I revisited this thread because, although it had seemed settled with the previous few posts 6 months ago,
this exchange in another thread made it clear it was not settled.
It seems I never really responded point by point before, to this post earlier in this thread. Sorry about that. Here goes.
cmloegcmluin wrote: ↑Sat Jun 20, 2020 4:20 am
Dave Keenan wrote: ↑Fri Jun 19, 2020 9:17 pm
If you need to follow the comma name with "up" or "down" then in what sense is the name itself directed?
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 —
I assume by "prime content" here, you mean "content of primes above 3".
Yes, it's good to maintain a distinction between the direction (greater or less than 1) of the comma itself, versus the direction of the simplest ratio it notates (the comma with 2's and 3s removed). These may coincide, as in the case of the 11-diesis
and the 55-comma
, or be opposed as in the case of the 5-comma
, the 7-comma
and the 7/5-kleisma
.
I don't believe I'm
conflating them. I'm simply taking "directed comma name" to mean "name of a directed comma" whereas you seem to be taking it to mean "directed name of a comma", specifically "name based on a directed 2,3-removed ratio, for an undirected comma".
— 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.
I agree, but I'd rather say that it's not quite as ambiguous, because if you happen to know which of the symbols
or
is associated with the 2,3-removed value greater than 1 (the upward version of the "prime content"), then you have the key to unlocking the orientation of the prime content in the comma.
But why ask people to deal with that?
Because it is the most useful thing to learn first anyway, as depicted here:
Harmonics are real and otonal chords are common. Utonal chords are less common and subharmonics are extremely rare. So you learn which way the symbol points for each prime harmonic. And no matter which way the symbol (and hence the comma) points you call it the <prime>-comma when it notates the harmonic, and you call it the 1/<prime>-comma when it notates the subharmonic.
You extend this to commas for notating ratios between harmonics, by learning the direction of the symbol (and hence the comma) for the ratios greater than 1. So you learn that 7/5 is notated with a downward symbol
. Actually you can figure that out when you know that 7 and 5 are both notated with downward commas and the comma that notates 7 is bigger.
It seems reasonable to me, that the "7-comma" should be the "comma that notates 7", namely the downward comma 63/64, as opposed to the comma that notates 1/7, which is 64/63 and should be called the 1/7-comma.
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.
I'm impressed by volleo's example, but only as a nice piece of mathematics, not as anything a comma naming scheme has to worry about. But let's say volleo finds a similarly ambiguous example with smaller numbers, so that they have relevance to human ears. Then I would either modify my "<n>-complex" scheme to give them distinct names, or come up with some additional adjectives to disambiguate them.
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.
Well no. We don't have two names for the same thing. We call the upward comma 1/5C (because it notates the subharmonic) and we call the downward comma 5C (because it notates the harmonic).
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?
That's always going to be a problem. It's just something you have to either learn or look up. But you can instead think of it as learning which primes have commas whose direction
coincides with the direction of their 2,3-removed value, and which are
opposed.
You can do that in two different ways, and there need not be any conflict between the two ways. One is, as you suggest, to learn the names of the upward commas: 1/5C, 1/7C, 11M. The other, which I prefer, is to learn the directions of the commas that notate the upward primes (the harmonics). I do this by learning the directions of the symbols (at the same time that I learn the shapes of the symbols): 5C
, 7C
, 11M
.
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.
Yes. It is important. But I don't feel the need to
require it, only to
allow it.
Going the way I've suggested, all I'm asking the community to do is start calling the 5C the 1/5C.
I think that's just too much to ask. We shouldn't be asking people to adopt new ways of thinking about commas. We should be trying to accommodate all the ways that they currently think about them (in so far as they don't conflict with each other). That's why we abandoned the undirected names (the ones with colons). But I'm also keen to allow your way of thinking about them, as above.
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.
That's fine. I'm not trying to take any of that away from you.
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).
I think it's too much to ask people (including me) to stop using the term "7-comma" (or "septimal comma" which I take to be synonymous with "7-comma"). The difference now is, if you don't follow it with the word "up" it refers to the
downward comma 63/64.