## [Audacity-nyquist] Pythagoran ratios converted into Nyquist steps

 [Audacity-nyquist] Pythagoran ratios converted into Nyquist steps From: David R. Sky - 2007-09-02 16:42:14 ```Hi, for Paul and others who are interested, I calculated the semitone (step) values corresponding to the Pythagoran scale frequency ratios. Load a dummy audio signal into Audacity, select it, and apply Pythagoran steps to it. The plug-in below does the calculations and displays them in the Nyquist debug window. ratio - step/semitone increment 1/1 - 0.0 2187/2048 - 1.13685 9/8 - 2.0391 32/27 - 2.94135 81/64 - 4.0782 4/3 - 4.98045 729/512 - 6.1173 3/2 - 7.01955 128/81 - 7.9218 27/16 - 9.05865 16/9 - 9.9609 243/128 - 11.0978 2/1 - 12.0 Concert A is 440hz step 69.0. If it's the tonic, for the next step (B flat) add 1.13685, or 70.13685. It is indeed a strange-sounding scale when I put the steps corresponding to a major scale into the sequencer (the zeroeth, second, fourth, fifth, seventh, ninth, eleventhth and twelvth step values). It's recognizeable as the major scale but something sounds "weird" or "missing". David ;nyquist plug-in ;version 1 ;type process ;name "Pythagoran steps..." ;action "Pythagoran steps..." ; "dummy" Nyquist process (mult .1 s) ; the following information is displayed in the Nyquist debug window (format nil "~a ~a ~a ~a ~a ~a ~a ~a ~a ~a ~a" (- (hz-to-step (* 440.0 (/ 2187 2048.0))) 69.0) (- (hz-to-step (* 440.0 (/ 9 8.0))) 69.0) (- (hz-to-step (* 440.0 (/ 32 27.0))) 69.0) (- (hz-to-step (* 440.0 (/ 81 64.0))) 69.0) (- (hz-to-step (* 440.0 (/ 4 3.0))) 69.0) (- (hz-to-step (* 440.0 (/ 729 512.0))) 69.0) (- (hz-to-step (* 440.0 (/ 3 2.0))) 69.0) (- (hz-to-step (* 440.0 (/ 128 81.0))) 69.0) (- (hz-to-step (* 440.0 (/ 27 16.0))) 69.0) (- (hz-to-step (* 440.0 (/ 16 9.0))) 69.0) (- (hz-to-step (* 440.0 (/ 243 128.0))) 69.0) ) -- David R. Sky http://www.shellworld.net/~davidsky/ ```

 [Audacity-nyquist] Pythagoran ratios converted into Nyquist steps From: David R. Sky - 2007-09-02 16:42:14 ```Hi, for Paul and others who are interested, I calculated the semitone (step) values corresponding to the Pythagoran scale frequency ratios. Load a dummy audio signal into Audacity, select it, and apply Pythagoran steps to it. The plug-in below does the calculations and displays them in the Nyquist debug window. ratio - step/semitone increment 1/1 - 0.0 2187/2048 - 1.13685 9/8 - 2.0391 32/27 - 2.94135 81/64 - 4.0782 4/3 - 4.98045 729/512 - 6.1173 3/2 - 7.01955 128/81 - 7.9218 27/16 - 9.05865 16/9 - 9.9609 243/128 - 11.0978 2/1 - 12.0 Concert A is 440hz step 69.0. If it's the tonic, for the next step (B flat) add 1.13685, or 70.13685. It is indeed a strange-sounding scale when I put the steps corresponding to a major scale into the sequencer (the zeroeth, second, fourth, fifth, seventh, ninth, eleventhth and twelvth step values). It's recognizeable as the major scale but something sounds "weird" or "missing". David ;nyquist plug-in ;version 1 ;type process ;name "Pythagoran steps..." ;action "Pythagoran steps..." ; "dummy" Nyquist process (mult .1 s) ; the following information is displayed in the Nyquist debug window (format nil "~a ~a ~a ~a ~a ~a ~a ~a ~a ~a ~a" (- (hz-to-step (* 440.0 (/ 2187 2048.0))) 69.0) (- (hz-to-step (* 440.0 (/ 9 8.0))) 69.0) (- (hz-to-step (* 440.0 (/ 32 27.0))) 69.0) (- (hz-to-step (* 440.0 (/ 81 64.0))) 69.0) (- (hz-to-step (* 440.0 (/ 4 3.0))) 69.0) (- (hz-to-step (* 440.0 (/ 729 512.0))) 69.0) (- (hz-to-step (* 440.0 (/ 3 2.0))) 69.0) (- (hz-to-step (* 440.0 (/ 128 81.0))) 69.0) (- (hz-to-step (* 440.0 (/ 27 16.0))) 69.0) (- (hz-to-step (* 440.0 (/ 16 9.0))) 69.0) (- (hz-to-step (* 440.0 (/ 243 128.0))) 69.0) ) -- David R. Sky http://www.shellworld.net/~davidsky/ ```