Dave Keenan wrote: ↑Sun Apr 26, 2020 1:45 pm
Not a bad idea.
But I don't like the
for 1/324 octave due to the size reversal. And that it's so far from its untempered size.
When you say size reversal, what did you mean exactly? It looks like those symbols are both decreases from
in both tempered size and untempered size. But maybe you meant the appearance of the symbol, how its flags take up more space.
I considered 1/324 octave as
as secondary comma 11:35k (2816:2835)? Tempered size 3.822 ¢. Trouble is, it's visually way too similar to
.
might be a good candidate, if we switch to using untempered sizes one step earlier, before going into the diacritics; its untempered size is 3.378 (tempered -2.487). Visually it works since it looks smaller than the other symbols.
It would be useful to include a column in your tables that says what comma the tempered and untempered sizes are based on, and whether this is the symbol's primary definition.
Interesting. I had not yet even considered commas other than the primary commas of each symbol. Here's what the original table would have looked like (also correcting my completely wrong information about the schima diacritic):
cents symbols tempered size untempered size EDO step comma primary?
±100 
100.000 113.685 12 apotome yes
±33.33333333 
31.174 27.264 36 7C yes
±11.11111111 
11.199 24.884 108 5:19C yes
±3.703703704 
2.487 20.082 324 19C yes
±1.234567901 
-13.686 1.954 972 5s yes
±0.4115226337 
4.333 0.423 2916 455n yes
And here's another suggestion, including that insight:
cents symbols tempered size untempered size EDO step comma primary?
±100 100.000 113.685 12 apotome yes
±33.33333333 31.569 29.614 36 3125C no
±11.11111111 11.199 24.884 108 5:19C yes
±3.703703704 
3.802 7.712 324 7:25k no
±1.234567901 -13.686 1.954 972 5s yes
±0.4115226337 4.333 0.423 2916 455n yes
Even though there were symbols with secondary commas that came closer to 33.333 and 11.111 cents, I decided to keep
and
, because they are actually used in 36edo and 108edo and it would seem strange not to use them for that same step size here.
You'll see that I went with
over my earlier suggestion of
. One thing
has going for it is that it symbol-element-wise it is a strict reduction from
which is the smallest defined 12R symbol cutting off just about here, at around 4¢.
Finally, re: the name issue:
When I was on that video call with Stephen the other morning, he expressed some confusing about the name "12R". He didn't know when to use "12N" and when to use "12R". He knew that "N" was just a variable/multiple and that "R" stood for "relative", but still found it confusing that both were used. Actually "12N" or "12-n" or any such variation does not even appear in the Xenharmonikon article (although maybe the title of Figure 10
should be "Trojan Symbol Sequences for 12N Equal Divisions"?). But people I think are generally quite familiar with this 12N concept, and so I think that for Stephen, the name "12R" clouded his ability to see it as being a notation should use for anything other than a 12-N EDO (I had to explain to him how I used 12R for a couple different proprietary tunings of mine that were not EDOs, but either also weren't JI or didn't really use fifths, and also weren't going to be performed by specifically microtonal-obsessed players, and that therefore the best notation for me was going to be one relative to 100 cent intervals).
So I wonder if maybe we could consider a name other than 12R. I mean, I think it is important that we encourage people to recognize that "this is the notation where everything is relative to the familiar 12 equal divisions of an octave into 100¢ intervals", but maybe instead of focusing on the 12 equal divisions part, we could focus on the 100¢ part? Like call it "100 Cent Notation" or "100 Cent Relative Notation"? I like that because:
- it emphasizes how the capture zone diagram for it ranges from 0 to 100.*
- it simplifies the description of the system from being based on two values (12 divisions of the interval 2/1, to simply 100¢ repeating. Would it be accurate to say it reduces it from a rank-2 to a rank-1 name, then? In any case, it occurs to me that if we ever get around to notating Bohlen-Pierce, it would probably want a stack of 13R EDOs in the same manner as Trojan's 12R EDO stack. But then in one place the R means EDOR and in the other it means EDTR. I'd rather say 100¢R than 12EDOR myself.
How about instead of Binary and Trinary we call it "Bisect" and "Trisect"? The latter, in a single word, also captures the equal-sectioning up of the interval. Unfortunately, they lose the implication of being polysagittal, because "binary" and "trinary" suggest digital systems, which each next digit being one order of magnitude greater. So maybe we should stick to our guns on Binary and Trinary.
Was there something of particular importance to the "balanced" word you've oft included along with "trinary"?
So... a bit weird, but "CCR Notation" (C, Roman numeral for 100; C, cents; R, relative)? Okay I suppose we don't folks to confuse it with Creedence Clearwater Revival notation, though
How about: 100cr Notations, including all 12n EDOs.
Then also we have Binary 100cr Notation and Trinary 100cr Notation.
* Although there is an argument that to be more similar to the capture zone diagram for JI precision levels it should only go up to 50 cents, and provide the Revo flavor of the upper half as a supplement soon thereafter (perhaps same thing for the rest of the EDOs in the paper... that quite confused Stephen as well). But it should probably still be called 100 Cent Notation over 50 Cent Notation, because 50 Cent would not work for this trinary notation.
