48 rows can be created from a single twelve-tone row: the prime, retrograde, inversion and the retrograde inversion with 12 transpositions each. Here I show how to make nice tables of these 48 transformations. For example the row of Arnold Schönbergs Variations for Orchestra op. 31:
In the following an old version is described, which uses LilyPond and LaTeX. A new version, which only depends on LilyPond, is to be found on GitHub. There is also to be found an executable, which doesn't require any Common Lisp implementation.
A Common Lisp Implementation is needed (I use LispWorks) and ASDF must be available. It only works on platforms with Shell like Max OSX or Unix, because the communication with the operating system is done via asdf:run-shell-command.
The paths to LilyPond, pdflatex as well as the twelve-tone row can be adjusted in the first few lines of the code. The note names of the row must be the English names for natural tones (c d e f g a b) with is resp. es for sharp or flat. (E.g. that means E♭ must be notated as ees.)
Concerning questions, remarks or whatever: You can conctact me!
;;; -*- mode: Common-Lisp; Base: 10 ; Syntax: ANSI-Common-Lisp ; coding: utf-8 -*-
;;; make 12 tone row table pdf files with LilyPond and LaTeX
;;; This work is licensed under a Creative Commons Attribution 3.0 Unported License.
;;; Frank Zalkow, 2010-2013
;; adjust these paths to your needs
(defparameter *row* '(bes e ges ees f a d cis g gis b c))
(defparameter *lilypond* "/Applications/LilyPond/LilyPond.app")
(defparameter *pdflatex* "/usr/texbin/pdflatex")
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; ASDF
(require 'asdf)
(unless (find-package 'asdf)
(error "ASDF is not installed!"))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; ARBITRARY NOTE NAMES TO NOTE NUMBERS
(defun name2number (note)
(let* ((diatonic '(("c" 0) ("d" 2) ("e" 4) ("f" 5) ("g" 7) ("a" 9) ("b" 11)))
(notestr (symbol-name note))
(nr (cadr (nth
(position (subseq notestr 0 1) diatonic :test #'string-equal :key #'car)
diatonic))))
(dotimes (i (/ (- (length notestr) 1) 2) nr)
(let ((substr (subseq notestr (+ 1 (* 2 i)) (+ 3 (* 2 i)))))
(setq nr (+ nr (cond ((string-equal substr "is") 1)
((string-equal substr "es") -1)
(T (error (concatenate 'string note " is not a valid note name!"))))))))))
;; ROW MANIPULATIONS: transpositions, retrograde, inversion, retrograde-inversion
(defun transposition (row interval)
(mapcar #'(lambda (n) (mod (+ n interval) 12)) row))
(defun retrograde (row)
(reverse row))
(defun inversion (row &aux (first (car row)))
(mapcar
#'(lambda (n)
(mod (+ (- first n) first) 12))
row))
(defun retrograde-inversion (row)
(retrograde (inversion row)))
;; GENERATING CODE FOR LILYBOOK
(defun generate-code (row-name &optional (stream T))
(let ((row-nr (mapcar #'name2number row-name)))
; converting a list of note numbers into a lilypond string
(labels ((row2str (row)
(let ((notes (mapcar #'(lambda (n)
(nth (position n row-nr) row-name))
row)))
(string-downcase
(concatenate 'string
(symbol-name (car notes)) "'4 "
(format nil "~{~a' ~}" (cdr notes)))))))
(format stream "\\documentclass[landscape]{article}~%\\usepackage{array}~%\\usepackage{geometry}~%\\geometry{a4paper,left=10mm,right=10mm, top=10mm, bottom=10mm} ~%~%\\begin{document}~%~%\\begin{center}~%\\thispagestyle{empty}~%~%\\Large \\textsc{Twelve-tone-row table}\\\\[2cm] \\normalsize~%~%\\newcolumntype{C}{>{\\centering\\arraybackslash} m{6cm}}~%\\newcolumntype{D}{>{\\centering\\arraybackslash} m{0.5cm}}~%\\begin{tabular}{|D|CCCC|}\\hline~% & prime & retrograde & inversion & retrograde-inversion\\\\ \\hline~%")
(dotimes (transp 12)
(format stream "~d & " (+ transp 1))
(dolist (func '(append retrograde inversion retrograde-inversion))
(format stream "\\begin{lilypond}[fragment,staffsize=12]~%")
(format stream "#(set-accidental-style 'dodecaphonic)~%\\override Staff.TimeSignature #'stencil = ##f~%\\override Stem #'transparent = ##t~%\\cadenzaOn~%")
(format stream (row2str (transposition (funcall func row-nr) transp)))
(format stream "~%\\end{lilypond} ")
(unless (eql func 'retrograde-inversion) (format stream " & ~%")))
(format stream "\\\\ \\hline~%"))
(format stream "\\end{tabular}~%\\end{center}~%\\end{document}"))))
;; ADDING A STRING TO AN ENVIRONMENT VARIABLE FOR DIFFERENT LISP IMPLEMENTATIONS
(defmacro add-env-path (pathname &optional (name "PATH"))
(let ((env
#+LISPWORKS `(lispworks:environment-variable ,name)
#+CMU `(cdr (assoc ,name ext:*environment-list* :test #'string=))
#+Allegro `(sys:getenv ,name)
#+CLISP `(ext:getenv ,name)
#+ECL `(si:getenv ,name)
#+SBCL `(sb-unix::posix-getenv ,name)
))
`(if (and ,pathname (not (string= ,pathname "")))
(setf ,env (concatenate 'string ,env ":" ,pathname))
,env)))
(defun double-tilde (str)
(substitute "~" "~~" str))
;; EXECUTE SHELL COMMANDS AND CREATE PDF
(defun create-pdf (row)
(let* ((tempdir (concatenate 'string "/tmp/twelve-tone-row-table-" (write-to-string (random 9999999999)) "/"))
(lytex-file (merge-pathnames tempdir "myrowtable.lytex"))
(tex-file (merge-pathnames tempdir "myrowtable.tex"))
(pdf-file (merge-pathnames tempdir "myrowtable.pdf"))
(lilybook (concatenate 'string *lilypond* "/Contents/Resources/bin/lilypond-book")))
; if pdflatex directory is not in path environment, add it
(let* ((pdflatex-dir/ (directory-namestring *pdflatex*))
(pdflatex-dir (subseq pdflatex-dir/ 0 (- (length pdflatex-dir/) 1))))
(unless (search pdflatex-dir (add-env-path NIL))
(add-env-path pdflatex-dir)))
; create files
(ensure-directories-exist tempdir)
(with-open-file (filestream
lytex-file
:direction :output
:if-exists :supersede
:if-does-not-exist :create)
(generate-code row filestream))
(unless (probe-file lytex-file) (error (concatenate 'string (namestring lytex-file) " could not be created!")))
(format T "\; call lilypond-book - this can take awhile")
(format T "~a"
(nth-value 1 (asdf:run-shell-command
(double-tilde (concatenate 'string lilybook " --output=" tempdir " --pdf " (namestring lytex-file))))))
(unless (probe-file tex-file) (error (concatenate 'string (namestring tex-file) " could not be created!")))
(format T "\; call pdflatex")
(format T "~a"
(nth-value 1 (asdf:run-shell-command
(double-tilde (concatenate 'string "cd " tempdir " ; " *pdflatex* " -output-directory=" tempdir " " (namestring tex-file))))))
(if (probe-file pdf-file)
(format T "~a created!" (namestring pdf-file))
(error (concatenate 'string (namestring pdf-file) " could not be created!")))
(format T "\; open pdf")
(asdf:run-shell-command
(double-tilde (concatenate 'string "open " (namestring pdf-file))))))
(create-pdf *row*)