Aesthetic Analyze of Computer Music

 

Teacher Maria Goga, Msc

School of Music Nr. 5,Bucharest, Romania,

email: goga_man@computermail.net

 

Postdoc Nicolae Goga

Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven,

email: n.goga@tue.nl

 

 

 

Abstract

 

The improvement of the aesthetic of the melody line of the music generated by the computer is a big challenge for the scientific world today.  The research presented in this paper is trying to give a solution to this problem. A first experiment consisted on the following: 1) a tool for music generation was created;  2) some simple melodies for Bass were created and all the possible solutions for Tenor, Alto and Soprano were generated;a musical analyze from an aesthetic and musical form points of view was made; 3) a set of rules were derived from the analyze such that the aesthetic of the melody line of the music generated by the tool would improve.Out of this first experiments we derived a theory for feelings based music generation. Examples generated according to this theory will be also presented in this paper .

 

     1. Introduction

 

  The improvement of the aesthetic of the melody line of the music generated by the computer is a big challenge for the scientific world today. There are programs and mathematic theory [1] for computer music generation. Usually, this music is produced in conformance with the laws of harmony [3]. But when a computer scientist gives to a musician some music originated from the computer too often the musician is saying: I do not want only a music which is harmonic good, but also a music which will sound good. On another hand, for a mathematician, only employing the harmonic laws for the computer music generation still leaves a lot of freedom for the notes generation, and, consequently the number of possible solutions (for a simple leading melody) is usually very big. For example, when Bass is given, and its melody has a small size (13 notes), the computer can still produce millions of solutions for the melodies of Tenor, Alto and Soprano (all the  solutions being harmonic good).

 

 The research presented in this paper is trying to give a solution to the problems above mentioned. The team was formed by researchers from music and computer science. In main the experiment consisted on the following: 1) a tool for music generation was created; the tool implements the laws of classical harmony; 2) some simple melodies for Bass were created and all the possible solutions for Tenor, Alto and Soprano were generated; a musical analyze from an aesthetic [2] and musical form points of view was made; the principles of the classical music for a choir were engaged in the analyze; 3) a set of rules were derived from the analyze so that the aesthetic of the melody line of the music generated by the tool would improve.

 

 This was a first experiment concerned with the computer music aesthetic. In our later experiences we took into account the set of rules derived from our first experiences. From this experiences we derived also a theory for feelings based music generation. The concepts of this theory are also applied and presented in this paper.

 

The paper is organized as follow. Section 2 briefly presents the harmonic laws implemented by the tool. Section 3 describes the tool. Section 4 presents the first experiment related with the aesthetic music analyze. Section 5 deals with the theory of feelings based music generation. Section 6 gives examples of applications of this theory. These examples are analyzed also esthetically. Section 7 outlines the conclusions.

 

 

 

     2. The harmonic law

 

The music is a revelation higher than any wisdom and philosophy (Ludwig van Beethoven)

 

 The music (the sound art) revealed in the time of the centuries to be a main component of  the human culture. The musical art has a theoretical system which is composed by a number of disciplines with different visions. In this way the musical theory, the harmony, the polyphony, the forms, the instrumentation and orchestration, the musical aesthetic and the composition, treat step by step the aspects studied by this art. From the multitude of disciplines enumerated above, the present paper is willing to `touch' only some aspects of the classical harmony, aspects which today can be used by the computer.

 

The  chord -- the principal element of the harmony The chord is a sonorous unit formed by more simultaneous sounds [5] with a sonorous structure and aesthetic structure well organized.

 

 In the natural resonance of the sounds the fundamental is repeated the most, the third is on the second place and the fifth is on the third place. It is not an accident that the sounds  do (the fundamental), mi  (the third) and sol (the fifth) represent the constitutive elements of the major chords.

 

 The chords and the harmony are linked to the occurrence of the tonal system.From the necessity that the musical sounds must support each other, must have a weighting center, the idea of tonality was born. From the sounds of a tonality, a chord can be built on every musical degree. A chord is formed from third overlaps. Every sound takes the function given by its correspondent degree.

 

From the point of view of their functions, two kinds of chords can be distinguished: principal and secondary. The degrees of the principal chords are: the tonic (I), the subdominant  (IV) and the dominant (V). The rest of the degrees are secondary : the supertonic (II) , the mediant (III), the submediant (VI), the leading tone  (VII).

 

The harmony for four voices The present work treats the human voice harmony, especially the harmony of the principal voices -- Soprano, Alto, Tenor and Bas. According to their setting in the choir assembly the voices are divided in external voices (Soprano, Bas) and internal voices (Alto, Tenor). Usually, the melody is given by Soprano. Sometimes the other voices contribute also to the melody. The most used chords are the ones with 3 sounds (triads) which are distributed to 3 voices. The fourth voice doubles the tonic or the fifth (the third is doubled rarely).

 

In some chords some   elements can be omitted. The tonic can not be omitted because it is the one which generates the chord. The same holds for the third because it gives the scale: minor or major. Consequently, the only element which can be omitted is the fifth.

 

The distance between voices For ensuring a homogeneous and balanced sonority a maximal distance should be respected among neighbour voices. For example, among Soprano and Alto the maximum  distance is of an octave.

 

The melodic movements of the voices For having a cantabile  song, some intervals, difficult to be singed, are not allowed:

 

 

 

 

The harmonic movement of the voices In the melodic movement we observed the horizontal development of one voice, but in the harmonic one we will observe two voices which moves simultaneously.The following movements between voices exists (self-explanatory by name): the direct movement, the parallel movement, the oblique movement, the counter movement and the counter-parallel movement.

 

The direct fifth and octave For the external voices, the direct fifth and octave are allowed if and only if the superior voice goes  gradually.

 

The parallel unison, fifth and octave It is not allowed to have two voices which go in parallel in unison, fifth and octave when the voices go through  two different chords.

 

The counter-parallel fifth and octave The succession of fifth and octaves between the same voices are  not allowed for a counter-parallel movement.

 

 

 

     3. A tool foor music generation

 

In this section we will present the  tool for music generation. The tool which is especially built for our experiments can be used in the following way: a Bass melody is given as the input for the tool and the melodies of Tenor, Alto and Soprano are generated such that the constraints imposed by the harmonic laws are respected. However, the tool can easily be updated so that it will help  the user to compose melodies for all the voices (Bass, Tenor, Alto and Soprano ), melodies harmonically good.  The tool can be easily be adapted to be  an interactively process in which the user gives notes for Bass, Tenor, Alto and Soprano to the tool and the tool tells to the user whether his/her choice is correct or not harmonically.

 

 The main engine of the tool is the procedure Verify. This procedure has as parameters four arrays of notes (for Bass, Tenor, Alto and Soprano). The procedure verifies whether the musical composition formed by the notes of Bass, Tenor, Alto, Soprano  is harmonically good. First it checks whether the distances between the notes of Bass and Tenor, Tenor and Alto, Alto and Soprano are in the allowed intervals (see Section 1). The next steps is to apply the procedure VerifyVoices to all the possible combinations between the four arrays of notes for Bas, Tenor,  Alto and Soprano. The first 3 steps of the procedure VerifyVoices is to verify that there is not a direct octave, fifth or unison between  two voices. After that it checks that there is not a parallel octave, fifth or unison between  two voices, at the end it looks for counter-parallel octaves or fifths.

 

 As  explained above the constraints imposed by the harmonic law are checked out by the procedure Verify. The generation of the notes  Tenor, Alto and Soprano is done by  a back tracking procedure. The algorithm  generates notes for Tenor, Alto and Soprano in a size equalling the length of the Bass melody. First, it fills the first position by generating  three notes for Tenor, Alto and Soprano. After that it goes to the next position and generates again notes for Tenor, Alto and Soprano.  This is done till a complete melodic solution is constructed. At each position the back-tracking algorithm verifies whether the melody generated is harmonic good (this is done by using Verify).  After a first solution, the algorithm generates other solutions. It stops only when all the possible combinations for every position are tried and, consequently, all the possible solutions for the melodies of Tenor, Alto and Soprano are produced.

 

 The tool have also the possibility to accept pattern functions for the Soprano voice. An example of such a pattern is: the voice is moving gradually. A first use of the patterns is to  generate music when the pattern and the Bass are given. Another possibility is to ask the tool to generate all the voices when a pattern of the Soprano is given. This option was used for the feelings based music generation experiment.

 

 

    4. The first experiments

 

The melody is the most expressive way of communication of the music. The melody is a general reference for the compositional, aesthetic, theoretical and historical characteristics of the sound art. The melody is the center to which all the characteristics of the musical image converge.

 

A melody can be well composed  harmonically but, sometimes, it does not sound well. In the work presented here, there  are many musical examples which confirm this truth. The same Bas can generate, on the basis of the harmonic laws, melodies which are correct from an harmonic point of view but which do not sound well. More precise, these melodies do not have a beginning, a culmination and an end.

 

 The Bas given (imposed) is in a pedagogical style, arranged in such a way to make easy the analyze of the melodies generated.   The harmonic laws of the classical style are used. From this reason the analyze of the melodies are made also from a classical point of view. The Bas of each of  the three melodies which are used in the first experiments is formed from the principal degrees of the do major scale. The rhythm is the element which differentiates the melodies.

 

 Because the  number of solutions generated was too big we considered randomly the same number of solutions for each melody, we made observations related with the aesthetic problems encountered. What is interesting for us is to observe whether the melodies created for Soprano (and for Alto and Tenor) can be interpreted and whether the aesthetical  melodical curve which keeps the idea of a beginning, a culmination and an end exists. We call correct  melodies (37% in our case) the ones which correspond to the harmonic laws and the aesthetic laws.

 

 There are exceptions from the aesthetic rules, melodies which do not respect strictly the `melodic-aesthetic` curve which gives the criterion of correctness. In a number of cases, the culmination is at the beginning, or at the beginning and at the middle, or at the middle and at the end, or at the end  (46% exceptions). It is common to have the culmination only once (around  the middle of the melody ), for such a small size.

 

Another problem encountered is that some melodies from the exception group can not be easy interpreted,  are not  easy-cantabile because the culmination (the notes in the acute register ), bypasses the admitted limit (goes too high), and, consequently, the other two support voices, Tenor and Alto, go also too much in the acute.

 

So called non-correct  melodies can not be called melodies, because they consist of one or two sounds which are repeated continually and we can not speak about a beginning (in the medium register of the voices), a culmination (in acute) and an end (in medium).

 

 

 

 5. Feelings based music generation theory

 

 In the previous chapters we presented a tool, aesthetical and classical musical form analyses and general rules of improvement (derived from the analyses performed) for the computer music. In the current chapter we propose a new theory for the music generated by the computer. We experimented with it on the tool presented in this paper. 

 

 When a composer is involved in his compositional process, especially when he/she tries to compose music for different texts, the composer wants the music to awake different feelings in the hearers of the music. The feeling can be decided by the composer or can be derived from the text. For example, a piece of text expresses joy, another one violence or peace, etc. On another hand it is a known fact that using some general rules for composing music can produce in the audience some reactions. For example, repeating  a small sequence of notes many times make a hypnosis state to be induced. The joy can be produced in many ways; for example by a melody which goes upwardly and  gradually.

 

 We propose to generate music according to a similar process used by the composers. Our method applies especially for texts which need to be sustained by melodies. When looking to the text, the human (a composer or a non-specialist) decides each portion of the text which feeling needs to awake. The feeling can be derived from that portion of  text or can be decided by the human. The computer receives as an input data the set of feelings and for each feeling the length of the melody which needs to be generated. Now, from its data base, for each feeling from the set, the tool will choose rules or a pattern which express that feeling and will generate music, till the whole melody is constructed. The human will receive back the set of melodies generated and he/she can choose one of these or get inspiration from this set in his/her compositional process.

 

 Of course a key element of the whole process is the knowledge (the data base) which the tool have related to the melodically patterns  which induce a given  feeling. In the current paper we worked out a list (which is not exhaustive) containing feelings and their associated pattern. One important observation is that one feeling can be  awaked by more patterns. The tool has the possibility to choose from more patterns for a given feeling, therefore its  creativity is enlarged.

 

The list of sentiments and their correspondent patterns are given below. This list is not exhaustive and it was worked out by the authors of this article with the help of the existing literature (see for example [5]).

 

1.     Restlessness:

 

a)      Gradually descendent movement combined with ascending movement having short breaks which suggests the restlessness idea.

 

 

 

 

 

 


b) At the beginning of the melodic sequence gradually movement followed by jumps of fifths or sixths; the melody is formed by the repetition of this melodic sequence.

 

 

 

 

 

 


2.     Peace

 

a)      Gradually ascending  movement combined with a descendent  jump of a fifth

 

 

 

 

 

 

 

 

 


b)      Gradually ascending movement followed by a descendent jump of a third combined with a ascending jump of a sixth and after that again a descending  jump of a third

 

 

 

 

 

 

 

 

 

 


3.     Consolation

 

a)      Gradually ascending movement combined with gradually descending movement

 

 

 

 

 

 

 


4.     Innocence

 

a) Gradually ascending movement which contains a short  musical proposition which will be combined with the same musical  proposition transposed  to a range of a fourth.

 

 

 

 

 

 

 

 

 

 


a)      Gradually ascending movement combined with a gradually  descending movement and everything repeated (short values for the times of the notes)

 

 

 

 

 

 

 

 


5.     Delicately

 

a)      Jump of a sixth at the beginning followed by a gradually descending movement combined with a gradually ascending movement (short values for the  times  of  the notes)

 

 

 

 

 

 

 


b)      At the beginning the repetition of the sound once followed by a jump of a sixth combined with descending jumps of thirds and ascending movement in jumps (short values for the  times of  the notes)

 

 

 

 

 

 

 

 

 


6.      Sadness

 

a)      The first sound repeated five or six times combined with gradually ascending movement

 

 

 

 

 

 


b)      Gradually descending movement followed by descending movement in jumps combined with ascending movement in jumps (large values for the times of the notes)

 

 

 

 

 

 

 

 


7.     Trust

 

a)      Ascending jump of a fourth followed by a repetition of the same sound (three or four times) combined with the repetition of a sound obtained from a ascending and gradually movement  (middle values for the times of the notes) 

 

 

 

 

 

 

 


b)      The first sound repeated twice or three times combined with an ascending and descendent movement with  jumps of thirds (middle values for the times of the notes)

 

 

 

 

 

 

 


 

8.     Love

 

a)      Gradually ascending movement followed by gradually  descendent movement combined with jumps of  fifths and followed by the repetition of the same sound

 

 

 

 

 

 

 

 


b)      Descendent movement in jumps of thirds combined with ascending movement in jumps of thirds followed by large values of times on the same sound

 

 

 

 

 

 

 

 


9.     Joviality

 

a)      At the beginning jump of a sixth followed by gradually ascending movement combined with an gradually movement or movement with jumps of thirds

 

 

 

 

 

 


b)      Gradually ascending movement followed by descendent  jumps of sixths or sevenths  combined with jumps of fourths followed by a gradually descending movement

 

 

 

 

 

 

 

 


10.    Joy

 

a)      Descendent movement with jumps of thirds (unison for all the voices) combined with ascending  jumps of thirds.

 

 

 

 

 

 

 


The music is a strange and subtle form of art. It is formed from different  ingredients: rhythm, harmony, melody, their mixture, etc. In function of the presence and the equilibrium of each of these ingredients the music can be peaceful or invigorating, profane or noble, philosophical or orgiastic. The music aims to influence the systems of our emotions.

 

It is interesting to observe and to analyse from a medical point of view how the musical patterns listed above induce their correspondent feeling (listed also above). But the way in which the musical sound from its entrance in the external hear induces the feeling production is not in the focus of the current article. Therefore we will explain this only for the variant a) of point 1) above: how the musical pattern induce the feeling of restlessness.

 

This musical pattern has short breaks at the beginning of the three cumulated values which go always from the acute register to the grave register. Another characteristic is the syncope which is used repetitively. The syncope reverses the natural rhythm of the body which induces a sensation of anxiety which conduct to restlessness.

 

 According to the medical experts [4], this musical pattern modifies the respiration and the blood circulation. This can lead also to the modification of the percentage of the sugar in blood. Under the influence of this music the pupil reflexes and the brain circumference can be changed. These modifications provoke anxiety, agitation, leading to restlessness.

 

 We worked out examples according to this theory with the tool described in the previous chapters. In the examples worked out, we choose some texts, we decided the feelings and we gave them to the tool together with the associated lengths. The tool produced music, which was analyzed from an aesthetical and musical form point of view.  These are presented in the next chapter.

 

 

 

  6. Implementing the  feelings based music generation theory

 

 

 

 In the current article we showed musical patterns based on ten types of feelings. For every feeling we presented two musical variants which induce that feeling. For the feeling of happiness we worked out an example. This is based on a text from the book Psalms of the Bible (Ps. 148, 1)

 

‘Praise the Lord from the heavens’

 

This text expresses feelings of praise for the Lord, happiness from the deepness of the heart. These feelings can be induced by different patterns. A first pattern is one in which the melody of Soprano has a jump of a fourth in the beginning followed by a gradually and descendent movement. The second pattern for Soprano has the culmination at the beginning of the melody (in acute) followed by a  movement which has jumps of maximum of thirds.

 

 The jump of a fourth for the first variant expresses the joy found in the text. The gradually descendent movement suggests the trust in the Almighty God which embraces gradually the soul of the composer (listener). The culmination of the second variant expresses an explosion of joy. This is followed by a gradually stabilisation of the trust in God (expressed by the movement which has small jumps).

 

 

 

 

 

 

 


              Praise     the                Lord          from          the          hea        vens

 

 

 

 

 

 


  

We succeeded to generate melodies for both patterns. Both melodies has a nice sonority. The harmonic law implemented by the tool are respected. We did not encounter aesthetic problems.

 

 

 

  7. Conclusions

 

We created a tool for music generation. The tool is based on a backtracking algorithm which explores all the possible solutions and chooses the only ones which respects the constraints

imposed by the harmonic laws. When the melody of Bass is given it can  generate  all the solutions for the melody of  Tenor, Alto and  Soprano. This functionality of the tool was used for the aesthetic music analyze of our first experiences. The tool can be used also for imposing a pattern to the Soprano voice and to generate all four voices for a given pattern (or sets of patterns).

 

 In our first experiments we used melodies of small size (8 -- 13 notes) which were made in a pedagogical style, with imposed bass. For this experiment, we used  chains of major principal chords. Many solutions given by the computer were distributed in the acute register which for a professional choir is not always easy to be intonated; for an amateur choir this is almost impossible. We also observe from the examples generated that the melody does not have a musical form with introductive part, culmination and ending of the musical phrase. So we found the culmination in the beginning and sometimes remaining in the melody movement. In many examples, the soprano voice remained on the same notes which does not correspond from the aesthetic or musical form points of view. These are only some negatives aspects met in the examples produced by the computer.

 

 Out of these experiments we derived a theory  feelings based music generation. We employed the principles of this theory for generating music and we analyzed it from an aesthetic point of view.

 

 We will continue the study of the quality of the music generation in other domains (such as for a specific instrument). We will implement also other kind of harmonic laws such as the modern and contemporary harmonies and improve the quality of the computer music. Another possible fellow-up of this research is to observe how such tools can be used efficiently in the domain of education, by teachers and students.

 

 

 

 

 

References

 

[1] Jackendoff, R. S. and F. Lerdahl (1996). A generative theory of tonal music. Publisher: MIT Press.

 

 [2] Leopoldo, H. (1971). Introduction a la estetica de la musica. Publisher: Editorial Paldos, Argentina.

 

[3] Schoenberg, A. (1900). The theory of music. Germany.

 

[5] Schullian, D. and Schoen, M. Music and Medicine. USA.

 

[5] Wyatt, K. and Schroeder, C (1998). Harmony and Theory. Publisher Hal Leonard, USA.