Hi all, I'm new to both Opusmodus and just intonation. I'm working through the book "The Arithmetic of Listening" by Kyle Gann, and interested in exploring these topics in Opusmodus. I see the command for ratio-to-cent (documentation excerpt pasted below) which gets me part of the way to what I'm interested in, but what if I want to actually here this scale? Or tune my music to match this scale? I think I can understand how to build out any just intonation scale, but just not sure how to actually hear and write music using the scale. Any advice?

LaMonte Young's Well-Tuned Piano:

(ratio-to-cent

'(1/1 567/512 9/8 147/128 1323/1024 21/16

189/128 3/2 49/32 441/256 7/4 63/32 2/1))

=> (0 177 204 240 444 471 675 702 738 942 969 1173 1200)

(setf ratios '(1 567/512 9/8 147/128 1323/1024 21/16 189/128 3/2 49/32 441/256 7/4 63/32 2))
(setf cents (ratio-to-cent ratios))

(setf pitch (vector-to-pitch '(c4 c5) cents :quantize 1/2))
=> (c4 d4 d4 d4 e4 f4 g4 g4 g4 a4 bb4 c5 c5)

(setf cent-rem (vector-to-pitch '(c4 c5) cents :quantize 1/2 :remain t))
=> (0 -23 4 40 44 -29 -25 2 38 42 -31 -27 0)

(setf cent-att (cent-to-attribute cent-rem))

(make-omn :length '(q)
          :pitch pitch
          :span :pitch
          :articulation cent-att)

;; With quantize set to 1/8

(setf pitch (vector-to-pitch '(c4 c5) cents :quantize 1/8))
=> (c4 cs4.. d4 d4+ e4+ e4.. fs4.. g4 g4+ a4+ a4.. b4.. c5)

Hi @opmo thank you for your response. This helps me get started. I'm having trouble with playing notes simultaneously. I can verify that in playback of a single line, they cents articulation is observed:

(setf cent-rem-third (cent-to-attribute (list '-95 '0 '95)))
(setf third (make-omn :length '(w. w. w.)
                      :pitch '(e4 e4 e4)
                      :articulation cent-rem-third))

I chose nearly whole steps of offset, and the difference in the three notes is quite audible. However, when I try to add a second line, to form the root of a chord, the articulation is not observed in playback.

(setf root (make-omn :length '(w. w. w.)
                     :pitch '(c4 c4 c4)))
(ps 'gm
    :p (list root third)
    :key-signature 'chromatic
    :time-signature '(4 4)
    :tempo 80)

Any advice on how to play these lines together?

(setf cent-val '(-95 0 95))
(setf cents (cent-to-attribute cent-val))

(setf rh (make-omn :length '(w. w. w.)
                   :pitch '(e4 e4 e4)
                   :articulation cents))

(setf lh (make-omn :length '(w. w. w.)
                   :pitch '(c4 c4 c4)))

(def-score cents
    (:key-signature 'chromatic
     :time-signature '(4 4)
     :tempo 80
     :layout (piano-solo-layout 'rh 'lh))
  
  (rh :omn rh
      :tuning (cent-to-tuning cent-val)
      :channel 1
      :sound 'gm
      :program 'acoustic-grand-piano)
  
  (lh :omn lh
      :channel 2)
  )

Cents notation is used to indicate micro-tuning of pitch.

To hear the cents in a score, I suggest using microtonal notation (1/4 or 1/8 tones) or tuning values that correspond to the cent values.

Thanks @opmo . Do you mind explaining what you mean by "tuning values that correspond to the cent values"? How do I do this?

Hi jacobcvt12,

If you are specifically interested in just intonation (JI), then a quantisation of the intervals you are interested in to a 1/4 or 1/8 tones resolution is a rather crude solution, in my view. In case you are already familiar with some JI terminology: 1/4 or 1/8 tones (i.e. 24-EDO or 48-EDO) does not give you a good approximation of 5-limit and 7-limit intervals (though it gives you a reasonably good approximation of 3-limit and 11-limit).

LaMonte Young was specifically interested in highly accurate JI tunings. His Well-Tuned Piano tuning does not include 5-limit intervals, but it does include 7-limit intervals prominently, and tuning it with a 1/4 or 1/8 tones resolution is not doing it justice. It would sound wrong, at least for my ears.

A resolution with cent accuracy, however, would be a good solution for reasonably accurate pitches.

Alternatively, as long as you are only working with tunings using only 12 different JI tones at the time (like the Well-Tuned Piano scale) then a more simple solution might be to not care about tuning details within Opusmodus itself, and to instead accurately tune the instrument you want to use directly. What instrument(s) are you using? Does it support directly tuning individual notes, e.g., by importing Scala files (https://www.huygens-fokker.org/scala/scl_format.html). Then you could import a Scala file with the ratios you shared in your initial message. (I am sure a Scala file for the Well-Tuned Piano scale also exists already somewhere.) Alternatively, if your instrument(s) support MPE or MTS-ESP, then you could tune it using the corresponding plugins by (Oddsound, https://oddsound.com/usingmtsesp.php). Does that make sense?

At some stage I started to add some more flexible microtonal tuning support to Opusmodus that goes beyond 24-EDO or 48-EDO, but supports arbitrary regular temperaments -- including arbitrary JI intervals (up to 61-limit) and arbitrary equal temperaments, see https://github.com/tanders/tot/blob/master/sources/tuning.lisp. For this, I basically tried to expand OMN by custom JI accidentals (i.e. accidentals for all sorts of commas like the syntonic comma etc.), which could then be quantised to a chosen temperament. However, this work is still not really finished.