powerful computers programmed with artificial intelligence are routinely
carrying out brain-work -- thinking, judging, selecting, creating
-- which we humans once thought only we could do. There are several
programs which produce music in different styles.
page outlines my own attempts to write a suite of programs to carry
out the basic carpentry tasks in inventing music. It does not used
artificial intelligence; instead the algorithms are based on 'rules'
to create the sequences of chords, vocal lines and melodic decoration
in common practice in the 18th century -- Bach and Haydn's time
-- as set out in the many textbooks on musical theory.
writing these many years ago using the BBC Basic language and have
continued to use it. My methods are not sophisticated and the results
are modest. As an examples, here
is an example of an organ prelude in an antique style (see Figure
67 in the article). I am still working to develop other ways of
decorating a farmework of chords..
has been to build up a short piece of music (or section of a longer
piece) in stages. First a list is created denoting, in the usual
Roman numerals notation, a sequence of triads which make musical
sense -- for example I, IV, I, V, VI, II, V, I. This lst is converted
into a piece in crude 3-part or 4-part harmony in a major or minor
key, and in 2, 3 or 4 beats per bar as the user specifies. The shapes
of the 4 voices are guided by curves effectively drawn across the
staves by the user. An further program cleans up this harmonisation
by removing bad parallels between voices and ensuring that each
chord has all three notes of the triad sounding. Yet a further program
will insert sequences of parallel chords called linear intervallic
patterns. The output is a series of block chords sounding rather
like an antique hymn tune (chorale). Here
is an example in a minor key, which appears as Figure 56 in the
programs in the suite elaborate this hymn tune in various ways,
again under some control by the user, though most of the changes
are made automatically using decision algorthims and some random
numbers. One basic elaboration is to add passing notes. When the
above hymn tune has had some passing notes randomly added into each
voice, it typically sounds like this
(see Figure 57 in the article0.
elaboration of the basic hymn tune uses suspended notes and accented
passing notes on the first neat of a bar (called appoggiaturas)
to give a different feel to the piece, as illustrated here.
type of decoration is to replace some of the remaining longer notes
with a patterns of shorter neighbouring (auxiliary) notes. These
are notes which differ from the given harmony note by only one scale
step up or down. The user can control how many such decorations
are inserted -- it is quite possible to go well over the top and
produce a musical jumble, though the algorithm largely prevents
clashing discords. Here
is another version of the organ prelude quoted above, though
played on a different organ. The difference is in the random way
the longer notes have been embellished with auxiliary notes.
of the sounds is largely automated, since I use the free downloadable
programs Lilypond and GrandOrgue. My programs save the created voice
lines in a code which denotes the pitch and duration of each note.
This is converted by another program in the suite into a Lilypond
file (www.lilypond.org) which, when run, generates both a pdf file
of the engraved sheet music and a MIDI file. GrandOrgue, as its
name implies, is a virtual pipe organ which can be played from a
MIDI keyboard as well as from a loaded MIDI file. It too is free
and is supported by free sampled sounds from several real organs,
all available through www.sourceforge.net. I am most grateful to
the authors of this free software -- a wonderful resource. I used
the sample sounds of Polish and other European organ on the web
site of Piotr Grabowski.
not intend to publish the suite of programs themselves because they
are not in a sufficiently tidy and robust state for other users.
The article here, however, gives an account of the algorithms and
the thinking behind them.
are the sections in the article, in pdf format here:
2: gives an overview of the essential ideas behind Western tonal
3: presents a considerable body of data on the frequencies of occurrence
of various chords and chord sequences.
4: describes how I have used this data in Program 1, which generates
a string of triads in either the major or minor mode, labelled only
by Roman numerals, in an order which makes musical sense. A sub-section
discusses modulation to the dominant and relative minor keys.
5: is about voice-leading within one melodic line; it describes
Program 2 to generate a canto fermo melodic line in notes of equal
duration. Program converts the output of the note-generating programs
into a Lilypond file from which it is engraved as a musical score
and converted to sound as a MIDI file. Program 4 is a development
of Program 2 in which the shape of the melodic line is controlled
by a user-defined mathematical curve.
6: describes stages in the development of Program 5 which makes
a first attempt at 4-part SATB harmony. The approach is to lay four
voice-line guide curves across the sequence of triads generated
by Program 1 Once preliminary measures to prevent parallel unisons,
octaves and fifths have been put in place, the results are fair
but not perfect.
7: is a diversion from computer codes to a discussion of several
aspects of rhythm and the development of melody with rhythmic interest.
Subsections examine agogic accent in polyphonic music, cadences,
musical motifs, compound melody and sequences, and also the textures
used in 18th and 19th century piano writing. This section effectively
defines the challenges and sets out the agenda for developing algorithms.
8: outlines Program 6 with examples. This is a first steps towards
imposing form on the sequences of triads.. On the assumption that
a piece is constructed from a number of 4-bar blocks, Program 6
searches for chord pairs which could become cadences at suitable
positions through the sequence, allocates a number of beats according
to a user-selected time signature, and then allocates the other
triads to beats between the cadences. The output can be realised
as a piece of music using Program 5.
9: returns to the challenge of producing 'correct' 4- and 3-part
harmonisation of a sequence of triads. It builds upon Program 1,
Programs 6 and 5, applied in that order, to generate a crude first
harmonisation. Program 7 attempts automatically to correct the faults
in this first version by completing all triads with root, 3rd and
5th, and to correct parallel unisons, fifths and octaves.
10: is about inserting so-called linear intervallic patterns, a
type of musical sequence, into a piece.
Section 11 deals with inserting passing notes.
12 describes Program 10 which elaborates voices lines by allocating
rhythmic and patterns of shorter neighbouring notes to each long
13 is about the several ways of combining two or more voice lines
into one -- arpeggiation, pedal notes, compound melody, etc.
14: gives some examples of short pieces created using the suite
of programs as tools. (to be completed)
back to the point that these programs deal only in the elementary
procedures in the carpentry of musical composition. What is lacking
is that overall intelligent, tasteful sense of style and integrity
which gives a piece a definite character. It reminds us just how
rare really great music actually is. Perhaps it is best to regard
the 'music' produced by these programs as possible starting material
for a talented human musician to correct, elaborate and rewrite
-- a spur to innovation, but certainly not an end in itself.
"Some Simple Computer Programs to Simulate Construction of
Tonal Music "
article: Fitting mathematical curves to the typical shapes ofd