6.5 Playing Frequencies of Brass Instruments
309
For a musician, the intonation of the instrument is a critical quality factor. The
manufacturer can determine the frequencies of the input impedance peaks by a
suitable choice of bore profile (Chap. 4), but when the instrument is played, the
sounding frequencies will also depend on the performer’s choice of lung pressure,
windway shape and embouchure. We have seen that notes can be ‘lipped’ both
above and below a ‘pitch centre’ (Sect. 1.2.2), which is usually close to one of the
impedance peak frequencies (see, e.g. Boutin et al. (2015b)). Good intonation thus
implies that the frequencies of the pitch centres (rather than the impedance peaks)
should correspond to the musically desirable notes, usually taken to be frequencies
on the equally tempered (ET) scale with A4 = 440 Hz.
To establish the relationship between impedance peak frequencies and playing
frequencies in musical practice, Eveno et al. (2014) carried out a systematic study
in which four performers were recorded playing three trumpets with different bore
profiles. On each trumpet four different valve fingerings were used (000, 100, 110
and 111). For each fingering, the natural notes from the second to the sixth were
sounded at three dynamic levels (mf, p and f ). The performers were asked to play
the notes with the easiest emission, without trying to correct the intonation: in other
words, to find the pitch centre for each note. To establish consistency each test was
repeated three times, giving a total of 2160 recorded notes. The input impedances
of the 12 different bore profiles (4 fingerings on each of 3 trumpets) were also
measured.
An analysis of this large corpus of data was used to obtain Fig. 6.22. Each graph
in this figure corresponds to one of the played regimes (natural notes) and includes
the results from all three trumpets and four fingerings. The horizontal axis, labelled
F res (cents), is the pitch difference between the impedance peak nearest to the
played note for a given fingering and the nominal ET pitch of the note. The vertical
axis, labelled F play (cents), is the pitch difference between the played pitch and the
nominal ET pitch.
A striking feature of these results is the wide range of the playing pitches for a
given fingering and playing regime. Taking the example of regime 2, the pitches for
the fingering 000 are represented by black crosses. All of the crosses are slightly
to the left of the F res = 0 vertical line, indicating that the second impedance peak
is approximately 10 cents below the nominal pitch of B 3 for all three trumpets.
The playing pitches range from 25 cents below B 3 to 25 cents above. For the other
three fingerings, the vertical spread of the data exceeds 50 cents. The dependence
of playing pitch on dynamic level was found to be weak. It thus appears that two
players asked to play the same note on the same instrument may differ in assessing
the pitch centre by up to half a semitone.
It is also noteworthy that most (though not all) of the data points are above the
black line representing F play = F res . This is true for all the regimes, although the
playing frequencies of the second regime are shifted up to the greatest extent with
respect to the impedance peak frequencies. This observation can be related to the
inharmonicity of the resonances corresponding to the second regime. For regimes
3 to 6, playing frequencies are, on average, around 15 cents above the impedance
peak frequencies.
309
For a musician, the intonation of the instrument is a critical quality factor. The
manufacturer can determine the frequencies of the input impedance peaks by a
suitable choice of bore profile (Chap. 4), but when the instrument is played, the
sounding frequencies will also depend on the performer’s choice of lung pressure,
windway shape and embouchure. We have seen that notes can be ‘lipped’ both
above and below a ‘pitch centre’ (Sect. 1.2.2), which is usually close to one of the
impedance peak frequencies (see, e.g. Boutin et al. (2015b)). Good intonation thus
implies that the frequencies of the pitch centres (rather than the impedance peaks)
should correspond to the musically desirable notes, usually taken to be frequencies
on the equally tempered (ET) scale with A4 = 440 Hz.
To establish the relationship between impedance peak frequencies and playing
frequencies in musical practice, Eveno et al. (2014) carried out a systematic study
in which four performers were recorded playing three trumpets with different bore
profiles. On each trumpet four different valve fingerings were used (000, 100, 110
and 111). For each fingering, the natural notes from the second to the sixth were
sounded at three dynamic levels (mf, p and f ). The performers were asked to play
the notes with the easiest emission, without trying to correct the intonation: in other
words, to find the pitch centre for each note. To establish consistency each test was
repeated three times, giving a total of 2160 recorded notes. The input impedances
of the 12 different bore profiles (4 fingerings on each of 3 trumpets) were also
measured.
An analysis of this large corpus of data was used to obtain Fig. 6.22. Each graph
in this figure corresponds to one of the played regimes (natural notes) and includes
the results from all three trumpets and four fingerings. The horizontal axis, labelled
F res (cents), is the pitch difference between the impedance peak nearest to the
played note for a given fingering and the nominal ET pitch of the note. The vertical
axis, labelled F play (cents), is the pitch difference between the played pitch and the
nominal ET pitch.
A striking feature of these results is the wide range of the playing pitches for a
given fingering and playing regime. Taking the example of regime 2, the pitches for
the fingering 000 are represented by black crosses. All of the crosses are slightly
to the left of the F res = 0 vertical line, indicating that the second impedance peak
is approximately 10 cents below the nominal pitch of B 3 for all three trumpets.
The playing pitches range from 25 cents below B 3 to 25 cents above. For the other
three fingerings, the vertical spread of the data exceeds 50 cents. The dependence
of playing pitch on dynamic level was found to be weak. It thus appears that two
players asked to play the same note on the same instrument may differ in assessing
the pitch centre by up to half a semitone.
It is also noteworthy that most (though not all) of the data points are above the
black line representing F play = F res . This is true for all the regimes, although the
playing frequencies of the second regime are shifted up to the greatest extent with
respect to the impedance peak frequencies. This observation can be related to the
inharmonicity of the resonances corresponding to the second regime. For regimes
3 to 6, playing frequencies are, on average, around 15 cents above the impedance
peak frequencies.