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**View example: Shepard.lsp

Sound examples: major.ogg - minor.ogg - chroma.ogg - paradox.ogg - sweep.ogg

; Shepard tones and paradoxes ; to use try ; (playscale (majorscale 60)) ; (playscale (minorscale 60)) ; (playscale (chromascale 60)) ; (playparadoxscale (chromascale 60)) ; for shepard sweeps, try ; (play (sheptone-sweep 60 60 2 72 60 12 4)) ; the signature of sheptone-sweep should tell what the parameters do ; (defun sheptone-sweep (pitch-1 centerpitch-1 duration pitch-2 centerpitch-2 ; overtonesemi overtones ; &optional (wavetable *sine-table*)) ; Some notes about how this works: ; Shepard tones consist of harmonics that are an octave apart, thus ; the ratios are 1, 2, 4, 8, 16, etc. Note that the pitch is ambiguous ; in the sense that there could be a missing fundamental at 0.5, 0.25, etc. ; The other trick is that the spectral shape is constant. The amplitude ; of each harmonic is a function of its absolute frequency. Here, the ; shape is triangular so that as the frequency sweeps upward, harmonics ; (which are ramping up in frequency) fade in, reach a maximum, and fade out. ; ; In this implementation, each harmonic is generated using an FM oscillator ; controlled by a frequency ramp. The harmonic is multiplied by an envelope ; to implement the spectral shape function. The envelope is computed by ; running the frequency control (with some scaling) into a SHAPE function ; that uses a triangular table to implement the spectral shape. ; ; Warning: Although I have not analyzed this code too carefully, I (RBD) ; believe that the oscillators keep sweeping up to higher and higher ; frequencies even after the amplitude drops to zero. This is not only ; wasteful, but when oscillators start to alias, they run slower. If you ; generate a very long Shepard tone with harmonics spanning many octaves, ; the run time could get to be very large. A better implementation would ; start the harmonics when they enter the non-zero part of the spectral ; envelope and end them when they leave it. (setf *onepi* 3.141592654) (setf *twopi* (* 2 pi)) (setf *halfpi* (/ pi 2)) ; envshaper is a raised cosine curve used to control ; the spectral shape. Its domain is 0 to 2 ; it transforms (0 2) into 0 1 ; it has to be used like ; (shape s (envshaper) 1) (defun envshaper () (mult (sum 1 (hzosc (const (/ 1.0 2.0) 2) *table* 270)) 0.5)) ; some utility functions ;; ISEQ-HELPER -- generates an integer sequence (defun iseq-helper (a b) (let ((mylist '())) (dotimes (i (1+ (- b a)) (reverse mylist)) (setf mylist (cons (+ a i) mylist))))) ;; ISEQ -- sequence of integers from a to b (defun iseq (a b) (if (> a b) (reverse (iseq-helper b a)) (iseq-helper a b))) (defun floor (x) (if (< x 0) (1- (truncate x)) (truncate x))) ; the main part (defun sheptone-sweep-helper (pitch-1 centerpitch-1 duration pitch-2 centerpitch-2 overtonesemi overtones &optional (wavetable *sine-table*)) (let ((mytone (const 0 duration)) (maxovertones (+ (floor (/ (float (max (abs (- pitch-1 centerpitch-2)) (abs (- pitch-1 centerpitch-2)))) overtonesemi)) overtones 2)) (ampshaper (envshaper))) ;; synthesize and sum maxovertones partials (dolist (i (iseq (- maxovertones) maxovertones) mytone) (progn ;; partials start at pitch-1, spaced by overtonesemi (normally 12) (setf startpitch (+ pitch-1 (* i overtonesemi))) ;; partials end at pitch-2 + offset (setf endpitch (+ pitch-2 (* i overtonesemi))) ;; f is the frequency modulation (in hz) (setf f (pwe 0 (step-to-hz startpitch) duration (step-to-hz endpitch))) ;; p is the pitch in steps (setf p (pwl 0 startpitch duration endpitch)) ;; c is the centerpitch curve ;; (probably we could compute this outside the loop) (setf c (pwl 0 centerpitch-1 duration centerpitch-2)) ;; normwidthfactor is used to map pitch curves into the spectral shape ;; function (range 0 to 2) (setf normwidthfactor (/ 1.0 (* overtones overtonesemi))) ;; a is the amplitude envelope: f(p - c) (setf a (shape (mult (diff p c) normwidthfactor) ampshaper 1)) ;; voice is one partial (setf voice (mult a (hzosc f wavetable))) ;; sum the partials into mytone (setf mytone (sum mytone voice)) ) ))) (defun sheptone-sweep (pitch-1 centerpitch-1 duration pitch-2 centerpitch-2 overtonesemi overtones &optional (wavetable *sine-table*)) (normalize ;; note: you might not want to normalize as is done here ;; use an envelope to get a smooth start and stop (mult (sheptone-sweep-helper pitch-1 centerpitch-1 duration pitch-2 centerpitch-2 overtonesemi overtones wavetable) (env 0.05 0 0.05 1 1 1 duration)))) ;; SHEPTONE is a special case of sheptone-sweep. ;; The spectral centroid and pitch is constant. (defun sheptone (pitch centerpitch duration overtonesemi overtones &optional (wavetable *sine-table*)) (sheptone-sweep pitch centerpitch duration pitch centerpitch overtonesemi overtones wavetable)) (defun majorscale (basepitch) (mapcar (lambda (x) (+ basepitch x)) '(0 2 4 5 7 9 11 12))) (defun minorscale (basepitch) (mapcar (lambda (x) (+ basepitch x)) '(0 2 3 5 7 8 10 12))) (defun chromascale (basepitch) (mapcar (lambda (x) (+ basepitch x)) (iseq 0 12))) ;; MAKE-TABLE turns a function of 0-1 into a lookup table (defun make-table (func-exp points) (let ((table (make-array points))) (dotimes (i points) (setf (aref table i) (funcall func-exp (/ (float i) (float points))))) (list (snd-from-array 0.0 points table) (hz-to-step 1) T) )) (defun erich-wave (skew) (make-table (lambda (x) (if (< (abs skew) 0.000001) (sin (* *twopi* x)) (* (/ (sin (* *twopi* x)) (- (/ 1.0 skew) (cos (* *twopi* x)))) (/ (sqrt (- 1.0 (* skew skew))) skew)))) 2048)) ;; NORMALIZE -- normalize a sound ;; (defun normalize (s &optional (maxvol 0.8) (maxlen 44100)) (let* ((mysound s) (vol (peak mysound maxlen))) (scale (/ (float maxvol) vol) mysound))) (defun playsafe (s) (play (normalize s))) ;; PLAYSCALE uses SHEPTONE to synthesize a scale that goes up on every ;; step, but never actually ends up an octave higher ;; (defun playscale (scaleseq &optional (duration 1) (wavetable *sine-table*)) (mapcar (lambda (x) (play (sheptone x 60 duration 12 4 wavetable))) scaleseq)) ;; PLAYPARADOXSCALE uses sheptone to go up by half steps, yet end up ;; an octave lower than it starts ;; (defun playparadoxscale (scaleseq &optional (duration 1) (wavetable *sine-table*)) (mapcar (lambda (x y) (play (sheptone x y duration 12 4 wavetable))) scaleseq (reverse scaleseq)))

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Sound example: sweep.ogg /
**View example: Shepard.lsp** /
View Example: Shepard Audacity Plugin
Audacity Support Forum /
Audacity and Nyquist /
Nyquist Reference Manual /
Nyquist Examples and Tutorials
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