Analysis of First-Counterpoint-Music Generator Based on Nyquist

Chencheng Liu

Data Science, University College London, London, U.K.

Keywords: Nyquist, Music Generator, First-Counterpoing-Music Generator.

Abstract: As a matter of fact, music composing based on software is widely analysed. This study introduces the

development and implementation of the first species counterpoint music generator based on Nyquist

programming. Reviewing early research on counterpoint music generators, including the pioneering work of

Hiller and Isaacson, and the use of Variable Neighbourhood Search(VNS) algorithms to optimize generators

in recent years, the author aims to create a music generator that can generate music according to the first

species counterpoint rules, and in experiment, author introduces four rules that must be met to generate music,

such as using only concertos and intervals and avoiding large leaps. By modifying the range and rules, the

generator can quickly generate the music conforming to the counterpoint method, but the rules are too strict

and the adjustment of the range is complicated. The summary points out that with the reduction of

programming algorithms, more and more music creators can use computers to generate specific styles of

music, Nyquist has great potential, especially in the composition of classical music.

1 INTRODUCTION

The first work on computer counterpoint dates back

to 1958, when Hiller and Isaacson used the ILLIAC

computer, a computer built at the University of

Illinois, to compile a generator that could quickly

generate music satisfying Fux counterpoint (Lejaren

& Leonard, 1958). By refining the rules of

counterpoint into regulations, and step by step, they

make the music generated by the generator meet the

corresponding requirements, proved that musical

concepts can be interpreted into computer language to

produce musical output. Next, considering about

generate music less imitative and restrictive in scope,

they wrote a program for the generation of dissonant

chromatic music, to make music more like it's made

by people and less like by machines. Finally, they

used second-order Markov chains to make abstract

musical rules mathematically embodied by

computers. After this, Lewin also compiled the music

generator, which generated music by adding "global

rules" to the original first species counterpoint,

making the generation more efficient, but less

aesthetically friendly (Farbood & Schöner, 2001). He

used his own understanding to change the rules,

making the original rules simpler and easier to

generate.

Although the pioneer research is half a century old,

in the last 10 years, there have been studies that have

changed the method of using programs to generate

music that meets counterpoint, constantly trying to

optimize the generator. Dorien and Kenneth

generated the score satisfying the first species

counterpoint through Variable Neighbourhood

Search (VNS) algorithm, which has been

implemented in Optimuse, a user-friendly software

(Komosinski & Szachewicz, 2015). The VNS

algorithm is also used in an Android software (FUX),

which has been able to generate music that satisfies

the fifth counterpoint according to the preset music

length (Herremans & Sorensen, 2013).

At present, although there are many counterpoint-

music generators, it is still necessary to study how to

build that generator. The creation of modern music is

not restricted only by the rules of counterpoint.

Different styles of music also have to meet different

rules, but it is less rigorous and convenient to evaluate

than traditional counterpoint. Therefore, writing

counterpoint music generator will be an important

reference for computer composition.

Nyquist is a language for sound synthesis and

music creation that combines the functions of score

language and signal processing language, capable of

simultaneously processing musical events and sound

signals (Dannenberg, 2008). Based on an interactive

Liu and C.

Analysis of First-Counterpoint-Music Generator Based on Nyquist.

DOI: 10.5220/0013515800004619

In Proceedings of the 2nd International Conference on Data Analysis and Machine Learning (DAML 2024), pages 285-288

ISBN: 978-989-758-754-2

285

Lisp interpreter, Nyquist is flexible and easy to use,

allowing users to design instruments and generate

sounds with simple expressions. It supports multiple

platforms, including Linux, macOS, and Windows.

Nyquist's core language is Lisp and has expanded its

capabilities for sound synthesis and signal processing.

Because of Nyquist's ease of use and its support

for mathematical models (e.g., Markov chains), the

next generation of generators will be written entirely

on the Nyquist platform.The attempt to use Nyquist

to randomly generate music is not new (Li et al.,

2024). Although the attempt of this paper is also

random generation of music, it is very different from

their research in that this attempt pays more attention

to the generation of Nyquist sheet music.

Before jumping right into the topic, here is a brief

introduction to the first counterpoint method.

Counterpoint originated in ancient Europe, and the

first known book on counterpoint was parallel

organum (about 900 A.D), which was very different

from what is known today (Jeppesen, 2013). All the

theory of counterpoint introduced here are from

Johann Joseph Fux (Fux & Wollenberg, 1992).

In classical composition, musicians classify note

combinations (chords) by the relationship between

two notes played at the same time (intervals),

classifying them into perfect consonance, imperfect

consonance and dissonance (Blom et al, 2016;

Dannenberg, 2010). Perfect consonance: unison, fifth,

octave; imperfect consonance: third, sixth and

dissonance is any interval else. All chords that appear

in the first species counterpoint are consonance. Also

to be mentioned is the marching of music, where the

implication of direct motion is that the interval of the

previous chord coincides with the interval of the next

chord, which is forbidden exists between perfect

consonance in the first species counterpoint. With the

above foreshadowing, the research method will be

clearer.

2 DATA AND METHOD

The main goal of the project is to use Nyquist to

create a program that can randomly generate music

satisfying the first species counterpoint. At the

beginning, this study will refer to the work of Hiller

and Isaacson, and this study lists the rules that need

to be met to generate music as rules:

 Only consonances are included in the music

 Start and end are perfect intervals

 Avoid leaps of major 6th or greater to keep

the melody smoothly

 No direct motion to perfect interval

As a preliminary experiment, this study limited

the generated music to 2 parts and the tonal range to

8 white keys (The mode used for the counterpoint part

must be the same).

This research gave priority to programming the

basic parts necessary to generate music, such as score

generation and instrument functions. Since the listed

rules do not include the regulation of rhythm, this

paper naturally focused on the relationship of pitch

between notes. Taking advantage of the feature of

nyquist music score that can accept multiple notes to

generate chords at the same time, this study listed the

possible consonances and asked the music score to

obtain tones only from these chords to satisfy the first

condition. After making the generated music meet the

second rule through the score editing function in

Nyquist, it is found that the generated music was too

monotonous and bland. The more restrictions was

subjected to in the creation of music, the less diversity

of works it could create. On the contrary, more

freedom in the creation of music would make the

generated music more possible. Considering that the

music to be composed by the program would be

constrained by the first pair of positions (which would

be an extremely liberating constraint), this study

increased the range of tones from the original 8 white

keys to 10.

This study began to try to make the parallel notes

in the music conform to the corresponding rules. First,

this study classified chords with different intervals.

By using the Markov chain function in Nyquist and

the control of the first-order Markov chain, the perfect

chord could not reach the next perfect chord directly,

thus satisfying rule 4 (last rules). Meanwhile, in order

to satisfy the third rule, this research further grouped

chords with the same interval and modified the

previous Markov chain. Groups with too large a pitch

span cannot communicate with each other, so that the

music is always smooth and stable. At this point, the

program has satisfied all the rules listed above. In

terms of generating the timbre of music, in order to

restore the classical style as much as possible and

identify the tone better, this research chose the piano

sound effect brought by Nyquist as the playing

instrument for generating the score.

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Figure 1: Generated music (Photo/Picture credit: Original).

3 RESULTS AND DISCUSSION

In addition to auditory recognition, Nyquist's

program can further display the generated score,

which is a randomly generated score with a total

duration of 24 seconds and 0.5 seconds per syllable

as shown in ‘Figure 1’.

The first species counterpoint generator written

by Nyquist in above way can indeed generate music

that satisfies the first species counterpoint quickly and

strictly, and can adjust the length of the music as

needed. However, the current code still has many

shortcomings and improvements. First of all, the rules

in the generator cannot be freely deleted, and there are

too many restrictions between different rules, which

makes it difficult to change the rules later. Second,

the range of the current generator cannot be changed

quickly, and each change requires regrouping the

chords, which greatly increases the workload, and

later it may be possible to add some preconditions to

meet the fast grouping of different ranges.

As for the prospect of this generator, because this

attempt shows that it is feasible to use Nyquist to

achieve random music generation satisfying stricter

rules, it has certain guiding significance for the

second counterpoint and even the fifth counterpoint

music generation that may appear later. In addition, if

combined with the powerful timbre processing

function of Nyquist itself, in the case of meeting

certain rules of classical music, breaking the rules of

some traditional music generation, it may produce

more creative works different from the music in the

market today, and these works may not only be novel

but also beautiful.

Artificial intelligence is expected to play a bigger

role in the future. Automatic creation refers to the

computer through a certain algorithm to compose

music, assisted creation refers to the computer to

simplify the creation process. Through algorithmic

music creation, and DAW and related tools,

researchers can realize that some commonly used

music arrangement, mixing software can be included

in this list. It is worth mentioning that Band in a Box,

this software can automatically arrange and

orchestrate music in a variety of styles, reducing the

Analysis of First-Counterpoint-Music Generator Based on Nyquist

287

threshold of creation. In addition, some software (or

apps) with game entertainment can also be called

creative aid tools. For example, the Garage Band on

ipad has the so-called Smart Drum. Percussion parts

can be made by simply dragging the corresponding

instrument to a certain position on an 8 × 8 panel (the

vertical coordinate of the panel is loudness, the

horizontal coordinate is rhythm complexity)

instrument, electronic timbre and vocal synthesis:

Synthetic instrument timbre provides the

convenience of writing and listening for the creator,

and also reduces the cost of playing (much cheaper

than having the player record). Electronic timbre is an

area that is still being explored, but it has been widely

used and is also very important for electronic music,

which has many well-known synthesizers from

hardware to software. Music storage, retrieval and

dissemination storage. Storage is mainly related to the

technology in the field of signal processing, involving

lossy compression coding and lossless compression

coding. Lossless compression coding generally

makes use of the information redundancy of music

itself. In terms of retrieval, it mainly uses retrieval

methods other than meta information (song name,

singer name, etc.). For example, search by humming

melody, search by beating rhythm, search by song

style (mood), search by song, and so on. Music

appreciation and analysis Appreciation is the

reproduction of music through playback equipment,

modern electronic music, the reproduction of concert

recording (sound field reproduction) is a very

important topic, there are many efforts in this area,

such as stereo, such as head recording, automated

evaluation. One can use computers to identify good

and bad versions of works; use the computer to

identify the level of the performer (can be used for the

automation of the instrumental music test).

Computers analyze the structure, orchestration, mood,

and emotion of music.

4 CONCLUSIONS

Overall, this experiment does show that with the

lowering of the threshold of modern computer

programming, more and more music creators can use

computers to create their own music faster, and

through certain rules to let the computer generate the

corresponding style of music. In addition, although

the use of Nyquist to generate music that satisfies

certain conditions is not new, the generation of music

that satisfies the first pair method through specific

Markov chains also demonstrates the greater potential

of Nyquist, whose strict score generation function is

also well adapted to classical arrangements that attach

great importance to rules.

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