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

512 18. Music and Musical InstrumentsFigure 18.3. Three symbols used to indicate the C, or movable, clef.Figure 18.4. The positions of the C-clef for the soprano, alto, and tenor clefs.Figure 18.5. Sharp, flat, and natural designations: the sharp raises a pitch by a semitone,the flat lowers a pitch by a semitone, and the natural nullifies a sharp or flat to restore anote to normal.A note can be moved up in its pitch a half step or semitone; this is labeled asharp. The sharp is designated by the natural note preceded by the sign, as shownin Figure 18.5. A note can also be moved down a semitone, thus rendering that notea flat with the symbol , which is also shown in Figure 18.5. A natural designationnullifies a sharp or a flat, returning the note to normal. A note may be movedup by a whole step by a double sharp designation or ×. A note may be moveddown a whole note by a double flat . A standard system for the identificationof tones used in music is given in line 1 of Figure 18.6 (Young, 1939). The otherseven lines represent the various systems for identifying the musical tones withoutthe benefit of using the staff, but the system represented by the first line is themost logical one to use and understand. The reference standard frequency C 0 is16.352 Hz, which just about constitutes the lowest frequency that a human ear candetect. It is customary to consider C as the point to begin counting whole octaves.Figure 18.7 displays the frequencies of the notes in equally tempered scale in thekey of C from 16 Hz to 16 kHz.