Followup on post: https://opusmodus.com/forums/topic/3989-om-lydian-chromatic-concept-of-tonal-organization-george-russell/

According to LCCOTO chords which are derived from a parent scale have a nice property as they all lean on the same lydian parent-scale- tonic, hence may feel similar in harmonic environment.

This may be used for various compositional purposes.

Example:

A G7 -> Cmaj7 cadence is in LCCOTO basically a movement of F-lydian-parent-scale-tonic to C-lydian-parent-scale-tonic.

Moving clockwise on circle of fifths with regards to parent scales tonic.

G7 is a chord on mode 2 in f-lydian.

Cmaj7 is chord on mode 1 in c-lydian.

According to LCCOTO it should be possible to exchange G7

by various other chords as long as they are derived from F-lydian parent scale or derived ones, like F-lydian augmented, etc.

For that a function I called "find-chord-in-parent-scale" may be useful.

New function

;;; ---------------------------------------------------------------------------
;;;
;;; Find chord in a parent scale according to LCCOTO 
;;; for a list of chords quality symbols and a list of parent scales
;;;
;;;   Conceptual framework: 
;;;   Lydian Chromatic Concept of Tonal Organization, LCCOTO
;;;   by George Russell, 1953, Concept Publishing Company) 
;;;
;;; This function helps to get all possible chords in a parent scale
;;; given their quality, i.e. maj, m7, sus2, 7, etc.
;;; Parameter "quality" must be a list with elemens which comply to OMs 
;;; definition of chord-symbols (see docu chord-symbols.pdf).
;;;
;;; The parameters scale and quality are lists.
;;; The return value is a nested list.
;;;
;;; Version 1, 2025-11-17
;;; Author: Cliff Scherer
;;;
;;;
;;; v1: initial version
;;; 
;;; ---------------------------------------------------------------------------


(defun find-chord-in-parent-scale (scale quality)
  "Find chords in a list of parent scales and a list of chord qualities"
  
  ;; Main function for one scale
  (defun find-chord-in-parent-scale-one-scale (scale quality)
  
    ;; Main function for one chord quality
    (defun find-chord-in-parent-scale-one-chord (scale quality)
      "Find chords in one parent scale for one chord quaity"

      ;; We use the lydian parent-scale with lydian tonic c
      (setf parent-scale (flatten  scale))
      (setf parent-scale-pcs (get-pcs (expand-tonality parent-scale)))

      ;; Next we define a chord symbol
      (setf chord-symbol quality)

      ;; Prepare all possible chords for symbol and pcs of scale
      (setf chord-symbol-candidates (cartesian 
                               (list (integer-to-pitch parent-scale-pcs) 
                                     chord-symbol)))

      ;; Get their PC
      (setf chord-pc-candidates (get-pcs (expand-chord chord-symbol-candidates)))

      ;; Test for intersection
      (setf test-intersect-pc (mapcar (lambda (x) (intersection x parent-scale-pcs))
                                      chord-pc-candidates))

      ;; Test for full intersection
      (setf chord-size (length (first chord-pc-candidates)))
      (setf test-intersect-pc-complete (mapcar (lambda (x) 
                                                 (equal (length x) chord-size))
                                               test-intersect-pc))

      ;; Return chord symbols
      (setf result (remove nil
                           (loop for test in test-intersect-pc-complete
                                 for chord in chord-symbol-candidates
                                 collect (if test chord nil))))

      result

      )

    (mapcar (lambda (x) (find-chord-in-parent-scale-one-chord scale x)) quality)

    )

  (mapcar (lambda (x) (find-chord-in-parent-scale-one-scale x quality)) scale)

  )



;; Tests ---
;;

(find-chord-in-parent-scale '((c lydian)) '((maj)))
;; ((((c4 maj) (d4 maj) (g4 maj))))

;; Use of the nested list result may require use of (multiple) flatten-sublist calls
(expand-chord (flatten-sublist (find-chord-in-parent-scale '((c lydian)) '((maj)))))
;; ((c4e4g4 d4fs4a4 g4b4d5))

(find-chord-in-parent-scale '((c lydian)) '((maj)(m7)))
;; (
;;  ( -> for scale
;;   ((c4 maj) (d4 maj) (g4 maj)) -> for first quality
;;   ((e4 m7) (a4 m7) (b4 m7)) -> for second quality
;;  )
;; )

;; Use
(expand-chord (flatten-sublist (find-chord-in-parent-scale '((c lydian)) '((maj)(m7)))))
;; ((c4e4g4 d4fs4a4 g4b4d5) (e4g4b4d5 a4c5e5g5 b4d5fs5a5))


(find-chord-in-parent-scale '((f lydian)(c lydian)) '((maj)(m7)))
;; (
;;  ( -> for first scale
;;   ((f4 maj) (g4 maj) (c4 maj)) -> for first quality
;;   ((a4 m7) (d4 m7) (e4 m7)) -> for second quality
;;  ) 
;;  ( -> for second scale
;;   ((c4 maj) (d4 maj) (g4 maj)) -> for first quality
;;   ((e4 m7) (a4 m7) (b4 m7)) -> for second quality
;;  )
;; )



;; Experiments to exchange G7 in V7->Cmaj7 ---

;; First the original -
(assemble-seq 
 (flatten-sublist (flatten-sublist  (find-chord-in-parent-scale '((f lydian)) '((7)))))
 '(c4 maj7))
;; ((g4 7) (c4 maj7))


;; Try m7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((a4 m7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((d4 m7) (c4 maj7))

(assemble-seq 
 (third (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((e4 m7) (c4 maj7))

;; Try maj7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian)) '((maj7))))))
 '(c4 maj7))
;; ((f4 maj7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian)) '((maj7))))))
 '(c4 maj7))
;; ((c4 maj7) (c4 maj7)) :-)

;; Try dim7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian-diminished)) '((dim7))))))
 '(c4 maj7))
;; ((f4 dim7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f lydian-diminished)) '((dim7))))))
 '(c4 maj7))
;; ((gs4 dim7) (c4 maj7))

;; Try 7/b5 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((g4 7/b5) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((bb4 7/b5) (c4 maj7))

(assemble-seq 
 (third (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((cs4 7/b5) (c4 maj7))


(assemble-seq 
 (fourth (flatten-sublist (flatten-sublist (find-chord-in-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((e4 7/b5) (c4 maj7))


;; Stay inside similar parent scales with same tonic but vary the chord quality ---
;; See chord pregression below
(assemble-seq
 (find-chord-in-parent-scale '((f lydian)) '((maj7)(7/sus4)))
 (find-chord-in-parent-scale '((f lydian-augmented)) '((maj7)(aug)(m7)))
 (find-chord-in-parent-scale '((f lydian-diminished)) '((dim7)(aug)(m7)))
 (find-chord-in-parent-scale '((f lydian-b7)) '((m7)(7)(7/b5))))

The concept of movement on circle of fifths clockwise with regards to parent scale tonic is explained here:

Also the idea to substitute G7 by another chord from it's F-lydian parent scale.

New version v2:

• rename to "find-chord-for-parent-scale" to match the counterpart function "find-parent-scale-for-chord"

;;; ---------------------------------------------------------------------------
;;;
;;; Find chord in a parent scale according to LCCOTO 
;;; for a list of chords quality symbols and a list of parent scales
;;;
;;;   Conceptual framework: 
;;;   Lydian Chromatic Concept of Tonal Organization, LCCOTO
;;;   by George Russell, 1953, Concept Publishing Company) 
;;;
;;; This function helps to get all possible chords in a parent scale
;;; given their quality, i.e. maj, m7, sus2, 7, etc.
;;; Parameter "quality" must be a list with elemens which comply to OMs 
;;; definition of chord-symbols (see docu chord-symbols.pdf).
;;;
;;; The parameters scale and quality are lists.
;;; The return value is a nested list.
;;;
;;; Version 2, 2025-11-17
;;; Author: Cliff Scherer
;;;
;;; v2:
;;; - rename to find-chord-for-parent-scale, to match 
;;;   the counterpart find-parent-scale-for-chord
;;; 
;;; v1: initial version
;;; 
;;; ---------------------------------------------------------------------------


(defun find-chord-for-parent-scale (scale quality)
  "Find chords in one parent scale and a list of chord qualities"
  
  ;; Main function for one scale
  (defun find-chord-in-parent-scale-one-scale (scale quality)
  
    ;; Main function for one chord quality
    (defun find-chord-in-parent-scale-one-chord (scale quality)
      "Find chords in one parent scale for one chord quaity"

      ;; We use the lydian parent-scale with lydian tonic c
      (setf parent-scale (flatten  scale))
      (setf parent-scale-pcs (get-pcs (expand-tonality parent-scale)))

      ;; Next we define a chord symbol
      (setf chord-symbol quality)

      ;; Prepare all possible chords for symbol and pcs of scale
      (setf chord-symbol-candidates (cartesian 
                               (list (integer-to-pitch parent-scale-pcs) 
                                     chord-symbol)))

      ;; Get their PC
      (setf chord-pc-candidates (get-pcs (expand-chord chord-symbol-candidates)))

      ;; Test for intersection
      (setf test-intersect-pc (mapcar (lambda (x) (intersection x parent-scale-pcs))
                                      chord-pc-candidates))

      ;; Test for full intersection
      (setf chord-size (length (first chord-pc-candidates)))
      (setf test-intersect-pc-complete (mapcar (lambda (x) 
                                                 (equal (length x) chord-size))
                                               test-intersect-pc))

      ;; Return chord symbols
      (setf result (remove nil
                           (loop for test in test-intersect-pc-complete
                                 for chord in chord-symbol-candidates
                                 collect (if test chord nil))))

      result

      )

    (mapcar (lambda (x) (find-chord-in-parent-scale-one-chord scale x)) quality)

    )

  (mapcar (lambda (x) (find-chord-in-parent-scale-one-scale x quality)) scale)

  )



;; Tests ---
;;

(find-chord-for-parent-scale '((c lydian)) '((maj)))
;; ((((c4 maj) (d4 maj) (g4 maj))))

;; Use of nested lest may require use of (multiple flatten-sublist calls
(expand-chord (flatten-sublist (find-chord-for-parent-scale '((c lydian)) '((maj)))))
;; ((c4e4g4 d4fs4a4 g4b4d5))

(find-chord-for-parent-scale '((c lydian)) '((maj)(m7)))
;; (
;;  ( -> for scale
;;   ((c4 maj) (d4 maj) (g4 maj)) -> for first quality
;;   ((e4 m7) (a4 m7) (b4 m7)) -> for second quality
;;  )
;; )

;; Use
(expand-chord (flatten-sublist (find-chord-for-parent-scale '((c lydian)) '((maj)(m7)))))
;; ((c4e4g4 d4fs4a4 g4b4d5) (e4g4b4d5 a4c5e5g5 b4d5fs5a5))


(find-chord-for-parent-scale '((f lydian)(c lydian)) '((maj)(m7)))
;; (
;;  ( -> for first scale
;;   ((f4 maj) (g4 maj) (c4 maj)) -> for first quality
;;   ((a4 m7) (d4 m7) (e4 m7)) -> for second quality
;;  ) 
;;  ( -> for second scale
;;   ((c4 maj) (d4 maj) (g4 maj)) -> for first quality
;;   ((e4 m7) (a4 m7) (b4 m7)) -> for second quality
;;  )
;; )




;; Experiments to exchange G7 in V7->Cmaj7 ---

;; First the original -
(assemble-seq 
 (flatten-sublist (flatten-sublist  (find-chord-for-parent-scale '((f lydian)) '((7)))))
 '(c4 maj7))
;; ((g4 7) (c4 maj7))


;; Try m7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((a4 m7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((d4 m7) (c4 maj7))

(assemble-seq 
 (third (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian)) '((m7))))))
 '(c4 maj7))
;; ((e4 m7) (c4 maj7))

;; Try maj7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian)) '((maj7))))))
 '(c4 maj7))
;; ((f4 maj7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian)) '((maj7))))))
 '(c4 maj7))
;; ((c4 maj7) (c4 maj7)) :-)

;; Try dim7 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian-diminished)) '((dim7))))))
 '(c4 maj7))
;; ((f4 dim7) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f lydian-diminished)) '((dim7))))))
 '(c4 maj7))
;; ((gs4 dim7) (c4 maj7))


;; Try 7/b5 -
(assemble-seq 
 (first (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((g4 7/b5) (c4 maj7))

(assemble-seq 
 (second (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((bb4 7/b5) (c4 maj7))

(assemble-seq 
 (third (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((cs4 7/b5) (c4 maj7))


(assemble-seq 
 (fourth (flatten-sublist (flatten-sublist (find-chord-for-parent-scale '((f whole-half-tone-scale)) '((7/b5))))))
 '(c4 maj7))
;; ((e4 7/b5) (c4 maj7))





;; Stay inside same parentscale tonic but vary the chord quality ---
;; See chord pregression below


(assemble-seq
 (find-chord-for-parent-scale '((f lydian)) '((maj7)(7/sus4)))
 (find-chord-for-parent-scale '((f lydian-augmented)) '((maj7)(aug)(m7)))
 (find-chord-for-parent-scale '((f lydian-diminished)) '((dim7)(aug)(m7)))
 (find-chord-for-parent-scale '((f lydian-b7)) '((m7)(7)(7/b5))))