How best to use directed comma names

[Dave Keenan]

[Moderator note: This post (and the following 8 posts) were moved from the topic "Extending Trojan notation to finer resolution" where they followed this post.]

I forget — do you have a better way of getting my previous post back besides using ChromeCacheView or the like?

No. Nothing better. Unless I realise soon enough that I can just hit my browser's Back button to recover the original.

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?

If you need to follow the comma name with "up" or "down" then in what sense is the name itself directed?

Surely is simply 1/5C and is 5C. Or is it 5/1C? In the case of being 11C, is that directed or undirected notation. There's no comma or slash. Are we now forced to write 1:11C for undirected? I want the new kid on the block to accomodate the old guy. (and I'm not referring to you and me). In the old undirected way we would write:
= 5C up
= 5C down
So I think, in the new directed way, we should write:
= 1/5C
= 5/1C

And hence, I think the apotome should be:
= 3/1A
= 1/3A

Perhaps reread Juhani's criticism here:
viewtopic.php?p=73#p73
But this time with the benefit of knowing in advance, that he does not read ":" as undirected, but as being exactly the same as "/".

[volleo6144]

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.

...You mean, like, 240edo nickels? (Also I just love doing things 5.5 times...)

I think the apotome should be called "3A". If is 1A, what is  ?
Surely is simply 1/5C and is 5C. Or is it 5/1C? In the case of being 11C, is that directed or undirected notation. There's no comma or slash. Are we now forced to write 1:11C for undirected? I want the new kid on the block to accomodate the old guy. (and I'm not referring to you and me). In the old undirected way we would write:
= 5C up
= 5C down
So I think, in the new directed way, we should write:
= 1/5C
= 5/1C
And hence, I think the apotome should be:
= 3/1A
= 1/3A

And then we get the issue with the two 5^146MS+A's, in a different form: aren't [336 2 -146> and [342 -2 -146> both 1/5^146MS+A's?

Also I thought the name itself being directed was only to help illustrate relationships like 1/5C + 55/1C = 11/1M ( + = ), which is "obscured" by non-directional naming: 5C + 55C = 11M, but 5s + 55C = 275C.

[cmloegcmluin]

I forget — do you have a better way of getting my previous post back besides using ChromeCacheView or the like?

No. Nothing better. Unless I realise soon enough that I can just hit my browser's Back button to recover the original.

Okay. I just re-ran my steps for ChromeCacheView and unfortunately it didn't turn up. There's a chance I did it on my work computer during a boring meeting. In any case it wasn't that much intellectual lifting. I'll recreate it soon.

If you need to follow the comma name with "up" or "down" then in what sense is the name itself directed?

Well, this is a fun one! If I was attempting to respond to this on a typewriter or pen and paper, I would have a huge pile of crinkled up dead trees in the room by now, because I'm finding it excruciatingly difficult to articulate my response.

@Dave Keenan, I think you are conflating the notion of directing the name in the general case with the notion of indicating direction in specific instances. The purpose of encoding the direction into the name is to disambigutate the orientation of the comma's prime content with respect to whether you are moving up or down by it. By trying to have the name carry the weight of up vs down movement as well as the orientation of the prime content in the comma, you are proposing something that is almost as ambiguous as it was before — it is not quite as ambiguous, because if you happen to know which of 5(/1)C and 1/5C is associated with the upwards symbol, then you have the key to unlocking the orientation of the prime content in the comma. But why ask people to deal with that?

So I'm going to side with @volleo6144 on this one, for both reasons, which are really just two sides of the same coin. If we use 1/5C for and 5(/1)C for then we removed the direction from the name, insofar as it reintroduces the ambiguity in cases such as the impressive example of [336 2 -146⟩ and [342 -2 -146⟩. That alone is enough, I think, to end the debate. Whether it is the 5(/1)C or the 1/5C must remain separate information from whether it is up or down.

Look at this way. Say I'm well aware that a Comma-sized comma with prime content 5 exists. I used to call it the 5C (up or down). I never really thought before about whether the 5 content was in the numerator or denominator when I moved up by this comma, and Sagittal didn't help me be aware of that. Now I've learned that we call it the 1/5C and the 5(/1)C. We have two names for it now, which frustrates me. And now I have to keep track of which one is up and which one is down. And it's a tad counterintuitive for me because the one which looks subharmonic is actually the upward movement (as it is in the case for about half of the commas). Imagine someone asks me to modulate by a 5/1C — ahhh, is that up or down? The up-ness or down-ness is such an important thing, I feel like we must require that to be explicit when describing a specific pitch change, and not bury it inside the name cross-referenced with the player's memorization of the prime content orientation.

Going the way I've suggested, all I'm asking the community to do is start calling the 5C the 1/5C. There's a bit of overhead in learning the new name, and the slight inconvenience that the new name is a tad longer, but a big win: I now know the orientation of its prime content. I don't have to memorize it; I'm reminded of it constantly. And it still works the same way: you can move up by it, or down by it. If I'm searching something for all references to this comma, I don't have to remember to look for 5C and 1/5C; it's all 1/5C (I had that in the old world, when everything was just 5C, and I don't want to regress on that front).

[Dave Keenan]

Okay. I just re-ran my steps for ChromeCacheView and unfortunately it didn't turn up. There's a chance I did it on my work computer during a boring meeting. In any case it wasn't that much intellectual lifting. I'll recreate it soon.

You were so polite about not saying who had accidentally edited-instead-of-quoted whose post (a hazard of the moderator powers we both have), that I only just understood that it was me who had edited-away your post. My humble apologies. I have now restored it from my browser cache. I also left some of your own attempt to recreate it from memory, which seemed like it might be usefully different. You decide. See viewtopic.php?p=1733#p1733

[Dave Keenan]

When I wrote:

Perhaps reread Juhani's criticism here:
viewtopic.php?p=73#p73
But this time with the benefit of knowing in advance, that he does not read ":" as undirected, but as being exactly the same as "/".

I should have been more forceful than "perhaps", and I should have said "and read his next 3 posts".

Here are the most relevant sentences. I've substituted "/" for ":" , except where he's effectively quoting me, because Juhani makes it clear later, that ":" means to him what "/" means to us.

By the way, the chart on page 9 of the Sagittal article would be much clearer if the ratios were actually written in the correct order, i.e. the accidentals were not 'up' when the ratios are 'down' - is 33/32, not 32/33 and so on.

But what I mean is simply this: means 33:32 up = multiply by 33/32. means multiply by 32/33. Although in Sagittal symbols the direction is usually obvious (as opposed to Johnston's, for example, where an inverted seven L means 36:35 up), it would still be clearer if the ratio of the comma and its direction (less or more than 1) would match.

[Dave Keenan]

What do you think of the way the relationships between symbols and primes are given here:
https://en.wikipedia.org/wiki/Just_into ... f_notation

Of course, none of these show symbols with more than one prime above 3, but the common thing seems to be to either:
(a) (Johnston and Sagittal) show only the symbols that represent the primes themselves (upward for 11, downward for 5, 7 and 13), or
(b) (EHEJIPN) show the symbols for the primes in one column and the symbols for their reciprocals in another column.

So it's sufficient to remember the direction of the symbol for each (unreciprocated) prime, rather than the direction of the comma for each upward symbol.

But I don't see any way to generalise that to symbols for two primes-above-3 on opposite sides of a ratio, like and for 5:7k.

[Dave Keenan]

And then we get the issue with the two 5^146MS+A's, in a different form: aren't [336 2 -146> and [342 -2 -146> both 1/5¹⁴⁶MS+A's?

Yes, under the current naming system they would have the same name. But, as you said when you first gave them, these examples probably don't have any musical relevance. I can't see any relevance to Sagittal notation.

In any case, it seems more a problem about how to give them distinct names. I initially thought that using directed names for them in their upward (positive cents) variant only, would be a solution. But I now realise it would not, as people would still assume one was the reciprocal of the other, when in fact their absolute values differ by 3.6¢. We'd still need to name them something like "the lesser 1/5¹⁴⁶MS+A" and "the greater 5¹⁴⁶MS+A".

Also I thought the name itself being directed was only to help illustrate relationships like 1/5C + 55/1C = 11/1M ( + = ), which is "obscured" by non-directional naming: 5C + 55C = 11M, but 5s + 55C = 275C.

That is certainly an important reason to use directed names, but it doesn't have to be the only reason. And this works just as well for 5/1C + 1/55C = 1/11M ( + = )

[cmloegcmluin]

I should have been more forceful than "perhaps", and I should have said "and read his next 3 posts".

I had indeed re-read that thread to prepare for my previous post. In some sentences I wrote (which apparently didn't make the final cut) I even explicitly referenced it. Clearly there's something in there that you think I've still failed to appreciate, though, but I can't figure out what it is. Reproducing these quotes isn't making it any more obvious to me... sorry about that.

Honestly, I'm a loss of how to respond well here. Because you did not respond directly (inline) to a single sentence I wrote, I don't understand what your objections are to any of them. Or if you actually have any objections. It seems like you do have some objections. It almost feels like you didn't see them at all, or chose to completely ignore them, especially since you did respond directly to volleo6144's words. I was building upon those, so I do have some sense where you stand on the stuff I said, but not many of my key points.

What do you think of the way the relationships between symbols and primes are given here:
https://en.wikipedia.org/wiki/Just_into ... f_notation

You're bringing ratios into the discussion, but I'm concerned that only clouds things, since the full ratios still have the 3's and 2's in them, so it's easy to tell which is bigger — the numerator, or the denominator — and thus whether the directed ratio represents a move upwards or downwards. We trade that ability away in the comma naming scheme for the ability to quickly identify the part of the prime content which is meaningful (those primes greater than 3).

So it's sufficient to remember the direction of the symbol for each (unreciprocated) prime, rather than the direction of the comma for each upward symbol. But I don't see any way to generalise that to symbols for two primes-above-3 on opposite sides of a ratio, like and for 5:7k.

I'm still very confused where you're going with this, but it seems like maybe you're focusing on Prime Factor notation when we need something that works for all the commas in Sagittal. Which you yourself acknowledge there.

And re: that first sentence I quoted of yours just above, specifically, I'll repeat something I wrote in my previous post that might have gotten buried:

Going the way I've suggested, all I'm asking the community to do is start calling the 5C the 1/5C. There's a bit of overhead in learning the new name, and the slight inconvenience that the new name is a tad longer, but a big win: I now know the orientation of its prime content. I don't have to memorize it; I'm reminded of it constantly.

So I don't know what you mean by "rather than [remembering] the direction of the comma for each upward symbol". I don't think you have to remember it. You get reminded of it every time you use the comma.

It does seem like in that first sentence you're hinting at having read something else that I wrote:

The purpose of encoding the direction into the name is to disambigutate the orientation of the comma's prime content with respect to whether you are moving up or down by it. By trying to have the name carry the weight of up vs down movement as well as the orientation of the prime content in the comma, you are proposing something that is almost as ambiguous as it was before — it is not quite as ambiguous, because if you happen to know which of 5(/1)C and 1/5C is associated with the upwards symbol, then you have the key to unlocking the orientation of the prime content in the comma. But why ask people to deal with that?

But under your false characterization of my side of the "rather", I don't understand what the advantage of your side would be over it...

these examples probably don't have any musical relevance. I can't see any relevance to Sagittal notation.

I agree with that. I retract my previous statement that "[volleo6144's counterexample] alone is enough, I think, to end the debate". The Secor-Keenan comma naming scheme is independent from Sagittal indeed. And after all, your name is on the naming scheme. @volleo6144 and I are guests here.

And this works just as well for 5/1C + 1/55C = 1/11M ( + = )

Agreed, but it's completely redundant with 1/5C + 55C = 11M. My point is that ever having to see the characters "5/1C", "1/55C", or "1/11M" is unnecessary, creates extra work for users, and potentially confuses them.

Sorry if this comes across as exasperated. It seems likely that you're resistant to the idea of "1/5C is the name of the comma in Sagittal; is up and is down, and you know the orientation of the prime content because the name corresponds to the upward symbol" but I don't understand what your objections are my attempt to illustrate the clear advantages of that over the old "5C is the name of the comma in Sagittal; is up and is down, but you're in suspense about the orientation of the prime content" or your proposed "the comma has two names: 1/5C and 5/1C, and make sure you remember that 1/5C is the upward one and 5/1C is the downward one ".

[Dave Keenan]

I'm hiking today, so this is just a brief response to say, don't worry, I'll respond to your earlier points eventually. What I believe we want to do is figure out how most of our potential users view this stuff. What is the way of presenting this symbol/comma relationship in educational material, so it will be the best match to the way they already view things.

I totally agree we don't want to present them with a 4-way relationship (two symbols to two names) for every comma, and the old (undirected names) way of doing things was bad.

I just wanted to get more data on the table first.

[Dave Keenan]

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.

...You mean, like, 240edo nickels? (Also I just love doing things 5.5 times...)

I eventually got this, after I looked up what a "nickel" was.