It will be recalled that in the section ([10]) dealing with quality the statement was made that quality depends upon the shape of the vibrations; it should now be noted that it is the form of these vibrations that determines the nature and proportion of the overtones and hence the quality. Thus e.g., a tone that has too large a proportion of the fourth upper partial (i.e., the third of the chord) will be reedy and somewhat unpleasant. This is the case with many voices that are referred to as nasal. Too great a proportion of overtones is what causes certain pianos to sound "tin-panny." The tone produced by a good tuning-fork is almost entirely free from overtones: it has therefore no distinctive quality and is said to be a simple tone. The characteristic tone of the oboe on the other hand has many overtones and is therefore highly individualistic: this enables us to recognize the tone of the instrument even though we cannot see the player. Such a tone is said to be complex.
12. The mathematical ratio referred to on [page 134], if strictly carried out in tuning a keyboard instrument would cause the half-steps to vary slightly in size, and playing in certain keys (especially those having a number of sharps or flats in the signature) would therefore sound out of tune. There would be many other disadvantages in such a system, notably the inability to modulate freely to other keys, and since modulation is one of the predominant and most striking characteristics of modern music, this would constitute a serious barrier to advances in composition. To obviate these disadvantages a system of equal temperament was invented and has been in universal use since the time of Bach (1685-1750) who was the first prominent composer to use it extensively. Equal temperament means simply dividing the octave into twelve equal parts, thus causing all scales (as played on keyboard instruments at least) to sound exactly alike.
To show the practicability of equal temperament Bach wrote a series of 48 preludes and fugues, two in each major and two in each minor key. He called the collection "The Well-tempered Clavichord."
13. Various standards of pitch have existed at different times in the last two centuries, and even now there is no absolute uniformity although conditions are much better than they were even twenty-five years ago. Scientists use what is known as the "scientific standard" (sometimes called the "philosophic standard"), viz., 256 double vibrations for "middle C." This pitch is not in actual use for musical purposes, but is retained for theoretical purposes because of its convenience of computation (being a power of 2). In 1885 a conference of musicians at Vienna ratified the pitch giving Middle C 261 vibrations, this having been adopted by the French as their official pitch some 26 years before. In 1891 a convention of piano manufacturers at Philadelphia adopted this same pitch for the United States, and it has been in practically universal use ever since. This pitch (giving Middle C 261 vibrations) is known as "International Pitch."
Concert pitch is slightly higher than International, the difference between the two varying somewhat, but being almost always less than one-half step. This higher pitch is still often used by bands and sometimes by orchestras to give greater brilliancy to the wind instruments.
References
Lavignac—Music and Musicians, pp. 1-66.
Broadhouse—The Student's Helmholz.
Helmholtz—Sensations of Tone.
Hamilton—Sound and its Relation to Music.