13-limit JI

Juhani
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Re: 13-limit JI

Postby Juhani » Thu Dec 17, 2015 5:21 am

Is there any notation software available now that allows multiple accidental characters against a single note?

In Finale you can freely add symbols on the stave to create a single compound symbol; however, you can't get correct microtonal playback that way as you can only designate a single pitch bend or other midi value to such a symbol; they're not cumulative. (And these are not real accidentals in Finale, they're expression symbols. You can also have real microtonal accidentals in Finale but only for a closed system, using a single font for the accidentals of an EDO.) I do hope that Steinberg will change that. Do they know that this is the way we want to use microtonal accidentals? Judging from their list of Johnston symbols and ligatures, that may indeed be the case.

The minus symbol should never be written on the stave.
Where should it be written?


Sorry, I meant on the staff line.

Juhani

Juhani
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Re: 13-limit JI

Postby Juhani » Fri Dec 18, 2015 10:49 pm

I was in contact with Steinberg. They will not implement cumulative accidentals. And the microtonal playback will only work for EDOs.

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Dave Keenan
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Re: 13-limit JI

Postby Dave Keenan » Sat Dec 19, 2015 11:21 pm

Juhani wrote:I was in contact with Steinberg. They will not implement cumulative accidentals. And the microtonal playback will only work for EDOs.

That's very disappointing. Thanks for contacting them about this. The EDO playback we could live with, since one can always find an EDO that is close enough for any given piece (except perhaps some Lamonte Young). The question is only how finely divided it needs to be. But the lack of cumulative accidentals is just silly. Even if they only allowed two accidentals per note, it would be a major improvement.

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Re: 13-limit JI

Postby Juhani » Mon Dec 21, 2015 8:45 am

The EDO playback we could live with, since one can always find an EDO that is close enough for any given piece (except perhaps some Lamonte Young). The question is only how finely divided it needs to be. But the lack of cumulative accidentals is just silly.

Well, sure, but it may be more complicated than that. If the system is similar to the that in Finale, it's very difficult to implement JI accidentals with playback, and Johnston's seem impossible. If everything in the playback were rounded to 72edo that would be fine for midi sketches (but in fact, not for demo recordings for players who must hear the pitches as close to the intended tuning as possible - tuning forks cannot be off, can they?). But in 72edo, you can only fit less than an octave on a midi channel, and I doubt that Steinberg has designed a system that allows the accidentals to change midi channels - which would be necessary for the hundreds of midi notes needed per instrument. As in Finale, the accidentals in Steinberg do not affect pitch bend or other tuning parameters, they do the transposing as number of steps (midi notes) in the EDO, the sound source being tuned to the EDO using a tuning script such as MTS, .scl etc. For a JI system, a lot of accidentals could be given the same value in steps for the playback. Now, in Finale, this is not possible, as the microtonal accidentals have to be called by pressing the + or - key on the computer keyboard, for one step sharp / flat. Obviously there is no progression in an open JI system for 1 step, 2 steps, 3,... So that's the first thing I'm going to ask the Steinberg team - please make it possible to choose any accidental from a palette. In Johnston's notation there's another problem: the nominals - the diatonic scale - is not equal, it's 5-limit JI. So the playback of the accidentals can't be handled with midi notes only; the nominals would have to be tuned to the 5-limit major scale first, using .scl etc., and the accidentals would then affect the tuning of the notes on top of that, using pitch bend.
As to the compound accidentals, Steinberg will allow adding your own compound accidentals in your library as you go along but not combining several accidentals on the same note. I will ask them this but I'm pessimistic. It seems like something that no notation software programmer wants to or knows how to do.
ADDENDUM: I got an answer from Steinberg to some of the above questions. At the moment, they do not actually know how they will implement microtonal playback, as the Cubase audio engine has not yet been incorporated. They believe that Halion, the sampler in Cubase, and therefore in the notation software as well, supports a draft of the HD MIDI specification which would allow full microtonality without the use of multiple MIDI channels.

Juhani
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Re: 13-limit JI

Postby Juhani » Tue Jan 12, 2016 2:40 am

Just a detail I noticed in one of the earlier posts; not important but I'll correct it anyway.
http://www.marcsabat.com/pdfs/EJItext.pdf
However, he appears to be in error when he writes, "In Johnston’s notation, septimal intervals above a note are indicated by adding a small 7 accidental. An inverted 7 simply means that the septimal interval was generated downward." He later contradicts this by writing, "The 7 sign alters a 9/5 interval (the 5-Limit minor seventh) downward by approximately a quarter-tone to produce the septimal minor seventh 7/4." This agrees with the SMuFL document linked below.


Sabat's wording is a little confusing but there's no error. He says that when a septimal interval is generated downward, the inverted 7 (L) is used. D7 is a 7:4 generated upward from E, and the 7 means that the D is thus flatter than a 5-limit minor seventh. EL is a 7:4 generated downward from D, and that interval is narrower than a minor seventh, so the E is sharpened.

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Dave Keenan
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Re: 13-limit JI

Postby Dave Keenan » Tue May 03, 2016 9:53 pm

I just emailed Daniel Spreadbury of Steinberg to encourage them to implement multiple accidental glyphs per note, and am pleased to post the following reply.
Daniel Spreadbury wrote:Hi Dave,

Thanks for your email.

As part of a tuning system in our application you will be able to define the number of EDOs, and then specify as many different accidentals as necessary that raise or lower the pitch by any number of the defined EDOs. EDOs will be defined as rational values (i.e. fractions) and so too will the delta defined for each accidental type. The graphical appearance of each individual accidental will indeed be defined by a single object, which is internally called a "composite". A composite allows you to impose together one or more glyphs from one or more fonts, and position and scale them relative to one another. There's no practical limit on the number of glyphs that can be combined in a composite.

So although you will not be able to set up complex behaviours by which you can define multiple accidentals that can themselves by combined together in some way, you can define accidentals that are themselves combinations of other accidentals.

We have not yet actually built the user interface that will make all of this possible, and although I do expect it will get done before the first public release, it's possible that it will be added in one of the free updates that comes along after the initial release.

You can post the above explanation in the Sagittal forum if you wish.

Daniel

Juhani
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Re: 13-limit JI

Postby Juhani » Tue Sep 13, 2016 7:33 am

Hi,
that's more or less the same answer I got from Mr. Spreadbury last December - after which I lamented here on the Sagittal forum that combining accidentals will not be possible in Dorico (as the Steinberg software is called). While it's true that we won't need a separate symbol for each combination in the font itself, we'll still need to build a potentially ever-growing palette of such symbols inside Dorico. What we want, however, is the possibility to add individual accidental symbols to an existing note on the page: to first input, say, :#:, and then add :/|\: , instead of having to have :#: :/|\: in the palette.

Moreover, Dorico will only support EDOs, so JI will have to be handled as a large EDO. They probably haven't solved microtonal playback at all in the first version that comes out this year.

Juhani

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Re: 13-limit JI

Postby Dave Keenan » Tue Sep 13, 2016 1:21 pm

Juhani wrote:While it's true that we won't need a separate symbol for each combination in the font itself, ...

This is the most important difference, as it is the difference between JI notations being possible rather than impossible (with SMuFL compliant fonts).

... we'll still need to build a potentially ever-growing palette of such symbols inside Dorico (as the Steinberg software is called). ... Moreover, Dorico will only support EDOs, so JI will have to be handled as a large EDO.

The necessary palette of such symbols for JI is not really so large. 224-EDO is an extremely good approximation and divides the apotome (the alteration corresponding to a sharp or flat) into only 21 degrees, and every ratio in the 15-limit diamond is notated using a different number of degrees. Of course this doesn't help with playback of Johnston notation if Dorico assumes the 7 nominals are contiguous on a chain of the EDOs best fifths, but you already know what I think about Johnston's choice of the 5-limit JI major scale for his nominals.

Juhani
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Re: 13-limit JI

Postby Juhani » Tue Sep 13, 2016 4:39 pm

But you are now talking about a notation system for 224edo, aren't you? Of course such a system, and indeed a much smaller one, is fine for playback. Some EDO will be used in a playback engine, anyway - 1200EDO is common in hardware synths.
But by JI notations I always refer to a one-symbol-per-prime system such as Multi-Sagittal and Sabat-v.Schweinitz, with 3-limit nominals, as well as Johnston's system.
Can you explain how the library of combined symbols will not quickly grow when using such a system? The coverage of the 15-limit diamond is minuscule.

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Re: 13-limit JI

Postby Dave Keenan » Wed Sep 14, 2016 1:16 am

Juhani wrote:But you are now talking about a notation system for 224edo aren't you? Of course such a system, and indeed a much smaller one, is fine for playback. Some EDO will be used in a playback engine, anyway - 1200EDO is common in hardware synths.
But by JI notations I always refer to a one-symbol-per-prime system such as Multi-Sagittal and Sabat-v.Schweinitz, with 3-limit nominals, as well as Johnston's system.
Can you explain how the library of combined symbols will not quickly grow when using such a system? The coverage of the 15-limit diamond is minuscule.


No, I wasn't talking about a notation for 224-edo. What I mean is that it would be OK if every combination of symbols that is actually used, from some JI notation such as Multi-Sagittal or Sabat-v.Schweinitz, was mapped to the appropriate number of degrees of 224-EDO, assuming the nominals are in a chain of its best fifths. 224-EDO is better than 1200-EDO in many ways.

But I take your point that, when using one symbol per prime, the number of combinations does not depend on which EDO is used to approximate it. It does however depend on your choice of nominals. I suspect that Chrysalid Requiem (to take an extreme example) would not require so many combinations, and the combinations that are required would not contain so many symbols, if it was notated using Pythagorean nominals.

I suspect that after about 50 JI accidental combinations have been defined, the rate at which new ones would need to be added would be very slow.

I mentioned the 15-limit diamond because its notes are represented uniquely in 224-EDO whereas in other EDOs some of them map to the same note, such as 15/14 and 16/15 in 72-EDO.

Since the primes 2 and 3 are handled by the nominals and sharps and flats, then the accidental combinations only need to correspond to combinations of primes 5 and above (which will then also need to be combined with sharp and flat).

I pointed out that the frequency of use of such combinations in the Scala scale archive falls off faster than Zipf's law.
I show the first 42 here:
http://forum.sagittal.org/viewtopic.php?p=258#p258
You can see that by the 42nd combination, we are down to accidental combinations that occur only once in 600 scale pitches. When it comes to notating musical pieces rather than scales, the fall-off in usage frequency will be even more rapid, since the most commonly used scales will tend to be those with the more common pitches, and the more common pitches will tend to be repeated more often in a piece.

Here's a list of such combinations generated by a simple algorithm, in an order that approximates the frequency order from the Scala archive:
http://forum.sagittal.org/viewtopic.php?p=299#p299


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