MUSIC record where the voice has never acquired the pitch characteristic of manhood ; thus, M. Du- pont, who often sings at the celebration of high mass in Paris, has a remarkably fine soprano voice, yet he is 36 years old (1874), and is the father of several children. In music we con- sider the ratios of the numbers of vibrations of definite sounds more than the absolute num- ber of the vibrations, or pitch, of these sounds. From the most ancient times it has been known that the most harmonious concords are pro- duced by means of the simultaneous sounding of strings whose lengths bear to each other simple ratios. Pythagoras, who probably de- rived the fact from the Egyptians, says that when the ratio of the lengths of the strings was as 1 : 2, the grave note sounded in unison with its octave, while the ratio 2 : 3 gave the quint, and 3 : 4 gave the quart. We now know that the numbers of vibrations of similar strings are inversely as their lengths, so that the existence of the above consonant intervals depends alone on the ratio of the vibrations of the strings, and not on the absolute number of vibrations of the fundamental note of the chord. (See HARMONY.) When we double the number of vibrations corresponding to a note, we obtain the octave of this note, and the sen- sation caused by this higher octave seems to repeat that which corresponded to the lower. This interval of the octave, which includes all the notes of any musical system, is established by our physiological constitution, and was de- termined long before it was known that to obtain the octave of a note we had to double the number of its vibrations. Modern science has shown that the following musical conso- nances are only obtained when their constitu- ent notes have the following vibration ratios : octave, 1:2; fifth, 2:3; fourth, 3:4; major third, 4:5; minor third, 5:6; major sixth, 3:5; minor sixth, 5 : 8. Within the compass of the octave are seven distinct steps of pitch, constituting the gamut. We here give the names of the notes of the natural gamut in English and German, and in Italian and French notation. Under these names we give the relative numbers of their vibrations in whole numbers and in fractions ; and in the succeeding line are the intervals between the notes of the gamut : j C DE F . G A B C (utordo re mi fa sol la si do Batio of vibra- tions. 1 24 1 Intervals be- ) tween succes- V -|. eive notes. 27: 30 t : * V 1 32 : 36 : 40 fV|:| 45 : 48 I The gamut does not suppose a knowledge of the absolute height of the notes ; it only fixes the ratios. The first note, or tonic, can have any pitch ; but once fixed upon, all the others must follow in the ratios of the above numbers ; thus, if makes 240 vibrations, then D in the same time must give 270, E 300, F 320, and so on. One gamut is continued by a second, formed by simply doubling the numbers of vi- brations constituting the first, and another by doubling the vibrations of the second, and so on. The ratios between the successive notes of the gamut and the first note, or tonic, are denominated their musical intervals. In the following table we give the names of the in- tervals preceded by the names of the notes. These intervals are designated by the position of the notes in the gamut : C: C:D C:E C:F C:G 0: A 0:B 0: C 3 C:D 3 0:E 3 0:F 2 C: G a Unison 1: 1 Second 8: 9 Third 4:5 Fourth 3:4 Fifth 2: 3 Sixth 3:5 Seventh 8: 15 Octave 1 : 2 Ninth 4: 9 Tenth 2 : 5 Eleventh 3: 8 Twelfth 1 : 3 Double octave 1 :4 Seventeenth 1 :5 &c. &c. C:C 3 C:E 8 &c. The first six notes received their present Italian names from the Benedictine Guido Aretino in 1026. They are the first syllables of the words taken from the following stanza of the hymn to St. John the Baptist : UT queant laxis .RjEfconare fibris J/7ra gestorum FAmull tuorum, SOL& polluti Z-4bii reatum, Sancte Johannes. The air to which this hymn is now sung at Rome on St. John Baptist's day is altogether different from that used by Guido, for in an- cient times the six syllables were sung to the notes which these syllables designated. The word si, derived from the fourth line (S and I), was first used by Francois Lemaire in 1684 to designate the seventh note of the gamut. The use of these words in solmization caused the Italians to change the ut into do. These names for the notes did not spread very rapidly, for during the time of Jean de Muris, in the 14th century, they still sang at Paris the syllables pro, to, no, do, tu, a; but finally Guide's names prevailed, except in Germany and Eng- land, where the notes are generally designated by the letters 0, D, E, F, G, A, B (or H). The origin of the latter nomenclature is as follows : Before the 6th century, certainly during .the time of Gregory the Great, they formed a se- ries of gamuts corresponding to the ordinary range of the notes of the human voice, and of the principal musical instruments then in use. The notes were designated by the first seven
