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The Multiperiodic Pulsating Star Y Cam A as a Musical
Instrument
B. Ula¸s
˙
Izmir Turk College Planetarium, 8019/21 sok., No: 22, ˙
Izmir, Turkey
bulash@gmail.com
July 28, 2015
Abstract
In this study we generate musical chords from the
oscillation frequencies of the primary component of
oscillating eclipsing Algol system Y Cam. The pa-
rameters and the procedure of the musical chord gen-
eration process from the stellar oscillations are de-
scribed in detail. A musical piece is also composed
in appropriate scale for Y Cam A by using the gen-
erated chords from the results of the asteroseismic
analysis of the stellar data. The music scores and the
digital sound files are provided for both the gener-
ated chords and the musical composition. Our study
shows that the further orchestral compositions can
be made from the frequency analysis results of sev-
eral pulsating stars by using the procedure stated in
present study.
keywords— stars: binaries: eclipsing — stars: os-
cillations (including pulsations) — stars: individual:
(Y Cam)
1 Introduction
The efforts on combining the celestial objects with
music have been made for ages. Pythagorians'philo-
sophical concept, Musica Universalis, pointing a har-
mony in celestial movements and Kepler’s works on
relating the planetary motions to musical consonance
can be given as examples. There are also modern
studies focused on combination of the music with pul-
sating stars in more mathematical and efficient ways.
For instance, in their extensive work, Koll´ath and
Keuler (2006) made a musical composition by devel-
oping a software to transform the stellar oscillations
that can be based on the note C. The authors consid-
ered the internal structures of stars while determining
their criteria in selecting some certain pulsating stars
as musical instruments. They also analyzed their
composition in musical point of view. An agreement
between musical scales and the frequencies of multi-
periodic stellar pulsations were investigated by Ula¸s
(2009). The author concluded that the best agree-
ment was reached for the binary system Y Cam and
the Diminished Whole Tone Scale. Various digital
sound files made by transforming the stellar pulsa-
tions to audible range also can be reached online1.
We describe the chord generation from the results
of the frequency analysis of a pulsating star in de-
tail in the next section. The third section focuses
on a musical composition in an appropriate musical
scale made by using a digital piano and the generated
chords from the oscillations of the primary compo-
nent of Y Cam. We concluded the results in the last
section.
2 Chord Generation from Stellar Oscil-
lations
A chord is defined as simultaneous sound of three
or more different tones which are formed by follow-
ing the certain intervals (Apel, 1944). It can be
1https://goo.gl/FFhpEV
1
arXiv:1507.07307v1 [physics.pop-ph] 27 Jul 2015
thought that a chord is a group of sound waves hav-
ing many frequencies emerged simultaneously from a
musical instrument. This phenomenon shows analogy
to the light received from a multiperiodic pulsating
star. The light curve of a multiperiodic pulsating star
exhibits a wave containing many sine like variations
with certain frequencies, amplitudes and phase shift
values which can be determined by analyzing the light
emerged from the star. This similarity were used in
generating a chord from the asteroseismic results of
the multiperiodic pulsating component of Y Cam in
this study.
We first defined three dimensionless transforma-
tion parameters in order to generate a musical chord
from the stellar oscillations: The relative frequency
was defined as f0=fi
fmin where fis are the derived
oscillation frequencies for a pulsating star and fmin
is the minimum frequency value among the derived
ones. The loudness parameter, L=Ai
Amax , refers to
the relative loudness of a signal and it is the ratio of
Ai, amplitude value for a given oscillation frequency
of star, to Amax, maximum amplitude value within
the derived frequency group. pparameter denotes
the starting time of the signal and is the difference
between the phase shift value of a given frequency
and the minimum phase shift value (p=φi−φmin)
among the derived parameters from oscillations of the
star.
We calculated the three parameters (f0, L, p) for
the oscillation frequencies of Y Cam A derived by
Kim et al. (2002). Following their results we cal-
culated the necessary quantities for the transforma-
tion as fmin = 15.0473 c/d,Amax = 5.8mmag and
φmin =−1.31. In order to generate a chord which
is unique for the star we first generated the tones
for the mentioned chord using the necessary param-
eters described above. Table 1 lists the calculated
values for the parameters which were used to gen-
erate the tones by using the Audacity2audio ed-
itor. The program can generate tones for a given
frequency, normalized amplitude and starting time
values. Three steps in the process of tone generation
were followed: (i) We multiplied all f0values with
the frequency value of the desired musical note. For
2http://www.audacityteam.org/
Figure 1: The Diminished Whole Tone Scale on F ]
in staff with the Gclef.
instance, when we wanted to transform the smallest
frequency to the fourth octave note Gwe multiplied
f0values with 392.0 Hz3and we derived four new fre-
quency values (392.00 Hz, 398.00 Hz, 469.09 Hz and
483.65 Hz). These values were applied to the pro-
gram as the frequencies of four tones. (ii) The Lval-
ues were directly entered the program as normalized
amplitudes. (iii) the pparameters were the input val-
ues characterizing the starting times of the generated
tones. When finished with those three steps we gen-
erated four tones (one for each oscillation frequency)
which can be played together to generate the chord on
the desired note. The same procedure was followed
for the notes G,A,Cand D. The frequency values of
the tones based on these notes are listed in Table 1.
A group of digital sound files for the generated chords
on the mentioned notes were also produced and can
be found in an online playlist4
3 Musical Composition using Stellar
Chords
Since the oscillation frequencies of the primary com-
ponent of the eclipsing binary system Y Cam shows
an agreement with the Diminished Whole Tone Scale
(Ula¸s, 2009) we planned to compose a piano piece in
mentioned scale and accompany the chords generated
from the oscillations of the star in the previous sec-
tion. A musical scale is defined as series of countless
variety of selected musical notes (Wood, 1964). The
Diminished Whole Tone Scale on F ] was selected as
the scale during the composition. The places of the
musical notes in Diminished Whole Tone Scale on F ]
on the staff is given in Fig. 1. The MuseScore5soft-
3http://www.phy.mtu.edu/∼suits/notefreqs.html
4https://soundcloud.com/bulash/sets/chordsycamb
5https://www.musescore.org/
2
Table 1: The oscillation properties of Y Cam together with the calculated transformation parameters of
chord generation. The second, third and fourth columns list the frequency, amplitude and phase shift values
of the pulsating component derived by Kim et al. (2002). Headers of the last four columns indicate the
musical notes whose frequencies were multiplied by f0values when generating the tones for the chord. The
indexes 4 and 5 refer the octave number of the notes, i.e. C5means the fifth octave note C. An octave is
the interval between first and the eighth tones of eight consecutive diatonic tones (Baker, 1904).
f(c/d) A(mmag) φ f0L p G4(Hz)A4(Hz)D5(H z)C5(Hz)
f115.0473 5.8 -0.89 1.0153 1.0000 0.4200 398.00 446.74 596.33 531.26
f218.2852 3.9 1.06 1.2338 0.6724 2.3700 483.65 542.87 724.64 645.58
f314.8203 3.4 -1.31 1.0000 0.5862 0.0000 392.00 440.00 587.33 523.25
f417.7348 2.8 -0.35 1.1967 0.4828 0.9600 469.09 526.53 702.83 626.15
ware is used to form a sheet music for the composed
piece (Fig. 2a and 2b). The program allows the user
to put numerous musical notations on a blank sheet
in digital media to prepare a sheet music. We cre-
ated a digital sound file for the composition in two
steps. First a sound file6was created by recording the
piano performing by the author; then, the recorded
sound file mixed with the previously generated stellar
chord files following the notation on the sheet music
for the composition. The mixing process was carried
out using the digital audio editor GoldWave7. The
resulting sound file for the final composition can be
found online8.
Fig. 2a and 2b demonstrates the music scores of
the whole musical composition. First two staffs from
the top (accolade) on the sheet show the piano par-
tition of the piece. The third staff with unusual no-
tation contains the star signs locate on the staff lines
and refer to the notes for the smallest frequency of
the generated chord, namely the smallest oscillation
frequency of Y Cam A after it was transformed to
the desired musical notes following the directions de-
scribed in the previous section. The star signs on
the third staff also show the places where the chords
are played through the composition. The duration
of the chord playing was set according to selected
time of the composition, three-four time. This type
of notation for the third staff was used because of
the impossibility of displaying the second, third and
6https://soundcloud.com/bulash/akycampiano
7http://www.goldwave.com/
8https://soundcloud.com/bulash/akycam
fourth frequencies of the generated chords by using
any musical notation on staff with the Gclef.
4 Conclusion
A short musical composition was made by using the
frequency analysis data of the binary system Y Cam
(Kim et al., 2002) whose oscillation frequency ar-
rangement of the primary component shows the best
agreement with the Diminished Whole Tone Scale ac-
cording to Ula¸s (2009). We also explained the general
properties of the transformation procedure for the os-
cillation frequencies of pulsating stars to the musi-
cal chords on desired note. The procedure is based
on the mathematical analogy between musical chords
and the observed frequency group of a multiperiodic
pulsating star.
The whole procedure can be summarized as con-
verting the oscillation phenomenon seen on the pri-
mary component of Y Cam to a musical instrument
which plays its unique chord on various notes. These
chords were placed proper to the tempo and the time
of the composition which is composed in appropriate
scale and given in Fig. 2a and 2b. The quality of the
composed music is controversial, however, the basic
steps explained here for one piano and one pulsat-
ing star can also be applied to make an orchestral
composition using several musical instruments and
pulsating stars which will enrich the quality and the
listening for the audiences. The digital artificial ef-
fects can also be added to orchestral composition by
3
Figure 2a: Sheet music for the composition.
4
Figure 2b: (Cont.)Sheet music for the composition.
5
using contemporary sound editors. The present study
was planned to be grown in that route.
References
Apel, W., 1944, Harvard Dictionary of Music, 2nd
edition, Harvard University Press
Baker. T, 1904, A Dictionary of Musical Terms, 8th
edition, New York: G. Schirmer
Kim S.-L., Lee J. W., Youn J.-H., Kwon S.-G., Kim
C., 2002, A&A, 391, 213
Koll´ath, Z., Keuler, J., 2006, Musicae Scientiae, 10,
161
Ula¸s, B., 2009, CoAst, 159, 131
Wood, A., 1964, The Physics of Music, Davies Press
6
