What it shows:

Demonstrate musical intervals, the relation of pitch to frequency, and autocorrelation in psycho-acoustics.

How it works:

A 25 cm diameter metal disk has a number of concentric rows of regularly spaced holes. When rotated at a uniform speed while blowing air at a row of holes, a musical note is produced by the sequence of regular puffs of air issuing from successive holes. The frequency is determined by the speed of rotation and the known number of holes.

The numbers of holes in the successive rows are 24, 27, 30, 32, 36, 40, 45, and 48 allowing for a complete octave to be played in the so-called Scientific or Just Scale (a.k.a. Diatonic Scale). Although the pitches emitted by all rows rise with increase in speed of rotation, the musical intervals between them remain unchanged. For example, rows 36 and 24 always produce a perfect 5th since their ratio is 3/2. Rows 30 and 24 always produce a major third (which is a ratio of 5/4 in the Just Scale). Chords may be played by blowing through more than one row of holes at a time.

A second disk has four rows of holes numbering 24, 30, 36, and 48 giving the root, major third, perfect fifth, and octave, and thus producing a major chord if played together. There is an additional fifth row, also with 24 holes in the row. What makes this row special is that the 24 holes are grouped into 8 groups of 3 holes. The grouping is subtle and not immediately obvious by visual inspection. However, the pitch you hear from this row is quite obvious — it is 2 octaves lower than the other row with 24 holes!

A third disk was fabricated to replicate one described by F.W. Opelt in his book, Allegemeine Theorie der Musik (Leipzig, 1852). The following illustration is copied from Opelt's book.

The disk has seven rows of holes labeled G (grundton or root) with 8 holes, T (terz or major 3rd) with 10 holes, Q (quinte or perfect 5th) with 12 holes, O (octave) with 16 holes. The outermost row, labeled D, consists of all the holes that make up G, T, Q, and O, and is meant to sound like the four rows together. It does, although it does not sound as rich -- it sounds a little "tinny." The two innermost rows are labeled Z and R.  Z is interesting in that it is comprised of 16 holes but does not sound like the octave, which also has 16 holes. This is because the holes are spaced in groups of three followed by 1. It sounds very much like the perfect 5th, but much "richer" and fuller in sound. An autocorrelation of row Z shows a strong correlation every 30˚, which is consistent with the 5th whose holes are equally spaced every 30˚ and an equally strong correlation every 60˚. The latter would correspond to a "subharmonic" and makes sense that that would make it sound "richer." It's interesting to compare and contrast what you hear with this row and the fifth row of the second disk (described in previous paragraph). Finally, row R consists of 10 holes spaced every 37˚, leaving 26˚ spacing between the last and first hole in the row. Paraphrasing Opelt's description on page 35, he posits that one should still hear a distinct tone, notwithstanding the odd spacing between the last and first hole in the row. An autocorrelation shows a strong correlation every 37˚ and the row indeed sounds close to the major 3rd (which has holes every 36˚) but a little "flat."

Setting it up:

A plastic 10 mL pipette attached to a length of Tygon tubing and a large nitrogen cylinder with regulator serves well for a source of air. You can also use your mouth as a source of air if the nitrogen cylinder is not handy. Two pipettes can be used at the same time with the Y-connector. The second disk with five rows of holes has a special nozzle that allows you to blow in all five rows selectively or simultaneously. The spacing of rows on the Opelt disk was made so as to also be compatible with this nozzle.

Comments:

Helmholtz was the first to design a siren for research purposes and it was subsequently produced by König for sale, largely for demonstration purposes. It was the first instrument to give absolutely precise ratios of frequency and remained the only really precise one until the advent of digital synthesis.