Using this expression

(harmonics 'a2 8 :quantize nil :type :hertz)

I am getting

(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

but I am expecting

(110.0 220.0 330.0 440.0 550.0 660.0 770.0 880.0)

What am I understanding wrong?

Best, Achim

(setf harm (harmonics 'a2 8 :quantize 1/2 :type :hertz))
=> (110.0 220.0 329.62756 440.0 554.3653 659.2551 783.99085 880.0)

(hertz-to-pitch harm)
=> (a2 a3 e4 a4 cs5 e5 g5 a5)

(hertz-to-pitch '(110.0 220.0 330.0 440.0 550.0 660.0 770.0 880.0))
=> (a2 a3 e4 a4 c5.. e5 fs5.. a5)

What is quantize NIL doing?

49 minutes ago, born said:

What is quantize NIL doing?

Nothing.

Jesper

:quantize nil
(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

:quantize 1/2
(110.0 220.0 329.62756 440.0 554.3653 659.2551 783.99085 880.0)

not exactly the same numbers ...
question remains.

Your first example doesn't quantize, and your second example quantizes to the closest semitone, I guess.

Sorry, didn't read carefully enough in my deleted answer.

Jesper

Sorry to insist in this, but my first example is somehow quantizing because the result should be
(110.0 220.0 330.0 440.0 550.0 660.0 770.0 880.0)

when calculating a harmonic scale in frequencies and not
(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

Achim

Only Janusz knows.

Could it be that the default is a tempered scale?

(harmonics 'a2 8 :quantize nil :type :hertz)

=>(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

(* 220 (expt 2 7/12)) ;;tempered fifth

=>329.62756

Jesper

Not quite. There ist still a difference in the 5. and 7. overtone compared to the semitone version of Janusz (5. and 7. overtone):

(setf harm (harmonics 'a2 8 :quantize 1/2 :type :hertz))

(110.0 220.0 329.62756 440.0 554.3653 659.2551 783.99085 880.0)


(setf harm (harmonics 'a2 8 :quantize nil :type :hertz))

(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

The quanize with nil will round all to 1/8 tone (which can be expressed in the notation).

Then I would suggest to set :quantize NIL to not quantize at all.

And as a feature request: It would be nice to add a functionality to be able to start the harmonic scale from any arbitrary overtone.

Achim

Don't know if this simple function will be of use for now.

Jesper

;; for single pitches

(defun harmonics2 (start-pitch length &key (partial 1) quantize)

(let ((sp (pitch-to-hertz start-pitch)) (part (max partial 1)) res)

(setf res (loop for i from part to (+ length (1- part)) collect (* i sp)))

(if quantize (pitch-to-hertz (micro-quantize (hertz-to-pitch res) :quantize quantize)) res)))

(harmonics2 'a2 8)

=>(110.0 220.0 330.0 440.0 550.0 660.0 770.0 880.0)

(harmonics2 'a2 8 :partial 4)

=>(440.0 550.0 660.0 770.0 880.0 990.0 1100.0 1210.0)

(harmonics2 'a2 8 :partial 1 :quantize 1/8)

=>(110.0 220.0 329.62756 440.0 546.4174 659.2551 772.751 880.0)

(mapcar (lambda (x) (harmonics2 x 4)) '(a2 c3 d3))

=>((110.0 220.0 330.0 440.0) (130.81278 261.62555 392.43832 523.2511) (146.83238 293.66476 440.49713 587.3295))