# mapping intervals as steps

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short question...

is there a function in OM to map an interval-list directly on a TONALITY or a SIEVE? in a way that the intervals are like steps? ..i coded that alreday for myself, but perhaps there is an OM-solution for such things?

nonsense-example:

(setf intervallist '(1 1 0 -2))

(setf pitches '(c4 e4 g4 b4))

=> :start 'c4

=> result: '(c4 e4 g4 g4 c4)

thanx

andré

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INTERVAL-TO-PITCH

I would explore all the interval functions.

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i'm not sure -> but interval-to-pitch works on "chromatic" only!? and not on other TONALITIES...?

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Intervals (direction and size) are nor chromatic or bound to any tonality.

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this is probably a misunderstanding...

intervals in a sense of STEPS, not as second/third/... as steps in a predefined/organized pitch/frequency-space...

```;;; like that

(defun interval-projection-on-pitchfield (&key pitchfield intervals (base 0))
(let ((integers (pitch-to-integer (interval-to-pitch intervals)))
(base-0-integers)
(centering)
(pos))
(setq base-0-integers (loop for i in integers
collect (+ (abs (find-min integers)) i)))
(setq centering (if (evenp (find-max base-0-integers))
(/ (find-max base-0-integers) 2)
(/ (1+ (find-max base-0-integers)) 2)))

(loop for i in base-0-integers
do (setq pos (+ i (* -1 centering) base))
when (< pos 0) do (setq pos 0)
when (> pos (1- (length pitchfield))) do (setq pos (1- (length pitchfield)))

collect (nth pos pitchfield))))

(interval-projection-on-pitchfield :pitchfield (expand-tonality '(c3 chromatic))
:intervals '(1 -1 2 -1 -1 -1)
:base 4)
;;; => (ds3 e3 ds3 f3 e3 ds3 d3)

(interval-projection-on-pitchfield :pitchfield (expand-tonality '(c3 whole-tone))
:intervals '(1 -1 2 -1 -1 -1)
:base 4)
;;; => (fs3 gs3 fs3 as3 gs3 fs3 e3)

(interval-projection-on-pitchfield :pitchfield (expand-tonality '(c3 major))
:intervals '(1 -1 2 -1 -1 -1)
:base 4)
;;; => (f3 g3 f3 a3 g3 f3 e3)

(interval-projection-on-pitchfield :pitchfield (expand-tonality '(c3 chromatic-permuted-diatonic-dorian-mixed))
:intervals '(1 -1 2 -1 -1 -1)
:base 4)
;;; => (e3 f3 e3 g3 f3 e3 d3)```

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Now I see what you were after.

Note: You can convert the intervals directly into the integers.

The DO-VERBOSE will stop printing the whole process in the Listener.

```(defun interval-projection-on-pitchfield (&key pitchfield intervals (base 0))
(do-verbose ("interval-projection-on-pitchfield")
(let* ((integers (interval-to-integer intervals))
(base-0-integers
(loop for i in integers
collect (+ (abs (find-min integers)) i)))
(centering
(if (evenp (find-max base-0-integers))
(/ (find-max base-0-integers) 2)
(/ (1+ (find-max base-0-integers)) 2)))
pos)
(loop for i in base-0-integers
do (setf pos (+ i (* -1 centering) base))
when (< pos 0)
do (setf pos 0)
when (> pos (1- (length pitchfield)))
do (setf pos (1- (length pitchfield)))
collect (nth pos pitchfield)))))```

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Hi André,

It is very interesting and totally "in line" with my practice of remapped pitch contours.

Generally, i use pitch as just melodic contours and use tonality map for constraint them.

(this melodic contours, naturally can comes from everything, vectors, intervals ...and finaly converted to pitch and passed thrught Tonality-map function)

The way you showed here is another interesting way.

Thanks

SB.

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STEP-TO-PITCH - function

...perhaps OM could implement such a STEP-TO-PITCH function (in a more professional programming way)?

...in that way it's simple to map any/same GESTALT(S) on any/different (pitch-)MEDIAS (like pitchfields/spectral/whatelse).

...would be the shortest way to "project" (certainly in varèse-way)  for example ALL MY DUCKS to whole-tone-/minor/messiane-x or on a inclined plane

"pseudo-code" for this non-sense-example:

-> (setf intervals (pitch-to-interval pitches-all-my-ducks))

-> (step-to-pitch intervals :tonality 'messiaen5)

@stephane

but - as i know - with tonality-map there sometimes "strange results" because it don't works by steps...

-> look at:

(tonality-map '(major)

'(c4 cs4 d4 ds4 e4 f4 fs4 g4 gs4 a4 as4 b4))

=> (c4 c4 d4 d4 e4 f4 f4 g4 a4 a4 a4 b4)

the GESTALT-transformation makes more sense by this STEP-concept

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"The GESTALT-transformation makes more sense by this STEP-concept"

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