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Lesson 04:
INTONATION SOUND WAVE FOR THE PIANO Seated, at the piano, strike an octave somewhere about the centre of the keyboard. The two notes should be struck exactly together - not one after the other - and held down until the sound has died away. If the octave is not quite true - and there are generally one or two on most pianos which are not - by listening intently the ear can be trained to detect a distinct wave or beat. The string of a musical instrument vibrates not only throughout its entire length, but also in equal or aliquot parts, each part producing a different note which is called a harmonic. The fundamental note is strongest, and the higher the harmonics are, the weaker they become. These harmonics are absolutely essential to a musical note - the more there are in a musical sound the more brilliant is the tone. The difference between sound and noise is that in the latter there are no harmonics. These harmonics are also called 'upper partials' or 'overtones', and if an octave is not quite correct some of these upper partials clash and make beats. If the octave is much out of tune, the dissimilar sounds will produce a harsh and jarring effect. If not very much out, by listening intently (and holding both notes down) a number of strong and rapid pulsations or beats will be heard. If the octave is only slightly out of tune, mere undulations or waves are audible. If in perfect tune a steady and continuous note will be heard with no waves or beats. The interval of an octave is divided into 12 semitones - the fifth having 7 semitones and the third 4 semitones. The fifth that is produced in Nature's scale of sounds and the fifth of 7 semitones on the piano are not exactly the same, the difference being .02 of a semitone. Nature's third is .14 less than the third on the piano. The fifth on the piano, therefore, must be slightly flattened and the third slightly sharpened. This alteration from Nature's intervals is termed 'Equal Temperament' or the 'Tempered Scale'. As before said, a musical sound is not a simple tone, but one comprising several tones. If the note C on the piano be struck and held down the fundamental tone will first be heard and then, very faintly, other notes or upper partials, as indicated here:-
The notes numbered 2 and 4, being octaves of a fundamental note cannot be detected by the unaided ear, but numbers 3, 5 and 6 can easily be heard. All these upper partials are faintly sounded with the fundamental note, and it is the presence of these which imparts the brilliancy to a musical note. If the student's piano is absolutely in tune there will be no waves or beats when an octave is played, but if, as is often the case, an octave is not quite in tune a distinct wave or beat is audible, and the more the notes are out of tune the quicker will be the beat. On the contrary, on a piano which is in perfect tune, beats between the fifths are present. As explained before, Nature's fifth and the fifth of 7 semi-tones on the piano do not quite agree, and the difference is indicated by the waves or beats. A tuner has to tune the fifths about two beats per second flatter than the perfect, or Nature's, fifth. This also applies to the third with this difference, that it must be slightly sharpened instead of flattened; Nature's third is 3.86 semitones as against the 4 semitones on the piano. It would be impossible to tune a piano by judging the pitch as a violinist does. The sound wave system is the method used by the piano-tuner. The student may find that he is unable to detect these waves or beats at the outset, but a little practice on the lines indicated, and also in attempting to detect all the upper partials enumerated above, will develop a fine and keen ear for pitch - for the lack of which many a good instrumentalist and singer remains in obscurity.
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