I want to be able to say that :\!: is the symbol for 5C = [4 -4 1⟩.
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Re: Naming commas and other intervals: a compilation of various sources

Post by cmloegcmluin »

Dave Keenan wrote: Wed Dec 09, 2020 12:04 pm I'm happy to thrash it out now-ish. Clearly I was confused — thinking I could have my cake and eat it too.


Yum yum!
Remember that I want to be able to write:

When you add the 5-comma symbol :\!: to the 11-diesis symbol :/|\: you get the 55-comma symbol :|\: because the downward and upward left barbs cancel each other out.

So I want to be able to say that :\!: is the symbol for 5C = [4 -4 1⟩.
I think that statement is compatible with my table.

Sure, inputting "5C" will give you [-4 4 -1 ⟩ if you don't specify "down", but that doesn't mean that [4 -4 1⟩ isn't also the 5C. It's just the 5C down.
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Re: Naming commas and other intervals: a compilation of various sources

Post by Dave Keenan »

cmloegcmluin wrote: Wed Dec 09, 2020 12:23 pm Yum yum!
An astoundingly appropriate image for my mixed metaphors. I salute your search skills.
Remember that I want to be able to write:

When you add the 5-comma symbol :\!: to the 11-diesis symbol :/|\: you get the 55-comma symbol :|\: because the downward and upward left barbs cancel each other out.

So I want to be able to say that :\!: is the symbol for 5C = [4 -4 1⟩.
I think that statement is compatible with my table.

Sure, inputting "5C" will give you [-4 4 -1 ⟩ if you don't specify "down", but that doesn't mean that [4 -4 1⟩ isn't also the 5C. It's just the 5C down.
Do you really think it still works just as well if I write:

"When you add the 5-comma down symbol :\!: to the 11-diesis symbol :/|\: you get the 55-comma symbol :|\: because the downward and upward left barbs cancel each other out."

or

"When you add the 5-comma down symbol :\!: to the 11-diesis up symbol :/|\: you get the 55-comma up symbol :|\: because the downward and upward left barbs cancel each other out."

I imagine a reader thinking: If I'm adding the 5-comma down to the 11-diesis (up), why isn't that the same as subtracting the 5-comma from the 11-diesis? And so why don't I end up with an 11/5-comma?
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Re: Naming commas and other intervals: a compilation of various sources

Post by cmloegcmluin »

Dave Keenan wrote: Wed Dec 09, 2020 2:25 pm An astoundingly appropriate image for my mixed metaphors. I salute your search skills.
Oh I knew what I was looking for and just grabbed the first result. I thought you set me up for that one! I guess dirt cake is just an American thing, though.
Do you really think it still works just as well if I write:

"When you add the 5-comma down symbol :\!: to the 11-diesis symbol :/|\: you get the 55-comma symbol :|\: because the downward and upward left barbs cancel each other out."

or

"When you add the 5-comma down symbol :\!: to the 11-diesis up symbol :/|\: you get the 55-comma up symbol :|\: because the downward and upward left barbs cancel each other out."

I imagine a reader thinking: If I'm adding the 5-comma down to the 11-diesis (up), why isn't that the same as subtracting the 5-comma from the 11-diesis? And so why don't I end up with an 11/5-comma?
I imagine the reader would think that too. Which is largely why I recommended directed comma names in the first place.

I don't have a problem with using the simplified form 5C in situations where it doesn't confuse the issues at hand. But in this particular context, maybe the answer is to just use the full name, the 1/5C? Why in particular do you "want" to write "the 5-comma" here?
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