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Visualization of concurrent tones in music with colours

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Visualizing music in a meaningful and intuitive way is a challenge. Our aim is to visualize music by interconnecting similar aspects in music and in visual perception. We focus on visualizing harmonic relationships between tones and colours. Related existing visualizations map tones or keys into a discrete set of colours. As concurrent (simultaneous) tones are not perceived as entirely separate, but also as a whole, we present a novel method for visualizing a group of concurrent tones (limited to the pitches of the 12-tone chromatic scale) with one colour for the whole group. The basis for calculation of colour is the assignment of key spanning circle of thirds to the colour wheel. The resulting colour is not limited to discrete set of colours: similar tones, chords and keys have similar colour hue; dissonance and consonance are represented by low and high colour saturation respectively. The proposed method is demonstrated as part of our prototype music visualization system using extended 3-dimensional piano roll notation.
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Visualization of Concurrent Tones in Music with Colours
Peter Ciuha
ALUO, Univ. of Ljubljana
Erjavˇ
ceva cesta 23
1000 Ljubljana, Slovenia
peter.ciuha@guest.arnes.si
Bojan Klemenc
FRI, Univ. of Ljubljana
Tržaška cesta 25
1000 Ljubljana, Slovenia
bojan.klemenc@fri.uni-lj.si
Franc Solina
FRI, Univ. of Ljubljana
Tržaška cesta 25
1000 Ljubljana, Slovenia
franc.solina@fri.uni-lj.si
ABSTRACT
Visualizing music in a meaningful and intuitive way is a
challenge. Our aim is to visualize music by interconnect-
ing similar aspects in music and in visual perception. We
focus on visualizing harmonic relationships between tones
and colours. Related existing visualizations map tones or
keys into a discrete set of colours. As concurrent (simul-
taneous) tones are not perceived as entirely separate, but
also as a whole, we present a novel method for visualizing a
group of concurrent tones (limited to the pitches of the 12-
tone chromatic scale) with one colour for the whole group.
The basis for calculation of colour is the assignment of key
spanning circle of thirds to the colour wheel. The resulting
colour is not limited to discrete set of colours: similar tones,
chords and keys have similar colour hue; dissonance and con-
sonance are represented by low and high colour saturation
respectively. The proposed method is demonstrated as part
of our prototype music visualization system using extended
3-dimensional piano roll notation.
Categories and Subject Descriptors
H.5.5 [Information Systems Applications]: Sound and
Music Computing—Methodologies and techniques, Systems;
H.5.1 [Information Systems Applications]: Multimedia
Information Systems—Animations, Audio input/output
General Terms
Experimentation
Keywords
music visualization, colour, concurrent tones, MIDI
1. INTRODUCTION
There are many possible ways to visualize music, but not
every visualization is meaningful and of practical use, so our
aim is to have a visualization that is not just to pleasing to
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the eye but can be used in analysis and comprehension of
music, is easy to understand and is of aesthetic value. The
basic idea behind our proposal is to interconnect similar as-
pects in music and in visual perception. In our visualization
we put emphasis on modelling harmony: affinity of tones
and consonance with colours. Our goal is to help under-
stand the harmonic relationships in music, which may be
sometimes difficult to comprehend for untrained people, but
may be clarified using visual clues. Furthermore, it could
be used in the other direction – for assistance in teaching or
when creating music: i.e. play-by-colour.
Existing visualizations use colour to visualize different as-
pects of music, one of possibilities is to represent pitch classes
with colours. To show harmonic relationships between pitch
classes, they can be organized into the circle of fifths. To get
the colour of a particular tone the colour wheel is assigned
to the circle of fifths. This also means when we have a group
of concurrent (simultaneous) tones, each tone is separately
assigned to a colour. However a group of concurrent tones
is not perceived by spectral pitches of tones alone, but also
as whole [9, 10, 13].
As the basic assignment of colour covers only pitch classes,
major and minor chords, we propose in this paper to address
this deficiency with a novel method of visualizing also tone
combinations (in our implementation concurrent tones). In
comparison to previous methods, the proposed method takes
into account also the loudness of tones, including dynamic
change of the loudness of a tone from start to end (decaying
of tones). The proposed method uses key spanning circle
of thirds, which was proposed by Gatzsche et al. [3]. The
key spanning circle of thirds is assigned to a colour wheel in
which tones are represented as vectors of appropriate direc-
tion and length. The resultant colour is obtained by vector
addition and is thus not limited to discrete set of colours.
The demonstration of the method is part of our system for
visualization of music based on MIDI input [5]. The visu-
alization itself uses a 3-dimensional piano roll notation and
allows interactive real-time observation of the resulting vi-
sualization.
The rest of the paper is organized as follows: in Section 2
relevant related previous work is reviewed, the method for
assigning initial colours and calculating common colour for
concurrent tones is presented in Section 3, Section 4 con-
tains description of implementation of the proposed method
as part of our music visualization system, the results are
presented and discussed in Section 5 and conclusions are in
Section 6.
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2. PREVIOUS WORK
Different attempts have been made at visualizing music.
Basic visualizations usually include a time axis and some
other value of interest on the other axis (e.g. pitch), some
also include colour in their mapping. Smith and Williams [12]
discussed visualizing MIDI music in 3-dimensional space and
using colour to mark timbre. The comp-i system [8] tries to
show the structure of music as a whole by using 3-dimensional
piano roll visualization and allow the user to visually explore
the underlying MIDI dataset. Music Animation Machine [6],
which is also MIDI based, encompasses a number of visual-
izations including a basic 2-dimensional piano roll notation
for visualizing structure. This visualization is additionally
expanded with colours based on pitch classes using the cir-
cle of fifths. Mapping of pitch classes into hue by aligning
related keys or tones into closely related colours was pro-
posed already by Scriabin (for a historical review of map-
pings of pitch to colour refer to Wells [14]). Mardirossian and
Chew [7] use colours based on circle of fifths for visualization
in Lerdahl’s 2-dimensional tonal pitch space. Bergstrom’s
isochord [1] visualizes consonant intervals between tones and
chords and is based on Tonnetz grid. Some other visualiza-
tion possibilities are summarized by Isaacson [4]. The ex-
isting visualizations using colour do not address the issue of
merging of concurrent tones.
3. ASSIGNING COLOURS TO
CONCURRENT TONES
3.1 Basic Assignment
The perception of consonance and dissonance is related
to ratios of frequencies [2,11]. In order of rising dissonance
the most consonant intervals between two tones are unison
(ratio of 1:1), followed by octave (1:2), perfect fifth (2:3),
perfect fourth (3:4), major third (4:5), minor third (5:6) etc.
Tones with simple ratios are also perceived similar. Perfect
fifth can be used to generate 12 tones of the chromatic scale,
which can be joined into the circle of fifths where tones which
sound consonant when played together are near each other
and the most dissonant are on opposing sides (Figure 1).
When mapping tones to colour we want to map similar tones
to similar colours and in colour wheel the colours that are
perceived similar are likewise close together and complemen-
tary are on opposing sides, so we can assign the colour wheel
to the circle of fifths. The sound of concurrent tones can
be anything from consonant to dissonant. Consonant tone
combinations are pleasing to the ears and are therefore rep-
resented by saturated colours and dissonant are unsaturated
or grey. For this purpose we take a colour wheel that has
zero saturation in the centre of the wheel and increases to
the outside.
3.2 Calculating colours
A tone is represented by a vector from centre in the di-
rection of the tone in the circle of fifths. The length of the
vector is proportional to the loudness of the tone. When
two or more tones sound concurrently, the tones which be-
long to the same pitch class, are represented as one vector of
length, which corresponds to the loudest tone in the given
pitch class. The colour of concurrent tones is calculated by
vector addition. The resulting vector length is normalized
by diving it with maximum resultant length, which could be
C
G
D
A
F
ae
h
f
c
g
Figure 1: Key spanning circle of thirds assigned to
the colour wheel. A particular tone is represented
by a radius vector pointing in the direction of circle
of fifths denoted by majuscule letters.
obtained by addition of given vectors, that is when all vec-
tors would be collinear. The direction of the resulting vector
in the colour wheel determines the hue and the length de-
termines saturation.
3.3 Solution for problematic intervals
The resulting colours are consistent with expectations re-
garding saturation and hue of pairs of tones that are very
consonant or very dissonant, for example: large saturation
for interval of unison, octave, perfect fifth and minimal satu-
ration for tritone and minor second. But for combinations of
tones which are an interval of major or minor third apart, the
resulting saturation is poor although they are not perceived
dissonant. The reason for this is that the angle between such
tones is from 90 to 120 degrees in the circle of fifths. This
is the consequence of circle of fifths showing relationships of
2:3 and 3:4, but not 4:5 and 5:6. To solve this problem the
key spanning circle of thirds [3] is used instead of circle of
fifths. The key spanning circle of thirds contains two circles
of fifths that are slightly rotated in correspondence to each
other (pitch classes in original circle of fifths are shown in
majuscule letters and that of the contorted circle of fifths
in minuscule letters) (Figure 1). Left and right neighbour
of a particular tone in this circle are the minor and major
third of the tone. Viewing from the viewpoint of keys in the
key spanning circle of thirds the parallel major and minor
keys are close together (for example C-major and a-minor).
The initial setup of colour wheel and key spanning circle of
thirds is presented in Figure 1. The setup is not fixed and
the circle could be rotated arbitrary or inverted.
Following the introduction of circle of thirds the calcu-
lating of resultant colour is modified: if a pair of tones is
encountered, where the second tone is a major third apart
from first and the first tone is louder or equally loud then the
second tone is represented by a vector pointing to the tone
1678
Figure 2: Screenshot of the main window of our
system for visualization of music showing coloured
3-dimensional piano roll of Tchaikovsky’s Swan Lake
demonstrating calculated concurrent colours.
of the same name in the contorted circle of fifths instead of
the original circle of fifths. If the second tone is louder, then
the angle between two circles is linearly interpolated. In
case of more tones, each tone is tested against all others and
converted to appropriate vector before the resultant vector
is calculated. In this way we attain consistent results such
that consonant intervals including major and minor third
result in saturated colours and dissonant intervals have low
saturation. Related chords have similar hues.
4. SYSTEM DESCRIPTION
The method for calculating colour of concurrent tones is
part of a system we developed for visualization of music [5].
The base of the system is a 3-dimensional piano roll nota-
tion (the dimensions are time, instruments and tone pitch)
expanded with colours for harmonic relations (Figure 2).
Loudness of tones is shown as transparency. The piano roll
notation enables us to visualize the structure of the music
and observe the calculated colours for the whole duration
of a composition. The system uses MIDI as input, which
is sufficient since the calculation of colours uses only the 12
pitch classes of the chromatic scale. Using MIDI also elimi-
nates the problem of tone extraction from sound recording.
The MIDI data itself can contain tones that have frequen-
cies in between the standard pitch classes – in that case the
colour computation algorithm rounds them to the nearest
pitch class, but the actual pitch is drawn in the piano roll
notation.
Because the resulting colour of concurrent tones is calcu-
lated for a given moment in time and changes in loudness
of input tones affect the resulting colour, the music would
have to be sliced in small time slices and the colour calcu-
lated for each one. Most of the time changing of loudness is
continuous; an important exception being the beginning of
the tone. Therefore the colours are calculated at boundaries
as such sudden change of tone loudness (events like note-off,
note-on and explicit change of loudness of a MIDI channel)
and interpolated linearly in between.
The visualization is dynamic and runs in real-time, allow-
ing live input. The resulting 3-dimensional object can be
interactively observed and studied.
5. RESULTS
No formal studies have been conducted with our visual-
ization system yet, but the feedback from users has been
positive.
The main purpose of our visualization is to visualize har-
monic relationship in music with colour but structure can
be seen as well and together they can give us greater insight
into nature of a musical piece. Consonant dyads (e.g. C
and G) have saturated colours and dissonant (e.g. C and
C,CandF) have low saturation. Major triads have hues
corresponding to hue between the root tone of the chord and
its fifth, minor triads have hues that correspond to hue of
minor third of the root (e.g. Am chord corresponds to hue
of C), but an augmented triad is dissonant and has therefore
zero saturation (grey), to name a few examples.
Examples from visualizations of excerpts of classical pieces
are presented in Figure 3. The visualizations are viewed
from side with time flowing from left to right and vertical
axis representing pitch (depth represents instruments, but is
omitted for clarity in the examples). An example of chord
progression can be seen in the initial part of visualization of
PachelbelsCanoninDmajor(D,A,Bm,Fm, G, D, G,
A) depicted in Figure 3(a). Resulting colour hues are cen-
tred around colour hue of D (orange in current assignment),
which is a consequence of tonality of the piece being D ma-
jor. An example of modulation can be seen in the excerpt in
Figure 3(a) where we can observe transition from A major
to D major to Bmajor then back to D major and then
to G major. An example of dissonant intervals can be seen
as grey areas in Tchaikovsky’s Swan lake (Figure 2), where
dissonance is caused by tritone interval. Dissonant inter-
vals are unstable and cause tension, so they are resolved,
which can be seen as saturation of colour increases in tone
combinations afterwards.
Currently broken chords may pose a problem to the vi-
sualization because the calculation of colour is limited to
concurrent tones. The problem could be solved by extend-
ing the analysis to broader group of tone concerning time
dimension.
Although presented examples are classical compositions,
the visualization also works for other genres such as folk
music, popular music, jazz etc. (additional examples are
presented in the accompanying video). In music, which uses
a lot of dissonant intervals, we can see colours of low sat-
uration, but problems outlined in connection with broken
chords make the results sometimes to colourful.
6. CONCLUSIONS
Visualizing music in a meaningful and intuitive way is a
challenge. In this paper we focused on visualizing harmonic
relationships between tones and colours. Related existing vi-
sualizations map tones or keys into a discrete set of colours.
As concurrent (simultaneous) tones are not perceived as en-
tirely separate, but also as a whole, we presented a novel
method for visualizing a group of concurrent tones with one
colour for the whole group. The method takes a group of
tones of the 12-tone chromatic scale as input and the result-
ing colour is not limited to a discrete set of colours. The
basis for calculation of colour is the assignment of key span-
ning circle of thirds to the colour wheel. In this way we map
similar tones and keys with similar colour hue. Dissonance
is represented with low saturation and consonant tone com-
1679
(a) Excerpt from Pachelbel’s Canon in D major
(b) Excerpt from Strauss’s An der sch¨
onen blauen Donau
(c) Excerpt from Debussy’s Clair de Lune
Figure 3: Examples of visualization of classical compositions.
binations have high saturation. Because loudness of tones
influences the perception of concurrent tones, it is also taken
into account in the proposed method.
The method is implemented as part of our prototype mu-
sic visualization system using MIDI input. We have shown
that the method works relatively well and could be used
to help visualize harmony in music. However, in some cases
there are still problems. Major and related minor chords are
differentiated but have very similar colours, failing to repre-
sent a psychological difference. Sometimes resulting colours
may be too saturated. Another limitation of the method is
that it is based on the pitches of the 12-tone chromatic scale.
The visualization could be improved by taking into account
a broader time range in addition to concurrent tones, as
human perception is not limited to a moment in time.
The colour model and our visualization system strive to
establish a unity of perception of two distinct senses, creat-
ing a form of synaesthesia. In consequence, it enables easier
understanding of music and thus colours may be used also
to facilitate learning of music.
7. REFERENCES
[1] T. Bergstrom, K. Karahalios, and J. C. Hart.
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[2] E. M. Burns. Intervals, scales, and tuning. In
D. Deutsch, editor, The Psychology of Music,
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[3] G. Gatzsche, M. Mehnert, D. Gatzsche, and
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[4] E. J. Isaacson. What you see is what you get: on
visualizing music. In ISMIR, pages 389–395, 2005.
[5] B. Klemenc. Visualization of music on the basis of
translation of concurrent tones into color space, Dipl.
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[6] S. Malinowski. Music animation machine.
http://www.musanim.com, 2007.
[7] A. Mardirossian and E. Chew. Visualizing music:
Tonal progressions and distributions. In 8th
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[8] R. Miyazaki, I. Fujishiro, and R. Hiraga. Exploring
midi datasets. In SIGGRAPH 2003 conference on
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[9] R. Parncutt. Harmony: A Psychoacoustical Approach,
chapter 2, pages 21–47. Springer-Verlag, 1989.
[10] R. Rasch and R. Plomp. The perception of musical
tones. In D. Deutsch, editor, The Psychology of Music,
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[11] E. G. Schellenberg and S. E. Trehub. Frequency ratios
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[12] S. M. Smith and G. N. Williams. A visualization of
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[13] E. Terhardt. Akustische Kommunikation, chapter 11.
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[14] A. Wells. Music and visual color: A proposed
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The author tells of events leading up to finding a possible link between musical harmony and visual color based on complementarity. He points out that an equal division of the musical octave into 12 half-steps permits one to recognize chords built on tones occurring at the interval of half an octave or the tritone interval as being complementary to each other. This corresponds to the equal spacing of 12 hues on a color circle in which complementary hues are located diametrically opposite each other. A circular form of the musical octave divided according to the chromatic scale of 12 half-steps places tones serving as roots for complementary chords diametrically opposite each other also. There seems to be a parallel between the equal division of the color circle into 3 primaries and 3 secondaries and the equal division of the musical circle into 6 whole steps or the whole-tone scale. In both circles, colors and chords that can be classified as secondaries are complementary to the primaries and vice versa. The near-complements of a color lying on either side of its complement are more subdued in contrast with the color than the complement is. Chords built on tones on either side of a tritone interval from a given tonal center on the musical circle also produce subdued contrast with a chord built on the tonal center. The relationship of the adjacent chords to a chord built on the tonal center is as of sub-dominant to tonic and dominant to tonic, which is the harmonic basis of the diatonic system.
Book
"Harmony: A Psychoacoustical Approach" explains aspects of the conventional theory of harmony in Western music in terms of psychoacoustics—experimentally-established, quantitative relationships between sound (acoustics) and sensation (psychology). The pitch properties of tones, chords, and chord sequences are calculated on the assumption that the human auditory system is familiar with the pitch pattern of the audible harmonics of complex tones such as speech vowels and musical tones. The model is tested experimentally, and subsequently applied in music theory, analysis and composition. (PsycINFO Database Record (c) 2012 APA, all rights reserved)