THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

510 18. Music and Musical Instruments18.2 Musical NotationAs pointed out by Olson, music can be memorized and passed from one personto another by the direct conveyance of the sound, but this does not constitute asatisfactory, nor an efficient method of communicating music to performers andpreserving the music for future performances (Olson, 1967). Accordingly, musicalnotations were developed to use symbols on paper to denote frequency, duration,quality, intensity, and other tonal characteristics. A human can typically distinguish1400 discrete frequencies, but in the equally tempered musical scale, thereare only 120 discrete tones ranging from 16 Hz to 16,000 Hz. Pitch is an attributeof aural sensation, dependent on the frequency of the sound. Musical tones are assignedspecific values, allowing for specific frequency values, and leaving out the“in-between” values. A principal reason that we can identify a musical instrumentis that the musical instruments are essentially resonant instruments and thereforeresponse only to certain frequencies. These resonant frequencies are fixed andcannot be altered, except for certain instruments such as those members of theviolin family and the trombone. Moreover, when same notes are played on differentinstruments, the overtones differentiate one instrument from another. With therelatively small number of fundamental frequencies designated in Western music,matters are greatly simplified in designating the discrete frequency characteristicsof tones.In the five-line staff of Figure 18.1, the pitch of a tone is denoted by placingnotes, , , on the lines and in the spaces between the lines. The pitch rangeof a set of lines is designated by the clef ( or ) which is placed at the left ofthe staff. The most common clefs are the treble or G clef and the bass or F clef,both of which are shown in Figure 18.1. The notes are designated alphabeticallyfrom A to G. The interval in pitch between two notes with the same letter is theoctave. As explained earlier in this text, the two sounds separated by an octavehave a fundamental frequency ratio of 2. The pitch interval between adjacent notes(i.e., between a note on a line and a note in the adjacent space, as designated bysuccessive letters) is a whole tone in the equally tempered scale. Pitches that arehigher and below the staff are designated by notes written upon and between shortlines called leger lines, as shown in Figure 18.1. The number of leger lines canhypothetically be extended without limit. The sign 8va above the staff denotes thatall tones are to be played an octave higher than their placement and, conversely, thesign 8vs placed below the staff indicates that all tones are to be played an octavelower. This is shown in Figure 18.2.There is also another clef—the movable or C clef—which was meant to accommodatemusic instruments with extended range (e.g., the bassoon, cello, or viola).In older musical manuscripts there are C-clefs for the soprano, alto, and tenor parts,Figure 18.3 shows the three different symbols to indicate the C-clef. The C-clefis placed on the middle C line. The old C-clef positions for the soprano, alto, andtenor are given in Figure 18.4. The position of the C clef always corresponds tothe middle C.