ModusXXI: An atonal melody generator based on Lars Edlund´s Modus Novus ear-training methodology

Alfonso Meave Escuela Nacional de Música, Universidad Nacional Autónoma de México (UNAM)

alfonsomeave@gmail.com - http://es.geocities.com/alfonsomeave

Felipe Orduña Centro de Ciencias Aplicadas y Desarrollo Tecnológico (CCADET), Universidad Nacional Autónoma de México (UNAM)

Felipe.orduna@ccadet.unam.mx - http://www.ccadet.unam.mx/~felipe.orduna

Proceedings of the fourth Conference on Interdisciplinary Musicology (CIM08) Thessaloniki, Greece, 3-6 July 2008, http://web.auth.gr/cim08/

Background on ear training. Ear training is a very important course in music education. Despite of a large existing amount of ear-training methodologies, the majority of it concentrates on the study of tonal music. One exception is the Modus Novus methodology that organizes the aural study of atonal melody structure on the «combinations of intervals that will break the bonds of the major/minor interpretation of each individual interval.» (Edlund 1963). Although there are other atonal ear-training methods (i.e. Ear Training for the Twentieth-Century Music), Modus Novus is the only one we know of, that concentrates on the study of the interval structure of atonal music. Unfortunately, the melodies for aural dictation and sight-reading contained in Edlund's book are not enough in number and diversity. So that, for a more extended and deeper study of this subject the generation of additional melodic material is necessarily required.

Background in computer science. At present, there are several procedures (i.e. probabilities, grammars, iterative algorithms, neural networks), languages and tools that facilitate music generation with computers. Object oriented computer languages have become the standard in computer programming because (among other reasons) they allow the creation of libraries that simplify programming. The Java language and the jMusic library are examples of that. With tools like these, it is possible and relative easy nowadays to develop computer applications that can be helpful on fields like ear training.

Aims. Our aim is to describe the development, function and use of ModusXXI, an atonal music generator able to create an unlimited number of atonal melodic dictations, or melodic material for sight-reading, during the study of Modus Novus, or during an ear training course on 20th century music.

Main contribution. ModusXXI is programmed in Java language and runs on many operating systems that support multimedia Java applications. In a friendly user environment, the user can control the degree of difficulty of the melody he wants to generate (based on Edlund´s methodology) and practice melody dictation as much as he needs.

Implications for musical practice and for musicological interdisciplinarity. ModusXXI is an interdisciplinary musicological product. It is the result of collaborative research in music education and music technology (Meave, 2007) at the Postgraduate Music Program of Universidad Nacional Autónoma de México, and opens the way to a broader research project. The consequent project aims to create a more advanced application also with a friendly graphical user interface that should be able to generate polyphonic music in specific styles, and serve as a didactic aid in the study of advanced ear training, counterpoint, harmony, etc.

ModusXXI is an atonal melody generator that follows the Modus Novus methodology from the Swedish composer and educator Lars Edlund. ModusXXI can generate an unlimited number of atonal melodic dictations, or melodic material for sight-reading, during the study of Modus Novus, or during an ear-training course of 20th century music. It can also be used to compose atonal musical motifs. ModusXXI is a music technology project, developed at the Postgraduate Music Program of Universidad Nacional Autónoma de México (UNAM) by Alfonso Meave and Felipe Orduña. As the application is written in the programming language Java, it runs on

many operating systems that support the Java Virtual Machine and multimedia (sound) applications.

Modus Novus Modus Novus is the first of two booksi written by the Swedish composer Lars Edlund (1922),- who was teaching at the Royal Academy of Music in Stockholm at that time. The book is dedicated to the study of sight-reading and ear training. Published in 1963, the Modus Novus is one of the first ear training methods that “attempts to tackle the problems connected with the reading of 20th-

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century music that is not mayor/minor tonal.”ii Edlund´s method concentrates on the atonal music composed during the first half of the century by twelve-tone technique composers like Schoenberg, Berg and Webern and less radical composers like Stravinsky, Bartok or Hindemith. Modus Novus does not deal with microtonal music and more radical music. It just focuses on the music created on the equal temperament system that divides an octave in twelve equal semitones and attempts to avoid all possible tonal relationships. What is the significance of this method, if it attends a relative small music style? The significance of the Modus Novus methodology lies, in our opinion, in the fact that it assumes musical intervals as capable of generating a musical discourse and not just as a simple ratio difference between two tones. Edlund writes in this context: “The student’s command (visual and aural) of the theory of intervals in the absolute sense of the word, however, is here merely a pre-requisite, for the study of what I would like to call the aural study of musical patterns.”iii Thus, one of Edlund’s main thesis is that “great accuracy in singing individual intervals is not always a guaranty of accuracy in reading atonal melodies…the most important thing now is to practice combinations of intervals that will break the bonds of the major/minor interpretation of each individual interval.”iv

Modus Novus’ organization Edlund offers a simple description about how the book is organized: “The melodic figures have been grouped together, according to the intervals they contain, in different chapters with an increasing degree of difficulty.”v Modus Novus is organized in twelve chapters as follows:

Chapter Intervals I Minor second, mayor second and

perfect fourth II Perfect fifth and the preceding

material III Minor third, mayor third and the

preceding material IV Examples of melodies from the

repertoire (Application exercises for chapters I-III)

V Tritone and the preceding material

VI Minor sixth and the preceding material

VII Mayor sixth and the preceding material

VIII Examples of melodies from the repertoire (Application exercises for chapters V-VII)

IX Minor seventh and the preceding material

X Mayor seventh and the preceding material

XI Examples of melodies from the repertoire (Application exercises for chapters IX-X)

XII Compound intervals: “Weitmelodik”

Table 1. Modus Novus Chapters Unfortunately, the melodies for aural dictation and sight-reading contained in Edlund's book are not enough in number and diversity. A more extended and deeper study of this subject requires necessarily the access to additional melodic material. A computer application able to generate this additional material is a powerful tool that helps to solve this problem.

ModusXXI ModusXXI is a computer application able to generate an unlimited number of atonal melodies based on the Modus Novus methodology. ModusXXI creates melodies by an stochastic method. The user defines parameters like desired intervals (taken from the Modus Novus methodology), rhythm values, time signature, tempo, duration, etc. The software creates subsets (arrays) of the selected intervals and rhythm values; and a random method, based on a uniform probabilistic function, selects some members of these subsets in order to generate a melody. In other words, when the members of the intervals and rhythm values subsets are defined, all of them have the same probability to be chosen.

Implementation ModusXXI has been programmed in the Java programming language. The software is organized in objects, classes and libraries,

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such as the jMusicvi library. jMusic is a Java package toolkit for instrument building, as well as music making, developed as a Queensland University of Technology (QUT) music research project. ModusXXI uses jMusic to define notes, rhythm values, time signature and tempo, and to generate the graphic notation file and play the melody.

Intervals and rhythm generation in ModusXXI The most significant process of melody generation of ModusXXI is presented below. More about the implementation of the program can be found in the diploma thesis Development of an atonal melody generator computer program based on Lars Edlund´s methodologyvii (text in spanish). The melody generation occurs basically on two classes: GeneradorMelodico.java (note generator) and GeneradorRitmico.java (rhythm generator). GeneradorMelodico.java randomly creates the melody pitches (MIDI notes) by selecting intervals, beginning note and register. Observe the following example:

Figure 1. Note generation Suppose the user selects C5 as first note and two octaves of register from C4 to C6. Also suppose he chooses the ascending minor second, the descending mayor second and the ascending perfect fourth (that could be part of the Modus Novus first chapter). The program will group these intervals in a list (array) of three elements. When the user

clicks the “Create melody” button, ModusXXI calls the random() method that includes the Math. Java library. This method randomly selects list indices and creates a new list with the selected indices, that represent the melody’s sequence of intervals. This is the programming code:

Figure 2. Programming code Taking into account the user’s selected rhythm values and the total melody duration, GeneradorRitmico.java randomly creates the rhythm sequence too. Look at the next example:

Figure 3. Rhythm sequence generation Suppose now that the user defines a total duration of six crotchets or equivalent, for example three bars in 2/4 time signature.

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Maybe he chooses the halfnote, the crotchet and the quaver. With this values ModusXXI will create a list of three elements. Again, the Math.random() method generates a new list with the randomly selected indices of this three element list, taking into account the total melody duration. This new list represents the melody’s rhythm sequence. If the user doesn’t want syncopes between bars, or in the bar, the bar duration (or the values) will be considered as a subdivision of the total duration. It is important to notice that, the sequence of actions in ModusXXI is organised so that rhythm values are generated before the intervals. That is because the number of intervals depends on the number of rhythm values.

ModusXXI (v.1.0) main window

Figure 4. ModusXXI main window The ModusXXI main window has two basic functions: • Collect user´s input data. • Execute the actions. The execution actions are basically three: • Create melody • View score • Play or stop melody The user supplies the following data: Time signature. The user can select from 2/4, 3/4, etc. to 9/4 time signature. ModusXXI generates melodies only with crotchet denominator time signature. This limit is imposed by the jMusic library version used in this implementation. That might be improved in up coming versions.

Duration. The user supplies the number of bars for the total melody duration. ModusXXI can generate melodies with a maximum duration of 67 crotchets or equivalent (also limited by the jMusic library version). Tempo. Melody speed in metronomic measurement. Register. The register selection includes following parameters: Beginning note, lowest note, highest note and register limit. If no register limit is selected, the register limit is the limit of the MIDI protocol. Intervals. The user can choose between three options: Manual selection of intervals, Modus Novus and Preparatory exercises. The first option allows the user to select intervals manually. The second chooses the intervals according to the selected Chapter of Modus Novus. Preparatory exercises allows melody generation with minor and mayor seconds and the specific new intervals presented on every Chapter of Edlund´s book. Rhythm values. The following rhythm values can be selected: whole, halfnote, crotchet, quaver, 16th, dotted half, dotted crotchet and dotted quaver. Syncopation. With this option it is possible to avoid syncopation between bars or to allow it. Subdivision. This option allows, or not, syncopation inside the bar. Once ModusXXI has generated a melody, the user can play it or view the score as in the following example:

Figure 5. Score window

First steps with ModusXXI ModusXXI generates atonal melodies with an intervallic structure. The user just needs to select some parameters and click the create

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melody button in order to get a melody. When a melody is created, the program opens a window with the message: “A new melody has been created. Click the play button or the view score button.” Thus, the user can decide if he wants to hear the melody in order to write it down or if he wants to see the score in order to sing it. Once a melody has been created, the user can play it as many times as he wants (or needs). It is also possible to change the tempo (speed) of the created melody at every moment. If the melody was created with a fast tempo (i.e. 150 beats per minute), he can re-play it with a slower tempo (60 b.p.m). When the user has transcribed the melody, he can view the score to control his transcription. The jMusic menu (it is opened when the view score button is clicked) allows, among other functions, to save the created melody as a MIDI file, or in other formats, and to change the MIDI instrument.viii

How can ModusXXI be used in the classroom or individual ear training? Dictation is a very important activity during an ear-training course, but not the only one, and requires a lot of time and continuous practicing. If a teacher spends a lot of time on dictation, other activities, such as sight-reading, melody harmonizing, etc. are disregarded. Another problem with dictation is the fact that every student has his own learning pace. Some students can learn to transcribe dictations in a relative fast way, whereas others need more time. With an application like ModusXXI, part of the ear-training course can be done with the aid of the computer. For example, the student can sing and harmonize the preparatory exercises and melodies of Modus Novus, with the teacher´s aid and supervision during class, and later, practice dictation with the program. He just needs to choose the respective chapter on the program and begin with dictation. Because ModusXXI can generate an unlimited number of melodies, the student can do so many dictations as he needs.

Controlling melody complexity with ModusXXI The control of the degree of melody complexity is also a very important feature in ModusXXI. It is possible, and easy, with ModusXXI to create very simple as well as very complex melodies. Time signature, bar durations, rhythm values, syncopes, among other parameters, let the user vary the complexity. We present three cases: Case A. Beginner. ModusXXI can generate very simple melodies that can help to identify interval direction. With a parameter selection of 2/4 time signature, one measure total duration, crotchets and the manual selection of minor second upward and downward, the program generates melodies with only two notes. Thus, beginners can practice the difference between ascending and descending intervallic direction. Case B. Learning with the Modus Novus methodology. The student wants to practice Modus Novus’ third Chapter. The “new” intervals are minor und mayor third but this chapter also includes minor and mayor second, perfect fourth und fifth. He can begin with ModusXXI preparatory exercises section 3. It includes just the new intervals (mayor and minor third) and seconds. It does not include the perfect fourth and fifth. Of course the student can control the rhythm and meter complexity while or practicing the new intervals. When the student has mastered this section, he can practice ModusXXI Chapter 3. This section includes all intervals of Modus Novus’ Chapter 3. Case C. Self teaching. Maybe the user does not attend an ear-training course and/or he does not have the Modus Novus. He can also use ModusXXI to create melodies for dictation or sight-reading. He just needs to select manually the intervals that he wants to practice. For example he can create melodies with a combination of perfect fifths and minor sixths. This combination is not considered in Edlund´s book but ModusXXI allows it. Rhythm complexity and register can also be controlled in ModusXXI. It has a syncope control that allows (or not) syncopation between bars and in bars. The program can also create melodies with or without register limits.

Software evaluation ModusXXI was tested with a group of 40 students. Based on the Mean Opinion Scoreix

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evaluation method. We used numbers to give marks from 5 to 1 (5=Excellent, 4=Good, 3=Satisfactory, 2=Poor and 1=Bad) to the following quality factors:

1. User interface Accuracy

2. Program Operability

3. Documentation

4. Program execution efficiency

5. Musical concepts (intervals, rhythm values, etc.) representation efficiency with objects like buttons, checkboxes, etc.

6. Usability for atonal ear training and Modus Novus practice

7. Efficiency to improve the musical ear

8. Usability as a group didactic tool

9. Usability as a private, individual tool for the atonal ear training and Modus Novus practice

The results are as follow: the best-qualified factor was number 7 (93,6% of acceptance). Most of the students consider that ModusXXI can improve efficiently their musical ear. The lowest qualified was factor 8 (80,8%). For a large group of students the application is not really a good group didactic tool. The program operability (factor 2) and the usability of ModusXXI for atonal ear training and Modus Novus practice (factor 6) were also well qualified (92,3% y 90,4% respectively). Factor 5 got 81,4% of acceptance and factors 1, 3, 4, and 9 were on the range between 89.1% y 88,5% of acceptance. It is important to notice that all questions had an acceptance over 80%, which corresponds to the “excellent” MOS qualification.

Figure 5. Evaluation results

Conclusions ModusXXI (v.1.0) fulfils our goal: it can generate an unlimited number of atonal melodies based on the Modus Novus methodology, that can be used for dictations or for sight-reading during an ear training course of the 20th century music. In the software evaluation ModusXXI gets an acceptance over 80%. The application also fulfils most of the software quality criteriax (operability, maintainability, transferability). Nevertheless there are some aspects that should be improved, remade or extended. Some of them are as follows:

• Score storing implementation

• Data input interface implementation

• Applet implementation (for access through the Internet)

• Melody transformation processes (inversion, retrograde, transposition, etc.) implementation. This could be helpful when trying to study another ear training techniques as Friedman’s method xi.

• Polyphonic sequences implementation. ModusXXI (v.1.0) generates only one-voice melodies.

• Develop a multiplatform application capable of generating an unlimited number of polyphonic sequences on different styles with an easy to use interface.

References Edlund, L. (1963). Modus Novus. Stockholm: AB

Nordiska Musikförlaget/Edition Wilhelm Hansen.

Edlund, L. (1967). Modus Vetus. Stockholm: AB Nordiska Musikförlaget/Edition Wilhelm Hansen.

Forouzan B. (2003). Foundations of Computer Science. California: Thompson Learning Inc.

Friedmann, M. (1990). Ear Training for the Twentieth-Century Music. USA: Yale University Press.

ITU (2007). http://www.itu.int/rec/T-REC-P.800.1-200607-I/en Last visited: 25/03/2008.

jMusic Library (1998) http://jmusic.ci.qut.edu.au Last visited: 25/03/2008.

Meave, A. (2007). Creación de una aplicación de cómputo generadora de melodías atonales

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siguiendo la metodología Modus Novus de Lars Edlund (Development of an atonal melody generator computer program based on Lars Edlund´s methodology). Music Technology Master Thesis. México: UNAM.

Shneiderman, B. (2006). Designing the user interfaces. New York: Pearson Education.

i The second book is the Modus Vetus and it is concerned with the study of the tonal music.

ii Edlund (1963) page 13

iii Edlund (1963) page 14

iv Edlund (1963) page 13

v Edlund (1963) page 13

vi jMusic (1998)

vii Meave (2007)

viii For more information about jMusic library, visit the jMusic website. See references.

ix ITU (2007)

x Forouzan (2003), Shneiderman (2006)

xi Friedmann (1990)