Harmonium acoustics

The acoustical effects described below are a result of the free-reed mechanism. Therefore, they are essentially identical for the Western and Indian harmoniums and the reed organ.

[edit]History of acoustics

In 1875, Hermann von Helmholtz published his seminal book, On the Sensations of Tone, in which he used the harmonium extensively to test different tuning systems:^[6]

"Among musical instruments, the harmonium, on account of its uniformly sustained tone, the piercing character of its quality of tone, and its tolerably distinct combinational tones, is particularly sensitive to inaccuracies of intonation. And as its vibrators also admit of a delicate and durable tuning, it appeared to me peculiarly suitable for experiments on a more perfect system of tones."^[7]

Using two manuals and two differently tuned stop sets, he was able to simultaneously compare Pythagorean to just and to equal-tempered tunings and observe the degrees of inharmonicityinherent to the different temperaments. He subdivided the octave to 28 tones, to be able to perform modulations of 12 minor and 17 major keys in just intonation without going into harshdissonance that is present with the standard octave division in this tuning.^[8] This arrangement was difficult to play on.^[9] Additional modified or novel instruments were used for experimental and educational purposes. Notably, Bosanquet's Generalized keyboard, constructed in 1873 for use with a 53-tone scale. In practice, that harmonium was constructed with 84 keys, for convenience offingering. Another famous reed organ that was evaluated was built by Poole.^[10]

Lord Rayleigh also used the harmonium to devise a method for indirectly measuring frequency accurately, using approximated known equal temperament intervals and their overtone beats.^[11] The harmonium had the advantage of providing clear overtones that enabled the reliable counting of beats by two listeners, one per note. However, Rayleigh acknowledged that maintaining constant pressure in the bellows is difficult and fluctuation of the pitch occurs rather frequently as a result.

[edit]Timbre

Reed organ frequencies depend on the blowing pressure; the fundamental frequency decreases with medium pressure compared to low pressure, but it increases again at high pressures by several hertz for the bass notes measured.^[12] American reed organ measurements showed a sinusoidal oscillation with sharp pressure transitions when the reed bends above and below its frame.^[13] The fundamental itself is nearly the mechanical resonance frequency of the reed.^[14] The overtones of the instrument are harmonics of the fundamental, rather than inharmonic,^[15]although a weak inharmonic overtone (6.27f) was reported too.^[16] The fundamental frequency comes from a traverse mode, whereas weaker higher traverse and torsional modes were measured too.^[17] Any torsional modes are excited because of a slight asymmetry in the reed's construction. During attack, it was shown that the reed produces most strongly the fundamental, along with a second transverse or torsional mode, which are transient.^[17]

Radiation patterns and coupling effects between the sound box and the reeds on the timbre appear not to have been studied to date.

[edit]Dynamics

The unusual reed-vibration physics have a direct effect on harmonium playing, as the control of its dynamics in playing is restricted and subtle. The free reed of the harmonium is riveted from a metal frame and is subjected to airflow, which is pumped from the bellows through the reservoir, pushing the reed and bringing it to self-exciting oscillation and to sound production in the direction of airflow.^[13] This particular aerodynamics is nonlinear in that the maximum displacement amplitude in which the reed can vibrate is limited by fluctuations in damping forces, so that the resultant sound pressure is rather constant.^[15] Additionally, there is a threshold pumping pressure, below which the reed vibration is minimal.^[16] Within those two thresholds, there is an exponential growthand decay in time of reed amplitudes .^[18]