;;; Missing fundamental - Frequency vs. Pitch ;;; ;;; Recomposition of 200 Hz and 250 Hz with 2 sines (a: partials 4 & 5; b: partials 3 & 4) ;;; ;;; Listening analytically we hear partial 4 of a (800 Hz) dropping to partial 3 of b (750 Hz). ;;; ;;; Listening synthetically we hear the virtual pitch of a: G3 (200 Hz) going up a major third to ;;; the virtual pitch of b: B3 (250 Hz). ;;; ;;; __________ 1000 Hz __________ 1700 Hz ;;; 5 4 ;;; __________ 800 Hz ;;; 4 __________ 750 Hz ;;; 3 ;;; ;;; ;;; ---------- 250 Hz ;;; ---------- 200 Hz ;;; a: G3 b: B3 ;;; (with-sound () (simp-clm 0.0 1.0 800.0 0.2)(simp-clm 0.0 1.0 1000.0 0.1) ;;; a (simp-clm 2.1 1.0 750.0 0.2)(simp-clm 2.1 1.0 1000.0 0.1)) ;;; b ;;; Adding one more partial to each sound the missing fundamentals are clearer. (with-sound () (simp-clm 0.0 1.0 800.0 0.2)(simp-clm 0.0 1.0 1000.0 0.1)(simp-clm 0.0 1.0 1200.0 0.1) (simp-clm 2.1 1.0 750.0 0.2)(simp-clm 2.1 1.0 1000.0 0.1)(simp-clm 2.1 1.0 1250.0 0.1)) ;;; with a full set of 10 partials for each sound the missing fundamentals seem to be part of the sounds. (with-sound () (loop for i from 0 to 10 and for j from 4 and for k from 3 do (simp-clm 0.0 1.0 (* 200.0 j) 0.1) (simp-clm 2.1 1.0 (* 250.0 k) 0.1))) ;;; Using our sine envelope instrument we fade-out lower of a 200 Hz tonepartials and continue feeling the ;;; missing fundamental (with-sound () (loop for i from 1 to 10 do (simp-clm-env 0.0 i (* i 200.0) 0.1 '(0 1 1 0)))) ;;; now the reverse, adding higher partials (with-sound () (do ((i 10 (1- i))) ((= i 1)) (simp-clm-env (- 10 i) i (* i 200.0) 0.1 '(0 0 1 1))))