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2.2 Pitch and the naming of notes
When we hear a musical instrument sound a note, we have a general sense of its pitch. For example, we know that the piccolo sounds relatively high frequency notes and the tuba sounds relatively low frequency notes. The names associated with these notes -- "A," "C#", etc. -- are determined solely by the pitch.
The most widely accepted naming convention for notes, in place since the mid-19th century, uses the following method to assign note names to specific frequencies. The frequency of 440 hertz is assigned the note A. This is the note you hear from the oboe when the orchestra is tuning up. You sound this note on a piano by striking the 40th key from the right, counting both black and white keys. There are thirteen named notes between 440 hertz and 880 hertz -- counting both boundary frequencies. These notes are A, A#, B, C, C#, D, D#, E, F, F#, G, G#, A -- where the symbol # is read "sharp." The ratio of the frequencies of any two successive notes in this list is approximately the same, i.e. the frequencies form a geometric sequence.
Thus, if you start at the 440 hertz key on the piano (40th key from the right) and strike it along with the next 12 keys to the right in order, you will play these notes. The first and last notes in this sequence have the same name -- "A." The same naming pattern applies to the notes between 880 hertz and 1760 hertz, and so on up and down the range of audible frequencies.
Thus, for any two successive notes with the same name, the frequency of the higher note will be twice the frequency of the lower note. It is said to be one octave above the original. (When you sing the do-re-mi scale, the do at the beginning and the do at the end are one octave apart.) A full-size piano has 88 keys and hence spans a little more than 7 octaves. The highest A note on the piano (third white key from the right end) has a frequency of 3520 hertz.
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| modules at math.duke.edu | Copyright CCP and the author(s), 1998 |
