The perception of closure in chord progressions


Master's Thesis, 2011

74 Pages, Grade: 2


Excerpt

Table of Contents

List of tables

Zusammenfassung

Abstract

Danksagung

1. Introduction
1.1 Aim
1.2 Music theoretical background
1.2.1 Chord Progressions
1.2.2 Cadences
1.2.3 Music theoretical developments in history
1.2.3.1 Medieval Ages (500-1400)
1.2.3.2 Renaissance Period (1400-1600)
1.2.3.3 Baroque Period (1600-1750)
1.2.3.4 Classical Period (1730-1820)
1.2.3.5 Romantic Period
1.2.3.6 20th Century Music
1.2.4 The circle of fifths
1.2.5 OCTs
1.3 Literature Overview
1.3.1 Riemann and Hauptmann
1.3.2 Schmuckler and Piston
1.3.3 Bharucha and Krumhansl
1.3.4 Rosner and Narmour
1.3.5 Eberlein and Fricke
1.3.6 Huron
1.3.7 Parncutt

2. Experiments
2.1 Introduction to two experiments
2.2 Palestrina’s analysis
2.2.1 Palestrina
2.2.2 Palestrina background
2.2.3 Palestrina Style
2.2.4 Analysis of Palestrina’s 1st Motet in “Canticum Canticorum”
2.3 Listening experiment: Closure in two-chord progressions
2.3.1 Introduction
2.3.2 Method
2.3.3 Apparatus
2.3.4 Design
2.3.5 Procedure
2.3.6 Results
2.3.7 Conclusion of the experimental data
2.3.8 Theoretical Predictions

3. Conclusion

4. Discussion, Limitations and Relevance
4.1 Discussion
4.2 Limitations and Relevance

5. References

6. Appendix
6.1: Results for the chord progressions “minor-minor”
6.2: Results for the chord progressions „major-minor“
6.3 Results for the chord progressions “major-major”
6.4: Results for the chord progressions „minor-major“

7. Questionnaire

8.: Motet „Canticum Canticorum“, written by Palestrina

List of figures

FIG. 1 CIRCLE OF FIFTHS

FIG. 2 SPECTRUM OF AN OCTAVE-COMPLEX TONE OVER THE RANGE OF HEARING

FIG. 3 SCHENKER’S „URLINIE“

FIG. 4 KRUMHANSL KEY PROFILE FOR MAJOR KEY (HURON, P. 151)

FIG. 5 KRUMHANSL KEY PROFILE FOR MINOR KEY (HURON, P. 152)

FIG. 6: SCHEMATIC ILLUSTRATION OF CHORD PROGRESSIONS IN BAROQUE MUSIC (HURON, P. 251)

FIG. 7 SCHEMATIC ILLUSTRATION OF CHORD PROGRESSIONS 20TH CENTURY (HURON, P. 253)

FIG. 8 CHORD PROGRESSION WITH HIGH PROBABILITY OF OCCURENCE (HURON, P. 252)

FIG. 9 CHORD PROGRESSION WITH LOW PROBABILITY OF OCCURRENCE (HURON, P. 252)

FIG. 10 FIRST BARS OF PATESTRINA’S MOTET WITH ONLY TWO VOICES

FIG. 11 THE FIRST TWO ANALYZED CHORDS IN PALESTRINA’S MOTET

FIG. 12 GRAPH ON COUNTED INTERVALS AND CHORDAL PROGRESSIONS 44 FIG. 13 RELATIONSHIP BETWEEN INTERVAL LABELS AND HEARD INTERVALS

FIG. 14 MEAN RATINGS FOR MINOR-MINOR CHORD PAIRS FOR PARTICIPANTS (1= VERY HIGH EFFECT OF CLOSURE, 7=VERY LOW) 49 FIG. 15 MEAN RATINGS FOR MAJOR-MINOR CHORD PAIRS ( PARTICIPANTS)

FIG. 16 MEAN RATINGS FOR MAJOR-MAJOR CHORD PAIRS ( PARTICIPANTS)

FIG. 17 MEAN RATINGS FOR MINOR-MAJOR CHORD PAIRS ( PARTICIPANTS)

FIG. 18 THE DISTANCES BETWEEN THE TONES ON THE CIRCLE OF FIFTHS 55 FIG. 19 GRAPH OF PREDICTION FOR THE THEORY OF THE AMOUNT OF COMMON TONES (MINOR-MINOR)

FIG. 20 GRAPH OF PREDICTION FOR THE THEORY OF THE AMOUNT OF COMMON TONES (MAJOR-MAJOR)

FIG. 21 GRAPH OF PREDICTION FOR THE THEORY OF DIATONIC SCALES IN TWO CHORDS (MINOR-MAJOR)

List of tables

TABLE 1: TABLE OF USUAL ROOT PROGRESSION AFTER PISTON (1978)

TABLE 2: PREFERENCES FOR PROGRESSIONS AFTER ROSNER AND NARMOUR (1992)

TABLE 3: PSYCHOLOGICAL CHARACTER/ FEELING OF SCALE TONES (AFTER DAVID HURON, 2006)

TABLE 4: PROBABILITIES FOR VARIOUS CHORD PROGRESSIONS IN BAROQUE MUSIC (HURON, P. 251)

Zusammenfassung

Fallende Quinten und Quarten zwischen den Grundtönen aufeinanderfolgender Akkorde sind die am häufigsten gebrauchten Intervalle in der westlichen Musik. Sogar zu Zeiten von Palestrina (ca. 1515-1594) waren diese fallenden Intervalle beliebt obwohl es damals keine Lehre über Musiktheorie gab wie sie heute unterrichtet wird. Experimente haben gezeigt, dass Zuhörer fallende Quinten im Vergleich zu fallenden Quarten in der Schlusswirkung bevorzugen (Eberlein 1994). Das Ziel dieser Arbeit ist dies in einem weiteren Experiment zu überprüfen und es werden Erklärungen für diese Beobachtungen angestrebt.

In dieser Arbeit geht es um die Wahrnehmung der Schlusswirkung bei Akkordfolgen. Aus den synthetisch erzeugten Klängen wurden 70 Versuchspersonen 96 Akkordfolgen von jeweils zwei aufeinander folgenden Akkorden vorgespielt. Es gab 48 verschiedene Akkordkombinationen, die zweimal durchgespielt wurden, jedoch in zufälliger Reihenfolge. Die Akkorde bestanden aus Dur- und Molldreiklängen.

Die Versuchspersonen stellten sich vor, dass die gehörten Akkorde das Ende eines Musikstücks darstellen. In diesem Sinne mussten die Versuchspersonen die Schlusswirkung dieser beiden Akkorde bewerten. Es wurde angenommen, dass die Versuchspersonen fallenden Quinten eine höhere Schlusswirkung zuordnen als fallenden Quarten.

Insgesamt wurde herausgefunden, dass fallende Quinten eine größere Schlusswirkung haben als fallende Quarten. Dies gilt allerdings nur für die Akkordfolgen „Dur-Moll“und „Dur-Dur“. Eine mögliche Erklärung dafür wäre, dass die Dominante meistens in Dur steht und die Tonika meistens in Dur oder in Moll steht. Dies ist vermutlich auf Aspekte der Vertrautheit zurückzuführen und würde bestätigen, dass vertraute Akkordfolgen größere Schlusswirkung haben.

Abstract

Falling fifths are more common than falling fourths in western music. Even in the music of Palestrina those falling fifths between successive chord roots were more common than rising fifths. This tendency was larger in the 18th century (Eberlein). The goal of this thesis is to investigate the role of rising and falling fifths between chord roots in the perception of closure. There is no widely accepted theory for this asymmetry.

This paper examines the perception of closure of cadential chord progressions. 70 participants listened to 96 chord pairs made of synthetically generated sounds. There were 48 different combinations that were played twice but in random order. Each chord was either a major or a minor triad.

The test persons were asked to imagine that the heard chords represented the end of a piece of music. The participants were then asked to rate the closure. The prediction was that the test persons would rate the closing effect of falling fifths higher than of falling fourths.

The hypothesis was confirmed for the chord combinations major-minor and majormajor. A possible explanation was that the dominant chord is mostly major and the tonic chord can be major or minor. A possible explanation could be that the participants responded on the basis of familiarity. A chord progression sounds final if it’s often heard at the end of a piece.

Danksagung

Ich möchte mich hiermit bei Herrn Univ.-Prof. Dr. Richard Parncutt für die Betreuung meiner Masterarbeit bedanken. Ich möchte mich auch bei Gottfried Reichweger bedanken für die technische Hilfe bei der Programmierung der Versuche in Matlab. Einen herzlichen Dank an Herrn Martin Winter, der mir mit dem Statistikprogramm SPSS geholfen hat. Ich bedanke mich bei allen Versuchspersonen, die durch ihre Mitarbeit die Datensammlung für meine Masterarbeit ermöglicht haben.

Ich möchte mich zu guter letzt bei meinem Freund Johannes Hofer bedanken, der mich immer wieder mit Begeisterung motiviert hat. Auch möchte ich seiner Familie danken, die meinen Sohn Florian Matthias betreut hat während ich an meiner Arbeit geschrieben habe.

1. Introduction

1.1 Aim

The aim of this research is to try to find out which chord progressions produce stronger feelings of closure and what that depends on. Does it depend on whether the interval between the roots is falling or rising? Or does it depend on intervals between successive chord roots? Most prevalent chord progressions in tonal harmony have fourth and fifth intervals between successive chord roots. Are perfect fifth intervals so prevalent in music because they are the most consonant after the octave? What about fourths? Cuddy says that the fourth is the least stable after the fifth and the third interval (Cuddy 1995, p. 452). Parncutt tries to answer those questions through his theory of the cycle of fifth and through the common tones theory (see pp. 9-11).

Falling fifths are more common than falling fourths intervals in western music between successive roots. In his appendix Eberlein shows that falling fifths and thirds are more common than rising fifths and thirds in diatonic chord progressions (Eberlein 1994). It would be interesting to analyse early music in the same manner to find out whether there were the same tendencies in that time period. The goal of this paper is to investigate the perception of chord progressions.

The topic of this master’s thesis is the perception of closure in chord progressions. The goal was to find out which chord progressions produce stronger feelings of closure and why it does so. Does it depend on whether the interval between the roots is falling or rising? How do other researchers explain that?

Eberlein’s data suggests that falling thirds produce greater closure than rising thirds and that falling fifths produce a greater closure than rising fifths (or falling fourths). How can the prediction be tested? A possible approach would be to collect data on the perceived closure of different endings in different musical pieces in different musical genres. Another approach would be that test persons rate the endings of computer generated chord progressions. In this experiment the latter approach has been chosen because it is easier to generate sounds without analyzing the different aspects of contexts and to systematically cover all possibilities in a given domain.

When different musical pieces are chosen participants could be influenced by e.g. instrumental or timbral aspects which they are not even conscious about.

This thesis examines the perception of closure of cadential chord progressions. Here, synthetically generated sounds are represented as built from octave complex tones (OCT’s, in Parncutt 1993). An OCT is a tone made of pure tones that are situated in various octave registers. The reason why OCTs are used is that we want to test a theory that is octave generalized. It is octave generalized because the voicing of the chords is not relevant. There are three aspects of voicing. Voicing means 1) the inversion (which of the tones is situated in the base of the chord), 2) the spacing (whether there are close or open voicings), and 3) the doubling (which is putting the same pitch class in two different octave registers).

The literature overview is covering the topic of the importance of falling fourths and fifths intervals between successive roots in cadences in western music. In the first part of the thesis the music theoretical background and the literature overview will be presented. At first the basic music theoretical definitions will be explained in order to understand the rest of the thesis. The next part of the thesis consists of a literature overview. The relevant literature that deals with falling fifths and fourths intervals between successive roots in cadences in western music will be discussed. The second part of the thesis is about the two experiments I did. The first experiment is an analysis of one of Palestrina’s motets. The goal was to find out whether Palestrina’s music also consists of more falling than rising fifths and thirds between the successive roots of chord progressions.

The second experiment addresses the perception of closure in chord progressions. The goal was to find out which chord progressions produce stronger feelings of closure. The hypothesis was that falling fifths intervals between successive roots in cadences are rated as being more closed than the other intervals. The hypothesis was confirmed for the chord combinations major-major and major-minor. For the two other chord combinations the hypothesis was not confirmed. The goal of considering the literature of various researchers was to try to find support for an explanation of my testing results.

1.2 Music theoretical background

1.2.1 Chord Progressions

Parncutt explains in his book “Harmony: A Psychoacoustical Approach” the term chord progression as follows: In the middle ages and Renaissance the notes the most used from the so-called heptatonic scales were the first and the fifth note of the scale. In the Renaissance Period when the scales developed to major and minor scales those two intervals were then called tonic and dominant (Parncutt 1989, p. 5).

In our days the term “chord progression” is used for certain chords that follow each other. The chords are made out of three notes which are the tonic and the dominant note of the scale and a third interval in between. A chord progression is a made of several chords joined together. There are chord progressions in music that are favoured more than others. When they are set at the end of a phrase or of a piece, they are called cadences.

1.2.2 Cadences

The word “cadence” comes from the Italian word “cadenza” which implies that something is falling or declining. In speech and in music there is a tendency for ending phrases to hear a descending contour. This phenomenon is also seen in various cultures. Western musicians therefore tend to expect that notes descend at the end of a phrase (Huron 2006, p. 154). In western music cadences are found as well at the end of phrases as at the end of musical pieces. Cook says that “the emotional symbolism of major and minor chords has a biological basis. Across the animal kingdom, vocalizations with a descending pitch are used to signal social strength, aggression or dominance. Similarly, vocalizations with a rising pitch connote social weakness, defeat or submission [and therefore] changes in the fundamental frequency of the voice have intrinsic meaning” (Cook, 2007).

Any music theory book tells about the different ways a cadence can end. Each cadence has a different degree of closure which gives the listener a different feeling of ending. The “authentic cadence” for example (V-I) sounds very closed compared to a more open sounding cadence such as the “plagal” cadence (IV-I). Another cadence is the “half cadence” (n-V) where it always ends with chord V preceding any other chord. The “deceptive chord” is when chord V goes to any chord other than the tonic (I). In speech we set commas, semicolons and periods. In music there exist cadences that sound more final or more closed than others.

Typical cadences are made of following chord progressions: They usually start and end with the tonic (I). There is climax in the middle of the chord progression which signals that the chord progression has gone half way and will now probably go back to the tonic. The dominant (V) marks the middle of the chord progression. After the tonic the dominant is the most important or most used chord of the scale. The subdominant (IV) often appears just after the tonic at the beginning or just before the tonic at the end of the chord progression.

1.2.3 Music theoretical developments in history

1.2.3.1 Medieval Ages (500-1400)

Medieval music was both sacred and secular. The Gregorian chant which was typical for this time period was monophonic. Polyphony started to develop in the 13th and 14th century. In the Middle Ages the heterophony made of a plainchant melodic line accompanied by a line that was first sung at a fixed interval before small alterations of the bass line led to the beginnings of polyphony. The duplication of plainchant in parallel motion at the intervals of an octave, a fifth or a fourth was the normality. The motet was one of the first genres that came from the plainchant and gradually became the most popular form of medieval polyphony. In the Middle Ages the interval of the third was still perceived as dissonant. The vocal range is very narrow so that the individual had to cross each other very often (Christensen, 2002).

1.2.3.2 Renaissance Period (1400-1600)

According to musicologists the time period of the Renaissance Music was about 1300-1470s. The musical interval of the third now starts to be accepted as being consonant. The independent moving polyphonic voices start to get smoother. The vocal range grows which means that the vocal parts don’t cross each other anymore as they did in the Middle Ages. The music gets more interesting, since it was now possible to make greater timbral contrasts between the voices. At the end of the period the modal sound of Renaissance Music breaks up more and more since the use of fifths intervals in the bass voice start to gain more importance. Through the development of the third and the fifth interval, the music sounds more tonal (Christensen, p. 364-402).

1.2.3.3 Baroque Period (1600-1750)

The main characteristics of the Baroque Period are the use of complex tonal counterpoint, the use of the basso continuo and the continuous bass line. The Sonata form with its theme and variations starts to take shape. The tonalities of major and minor, modulations from one tonality to the next, dissonances and chromaticism now take full shape.

With the slowly changing feeling of tonality and harmony, the instrumentation starts to change. The instruments are getting classified into strings, brass, woodwinds and percussions. Trumpets for example get valves, and are now not only limited to play their overtones. Violas had six strings, while the violin will now have only 4 strings which are tuned in rising fifths. With the constructional changes in the instruments, the musical techniques changed. Composers and performers use more ornamentations and change their musical notation. Baroque Music, in contrast to Renaissance music, gets more complex. The range and possibilities of performance grow as did the size of instrumental performances. With the changes in instruments, the musical pieces change. Music is now written for larger ensembles, orchestras, operas, musical dramas, chamber music, etc (Christensen, 2002).

The music is still very polyphonic with its use of counterpoint as it was in Renaissance music. In contrast to Renaissance music, Baroque music starts to develop virtuoso solo parts for singers and instrumentalists. Solo singers of instrumentalists are expected to improvise on their solo parts. A cappella music recedes in importance. The figured bass starts to change musical thinking. Harmony makes that all individual parts get one huge unity. The use of the tritone as a dissonance, the use of harmonic progressions and the use of the seventh chord make the music sound tonal. Music is now thought of as in chords, rather than in notes. A sense of closure through harmonic progression starts to develop. Those are the fundamental aspects of what is understood as tonal music in our days.

1.2.3.4 Classical Period (1730-1820)

Many norms of composition and style that are usual in our days come from the Classical Period. The piano becomes the predominant keyboard instrument. Chamber music grows, serenades and symphonies and the opera buffa are now marking important regional differences in Italy, France and German-speaking areas. The concerto setting gets more and more attention from composers and performers (Christensen, 2002).

1.2.3.5 Romantic Period

In the Romantic Period melodic lines start to extend and get more expressive and emotional. The strict forms of the Classical Period start to break down. There are more and more musical pieces with free-forms such as nocturnes, fantasias, preludes with developing themes, etc. The music becomes more chromatic and dissonant. Composers choose colorful tonalities, rich timbres and more tensions (Christensen, 2002).

1.2.3.6 20th Century Music

In the 20th Century music is characterized by its technological advancements in recording and synthesizing music electronically. Composers have much more possibilities of composing. They start to experiment with technical effects, amplification, etc. All rules that were set up until the 19th century are allowed to break. Harmonically this means, that the chord progressions: I, IV, V, vi and ii (see Fig. 7, p. 32). Nevertheless, the musical styles vary between electronic music, folk music, Bluegrass and Popular music, Blues, Country, Jazz, Rock and Roll, Progressive Rock, Punk and Alternative Rock, Soul, Funk, Salsa, Disco, World music and New Age music. David Temperly and Trevor de Clercq (2010) analyzed about 100 songs of the 1950s to the 1990s on the conventional harmonic progressions. They found out that the harmonic norms in rock music are opposite to those of common-practice music. An example for this is the favored “root motion by ascending fifths rather than descending fifths” (Temperly, p. 254). They also found out that chord IV is the most common chord in rock music after chord I. The next more frequent chords are V, bVII, and VI. Chord IV is also the most common chord preceding and immediately following chord after chord I (Temperly, p. 254).

1.2.4 The circle of fifths

The circle of fifths (see Fig. 1) is a schematic representation of the relationship between the twelve tones of the chromatic scale, their corresponding key signatures in all major and minor modes.

Fig. 1 Circle of fifths

Abbildung in dieser Leseprobe nicht enthalten

The distance between the individual steps on the circle of fifths is a fifth interval. When starting at any pitch and going clockwise, one can add up a perfect fifth to that tone. When arriving at the end of the circle, all twelve tones of the chromatic scale have been used. The same can be done counter clockwise when perfect fourths are added.

1.2.5 OCTs

An octave-complex tone (OCT) is made of pure tones that are situated in various octave registers. That means that an OCT does not have a definite pitch. The tone „C“for example comprises all other „C‘s“oft he whole register. When OCTs are played, listeners cannot find out in which register the OCT is located. Each pure tone is tuned to the same pitch class. All partials in the OCTs have the same sound pressure level. OCTs are used in this thesis so that listeners do not recognize at which exact pitch the chords are located. Gottfried Reichweger shows a diagram where the spectrum of an octave-complex tone is represented (see Fig. 2).

Fig. 2 Spectrum of an octave-complex tone over the range of hearing

Abbildung in dieser Leseprobe nicht enthalten

Fig. 3 Schenker’s „Urlinie“

Abbildung in dieser Leseprobe nicht enthalten

In contrast to Hugo Riemann, Schenker (see Fig. 3) regards only chord I and V as being most fundamental. Riemann regarded the subdominant (chord IV) as equally important as the dominant (V) chord. Riemann regards the chord progression I-IV-V-I as being the basic chord progression. Nevertheless, both theorists acknowledge falling fifths (V-I) as the most fundamental chord progression of tonal music.

1.2.5.1 A general approach to the structure of the remaining master’s thesis

In the first part of this master’s thesis I presented music researchers who have worked on that subject matter. The second part of the master’s thesis consists of the experimental part. An experiment about the perception of closure in chord progressions especially regarding falling thirds and fifths chords has been done.

First the different possible thesis of the experiment will be presented. Then the method including the design and procedure of the experiment will be explained. Then the results of the experiment will be analyzed. A discussion part with the possible limitations and its relevance for further music research will be presented.

1.3 Literature Overview

“The absence of expectation evokes a sense of closure”

(Margulis 2003, p. 39).

Various researchers try to find explanations for the asymmetries between falling fourths and falling fifths intervals between successive roots in cadences in western tonal music. Some researchers discuss the importance of harmonic and melodic hierarchies or stabilities of the individual tones and chords. Other researchers try to see the problem from a cultural point of view. On the one hand researchers try to solve the problem through a historical way while others try to analyze the problem with the help of music theory or music psychology. All such approach can be fruitful. It is important to look at all different aspects and then to try to find a general explanation. In this part of the thesis various points of view will be looked at.

1.3.1 Riemann and Hauptmann

Riemann regarded the I-IV-V-I progression as the “prototypical tonality-defining structure” (in Huron 2006, p. 154). Riemann’s definition for closing effect (“Schlusswirkung”) is the following: He says that the harmonic partials (“Partialtöne”) always go back to the tonic chord which is the so-called unification point (“Einigungspunkt”) where all chord progressions finally end. He explains that the chord progressions always end in the tonic because the latter sounds satisfying (Kurth, p. 96). As Kurth says this thesis does not explain why the dominant chord tends to move to the tonic chord.

The idea of Riemann and August Halm (in “Harmonielehre”, in Kurth p. 122) was that the major and minor tonalities are like opposed forces. Major and minor tonalities represent positive and negative directions of movement that tends to seek for a resolution. On the one hand the resolution seems to be a tonic chord, but on the other hand the resolution seems to be a tonic chord without the third interval in the middle. The reason for this is that the third interval still implies a certain kind of movement. Therefore, so Riemann, the point of absolute calmness can never be reached (Kurth, p. 122).

Riemann claims that there are two dominant chords in music: the dominant and the subdominant chord. Riemann tries to set the dominant and the subdominant chord in a certain relation to each other so that the two dominant chords can be easily compared to the major and minor tonalities. In his book “Handbuch der Harmonielehre” (Kurth, p. 97) Riemann says that all chordal relations that are dominant-like sound major-like. All chordal relations that are subdominant-like are minor-like. Riemann gives a general musical example: In a minor tonality it is impossible to imagine a major subdominant chord, but a major dominant chord is absolutely common practice. In a major tonality it is common to find minor subdominant chords, but rather seldom or even unthinkable to encounter a minor dominant chord.

When regarding the literature of Riemann it is important to keep in mind that his theories date from 1849-1919. The strictness about do’s and don’ts concerning the melodic and harmonic relationships of chord progressions varies after the 20th century.

M. Hauptmann (Kurth, 1913) claims that rising and falling chromatic intervals have different effects in music. He didn’t prove this hypothesis empirically. Anyhow, his theory is the following: He says that in music rising chromatic intervals could be characterized by the words upswing, heightening and increase. Falling chromatic intervals could be characterized by the words atony, unsatisfied yearning, resignation or grief. In his opinion this is the reason why there is a difference in the outcome when the order of the chord sequence is either minor-major or major-minor (Kurth, 1913, p. 85). Daniela Prem (2008) has analyzed in her research the different usage of wording of timbre of professional jazz singers. This could be done for rising and falling chord progressions in a following research to work out the idea of M. Hauptmann (1913).

1.3.2 Schmuckler and Piston

Schmuckler’s research is about expectation in music. He investigates melodic and harmonic processes in musical passages. In his four experiments he examines the formation and generation of melodic and harmonic expectancies in full musical contexts. In the last experiment he examines the expectation of pianists for a same musical passage.

Schmuckler presents the listeners various chord sequences in a tonal context passage. The tonal passage has two voices: a melodic line and a harmonic accompaniment. The piece is written in E b major. The listeners hear all musical examples in the key of that piece. The listeners rated “how well the final event fit their expectations of what was to come next” (Schmuckler, p. 117). One of Schmucklers results is that he finds out that “contour-changing tones were more strongly expected than contour-continuing tones” for all probe tones (Schmuckler, p. 124). This means that melodic contour has an effect on the expectancy of the tones that come next. It also means that tones that are not part of the melodic contour are more expected than tones that are part of the contour.

This aspect is interesting for my work, since I look at the perception of closure in harmonic chord progressions. One of the theories that I will explain in the experimental part is that of the common tones. A graph of prediction with the semitones shall be varied with the number of common tones. The hypothesis is that when two chords share two or three common tones, then the chord progression sounds closed. This is similar to the idea of common tones in Schmucklers’ melodic contour theory.

Schmuckler develops a system of predictions where common progressions are evaluated in “typical chord sequences” (Schmuckler, p. 134). Schmuckler evaluates the ratings of the continuation of chords and then compares that with the predictions of Piston’s table of usual root progressions (see Table 1 (p. 131 in Schmuckler)).

Table 1: Table of Usual Root Progression after Piston (1978)

Abbildung in dieser Leseprobe nicht enthalten

Pistons’ goal was to find out about frequent chord progressions in western music. He counted how often which chords followed each other. It is unclear which musical period or which exact musical pieces he used for his analyses. However, this table (Table 1) shows his results of frequent chord progressions. According to his classification the most frequent chord continuation is “the triads built on the sixth scale degree (C minor), and finally triads based on the second and third scale degrees (A b and B b major), followed by the chord built on the sixth scale degree (C minor), and finally triads based on the second and third scale degrees (F minor and G minor)” (Schmuckler, p. 131).

In my experiment I found out that the chord progressions I-IV and I-V were the ones with the highest degree of closure. I then differentiated between falling and rising chord progressions, what Piston did not.

Though, Pistons research has been highly criticized by Schmuckler. He finds out that Piston’s table does not account for Schmucklers’ observed expectancy patterns. He supposes that the reason is the so-called context problem. He criticizes that Piston only analyzed one chord to the immediate neighboring chord. Schmuckler proposes to incorporate larger harmonic contexts as Bharucha and Stoeckig did in their research 1986-1987.

In my master’s thesis I did not consider the aspect of context, because the experiment would have been much longer and more complicated to evaluate. I preferred to work without context. I used synthetically generated sounds where neither the key nor the pitch could be detected by the listeners. In that way the answers were not influenced by any preferences of timbre or sound quality.

On the other side various other experiments showed that “tonal context significantly influences one’s perception of harmony”. A few examples for this show Krumhansl, Bharucha and Kessler (1982) where listeners had to rate “the perceived relatedness of chords drawn from three harmonically related keys relative to a tonal context” (Schmuckler, p. 129). The results were that the harmonies that were based on the first, fourth and fifth scale degrees were the chord the most related in that specific tonal context. Castellano (1982 in Schmuckler) repeated the experiment in three different contexts. His results confirmed that of Krumhansl, Bharucha and Kessler.

1.3.3 Bharucha and Krumhansl

Bharucha & Krumhansl (1983) tested chord progressions in two different context conditions. The chord progressions consisted of three-chord cadences (IV-V-I) followed by a pair of test chords. The keys were in C or in F# major. The three-chord cadence was supposed to state the keys and the context. The task was to evaluate how well the second chord fit the first chord on a seven-point scale.

Bharucha and Krumhansl suggest that “harmonically stable chords function as cognitive reference points for the system (Bharucha 1983, p. 63). In 1982 Krumhansl found three principles in her research. First she found that several chords from the same key form a cluster. The second principle she found was that the “I, IV and V chords form a cluster within the group of chords from each key, and 3) a chord pair in which the second chord is either I, IV or V and the first chord is not is [sic!] judged more closely related than the same pair in the opposite order” (Krumhansl in Bharucha 1983, p. 69). This means that the stable chords such as I, IV or V are the most important chords in a musical piece. All chord progressions at the end of a phrase or of a cadence lead to one of those chords which Bharucha calls “reference points”. In my experiment those three chords had the highest rating in the perception of closing effect.

Krumhansl (1982) presented her listeners chord pairs. On a seven-point scale the listeners were supposed to answer the question how well the second chord followed the first. In her results she found out that pairs of chords in strong harmonic and melodic relationships and of similar consonance tend to be more close to each other.

Bharucha further says that “less stable tones are perceived with reference to more stable tones” (Bharucha, p. 93). This means that each time a less stable tone is heard, it is heard in reference to a more stable tone. This would concur with my theory: When a chord V is heard, chord I is ultimately implied. When chord IV is heard, chord V or even stronger: chord I is anticipated. The problem with that theory is that it does not work for all chord combinations. As Piston already remarked in 1962: “Even though the VI chord is perceived as less stable than the tonic (I), the progression from VI to I has not traditionally been considered desirable” (Piston in Bharucha, p. 93). Another explanation for this effect still has to be found.

Krumhansl found in a study of 1982 that the chords in a certain key follow a hierarchical order: I, V, IV, VI, II, III and VII. This reflects the hierarchies of stabilities of the chords to each other. Krumhansl found that pairs of chords ending on the tonic were preferred than pairs of chords not ending on the tonic of the keys (Bharucha, 1983). In my experiment I found that chord pairs ending on the tonic, subdominant or dominant were associated with having a higher closure than endings on other chords. The second highest rating in the perception of closing effect after the tonic was the V- chord and then the IV- chord. This concurs with the results of Krumhansl’s study. Bharucha found that the chords I, IV and V were evaluated as being more closely related to each other than the chords II, III, VI and VII (Bharucha, p. 79).

Bharucha says primarily that the perception of tones, tonal hierarchies and tonal stability is contextual (Bharucha, p. 68-69). He observed that the chords in context were evaluated as more stable. Chords that were not in context were evaluated as less stable than if they were presented in context. For this experiment Bharucha concludes that chords in context are more often recognized than chords without context and that the context helped strengthen that perception (Bharucha, p. 91).

In my experiment I show that the perception of tonal relationships does not have to depend on context. I show that the tonal hierarchy and stability of chords is also present without context. The chord progressions that my test persons evaluated were computer generated chords that were played one after the other without context. On the other hand I didn’t have any data (with context) to compare with. In that way it was not possible to collect that data and to compare the significances. This could be worked out in a further investigation.

All in all Bharucha and Krumhansl (1983) conclude that chords as well as single tones are perceived according to their relationship towards the prevailing tonality. They also conclude that chords that were represented in context were rated as more stable than chords without context.

Bharucha explains that there are a few principles that are important for identifying the stability of chords toward each other. For example: metrical stress, grouping, proximity, good continuation and contour. All of those criteria are unique in music for the perception of stability of chords (Bharucha, p. 97). Those criteria are not given in language. They are found only in music. Bharucha therefore talks about innateness when identifying the stability of chords in music. He denies the idea of learnt process when it comes to identifying the stability of chords. He finally concludes that listeners have a very high structured internal representation and understanding of harmony.

[...]


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Details

Title
The perception of closure in chord progressions
College
University of Graz
Grade
2
Author
Year
2011
Pages
74
Catalog Number
V191295
ISBN (eBook)
9783656159957
ISBN (Book)
9783656160311
File size
3572 KB
Language
English
Tags
chord progressions, perception, closure, music, harmony, circle of fifths, musicology, quinten, quarten, Schlusswirkung, wahrnehmung
Quote paper
M.A. Stephanie Lüders (Author), 2011, The perception of closure in chord progressions, Munich, GRIN Verlag, https://www.grin.com/document/191295

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