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13-limit JI - The Sagittal forum

13-limit JI

Juhani
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13-limit JI

Postby Juhani » Fri Nov 06, 2015 9:10 am

Hi, I'm trying to get to grips with notating JI in Mixed Sagittal. Is there no dedicated symbol for the 13-comma (27:26)? As I understand it now has to be notated as 36:35 up from a flat :/|): :b: which is confusing. Sure, that's almost the same pitch but that notation doesn't tell you how to find it or where it is in the lattice - which is the whole point of the JI notation systems of Johnston, Sabat etc.

Juhani

Juhani
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Re: 13-limit JI

Postby Juhani » Sat Nov 07, 2015 4:07 am

Let me add that I do know that the recommended notation for 13 is the apotome complement of :/|): :b: , i.e. :(!/: from 27 but I find that even more confusing. The logic of the :(!/: accidental is not obvious for me. Why is it the horizontal mirror of 36:35? I don't see another example of an accidental whose apotome complement is its horizontal (-cum-vertical) mirror. I thought this was a pure-sagittal symbol only, but it's recommended for mixed Sagittal as well. (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).

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Dave Keenan
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Re: 13-limit JI

Postby Dave Keenan » Mon Nov 09, 2015 1:49 pm


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Re: 13-limit JI

Postby Dave Keenan » Mon Nov 09, 2015 2:29 pm


Juhani
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Re: 13-limit JI

Postby Juhani » Mon Nov 09, 2015 8:04 pm

Hi,
thanks! I'll read your explanations carefully and may come back with questions or comments. About the interval notation - "why should a JI major third be notated 4:5 when it forms part of a triad, but 5:4 as a bare dyad or interval?" - I know, but that's a very common convention in any case. 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.
Juhani

Juhani
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Re: 13-limit JI

Postby Juhani » Mon Nov 09, 2015 8:12 pm

"In that case, I don't understand why you said it "has to be notated as 36:35 up from a flat :/|): :b:"."

OK, that was because I assumed understanding the logic of the :(|\: symbol requires familiarity with pure Sagittal - which I don't want to refer to in my scores - but of course one can simply memorize that symbol.
Last edited by Juhani on Tue Nov 10, 2015 12:31 am, edited 1 time in total.

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Dave Keenan
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Re: 13-limit JI

Postby Dave Keenan » Mon Nov 09, 2015 10:28 pm

It appears that you and I think of ratios expressed with a colon ":" in very different ways. You seem to treat them as synonymous with fractions expressed with a slash "/", where I do not.

Yes it's very common for people to put the larger number to the left, in the case of a dyad, e.g. 5:4, even though we would never think of writing it E:C, but would always write it C:E. E:C would be 5:8. Because it's so common, I'm happy to accept it written either way, 4:5 or 5:4. But when I write it myself, I choose to use 4:5, as that is more consistent with 4:5:6 and C:E.

So I say that :/|\: means 32:33 up, just the same as it means 33:32 up, because 32:33 and 33:32 are exactly the same thing in musical terms. I'm sorry that you find that confusing. But in terms of multiplication, it is neither "multiply by 32:33" nor "multiply by 33:32" because multiplication is not defined on colon ratios. :/|\: means multiply by 33/32. :\!/: means multiply by 32/33.

It's safe to assume that, in Sagittal, an upward-pointing arrow will always correspond to multiplying by a fraction greater than one, irrespective of the "crazy" way we write our colon ratios. :)

"Otic"? Do you mean "acoustics"?

Yes, all single-shaft symbols are intended for use in mixed Sagittal, including those greater than a half-apotome, like :(|\:.

Juhani
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Re: 13-limit JI

Postby Juhani » Tue Nov 10, 2015 1:55 am

Hi,

"Sabat et al notations don't have a single symbol for 35:36 or any of the other combinations of primes for which Sagittal has single symbols."
Johnston has 5-limit nominals, so actually the single symbol for prime 7 is indeed for 35:36 but then 63:64 is notated with a combination of 35:36 and 80:81.
Even if Sagittal has more symbols for various commas, and they're single symbols, I still read them as following the logic of a combination of other comma symbols (two :/|: 's make a :/ /|: and so on). See below.


"it is neither "multiply by 32:33" nor "multiply by 33:32" because multiplication is not defined on colon ratios. :/|\: means multiply by 33/32. :\!/: means multiply by 32/33."

OK, I read now that that's how it is in mathematics but I learned the colon ratios differently in school (ie. as ordered, not unordered), and I also have ratio calculator software where a:b is used for a/b.

"Otic"? Do you mean "acoustics"? Sorry, odd typo. Logic.

I assume :(|\::': means 8192:8505 corrected by a 4095:4096 comma? But then the accidental is still derived in a complicated path from a 7-limit interval. That's what I mean by the logic of the accidentals. Assuming I never use the 7-limit comma 8192:8505 :(|\: I can tell the musicians that this is the accidental used for 13-limit intervals. All the other symbols for low-prime-limit intervals have their own symbol (5-comma, 7-comma, 11-comma), and how signs are combined to a single symbol is often clear ( :/ /|: for two syntonic commas etc.). I would have liked a separate symbol for 13 that is distinct from a combination of lower-limit intervals. I predict musicians won't always be satisfied with learning a symbol by heart but will try to understand it, like me, as a combination of symbols (intervals). And that's not how a 13:8 limit interval is played or sung. A musician playing in just intonation, from a Johnston score, for example, sees a 13-accidental and tunes the 13/8 interval by ear - NOT by tuning two 3/2's, one 5/4 and one 7/4 down, as the Sagittal symbol seems to be saying. But as I said, I can simply tell the musicians that this :(!/: is used for 13, don't worry why it looks like that. Maybe I'd add the number 13 above the note to remind that you're supposed to find the 13th harmonic here. I don't find that ideal, though.

"The symbols to use for that purpose have their descriptions given in bold in Table 1 on page 9. If you prefer to use Sagittal in that manner, then you would notate sharp-26:27-down as :/|): and 35:36 as :/|::|): or :|)::/|:." Table 1 doesn't show examples of those combinations of separate glyphs. It seems that's indeed what I'm after but then I'd need loads of new combined symbols in the font.

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Dave Keenan
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Re: 13-limit JI

Postby Dave Keenan » Tue Nov 10, 2015 10:19 am


Juhani
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Re: 13-limit JI

Postby Juhani » Wed Nov 11, 2015 9:09 am

"But you can see that we had a difficult job, to satisfy everyone. Some people say there are too many symbol." I understand this. But instead of the cumbersome clustering of symbols that you find in JI notation systems such as Johnston's there are now all these unique symbols to memorize. By reading a page of instructions from a Johnston score, or that of Sabat, one is instantly capable of notating and reading an almost arbitrarily complex just interval (at least up to 31-prime-limit beyond which Johnston never went), but I've come back to the Sagittal manual countless times over the years, and while this is the first time I haven't immediately given up, all the dedicated symbols for different commas of the same p-limit do frustrate me and I still have no idea how to notate even such a simple interval as the seventh harmonic of the seventh harmonic (49/32) which in Johnston would be two 7's horizontally and in Sabat two 7's vertically placed - nothing to memorize there.

Some years ago I wrote a piece for chamber choir in 11-limit JI, using Johnston's notation. I made rehearsal tapes for the conductor and met with him, but to teach the notation to the choir (they had no previous experience of extended just intonation, only modernist works with quarter-tones) took only an initial meeting of 45 minutes. When I later went to hear rehearsals, intonation was discussed, of course, but not the notation - even with the admittedly confusing 81/80 symbol logic of Johnston's 5-limit nominals. I wonder if this would be the case with Sagittal. Perhaps, judging from the success of Jacob Barton's praxis camps.

I do agree with you, I wouldn't want nor need dedicated symbols for very many prime limits, either, but even if Partch stopped at 11, many just intonation composers do use 13 and expect it to be tuned by ear - hence the need for the notation to show it clearly.
"You could even define :/|): as a the 35-comma (35:36) and :(|\: as the 13-comma (26:27)." This is fine - but need I tell you how much more easily Johnston's symbol for the 13th harmonic, which is, well, 13, is memorized than a symbol that looks very much like another one that designates a completely different (7-limit) interval?

"It's safe to assume that, in Sagittal, an upward-pointing arrow will always correspond to multiplying by a fraction greater than one" - & "what about the poor performer who sees :\!::|):. It is far from obvious what direction the overall alteration is" Yes, this is indeed an improvement on Johnston's accidentals and their combinations.

It worries me a little bit that no-one has taken to take the trouble of transcribing even a single movement of the existing JI masterpieces - Johnston's string quartets - to Sagittal. A JI cello piece of mine, originally written in Johnston's notation is going to be published and I was thinking of including additional versions in both Sabat's system (popular in Germany) and Mixed Sagittal but for the latter, I have to see if I can notate even the fairly simple ratios that are used in it, and how it looks like.
Last edited by Juhani on Tue Jan 12, 2016 2:25 am, edited 2 times in total.


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