## How best to use directed comma names

Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

I've run out of time again today despite working on nothing but Sagittal all day. But in short:
Dave Keenan stupidly wrote: But I don't see any way to generalise [only showing the symbols for the primes as opposed to their reciprocals] to symbols for two primes-above-3 on opposite sides of a ratio, like and for 5:7k.
The generalisation is bleedin' obvious. Only show the symbol used to notate the ratio that's greater than one.

So we can either present the information as:

= 5/7-kleisma (5120/5103)
= 1/5-comma (81/80)
= 11-M-diesis (33/32)
i.e. arrow always upward, new 1/p names for some commas.

or as:

= 7/5-kleisma (5103/5120)
= 5-comma (80/81)
= 11-M-diesis (33/32)
i.e. notated ratio always greater than 1, no new comma names (except a:b is now shown as max(a,b)/min(a,b)).

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.

One doesn't even need to think about the commas in order to use Sagittal. The first thing anyone should learn is that to convert a Pythagorean major third C:E to a just major third (4:5) you add a  to obtain C:E . Then you learn that a 4:7 is a minor seventh with  , e.g. C:B , and 8:11 is a perfect fourth with  , e.g. C:F . So you learn that primes 5 and 7 use a downward symbol while prime 11 uses an upward symbol. No mention of commas.
cmloegcmluin
Posts: 1704
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
Contact:

### Re: How best to use directed comma names

Dave Keenan wrote: Mon Jun 22, 2020 3:15 pm
volleo6144 wrote: Fri Jun 19, 2020 10:37 pm
cmloegcmluin wrote: Fri Jun 19, 2020 5:51 am 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.
How appallingly Americo-normative of us!

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"?
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.
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).
no new comma names (except a:b is now shown as max(a,b)/min(a,b))
So does 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)?
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.

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. 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)".
Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

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))
So does 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.]
cmloegcmluin
Posts: 1704
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
Contact:

### Re: How best to use directed comma names

Dave Keenan wrote: Tue Jun 23, 2020 9:31 am However we're very proud of our first-in-the-world windowed polymer notes, which are colour-coded, size-coded and tactile.
Nice! I've got some polymer bills in the closet here leftover from trips to Canada and Mexico. I didn't realize Australia pioneered them.
Hmm. As a scientist, that makes me feel uncomfortable.
How about as a ... "creative director"?

Well, here's an argument in favor of 7/5k and 5/7k (as opposed to 5/7k up and 5/7k down): we think of these names as names for the symbol, not for the comma. When you see a slash in the name it would mean it's directed, for the symbol, and when you see the colon, like 5:7k, that means it's for the comma — but here's the clincher - even though it's undirected, we conventionally write the comma name such that the first term is the numerator of the upward symbol.
Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

Please note that I significantly edited the last 3 paragraphs of my post above. But I clearly wasn't quick enough.

"Creative director"? Bah, humbug.

I think I feel more like a "lead notation engineer".
cmloegcmluin wrote: Tue Jun 23, 2020 9:50 am Well, here's an argument in favor of 7/5k and 5/7k (as opposed to 5/7k up and 5/7k down): we think of these names as names for the symbol, not for the comma. When you see a slash in the name it would mean it's directed, for the symbol, and when you see the colon, like 5:7k, that means it's for the comma — but here's the clincher - even though it's undirected, we conventionally write the comma name such that the first term is the numerator of the upward symbol.
At first I thought: If that works for you, I'm happy. I have no objections, although I don't think I need it. But then I started to think that perhaps I'm not fully seeing the consequences.

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.
cmloegcmluin
Posts: 1704
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
Contact:

### Re: How best to use directed comma names

That or I responded too quickly!

I think it was a Lead Notation Engineer who once wrote, when George proposed differentiating the split minas of the Extreme precision level of the JI Notation as "sub-boundaries" :
KISS.
There's probably close to no chance we could rally a sizable community around a scheme as complicated as the one I just threw out in my previous post.

= 7/5k (5103/5120) and = 5/7k (5120/5103) is good.
Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

Cool. I guess it's a kind of "sleight of hand". I'm saying it's better, when introducing a symbol, to invert the comma ratio (and hence the symbol) than to invert the ratio part of the comma name (which is also the ratio of the simplest pitch to be notated).

Hence, in replacing the old:

= 5-comma up (81/80)

I prefer:

= 5-comma (80/81)

over:

= 1/5-comma (81/80)

I suppose I think that people will object less to seeing the "5-comma" described as 80/81 instead of 81/80 (because hey, they're really just the same thing in a different direction) than they would to being told that 81/80 is now called the "1/5-comma".

But if you have to give them both, like in the SMuFL character map, then you have to give them both.
Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

But then I go and look at how the Johnston and EHEJIPN accidentals are described in SMuFL and I wonder if directed comma names (for Sagittal) make sense there at all. Maybe we shouldn't bother asking Steinberg to change the text with the existing symbols (except to correct errors).
cmloegcmluin
Posts: 1704
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
Contact:

### Re: How best to use directed comma names

This is currently the format I would have thought you wanted me to get the Sagittal-SMuFL-Map into:

accSagittal1v5Comma	1/5 comma, (1/5C), 1° up [22 27 29 34 41 46 53 96-EDOs], 1/12-tone up
accSagittal5Comma	5 comma, 1° down [22 27 29 34 41 46 53 96-EDOs], 1/12-tone down

Dave Keenan
Posts: 2180
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: How best to use directed comma names

cmloegcmluin wrote: Tue Jun 23, 2020 3:00 pm What about Johnston and EHEJIPN changes your view?
The fact that they use essentially the same style of description as the current Sagittal, except that they use"raised by" and "lowered by" instead of "up" and "down", and they use "7-limit comma" etc, instead of "7-comma" etc.
This is currently the format I would have thought you wanted me to get the Sagittal-SMuFL-Map into:

accSagittal1v5Comma	1/5 comma, (1/5C), 1° up [22 27 29 34 41 46 53 96-EDOs], 1/12-tone up
accSagittal5Comma	5 comma, 1° down [22 27 29 34 41 46 53 96-EDOs], 1/12-tone down

Yeah. That's what I thought I wanted until very recently. Although I had completely failed to realise the implications for the identifiers. I think it's a bad idea to change the identifiers. It may break software, like MuseScore.