; ****************************************************************
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; | OM-SRR, 2023-2025 M.Schumacher |
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; | |
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; | Library for spectral rhythm modeling via integer time ratios |
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; | (partials) as phase-aligned amplitude modulations. |
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; | |
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; | See https://steffenkrebber.de/research/sinusoidal-run-rhythm/|
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; ****************************************************************
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;
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;This program is free software; you can redistribute it and/or
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;modify it under the terms of the GNU General Public License
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;as published by the Free Software Foundation; either version 2
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;of the License, or (at your option) any later version.
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;
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;See file LICENSE for further informations on licensing terms.
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;
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;This program is distributed in the hope that it will be useful,
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;but WITHOUT ANY WARRANTY; without even the implied warranty of
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;MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;GNU General Public License for more details.
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;
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;You should have received a copy of the GNU General Public License
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;along with this program; if not, write to the Free Software
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;Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,10 USA.
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;
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;Authors: M. Schumacher
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(in-package :om)
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; GEN-PARTIAL
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(defmethod! gen-partial (subdivision &key (precision 0.01) (decimals 5))
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:icon 988
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:initvals '(2 0.01 5)
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:indoc '("subdivision" "precision" "decimals")
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:numouts 2
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(let* ((sampled-function (multiple-value-list
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(om-sample #'cos (* subdivision precision) 0 (* subdivision (* 2 pi)) decimals)))
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(x-points (second sampled-function))
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(y-points (third sampled-function)))
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(values (om/ x-points subdivision) y-points)
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)
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)
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; example
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; (gen-partial 8)
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; GEN-SRR
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(defmethod! gen-srr (&rest subdivisions)
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:icon 988
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:initvals '(nil)
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:indoc '("subdivisions")
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:numouts 2
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(let ((valuelist (mat-trans
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(loop for sub in subdivisions
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collect (multiple-value-list (gen-partial sub))))))
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(values (caar valuelist)
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(om* (expt 0.5 (length subdivisions))
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(om+ (length subdivisions) ;(apply 'om+ (second valuelist)))))
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(loop for i from 0 to (1- (length (car (second valuelist))))
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collect (reduce '+ (loop for list in (second valuelist) collect (nth i list)))
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))
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)
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)
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)
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)
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; legacy method
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(defmethod! gen-srr_2 (subdivision1 subdivision2 &key (precision 0.01) (decimals 5))
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;:icon 141
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;:initvals '(0 0.1 5)
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;:indoc '("subdivision" "sampling-factor" "decimals")
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:numouts 2
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(let* ((pointlist1 (multiple-value-list (gen-partial subdivision1 :precision precision :decimals decimals)))
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(pointlist2 (multiple-value-list (gen-partial subdivision2 :precision precision :decimals decimals)))
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)
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(values (first pointlist1)
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(om* 0.25 (om+ 2 (om+ (second pointlist1) (second pointlist2))))
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)
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)
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)
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; polar-plot
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(defmethod! polar-plot ((srr bpf))
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:icon 988
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(let* ((xpoints (x-points srr))
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(ypoints (y-points srr))
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(x-factor (/ 360.0 (* 2 pi)))
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(polar-values (multiple-value-list (ad->xy (om* x-factor xpoints) ypoints))))
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(simple-bpf-from-list (first polar-values) (second polar-values) 'bpc (decimals srr))
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)
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)
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; output the object or the point lists
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; optionally output cartesian or polar representation
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; Computation of Farey-Sequence
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; A Farey sequence of order n is the sequence of irreducible fractions between 0 and 1 that have denominators less than or equal to n, arranged in increasing order.
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(defun farey-sequence (n)
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"Compute the Farey sequence of order n."
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(let ((fractions '()))
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(loop for denominator from 1 to n
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do (loop for numerator from 1 to denominator
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when (and (>= numerator 0) (<= numerator denominator)
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(= 1 (gcd numerator denominator)))
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do (push (cons numerator denominator) fractions)))
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(sort fractions (lambda (a b)
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(let ((num-a (car a)) (den-a (cdr a))
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(num-b (car b)) (den-b (cdr b)))
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(< (* num-a (float den-b)) (* num-b (float den-a))))))
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))
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;; Example usage
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(print (farey-sequence 5))
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(farey-sequence 5)
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