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TMH-QPSR, KTH, Volume 47/2005
Speech, Music and Hearing, KTH, Stockholm, Sweden
TMH-QPSR, KTH, Vol. 47: 1-6, 2005
1
Intonation analysis of a multi-channel choir
recording
Harald Jers & Sten Ternström
Department of Speech Music and Hearing, Kungl Tekniska Högskolan, Stockholm
jers@speech.kth.se & sten@speech.kth.se
Presented at the Baltic-Nordic Acoustics Meeting 2004, June 8-10, Mariehamn, Åland, Finland.
Abstract
A multi-track recording of a 16-singer choir is analysed singer by singer with
regard to intonation, synchronisation, and to what extent the singers of a voice
section agree to each other. We try to find objective measures that might contribute
to a definition of the so-called “chorus effect”. The results show some expected
effects of intonation dispersion and also an unexpected lining up of vibrato.
1. Introduction
Amateur choir singing has improved greatly in
recent years, and many semiprofessional choirs
reach an almost professional quality. However,
in the field of choir acoustics, there has not been
much research that could help to improve
rehearsal methods. Ternström (2003) gave an
overview of earlier investigations, that dealt
mostly with F0-analysis, timbre and spectrum,
SPL and formant frequencies. Some measure-
ments were done with several singers singing
within a choir, sometimes synthetic signals were
used to simulate a choir, and some intonation
analyses were done with ensembles. One of the
particular properties of choral sound is the so-
called “chorus effect”, that is, the combined
sound of many sources that are similar but
uncorrelated at the level of the waveform of the
sound. To study the chorus effect, it is important
to know what each choir singer is singing. Only
a few recordings of a choir (as distinct from
quartets, etc) have been studied, and we have
found no detailed investigation with multi-
channel recording of separated choir singer
signals. With the advent of affordable multi-
track equipment, such recordings are now easier
to make than before. In his diploma thesis,
author Jers (1998) used multi-track recordings to
re-create “virtual choirs” in order to study the
effect of singer directivity with singer placement
and room acoustics taken into account. This
resulted in a large material which also can be
used for detailed studies of how the choir
singers sing together: intonation, synchron-
isation, timbral matching etc. This paper reports
on some attempts to assess choral intonation in
detail, and presents a preliminary analysis of a
complete choir recording concerning the degree
of similarity between singers in intonation and
vibrato.
2. Musicians and music
A multi-channel recording was done with the
County Choir of North-Rhine Westfalia in
Germany; an amateur choir with singers aged
20-32 years, recruited regionally. Some of them
had soloist training, but the majority had learned
by practising choir singing. The recording was
made in their normal rehearsal room. The music
should represent a real choir rehearsal situation,
and therefore an 8-bar canon by Praetorius was
chosen (Figure 1), and performed in unison,
females and males one octave apart. The range
of the piece is comfortable for every voice
group, it has some melismatic and some syllabic
parts, and some variety of different melodic
intervals. The piece was rehearsed with the choir
before and sung in German pronunciation of
Latin.
Jers & Ternström: Intonation analysis of a multi-channel choir recording
2
3. Data acquisition
A 16-channel recording system was used, with
16 miniature omnidirectional electret condenser
microphones (Monacor MCE-100), a mixer
(Target Q-Series 328+6), and two synchronised
Tascam D-88 8-track PCM recorders. The
microphones, purpose-built at the Institute of
Technical Acoustics in Aachen, had a flat fre-
quency response up to 10 kHz. Each micro-
phone was placed on the nose of a singer, close
to the mouth, outside the voice airstream, and
undisturbed by clothing etc. The error in fre-
quency response incurred by this placement was
later compensated for as described by Jers
(1998). The 8-bar piece was sung twice: in
normal tempo (
= 125 bpm) and in a slower
tempo (
= 80 bpm). At this point, the piece had
already been rehearsed many times, so the
training effect between these two takes should
have been negligible. After recording the data
was copied to a computer hard disc.
The choir consisted of 16 singers, four in
each voice section (Figure 2). The separation
between the singers was 80-100 cm. The
crosstalk between adjacent microphones was
about 20 dB, which is enough for our analysis.
4. Analysis and results
The fundamental frequency (F0) contours were
estimated using the correlogram utility of
Soundswell (Granqvist & Hammarberg, 2003),
which uses auto-correlation and manual segmen-
tation to produce F0 contours with a sampling
rate of about 1 kHz and a resolution of better
than 1 cent. These were converted into text files
and read into Microsoft Excel for further ana-
lysis and display.
There are several types of dispersion in
choral intonation. Each singer’s F0 has micro-
variations over time, so to get an intonation
value for one tone we must compute the average
F0 over the duration of the tone, MF0
N
. This
operation will also remove the vibrato, provided
that there is a whole or at least large number of
vibrato cycles in the tone. The standard
deviation SF0
N
over the tone is a measure of the
singer’s instability in F0, or, of the vibrato
extent (RMS). It is also interesting to compute
the average F0 of all singers or voices, MF0
V
,
reflecting the combined intonation of the
ensemble; and the corresponding standard
deviation SF0
V
, reflecting the dispersion in F0
between singers. For readability, we first
tabulate these symbols for the different F0
averages and standard deviations (Table 1).
Figure 2. 16-channel recording of a choir.
F
i
g
ure 1. Canon “Laudate Dominum” o
f
Michael Praetorius.
TMH-QPSR, KTH, Volume 47/2005
Speech, Music and Hearing, KTH, Stockholm, Sweden
TMH-QPSR, KTH, Vol. 47: 1-6, 2005
3
Table 1. Definition of symbols for different F0 averages and standard deviations.
Average Standard
deviation
Comment
Over time but within notes MF0
N
SF0
N
One value per note per singer. MF0
N
measures the F0 of one note, SF0
N
measures the F0 stability of one singer
Over voices/singers MF0
V
SF0
V
MF0
V
measures the average F0 of
several singers, SF0
V
measures the
scatter in F0 across singers.
Both change continuously with time
Over time-averaged notes and
over singers
MF0
V,N
SF0
V,N
One value per note. Measures the
mean MF0
N
and scatter in MF0
N
over
singers
-100
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 2 4 6 8 10 12 14 16 18 20
MF0
[cent]
V
Figure 3. Average of the whole ensemble, Standard deviation across all 16 singers, slow tempo.
4.1 Intonation
We will start by looking at the averages taken
over the entire ensemble and then progress to
lower levels of detail. Figure 3 is an analysis of
the low-tempo version. It shows the MF0
V
in
cents relative to the root, N=16 singers, and with
SF0
V
in a separate trace at the bottom.
It is easy to track the MF0
V
curve with regard
to the printed score, and the tone steps are
clearly seen. One may note that the intonation
on descending scales seems very accurate (in
SF0
V
Jers & Ternström: Intonation analysis of a multi-channel choir recording
4
equal temperament), while on the ascending
scales there seems to be a tendency of pitching
high, similar to an earlier investigation of
coloratura passages of Sundberg (1989). In
melodic intonation, the big intervals are
enlarged, for example the fifths and the octaves.
As might be expected, the standard deviation
SF0
V
at the transitions between the tones is high,
caused both by some desynchronisation of the
voices and by transient effects in arriving at the
next pitch. After a transition, the SF0
V
decreases
to a baseline level after approximately 0.3
seconds. The overall time average of SF0
V
was
39 cents. This value includes variations due to
vibrato and flutter. Although MF0
V
represents
an average across all singers, there is still a
clearly visible vibrato, increasing in extent to the
end of a note.
-100
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 2 4 6 8 10 12
MF0
V
[cent]
[s]
SF0
V
Figure 4. F0 averaged over all 16 singers, with standard deviation, normal tempo.
In the normal tempo version (Figure 4),
similar tendencies may be observed: the big
intervals are enlarged, steps upwards are
sharpened and the vibrato is still visible, with an
even larger extent than in the slow version. The
main differences seem to be some over- or
undershoots for the highest and the lowest tones,
a slightly bigger increased standard deviation
SF0
V
at the tone transitions and a more
glissando-like difference between tone steps.
Probably the fast tempo gives less time to find
the correct pitch of each note, thereby causing
this greater imprecision. Greater imprecision
was also found in the time average of SF0
V
,
which was 55 cents over the 8 bars, implying
that the F0 inaccuracies and/or instabilities
increased a little in the higher tempo.
To compare with an earlier investigation of
Ternström & Sundberg (1988), a statistical
analysis of the long notes of this piece was done
by calculating the SF0
V,N
. This gives informa-
tion about the degree of agreement in intonation
among the singers.
Figure 5. Notes of the choir piece chosen for further intonation and vibrato analysis.
TMH-QPSR, KTH, Volume 47/2005
Speech, Music and Hearing, KTH, Stockholm, Sweden
TMH-QPSR, KTH, Vol. 47: 1-6, 2005
5
0
5
10
15
20
25
30
Normal tempo Slow tempo
Sopranos
A
ltos Tenors Basses
[cent]
Figure 6. SF0
V,N
over singers and note A4 for each voice group, normal and slow tempo.
For this purpose the MF0
N
of the A4 of the
female (A3 of the male voices) was calculated
and the SF0
V,N
for each voice group is shown in
Figure 6. Like the SF0
V
, the SF0
V,N
is lower in
the slow version. There were no differences
between the choir sections in this regard.
Ternström & Sundberg (1988) found an average
SF0
V,N
of about 13 cents over six basses when
the choir was singing to the conductor’s
satisfaction, which is similar to the slow version
here.
4.2 Vibrato
There are many investigations of soloist vibrato,
but little has been looked at in choirs. Different
choral traditions use different amounts of
vibrato. In the choir studied here, some singers
had vibrato and others did not. It can be argued
that vibrato would be detrimental to choral
intonation, since it would tend to blur the
harmonies of the chords. From a perceptual and
motor-control perspective, it seems very un-
likely that singers would be able to consciously
synchronise their vibratos, but if it were
possible, then such a blurring might be less
F0 of female section - 1st note of bar 2 - slow version
2,9 3 3,1 3,2 3,3 3,4 3,5 3,6 3,7
time (s)
F0 Sop1
F0 Sop2
F0 Sop3
F0 Sop4
F0 Alt1
F0 Alt2
F0 Alt3
F0 Alt4
Avg Female
100 cent
Figure 7. Vibrato comparison of the female section – 1
st
note of bar 2 – slow version.
Jers & Ternström: Intonation analysis of a multi-channel choir recording
6
F0 of female section - 1st note of bar 6 - slow version
12,1 12,2 12,3 12,4 12,5 12,6 12,7 12,8 12,9
time (s)
F0 Sop1
F0 Sop2
F0 Sop3
F0 Sop4
F0 Alt1
F0 Alt2
F0 Alt3
F0 Alt4
Avg Female
100 cent
Figure 8. Vibrato comparison of the female section – 1
st
note of bar 6 – slow version.
objectionable to the listener. Figures 7 and 8
shows the F0 contours of the female singers on
the first notes of bars two and six (slow version).
Remarkably, most of the singers with vibrato
did exhibit some degree of synchronisation. This
is an interesting observation, but more experi-
ments are needed to determine whether it is a
common phenomenon. For the fast version, the
picture was similar, except that vibrato was
initiated immediately at the onset of the tones.
It can be argued that the vibrato oscillations
will be the same if the note onsets act as
synchronisation points, and we think that this is
what is happening. For example, in going to a
lower note from a higher note, singers typically
perform a small F0 undershoot, which would act
as the lower starting point for a vibrato cycle. In
notes of longer duration than those measured
here, it is possible that desynchronisation would
set in.
5. Conclusion
The present investigation shows some details of
intonation and vibrato behaviour of singers
within a choir. Although it is not possible to
draw general conclusions, it seems to be
possible to get closer to a definition of the
“chorus-effect” with this material, as well as
with further analysis. It has to be taken into
account that the sound pressure level was not
mentioned in this analysis, and we do not know
how these findings are related to how the choral
sound is perceived. Another 16-channel record-
ing is planned for comparison through listening
tests.
6. Acknowledgements
We would like to thank the Youth choir of
North-Rhine Westfalia and their conductors for
their help, and the Institute of Technical
Acoustics in Aachen for providing the measure-
ment equipment. This research was supported by
a Marie Curie Fellowship from the European
Commission.
7. References
Ternström S (2003). Choir Acoustics: An Overview
of Scientific Research Published to Date. Int J Res
Choral Singing, 1(1), 3-11. Available online at
www.choralresearch.org.
Jers H (1998). Investigations of implementation
possibilities of distributed sources for the room-
acoustic computer simulation by the example of the
choir (in German). Diploma work in physics,
Institut fuer Technische Akustik, RWTH Aachen,
Germany.
Granqvist S & Hammarberg B (2003). The
correlogram: a visual display of periodicity, J
Acoust Soc Am (JASA) 114/5: 2934-2945.
Sundberg J (1989). Synthesis of singing by rule. In:
Current Directions in Computer Music, MIT Press,
Cambridge, Mass.
Ternström S & Sundberg J (1988). Intonation preci-
sion of choir singers. J Acoust Soc Am (JASA)
84/1: 59-69.
