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Announcement: work on extending microtonal/xenharmonic music support in progress


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Briefly sharing some news: I started to work on greatly improving Opusmodus' support for microtonal/xenharmonic music. I am aiming for supporting arbitrary equal temperaments (both equal divisions of the octave and other intervals), just intonation (JI) for arbitrary prime limits, and arbitrary regular temperaments (https://en.xen.wiki/w/Tour_of_Regular_Temperaments ). I aim to have this whole tuning universe controlled by a single uniform notation embedded in OMN. Still, I try to keep things relatively clear and simple by introducing only a single actual new accidental symbol, and that symbol will then be combined with numbers (for prime limits) to express arbitrary JI pitches, which are then mapped to all the possible tunings. I also aim for some support for dynamic temperaments, so that the tuning can change during the course of a piece.

 

Now, this is all claiming rather a lot, and the result may not necessarily be perfect (e.g., controlling a non-octave-repeating equal temperament with a notation suitable for JI is possible and may actually work well for some situations, but is perhaps not to everyones liking). Anyway, I already have some rather solid foundation for all this. Will update you on more details at a later time. 
 

(Technically, pitch deflections will be expressed by articulations, as I cannot change the underlying OMN pitch format. All this depends of course on getting the cent articulations working properly, but I trust that will be sorted at some stage. 😅)

 

Best,

Torsten

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I am aiming for some state-of-the-art microtonal/xenharmonic support for Opusmodus. Here is a first preview.


It has been easier than expected to do what I planned when using some unifying ideas proposed by tuning math guys around 20 years ago. The core idea is that just intonation (JI), arbitrary equal temperaments (subdividing the octave or other intervals) and very many other tunings (https://en.xen.wiki/w/Tour_of_Regular_Temperaments ) can all be expressed as regular temperaments. You can find an informal discussion of regular temperaments, its context and motivation -- how it extends/generalises many other tone systems -- at this link: http://x31eq.com/paradigm.html


Importantly, regular temperaments can all be mapped to JI. Therefore, they can also all by notated by pitch notation capable of notating JI for arbitrary prime limits. So, as a unifying pitch notation for all these temperaments I am using such a JI notation. Many recent JI staff notations (I found so far 5 of them, one highly developed one is http://sagittal.org ) are all based on the same fundamental idea, which I am also using: the traditional pitch nominals (A, B, C...) and the traditional accidentals (sharp, double-sharp, flat...) are denoting Pythagorean tuning (when the notation is read as a JI notation), i.e. they notate all the pitches we can reach when stacking just fifths (plus their octaves).


We can express this in OMN with our standard pitch notation. Here is a dominant seventh chord, which in a JI interpretation would be tuned in Pythagorean tuning.

(setf pythagorean-seventh '(h c4e4g4bb4))


We can play this chord in JI with the new macro def-tempered-score, which does pretty much what the Opusmodus builtin def-score does, but it receives a temperament as one of its arguments. Also, there are multiple MIDI channels specified here, as simultaneous tones are played on different MIDI channels, so they can be tuned individually by pitch bend (I am simply using the def-score tuning argument in the background). Using multiple channels instead of multiple ports is more widely supported by existing MIDI MPE-supporting plugins. 

(def-tempered-score score-name
    (:temperament '11-limit-JI
     :time-signature '(4 4))
    (instr1
    :omn pythagorean-seventh
    :channel '(1 2 3 4)
        :sound 'gm))


OK, how about instead of the Pythagorean third we want to use a just major third -- and also a harmonic seventh. All pitches that go beyond Pythagorean tuning are expressed using new JI accidentals that express some microtonal inflection. The core idea of all the above-mentioned JI pitch notations is to introduce a new accidental for every prime limit (https://en.wikipedia.org/wiki/Limit_(music) ) comma (https://en.wikipedia.org/wiki/Comma_(music) ). These different notations mainly differ in what kind of symbols they propose for these commas. 


When extending OMN by microtonal accidentals, I am restricted to plain ASCII letters and numbers (most of the ASCII special characters are already used for something else, and OMN does also not really support unicode). So, I suggest to use the letter K for denoting that something is a Komma (similar to the Greek kappa, from where the word comma comes -- the letter C is already used for cent values) and then simply complement that letter with the prime of the comma in question. So, the 5-limit comma (syntonic comma, https://en.wikipedia.org/wiki/Syntonic_comma) is notated 5K and the 7-limit comma is 7K. These accidentals raise the pitch by that comma, for a comma flat, put a minus in front of the accidental. So, here is how we can notate and play the just harmonic seventh chord (1K is the natural sign and multiple accidental attributes for a chord are assigned in ascending order of chord tones).

(setf 7-limit-seventh '(h c4e4g4bb4 1K+-5K+1K+-7K))

(def-tempered-score score-name
    (:temperament '11-limit-JI
     :time-signature '(4 4))
    (instr1
    :omn 7-limit-seventh
    :channel '(1 2 3 4)
        :sound 'gm))


JI leads to an infinite number of different pitches. Temperaments reduce that number. So, how about we want to play the above chord in, say, 22-tone equal temperament (https://en.xen.wiki/w/22edo ). For that, we only need to define that temperament. Each regular temperament (including equal temperaments and also JI) is specified by only two settings: a small number of generator intervals, and a val for each generator. The vals together specify how each prime (up to the prime limit of the temperament) it is mapped to JI. I will explain these details in a later message and for now simply show the definition of 22-EDO, which is pretty brief. 

(deftemperament 7-limit-22-EDO
   ;; List of vals
    (list (list 22
        (+ 13 22)
        (+ 7 (* 2 22))
        (+ 18 (* 2 22))))
  ;; List of generators
  (list (/ 1200.0 22)))


Now, we can play the above chord (and any other 7-limit OMN intervals) in 22-EDO.

(def-tempered-score score-name
    (:temperament '7-limit-22-EDO
     :time-signature '(4 4))
    (instr1
    :omn 7-limit-seventh
    :channel '(1 2 3 4)
        :sound 'gm))


Similarily, we can define arbitrary other regular temperaments by simply specifying their vals and generators.

 

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