Chord Character Evaluation Model Based on Real
Acoustic Sources: Introduction to Differences inTimbre
Taiki Shimozono
Department of Human System Interaction, School of Science and Technology, Kwansei Gakuin
University, 2-1 Gakuen, 669-1337 Sanda, Hyogo, Japan.

Eriko Aiba
Graduate School of Information Systems, The University of Electro-Communications, 1-5-1
Chofugaoka, 182-0021 Chofu, Tokyo, Japan.

Takashi X Fujisawa
Research Center for Child Mental Development, University of Fukui, 3-9-1 Bunkyo, 910-8507
Fukui, Fukui, Japan

Noriko Nagata
Department of Human System Interaction, School of Science and Technology, Kwansei Gakuin
University, 2-1 Gakuen, 669-1337 Sanda, Hyogo, Japan
Summary
Chord is a factor as important as a melody and rhythm in the creation of music. However, it isunclear whether any acoustical features of each chord affect the impression of the chord. In
previous studies, psychophysical models were constructed to evaluate chord impression (i.e.,chord character evaluation models). These models can quantitatively evaluate the relevance ofphysical acoustical features, psychological impressions, and sensibilities of each chord.
Nevertheless, in previous chord character evaluation models, virtual acoustic sources were used
for evaluation. Thus, the correspondence between real acoustic sources and the output of the chord
character evaluation models has not been considered much. Therefore, differences in the timbre ofinstruments have not been able to be validated. In order to add the function to be able tounderstand the difference in timbre, peaks of frequency were extracted from real acoustics sources
and power and frequency were used to calculate the impression of the chords. In order to validate
the correlation between the psychological impression and chord character evaluation model, anexperiment that evaluates the impression of primary triads in theory of harmonics was performed
through the paired comparison method in the primary triads of the theory of harmonics. The
results suggest that the psychological impression differs depending on timbre. Furthermore,theoretical values that were calculated by previous chord character evaluation models and thechord character evaluation model proposed in this study were compared to the experimental r esult.
The results suggest that our proposed theoretical value had a stronger correlation withexperimental results than previous theoretical values. In the case of the same audio source, astronger correlation was found in the experimental results and theoretical values. In conclusion,
our study found that a timbre is one of the important factors that affect the impression of the chord.
PACS no. 43.66.+y1.

Introduction1

Chord is a factor that is as important as melody
and rhythm in the creation of music; and, as such,it is one of the most essential factors needed in
1(c) European Acoustics Association

order to evoke various emotions through music.
Various impressions brought about by a chord are
influenced by the sound that constitutes it, and thisunique feature is seen in every chord. For example,a major chord brings an impression of consonance(a combination of notes that sound pleasant to mostpeople when played at the same time), while
diminished or augmented triads give the impression

FORUM ACUSTICUM 2014
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Coustician, Sound: Template for EAA proceedingsof dissonance. This is a common reaction
regardless of cultural or social background, and has
been a widely used technique not only in works
such as film background music but also insoundscapes and sound design for media
transmissions. Many psychological models havebeen proposed on the relationship between physicalcharacteristics (such as tone frequency ratio) andpsychological characteristics of chords [1][2][3].
However, these studies have largely been restricted
to the most fundamental chord group (triads), and amodel that can be fully explained is yet to beconstructed.
In particular, in previous chord character
evaluation models, virtual acoustic sources wereused for evaluation. Thus, the correspondencebetween real acoustic sources and the output of thechord character evaluation models has not been
considered much. Therefore, differences in thetimbre of instruments have not been able to bevalidated.
In this study, in order to add the ability tounderstand the difference in timbre, theoreticalvalue was calculated by use of real acoustic
sources, which were compared with theexperimental result.

2.

In the psychological indexes, the instability
obtained from combining the dissonance level andtension level is reportedly similar to the results
obtained from the behavioral experiment, revealing
the human impression effect against chords. Theequation is shown below:
1 3(4)I   Di  T
3 i 1(a) Dissonance Curve

Previous Chord Character Evaluation
ModelCook et al. defined chord character as the “generalnature of sensibility given by chords.” They also
calculated a theoretical curve for psychologicalindexes such as the levels of dissonance (D,consonant-dissonant), tension (T, tensed-calm), andmodality (M, major-minor), with reference to thefrequency ratio of the two interval structures (a rootnote to a third tone, a third tone to a fifth tone) thatcompose a triad. Each equation is shown below [4]:n 1 n 1

D   vij 3 exp( 1 xij )  exp(  2 xij )(b) Tension Curve(1)

i 0 j  0

  x jk  xij  2 (2) T   vijk exp  i  0 j  0 k 0   
4n 1 n 1 n 1
 2( x  x )    ( x  x )  M    vijk  jk ij  exp   jk ij ijk   (3)4i 0 j 0 k 0   Here,  ,  ,  and  represent constant values,
x is an interval, n is the number of harmonicovertones used in the equation, and v is volume.
The expanded theoretical curves shown in Fig.1 (a),(b) and (c) are obtained by adding up each overtone
to six harmonic overtones. The intervals between
the root notes and the third tones in Fig.1 (b) and(c) are all five semitones.
n1 n1 n1(c) Modality Curve
Figure 1. Psychophysical Function of Chord Perception

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Coustician, Sound: Template for EAA proceedings

Figure 2. Chordal Stimulus

3.

Theoretical Calculation

Real acoustic sources were windowed in aHamming window and then a frequency analysis
was performed by use of FFT (Fast Fourier
Transform). In order to suppress pitch tolerance andnoise, frequency peaks were extracted from real
acoustics sources and power and frequency wereused to calculate the impression of the chords.

4.

“grouping.” In particular, each chord was played
three times, then a rest of between 1.2 and 1.4 beatswas inserted, then the next chord was played threetimes (Fig.3).

Experiment

The subjects consisted of fourteen university
students from ages twenty-one to twenty-three(years of musical experience between zero andseventeen years). An experiment that evaluates theimpression of primary triads in the theory ofharmonics was performed through the paired
comparison method in the primary triads of thetheory of harmonics. The primary triads of thetheory of harmonics that were used in anexperimental stimulus constituted five types(major, minor, diminished, augmented andsuspended fourth) (Fig.2). The inversions of thechord were three kinds (root, first inversion andsecond inversion) (Chord names henceforth werecalled “triad_inversion”). In order to suppress theimpression evoked by pitch, stimulus unified theroot note as C (261.6 Hz) and the added C1 (523.2Hz). There were twenty stimulus pairs in total.
The chordal stimuli were generated by piano via
SoundFont and organ via VSTi. The experiment
was performed on a PC via a speaker in asoundproof room. ”Dissonance,” one of the chord
impressions, was evaluated in five steps (“theformer chord was dissonant,” “the former wasslightly dissonant,” “almost the same,” “the latterchord was slightly dissonant,” and “the latter chordwas dissonant.”) Ura’s procedure, modified from
Scheffe’s Paired Comparison, was used for analysis.
Evaluative words related to “Dissonance” wereused an experimental stimulus and included fivekinds of words (dissonance, immiscible, unpleasant,unsteadiness, complexity). In order to suppress theimpression evoked by the chordal progression,stimulus presentations were designed to promote aFigure 3. Chordal Stimulus Presentation

5.

Results and Discussion

5.1.

Experimental Result

This experiment shows a stronger correlation
between each sub-experiment by using evaluative
words. Therefore, the results for each evaluative
word were compressed through the analysis ofeach principal component. These values represent“Dissonance.” Experimental results using twotimbres are shown in Fig.4. Significant differenceswere found in the following experimental results:
Major_R, Major_1st, and Sus4_R. The results
suggest that psychological impression differs
depending on the timbre.

Figure 4. Experimental Result

5.2.

Compare with Theoretical Value andExperimental Result

Theoretical values calculated by previous chord
character evaluation models and the one proposedin this study were compared to the experimental
results. The results suggest that the theoreticalFORUM ACUSTICUM 2014
7–12 September, Krakow

value we proposed had a stronger correlation withthe experimental results than previous theoreticalvalues. In the case of the same audio source, astronger correlation was found in the experimental
results and theoretical values (Fig.5, Table.1).
Therefore, theoretical values using real acoustic
sources fit better into the chord impression thanvirtual acoustic sources.

Coustician, Sound: Template for EAA proceedings

5.3.

Evaluation
Experience

DifferenceMusicalIn order to investigate evaluation difference inmusical experience, correlations between theevaluation of each subject and theoretical value
were calculated (Table.2). Correlation value
increases as the period of musical experience inpiano timbre increases. However, there were norelations between correlation value and the periodof musical experience in organ timbre. The results
show that evaluation of chord impression changes
depending on the period of musical experience.

Figure 5. Comparison between Theoretical Value andExperimental Results

Table 1. Correlation between Theoretical Value and Experimental Results* p<0.05, ** p<0.01
Table 2. Correlations between Evaluation of Each Subject and Theoretical Value(a) Piano timbre; (b) organ timbre* p<0.05, ** p<0.01

inFORUM ACUSTICUM 2014
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Coustician, Sound: Template for EAA proceedings* p<0.05, ** p<0.01

5.4.

Correlations between Theoretical Values

Table 3 shows the correlations between theoreticalvalues in piano and organ. Correlation indissonance level is low, while correlation in tension
level is high. The results show that dissonance levelis dissonance of timbre and tension level isdissonance of interval.
Table 3. Correlations between Theoretical Values

6.

Conclusion

In this study, in order to introduce the difference intimbre, theoretical values calculated using real
acoustic sources were compared with theexperimental results. The experimental results show3 key points. First, the psychological impression
differs depending on timbre. Therefore, theoreticalvalue through the use of real acoustic sources fitsbetter into chord impression than virtual acoustic
sources. Second, evaluation differs in musicalexperience. Finally, dissonance level is dissonanceof timbre, and tension level is dissonance ofinterval.
In the future, accurate signal processing, amplitudeenvelope and calculation of modality should beconsidered as the study problem.

References[1] H. v. Helmholtz, A. J. Ellis, and H. Margenau, On
the sensations of tone as a physiological basis for thetheory of music, 2nd ed. New York: Dover, 1954.
[2] R. Plomp and W. J. Levelt, “Tonal consonance andcritical bandwidth,” J Acoust Soc Am, vol. 38, no. 4, pp.
548–60, 1965.
[3] A. Kameoka and M. Kuriyagawa, “Consonance theory
part i: consonance of dyads,” J Acoust Soc Am, vol. 45,no. 6, pp. 1451–9, 1969.
[4] D. Cook Norman and T. Fujisawa X., “Thepsychophysics of harmony perception: Harmony is athree-tone phenomenon,” Empirical Musicology
Review, vol. 1, no. 2, pp. 106–126, 2006.