ABSTRACT
The representation of musical pitch can be confusing because a number of different notation systems are in use. In this book the system which uses A4 to represent the A above middle C has been adopted. The number changes between the notes B and C, and capital letters are always used for the names of the notes. Thus middle C is C4, the B immediately below it is B3, etc. The bottom note on an 88-note piano keyboard is therefore A0 since it is the fourth A below middle C, and the top note on an 88-note piano keyboard is C8. (This notation system is shown for reference against a keyboard later in the chapter in Figure 3.21 .)
3.1.1 Musical notes and their fundamental frequency When we listen to a note played on a musical instrument and we perceive it as having a clear unambiguous musical pitch, this is because that instrument produces an acoustic pressure wave which repeats regularly. For example, consider the acoustic pressure waveforms recorded by means of a microphone and shown in Figure 3.1 for A4 played on four orchestral instruments: violin, trumpet, fl ute and oboe. Notice that in each case, the waveshape repeats regularly, or the waveform is “ periodic ” (see Chapter 1). Each section that repeats is known as a “ cycle ” and the time for which each cycle lasts is known as the “ fundamental period ” or “ period ” of the waveform. The number of cycles which occur in one second gives the fundamental frequency of the note in hertz (or Hz). The fundamental frequency is often notated as “ f 0 ” , pronounced “ F zero ” or “ F nought ” , a practice which will be used throughout the rest of this book. Thus f 0 of any waveform can be found from its period as:
( in Hz)
(period in seconds) f0
(3.1)
and the period from a known f 0 as:
(period in seconds)
in Hz
0f (3.2)
For the violin note shown in Figure 3.1 , the f 0 equivalent to any cycle can be found by measuring the period of that cycle from the waveform plot from which the f 0 can be calculated. The period is measured from any point in one cycle to the point in the next (or last) cycle where it repeats, for example a positive peak, a negative peak or a point where it crosses the zero amplitude line. The distance marked “ T ” for the violen in the fi gure shows where the period
made in the laboratory to give the period as 2.27 ms. Using Equation 3.1:
1 2 27
2 27 10 440 5
. ( . ) .
