PITCH, MUSICAL. The pitch of a musical sound is precisely defined by a vibration number recording the frequency of the pulsations of a tense string, a column of air or other vi brator, in a second of time. In Great Britain and America the complete vibration to and fro is taken as the unit ; elsewhere the vibration in one direction only. The only official standard is the French, dating from 1859, preserved by a tuning-fork vibrating 870.9 (double vib. 435.45) at a temperature of 15° Centigrade (59° Fahr.) in a second. The vibration number stated in the edict establishing, in the year named, the diapason normal is 870 (435)• Vibrations increase in rapidity as a note rises and decrease as it falls. Any note may be a pitch note. For orchestras custom has settled upon a' in the treble clef, for organs and pianos in Great Britain c", and for modern brass instruments b flat'.
We are not without a clue to the pitch usual in the classic Greek and Alexandrian ages : the vocal octave to which the lyre was adapted was noted as from e to e'. As in choruses barytone and low tenor singers always prevail, d–d', at French or at medium pitch, would really be the Greek singing octave ; we may therefore regard it as a tone lower than that to which we are accustomed. But to sing the lower Greek modes in or near the vocal octave it was necessary to transpose a fourth upwards, which is effected in modern notation by a flat placed upon the B line of the staff; thus modulating from our major key of C to that of F. This transposition has had, as we shall see, much to do with the history of our subject, ultimately influencing the ecclesiastical chant and lasting until the 17th century of our era. It does not appear from any evidence that the keyboards— when there were more than one—of the early organs were ar ranged for transposition, but it is certain that the Flemish harpsi chords to 1650 were made with double keyboards to accommodate it (see Hipkins's History of the Pianoforte, 1897). But a positive identity of pitch cannot be claimed for any period of time, and certainly not for the early organs ; the foot-rule of the organ builder, which had to do with the lengths of the pipes, and which varied in every country and province, could easily cause a differ ence of a semitone. Scale and wind-pressure are also important factors. But with all these often opposed conditions, we find less variation than might be expected, the main and really important divergence being due to the necessity of transposition, which added a very high pitch to the primarily convenient low one.
The first to attempt to define pitch would seem to have been Arnold Schlick (Musica ausgeteutscht and ausgezogen, Heidel berg, 1511), who gives a measure, a line of 4 Rhenish inches, which, he says, multiplied sixteen times, should be the lowest F of a small organ. He gives no diameter or wind-pressure. Dr. A.
J. Ellis used this indication to have an organ pipe made which with one-sixteenth diameter and a wind-pressure of 3 at one fourth Schlick's length, gave f' 301.6, from which he derived a just major third of a' 377, which would compare very well with an old Greek a'. Schlick goes on to say the organ is to be suited to the choir and properly tuned for singing, that the singer may not be forced to sing too high or too low and the organist have to play chromatics, which is not handy for every one. Further, he says pitch cannot be exactly defined, because voices vary; he nevertheless gives the measure above mentioned for the low F, but if a larger organ is built to include the still lower C, then this C must be of the same measurement, the reason being that a greater part of church music ends in "grambus," a word under stood by Schlick's editor to mean the transposition of a fourth. The larger high-pitch organ will therefore be at a' 502.6.
The Halberstadt organ was, according to Praetorius, built in 1361, and repaired or rebuilt 1495. He gives the longest pipe of this organ, B natural, as 31 Brunswick feet, and the circum ference aft. He further tells us this pitch was a tone, nearly a tone and a half, higher than a suitable church pitch (Chor ton), for which he gives a diagram. Dr. Ellis had pipes (now preserved in the Royal Institution, London) made to repro duce both these pitches at 3/in. wind-pressure. The Halberstadt pitch was found to be a' 505.8; the Chorton, 424.2. Ellis used mean-tone temperament in calculating this lower pitch ; but as he used just intonation for the Halberstadt, it seems preferable to substitute it for the Chorton, thus reducing it to a' 422.8. Prae torius's Cammerton, or chamber pitch, formulated in his diagrams for voices and instruments, is, he says, a whole tone higher; equivalent, therefore, to a' 475.65. Nearly all the German organs were tuned to this higher pitch. The lower vibration number is justified by the three divisions of the male voice, bass, tenor and alto, as given by Praetorius, whose Cammerton very closely corresponds with Bernhardt Schmidt's Durham organ, 1663 1668, the original pitch of which has been proved to have been a' 474.1. The Halberstadt pitch is nearly a semitone higher, which again agrees with the statement of Praetorius, and also Schlick's high C organ. Yet it would seem that there had been a still higher pitch used in the old ecclesiastical music. In one pas.