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Musical Pitch

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The pitch of a musical sound is aurally defined by its absolute position in the scale and by its relative position with regard to other musical sounds. It is precisely defined by a vibration number recording the frequency of the pulsations of a tense string, a column of air, or other vibrator, in a second of time. In Great Britain and America the complete vibration to and fro (swing both ways of a pendulum) is taken as the unit; elsewhere the vibration in one direction only (swing one way of the pendulum). 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 the Diapason Normal is 870 (435), which for comparison will be here adhered to. The natural basis for a standard musical pitch is the voice, particularly the male voice, which has been of greater importance historically. There is no reason to suppose the human voice has varied, during the period of which we have evidence, more than other physical attributes. The only difference to be reckoned with may be in recent tendencies of solo vocalists to sing for effect, and so to extend the compass of the voice upwards. Otherwise we may assume no disturbing alteration has taken place for more than 2000 years in its position and extent. 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 2 , 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 O. As in choruses baritone 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 (yEraj30Xii) 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 arranged for transposition, but it is certain that the Flemish harpsichords to 1650 were made with double keyboards to accommodate it (see Hipkins' 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 difference 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, Heidelberg, 1 511), who gives a measure, a line of 4s 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 34 in., 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 understood 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, about which so much has been written, was, according to Praetorius ( Syntagma musicum, Wolffenbi ttel, 1618), built in 1361, and repaired or rebuilt 1495. He gives the longest pipe of this organ, B natural, as 31 Brunswick feet, and the circumference 31 ft. He further tells us this pitch was a tone, nearly a tone and a half, higher than a suitable church pitch ( Chorton ), for which he gives a diagram. Dr Ellis had pipes (now preserved in the Royal Institution, London) made to reproduce both these pitches at 31 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. Praetor ius'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 in his time were tuned to this higher pitch. Ellis offered the suggestion of a much higher pitch for this Cammerton in his lecture "On the History of Musical Pitch," read before the Society of Arts, London ( Journ. Soc. Arts, March 5, 1880), but the present writer is unable to accept it. The lower vibration number is justified by due consideration of 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 by Professor Armes to have been a 1 474.1. 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 there had been a still higher pitch used in the old ecclesiastical music. Upon this interesting question Praetorius is confused and difficult to understand, but he never wavers about the transposition of a fourth. In one passage he distinctly says the old organ high pitch had been a whole tone above his Cammerton, with which we shall find his tertia minore combines to make the required interval. The term tertia minore, or inferiore, is used by Praetorius to describe a low pitch, often preferred in England and the Netherlands, in Italy and in some parts of Germany. An organist, instead of transposing a whole ton g down from the Cammerton, would for the tertia minore have to transpose a minor third. A corroboration of this pitch is found in A. Silbermann's great organ in Strasburg minster (1713-1716), the pitch of which, taken in 1880 and reduced to J9° Fahr. (as are all pitches in this article), is a' 393.2. An old organ at Versailles (1789) was very near this example, a' 395.8. Sir Frederick Gore Ouseley ( vide Ellis's lecture) regarded the French ton de chapelle as being about a minor third below the Diapason Normal, a' 435, and said that most of the untouched organs in the French cathedrals were at this low pitch. Strasburg was French territory in 1713, but Silbermann's organ is not quite a whole tone below. Ellis quotes an organ at Lille, a' 374.2, but no other instance of the very low Schlick pitch is recorded, although trial of the French cathedral organs might perhaps result in the finding of examples. Ellis gives Dom Bedos ( L'Art du facture d'orgues, Paris, 1766) as authority for a mean tone a' 376.6. To return to the tertia minore. Dr R. Smith, of Cambridge, in 1759, had the organ of Trinity College, built by Bernhardt Schmidt, lowered a whole tone, to reduce it to certain Roman pitch pipes made about 1720. His determinations of pitch by a weighted wire are not trustworthy; Ellis thinks they are not safe within four or five vibrations per second, but gives a mean pitch for this organ, when altered, of a' 395.2. St Michael's church at Hamburg, built as late as 1762 and unaltered in 1880, had a 17th-century pitch, a' 407.9. This is about a semitone below the Diapason Normal, and a just minor third lower than the St Jacobi organ in the same city (1688), measured by Herr Schmahl, a' 489.2. What was remarkable in this organ was that it had one stop which was an equal minor third lower, a' 411.4'. The difference of a minor third, or, as we shall see later, a whole tone, had replaced the earlier fourth. Sir Frederick Gore Ouseley's comparison of the church and chamber pitches of Orlando Gibbons ( vide Ellis's lecture) clearly shows the minor third in Great Britain in the first half of the 17th century. But the narrowing continued. Bernhardt Schmidt, better known in England as Father Smith, was invited about 1660 to build the organ for the Chapel Royal, Whitehall; two years later he built the organ in Durham Cathedral a' 474.1, difference a whole tone, and practically agreeing with the Cammerton of Praetorius. The Hampton Court organ of 1690 shows that Schmidt had further lowered his pitch a semitone, to a' 4417. What happened at Durham was that at some subsequent date the pipes were shifted up a semitone to bring the organ into conformity with this lower pitch, with which it is probable Schmidt's organs in St Paul's and the Temple, and also Trinity College, Cambridge, agreed. This lowering tendency towards the low church pitch, and the final adoption of the latter as a general mean pitch throughout the 18th century, was no doubt influenced by the introduction of the violin, which would not bear the high tension to which the lutes and viols had been strained. Harpsichords had long been preferred at the tertia minore. The Chorton of Praetorius, a l 4 22.8, is practically the same pitch as that of the fork the possession of which has been attributed to Handel, a' 422.5. It is a very fair mean between G. Silbermann's 18th-century Dresden pitch, a' 415, and the organs of Renatus Harris, a' 428.7. Stein tuned Mozart's piano to a fork a' 421.6, and the Broadwood pianos used at the London Philharmonic Society in its first concerts (1813) were tuned to a fork c 2 506.8, which gives a mean tone a' 423.7.According to Schindler (Niederrheinische Musik-Zeitung, 1855, Nos. 8 and 9) and the report of the French Commission, 1859, the rise in pitch began at the Congress of Vienna in 1816, the military bands being the cause. With the improvements in wind instruments this continued, as a more brilliant effect was gained. In 1823 Weber's Euryanthe is recorded as having been played in Vienna at a' 437' 5, and in 1834 Kreutzer's Nachtlager at a' 440. The measurements are doubtful, but the upward tendency is clear. Scheibler, by his simple and accurate tonometer, has recorded pitches in Vienna about 1834 from a1 433.9 to 440.2. About that time, or it may be a few years earlier, Sir George Smart established a fork for the Philharmonic Society, a' 433.2. Forks intended for this vibration number, stamped "Philharmonic," were sold as late as 1846. But about that year the performing pitch of the Society had reached 452.5. Sir Michael Costa was the conductor 1846-1854, and from his acceptance of that high pitch the fork became known as Costa's, and its inception was attributed to him, though on insufficient grounds. In 1874 a further rise in the fork to a' 454 was instigated by Sir Charles Halle. The British army is bound by His Majesty's Rules and Regulations to play at the Philharmonic pitch, and a fork tuned to a' 452.5 in 1890 is preserved as the standard for the Military Training School at Kneller Hall. But the Philharmonic Society adopted the Diapason Normal in 1896, and the military bands have not gone with it. In point of fact, they are gradually going higher, and the brass bands, which are so important in the North of England and in Wales, are not behind them.It was the irrepressible upward tendency that caused the French government in 1859, acting with the advice of Halevy, Meyerbeer, Auber, Ambroise Thomas and Rossini, to establish by law the Diapason Normal. Other countries have gradually followed, and, with few exceptions, the low pitch derived from the Diapason Normal may be said to prevail throughout the musical world. Great Britain has been the last to fall in, but the predominance of the low pitch, introduced at Covent Garden Opera since 1880, is assured. The proprietors of Queen's Hall, London, did much for it when they undertook the alteration, at great expense, of their large concert organ, which had only just been erected. In 1896 the Philharmonic Society decided upon a performing pitch, ostensibly at 68° Fahr., of a' 439; and in 1899 Messrs Broadwood made a successful effort to get this vibration number accepted by their competitors in Great Britain. The high pitch remains only where there are large concert organs not yet lowered, and with the military and brass bands.The consideration of temperature as affecting the use of a standard pitch was not attended to when the French government issued its ordonnance. The 15° Centigrade attached to the description of the standard fork in Paris was intended for the definition and verification of the fork only. The alteration of the fork due to heat is scarcely perceptible, but wind instruments, and particularly the organ, rise almost proportionately to the increase in temperature of the surrounding air, because sound travels at an enhanced rate as the temperature rises. The coefficient of this rise is equivalent to half a vibration (o.5) per degree Fahr. per second. D. J. Blaikley (Essay on Musical Pitch, Catalogue of the Royal Military Exhibition, Chelsea, 1890), and Victor Mahillon ( Catalogue descriptif et analytique du Musee, Bruxelles, troisieme volume, appendice, 1900) have recorded their experience of wind instruments under changes of temperature. The French Commission, in establishing the Diapason Normal, should have chosen a temperature of 20° C.There would then have been less disturbance owing to the breath of the players and heat of the theatres or concert-rooms. It would be a great advantage to get this higher grade generally adopted. It was proposed in the Stimm-Conferenz at Vienna in 1885, but not carried. Table III., showing orchestral pitches obtained in 1899, for the measurements of which the writer is responsible, prove how chimerical it is to hope for greater accuracy than is found between 435 and 440 vibrations a second for a', inasmuch as temperature must always be reckoned with.