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1 The Musician’s Experience of Brass Instruments
Fig. 1.11 International pitch notation
Fig. 1.12 The pitches of the first 16 members of a harmonic series with fundamental C2
1.2.2 Natural Notes and Harmonics: The Musician’s View
When a trumpet is sounded without operating any valves, the player finds that a
number of notes at different pitches can be easily obtained by varying the lip tension
and blowing pressure. These notes are often referred to by musicians as ‘harmonics’.
Underlying this description is the idea of a harmonic series of frequencies, each
member of which is an integer multiple of the first member (sometimes called the
‘fundamental’). For example, the first few members of a harmonic series with a
fundamental of 110 Hz are 110, 220, 330, 440 Hz, etc.
Figure 1.12 shows the pitches of the first 16 members of a harmonic series
with fundamental 65.4 Hz (pitch C2). Although the difference in frequency between
successive members of the series remains constant at 65.4 Hz, the pitch intervals
become smaller as the series is ascended. Many of the notes shown in Fig. 1.12 are
members of a diatonic C major scale, but the 7th, 11th, 13th and 14th are not close
to any of the pitches on a piano keyboard. The ‘three-quarter flat’ sign on the 7th
harmonic is used here to indicate that the note is significantly flatter than B 4; in fact
it is 231 cents below C5. Similarly the ‘quarter sharp’ sign on the 11th harmonic is
used as a reminder that this note is slightly sharper than F4 (in fact, 151 cents below
G5), while the ‘quarter flat’ on the 13th harmonic indicates that it is slightly flatter
than A4 (in fact, 139 cents above G5).
1 The Musician’s Experience of Brass Instruments
Fig. 1.11 International pitch notation
Fig. 1.12 The pitches of the first 16 members of a harmonic series with fundamental C2
1.2.2 Natural Notes and Harmonics: The Musician’s View
When a trumpet is sounded without operating any valves, the player finds that a
number of notes at different pitches can be easily obtained by varying the lip tension
and blowing pressure. These notes are often referred to by musicians as ‘harmonics’.
Underlying this description is the idea of a harmonic series of frequencies, each
member of which is an integer multiple of the first member (sometimes called the
‘fundamental’). For example, the first few members of a harmonic series with a
fundamental of 110 Hz are 110, 220, 330, 440 Hz, etc.
Figure 1.12 shows the pitches of the first 16 members of a harmonic series
with fundamental 65.4 Hz (pitch C2). Although the difference in frequency between
successive members of the series remains constant at 65.4 Hz, the pitch intervals
become smaller as the series is ascended. Many of the notes shown in Fig. 1.12 are
members of a diatonic C major scale, but the 7th, 11th, 13th and 14th are not close
to any of the pitches on a piano keyboard. The ‘three-quarter flat’ sign on the 7th
harmonic is used here to indicate that the note is significantly flatter than B 4; in fact
it is 231 cents below C5. Similarly the ‘quarter sharp’ sign on the 11th harmonic is
used as a reminder that this note is slightly sharper than F4 (in fact, 151 cents below
G5), while the ‘quarter flat’ on the 13th harmonic indicates that it is slightly flatter
than A4 (in fact, 139 cents above G5).