Re: Ptolemy's scale
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Hi Paul and all others on the list,
> a better heading might be "Alternatives to the hideous TET-12" Common Music in principle is nothing but a pre-processor where you can set up your own arbitrary tuning and measurement systems, which then get automatically transformed into 12-TET MIDI + cents, so the music can be played with any arbitrary software or hardware synthesizer (which usually only understand MIDI in 12-TET pitch + cents). Nyquist goes in this regard much further, because the tunning and measurement as well as the synthesizer(s) all together can be defined in one and the same system. The synthesizer and the notation system with Nyquist are the same thing. Common Music on the first view seems for musicians easier to handle but in practice Nyquist gives much more flexibility. Also Common Music needs understanding of Common Lisp (like Nyquist needs understanding of XLisp of course) but Common Music (based on my experience) is much more tedious to set up and work with than Nyquist, where everything is already included from the beginning. There is a new version of Common Music working with Chicken Scheme but I personally prefer Nyquist because with Nyquist it's much easier to break the rules of classical tuning and music composition theory than with Common Music so in the long view learning Nyquist pays off. The reason why I sent you parts of the Common Music manuals is that it's for musicians with Nyquist sometimes really hard suddenly to think in terms of Hertz and seconds instead of the music notation systems they usually use to express their compositions. So I will now give an example how the Common Music tuning system can be used within Nyquist. A 12-TET MIDI notation system is already built into Nyquist (as you probably know). With Audacity, the Nyquist 12-TET system is defined at the beginning of the "nyquist.lsp" file in the Audacity "nyquist" directory from line 26 to line 62. Ptolemy's scale With Nyquist it's not a real problem to define a Ptolemy's scale. Since it is (what I call) a non-linear tuning system, based on a series of fractions, which cannot be computed from each other by using a simple constant multi- plication factor, you can define it in Nyquist similar to the Common Music examples I had sent you in a list of scaling factors and note names like: (defun make-ptolemy-notes () (let ((ptolemy-scale '((1.0 c) ((/ 16.0 15.0) cs df) ((/ 9.0 8.0) d) ((/ 6.0 5.0) ds ef) ((/ 5.0 4.0) e) ((/ 4.0 3.0) f) ((/ 45.0 32.0) fs gf) ((/ 3.0 2.0) g) ((/ 8.0 5.0) gs af) ((/ 5.0 3.0) a) ((/ 9.0 5.0) as bf) ((/ 15.0 8.0) b)))) (dotimes (octave 8) ; make notes from c0 to b7 (let ((octave-c (step-to-hz (* 12 octave)))) ; c of current octave (dolist (scale-element ptolemy-scale) ; for every line from scale (let ((factor (eval (car scale-element)))) (dolist (note (cdr scale-element)) (let ((note-name (read (make-string-input-stream (format nil "~a~a" note octave))))) (setf note-name (hz-to-step (* octave-c factor))))))))))) NOTE: if your mailbox scrambles the indentation of the code (like mine does) look into the attachment, there is a version with proper indentation, which is usually easier to understand, or look at the copy of this mail in the Audacity SF mailing list archive. By calling the "make-ptolemy-notes" function, afterwards Nyquist will work with notes from c0 to b7 in the ptolemy scale (in a "fake" TET-12 system like in Common Music) but there still is another problem. The Nyquist pitch transformation environment will continue to work in TET-12, so if you write Nyquist code like this: (transpose 5 behaviour) The "behavior" will not get transposed by 5 semitones in the ptolemy scale but by 5 semitones in TET-12. I don't know how much this is a real problem, because transposition wasn't possible with the ptolemy scale anyway, but I think with defining new tuning systems the behaviour of the Nyquist pitch transformation environment should change too. The key functions to change the pitch transformation environment are the Nyquist "step-to-hz" and "hz-to-step" functions but since this will become a major Nyquist system surgery I first whould like to hear wether this is necessarily needed at all. Thanks, - edgar -- The author of this email does not necessarily endorse the following advertisements, which are the sole responsibility of the advertiser: _______________________________________________________________________ EINE FÜR ALLE: die kostenlose WEB.DE-Plattform für Freunde und Deine Homepage mit eigenem Namen. Jetzt starten! http://unddu.de/?kid=kid@mf2 ------------------------------------------------------------------------- Check out the new SourceForge.net Marketplace. It's the best place to buy or sell services for just about anything Open Source. http://sourceforge.net/services/buy/index.php _______________________________________________ Audacity-nyquist mailing list Audacity-nyquist@... https://lists.sourceforge.net/lists/listinfo/audacity-nyquist |
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ptolemy-scale.lsp (1K)
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