is a possibility of keeping them in tune I do not like to find any organ without Oboe and Clarionet, even if it have only eighteen or twenty stops. (See Reed Stops.) The combination of Oboe with 8-ft. Wienerflöte and 4-ft. Flauto Traverso produces a charming effect, coupled with Flauto Dolce or Bourdon on the first manual, with Sub-Bass and Harmonica Bass, or the latter only, as a foundation. (See Combinations of Stops.)

This stop is on every organ itself to the Diapasons in The first Octave must be

Octave, Prestant, Diapason. without exception, and adapts character, intonation, and size. half as large as the largest Diapason, the second Octave must be half as large as the first Octave, and so forth.* A 16-ft. Principal, therefore, requires for the completeness of arrangement the 8-ft., 4-ft., 2-ft., but seldom 1-ft. Octave. As 2-ft. and 1-ft. tone it is often called Super-Octave. An 8-ft. Octave Bass (and, if possible, a 4-ft. Octave Bass for the performance, for example, of Bach's trios, with a cantus firmus on the pedal) is therefore necessary to the 16-ft. Principal Bass (as pedal stop). The Octave stops are sometimes called Prestants (from the Latin, præstare), when placed in the front (like the corresponding Principals). The Octave stops serve to strengthen the first harmonic, and therefore give more energy and clearness to the larger and deeper Principals. In very small organs, where Mixtures cannot be afforded, bright Octaves are absolutely necessary for the clearness of the stop. Where funds will allow, the 2-ft. Octave should never be missing in any but the smallest organs, it being a support to the Mixture stops,

*The calculations as to measurement are, it is true, mathematically not absolutely correct (compare Melde's "Acoustics," 1883, p. 277), but may be accepted as such in the technique of organ-building.

although already contained in the latter. (See Mixture and Flautino.)

The 4-ft. Octave on the Great manual is one of the most important of all organ stops, and is rightly termed in England the 4-ft. Principal (see Diapason), which it in reality is. This stop is generally used as the starting-point for tempering the organ. An alteration in the cycle of fifths must be made in such a manner that the twelfth fifth becomes identical with the foundation tone, or with one of its octaves; which result is obtained by tuning each. fifth a trifle flat. By these slight deviations from perfect attunement, beats (or pulsations of sound) are created, and hence the term described in German as "Temperament with equal beats," commonly known as "Equal temperament." The fifth is first correctly attuned, and then flattened till it gives a slow pulsation. (See Töpfer, vol. i. p. 827 and the following, on Temperament, and on Heinrich Scheibler's mathematical tuning, according to differences of vibration.)

By presupposing the Paris pitch, adapted by the Conference for deciding pitch at Vienna, the a', which is mentioned in every organ contract, makes eight hundred and seventy vibrations per second at 12° Reaumur (15° Celsius = 59° Fahrenheit). Compare Blaserna's "Sound," p. 87.

By taking as basis C (the so-called physicists' C, suggested by Sauveur, adopted later on by Chladni), of 512 simple or (French) half-vibrations (explanation follows), to which a tuning-fork, a', of 853 vibrations would correspond, the following numeric proportions, derived from the multiples of 2, are obtained :-32-ft. C with 32; 16-ft. C with 64; 8-ft. C with 128; 4-ft. C with 256; 2-ft. C with 512; and lastly-ft. C, the highest C on the organ having

16,000 half-vibrations per second (ex. Riga). Compare Du Hamel's "Organ-Builder," vol. iii. p. 137.

This is the proper place to mention the very interesting way in which one has succeeded, by means of the Double Siren (invented by Seebeck, improved upon by Cagniard de la Tour and Dove, and in its present form constructed by the great physiologist and physicist, Helmholtz), in determining with mathematical exactness the number of vibrations per second of a chord, an organ pipe, or a human voice. Long before there was anything known of vibrations and their calculations, Pythagoras (580-500 B.C.) had discovered that

if

you divide a string by a bridge in such a way that the two parts produce consonants, they must be divided as 1 to 6. If the string be divided so that two-thirds of the string remain on the right, and one-third on the left, this proportion of length-1 to 2-gives the interval of an octave; just as the proportion 2 to 3 gives the fifth, 3 to 4 the fourth, 4 to 5 the major third, and 5 to 6 the minor third. (The proportions of the inversions are obtained by doubling the smaller figure of the original interval.)

It was not until much later that it was discovered (Mersenne), from the laws regulating the movements of strings, that the simple proportions of length in strings apply in an equal manner to the number of vibrations of tones; therefore to the intervals of tone on all musical instruments, and also to that immediately under our notice, the organ. I have mentioned by way of example the simple relative vibrational numbers of the various octaves founded on C. Excellent illustrations, furnished with correspondingly clear explanatory text, of Helmholtz's Double Siren, to which we owe such exceedingly important results in physical acoustics, are found in Helmholtz's

"Sensations of Tone," part ii., chap. viii., p. 242; and in Tyndall's "Lectures on Sound," vol. ii. p. 91. I recommend the latter to my English readers, as the best work on this subject in the English language. Compare the chapter on Reed Stops and Sirens in Melde's "Acoustics," sect. 94, and in Blaserna's "Theory of Sound,” p. 120.

In illustration of the above-mentioned vibrational numbers, that for instance of 870 for a', I must add that, according to Tyndall, English and German physicists call a vibration a complete oscillation of the vibrating body, the wave of which bends the drum of the ear first inwards and then outwards. A French physicist, on the other hand, calls a vibration a backward or a forward motion of the vibrating body in one direction only. We have therefore to distinguish between whole vibrations and half-vibrations ; and as the Paris pitch (adopted by the International Conference at Vienna) goes by the latter, I have given the numbers accordingly. The a', for instance, mentioned as having 870 (French) vibrations, would have 435 complete German vibrations; the 32-ft. C would have 32 (French) vibrations, but only 16 complete German ones.

Octave Bass. See Flute Bass.

Octave Coupler engages the higher octave of the stop drawn on the manual (specimen: Petrikirche, Hamburg).

Ophicleide. An 8-ft. stop. This name, which at the first glance appears rather far fetched, is simply derived from the orchestral instrument Serpent (Greek opio, the snake; hence the name), which stop is still called Ophicleide in France. It is a reed stop, frequently found on the Great manual, as well as on the Swell, in large new organs (Riga, Boston). Its intonation is like that of the Clarionet, and its degree of strength is proportionate to the manual on

which it stands. An Ophicleide occurs as pedal stop of 16-ft. tone in Canterbury Cathedral, and in the organ at Garden City, U.S.A.

P.

Pasteboard as material for pipes. See Reed Stops.
Pedal Swell. See Crescendo.

Physharmonica is a very soft 8-ft. free reed stop, in which the metal tongue, instead of striking on the edge of the groove, vibrates freely within the groove. It is placed in a box, and has no real tube. If the Physharmonica has an appropriate swell, the most wonderful effects can be produced with it. It is arranged as 8-ft. and 16-ft. stop, with bells, in the Münster at Freiburg, Switzerland. (See Reed Stops.) In the cathedral organ at Magdeburg, there is an 8-ft. Harmonium, identical with the Physharmonica here described (Palme). A well-known effect is obtained by combining a good 4-ft. Flauto Traverso with an 8-ft. Flauto Dolce, accompanied by a Physharmonica with a tasteful Crescendo and Decrescendo. (See Combinations of Stops.)

Piccolo. See Flauto Piccolo.

Piffaro. A bright 2-rank flute of 4-ft. and 2-ft. tone.

Pneumatic Action. The pneumatic lever—that is, a lever set in motion by air-is a mechanical mediator between the pressure on the keys and the resistance of the trackers and pallets. In a box filled with air and hermetically closed, there are as many little bellows connected with the trackers as there are keys on the manual, and the finger has only