cmloegcmluin wrote: ↑Tue Jun 23, 2020 6:43 am
Wait just a minute here, y'all don't even have names for your coins? Do you actually call your 5-cent coin an "echidna"? Do you call the 20¢ one a "dodecagon"?
I'm embarrassed to say, we're incredibly boring in that regard. No, we call it a "5 cent piece". I doubt most Aussies could tell you what animal was on what coin without looking. Although my wife says she thinks she once heard someone refer to a 20 cent piece as a platypus. It's the 50 cent piece that's a dodecagon, but we certainly don't call it that. I just now searched online for slang terms for Aussie coins or notes and the only thing I could find was that a $20 note is sometimes called a "lobster", not because it has a picture of a lobster but because it is red. However we're very proud of our first-in-the-world windowed polymer notes, which are colour-coded, size-coded and tactile.
Dave Keenan wrote:The generalisation is bleedin' obvious. Only show the symbol used to notate the ratio that's greater than one.
This is making me think that if we had a ton of data about directed usages of microtonal accidentals, we might find that many commas are much more often used in one direction or the other.
That would be useful, but it's not necessarily about what is used more often, but about what is considered the canonical notation of an interval versus what is considered notating it as an inversion. The canonical form always has the "root" as the lowest note, with the root having a Pythagorean notation (at most sharps or flats, but no other accidentals). That means that the higher note, which necessarily has a ratio greater than one, relative to the root, is the one with the comma alteration, if any.
Putting it another way, octave equivalent pitch ratios are conventionally given as ratios between 1/1 and 2/1 (positive logarithm), not between 1/2 and 1/1 (negative logarithm).
notated ratio always greater than 1
To be clear, I think you mean something like "ratio part of the comma name always greater than 1", because what within the block of text immediately above this line I could most simply call the ratios — the things in parens, such as "(80/81)" — are not always greater than 1 (and this is of important difference from the alternate versions of them in the previous block).
Yes, I should have written "simplest
notated pitch ratio is greater than one". I note that the "ratio part of the comma name" is also the simplest pitch ratio that can be notated by combining the symbol for that comma with a nominal and possibly sharps or flats. And I claim that, for educational purposes, it is best thought of in that way. To me, that's why
we remove the factors of 2 and 3: So it can
be thought of in that way.
no new comma names (except a:b is now shown as max(a,b)/min(a,b))
not have a name, then? I thought it was the 5/7-kleisma (5120/5103) under this scheme. I recognize max(a,b)/min(a,b) as the formula for the super
-directed value (>1) of an undirected ratio. But don't we sometimes want the sub
-directed value (<1)?
Dear me. Of course it has a name. I completely agree it is the 5/7-kleisma (5120/5103). I was referring only to the style of introductory table that was immediately above those words, and comparing the names to the old style which would have been the misleading:
= 5:7-kleisma (5120/5103)
= 5-comma (81/80)
= 11-M-diesis (33/32)
I think that convincing people to refer to 81/80 as the 1/5-comma is a losing proposition. It was hard enough to get a few to call it the 5-comma. Most still call it the syntonic comma or something else without a "5" in it. It wasn't as hard to go from "septimal-comma" to "7-comma". In fact "7-comma" can just be read as "septimal-comma". But do you expect them to call it the "reciprocal septimal comma" or the "one on seven comma". Good luck with that.
I haven't begun to try. But I know you have. I think we should trust you on this one.
Hmm. As a scientist, that makes me feel uncomfortable.
I recognize that the things that appeal to me about the naming scheme where 1/5C + 55C = 11M may not be the same things that are best for the general users of Sagittal — composers and performers.
That thing appeals to me too, and I'm not proposing to eliminate it.
When I frame my goal more specifically as "I want to improve the line of the original Xenharmonikôn article which reads "The right barb |\ is therefore defined as the 55 comma (54:55), i.e., the 11M diesis minus the 5 comma", then maybe I just want to direct the existing ratio and surface the other two, as in: "The right barb |\ is therefore defined as the 55 comma (55/54), i.e., the 11M diesis (33/32) less the 5 comma (80/81)".
No. Your proposed alternative is simply false, since 33/32 "less" 80/81 would be (33×81)/(32×80) = 2673/2560 ≠ 55/54. This would be correct:
"The right barb |\ is therefore defined as the 55 comma (55/54), i.e., the 11M diesis (33/32) less the 1/5 comma (81/80)"
I guess what I'm saying is that we
can refer to 81/80 as the 1/5-comma, but we shouldn't expect others to do so, or to easily understand what we mean when we do so. So perhaps this would be preferable:
"The right barb |\ is therefore defined as the 55 comma (55/54), i.e., /|\ the 11M diesis (33/32) plus \! the 5 comma (80/81), where the upward and downward left barbs cancel."
[Edit: right barbs cancel -> left barbs cancel.]