In his treatise ([Cowell1930]) written in 1919 (but not published until 1930), Henry Cowell discusses the overtone series at length. He applies the overtone series to set up scales of metre, duration, and tempo, which are, in his treatment, the three elements that make up rhythm.
"It is difficult to find musical means to which overtones do not apply, or may not be applied, as they may be used to measure all relationships of steady pitch, no matter how subtle are the degrees of pitch chosen; and all rhythmical relationships can be derived from overtones, as will be shown. .." ([p. 20])
Cowell mentions "undertones", descending sequences of partials, what Stockhausen refers to as "subharmonic series of proportions". To Cowell, they arise naturally from properties of acoustics, and they are related to overtones, or ascending sequences of partials, in ways that parallel the relationship of "minor" intervals to "major" intervals. He is on a quest for "new musical resources", as is Stockhausen in his search for ways to parameterize and unify the microstructure and macrostructure of sound, but Cowell does not share Stockhausen's view that "modes", like this series of undertones, are inappropriate in his music.
Cowell sets up a scale based on tone-qualities (evidently referring specifically to the aspect of timbre dependent on the presence and relative amplitude of different harmonic overtones in a continuous tone). This characterization looks very much like the serial treatment of such a timbral parameter might look, except for the prominence of harmonic, instead of chromatic, qualities as his structural organizing principle:
"It will be seen that the problem of forming a related series of tone-qualities is the same as in other branches. A scale can be made by placing in the same group the tone-qualities in which overtones from the same proportion of the series are most prominent; thus a quality in which the first overtone is most evident might be number one in the scale; a quality in which the second overtone is most plainly heard might be number two, etc. A quality strongly posessing both the first and the second overtones would be a bridge from number one to number two in the scale, and might be classified as a `harmonic' quality, as it would be produced through a combination of sounds....
"If tone-qualities were arranged in order, and a notation found for them, it would be of assistance to composer and performer alike.... Tone-quality thus becomes one of the elements in the composition itself and ceases to be only a matter of performance.....Progress in the field of new or graduated tone-qualities in composition has been greatly hindered by lack of notation, as it has been justly felt that if music demanding new tonal values were set down in present notation, the desired effect would be likely to be entirely lost in the performance." ([p. 34])
Cowell is more systematic than Stockhausen in his definitions of terms that he uses. He defines duration, metre, and tempo as sub-divisions of a general "rhythm" category, and proceeds to develop the relationship of rhythm to sound-vibrations -- in Stockhausen's terms, the "sphere of duration"is considered in terms taken from the "sphere of pitch", over 35 years before Stockhausen's article.
"... one general idea will be dealt with -- namely, that of the relationship of rhythm to sound-vibration, and through this relationship and the application of overtone ratios, the building of ordered systems of harmony and counterpoint in rhythm, which have an exact relationship to tonal harmony and counterpoint.... In the discussion of musical rhythm in its elements, time, metre, and tempo, it will be seen that the problems here considered are not only related to, but based on, principles that are already familiar in the field of harmony and counterpoint -- that is, in the relation of tones to one another......" ([pp. 45 - 46])
Cowell constructs a chart showing that in one time interval, if a fundamental tone C = 16 cycles per second vibrates 16 times, the octave vibrates 32 times, the fifth 48 times, etc. Calling partial #1,2,4 by the note name "C", partial #3 "G", and partial #5 "E", he notes that the collection G, C, E (partial #'s 3,4,5) vibrate at 48, 64, 80 times in this interval, i.e. G vibrates 3 times, while C vibrates 4 times, and E vibrates 5 times, in one sub-unit of time.
This is simply stating the relationships of the frequencies of the partials to the frequency of the first partial, or fundamental. The number of vibrations in one fundamental cycle made by a given partial is just the number, in the overtone series, of that partial! i.e. partial #5, E, vibrates 5 times in the interval.
Then he extends this relationship to the sphere of rhythm as follows:
"If we anticipate for a moment what is to be said in regard to musical rhythm, and desire to represent graphically the result of playing simultaneously three parts which would equally divide a whole note into three, four, and five parts respectively, we should have a diagram of exactly similar form. The smaller units are the fractional notes that prefectly fill the measure. And the principle of beats that coincide, then separate, then coincide again, can be seen to be identical." ([p. 45])
Now he covers the three aspects of rhythm individually - time, metre, and tempo. He mentions that the fundamental unit of measuring musical time or duration is the whole note, and that it can be divided up by half, quarter, eight, sixteenth notes, etc., and also by combining these shorter units into so-called "figures".
Stockhausen, on the other hand, points out that this division of a largest fundamental durational unit into smaller and smaller partials is just one way of treating durations - Stockhausen also explores the multiplicaton of a smallest unit, yielding larger and larger partials, for example. We will see that Cowell also sets up such a scale when he treats metrical meter with the overtone series.
Cowell discusses the problem of notating the division of a whole note into three equal parts, into what we call a "triplet". We recall that Stockhausen began his construction of durational scales with similar questions about the inadequacy of traditional notation for duration:
"...there is no way of doing so except by the clumsy expedient of writing the figure 3 over three successive half-notes filling a measure. In other words the notes as written down have a certain time-value impossible under the circumstances, and the discrepancy is reconciled by explaining that in reality notes of a different time-value are intended. Were the use of such notes of rare occurrence, this method might be justifiable; since, however, these notes and others having a similar discrepenacy in time are very often used, should not an independent method of notation be found for them?" ([p. 50])
Cowell also makes the reverse connection, as Stockhausen does, namely that speeding up a periodic rhythmic figure by a sufficient amount will result in the perception of a continuous tone. He gives an example of taking two simultaneous melodies, one played twice as fast as the other, with the common underlying pulse indicated by the tapping of a stick,
"If now the taps were to be increased greatly in rapidity without changing the relative speed, it will be seen that when the taps for the first melody reach sixteen to the second, those for the second melody will be thirty-two to the second. In other words, the vibrations from the taps of one melody will give the musical tone C, while those of the other will give the tone C one octave higher. Time has been translated, as it were, into musical tone. Or, as has been shown above, a parallel can be drawn between the ratio of rhythmical beats and the ratio of musical tones by virtue of the common mathematical basis of both musical time and musical tone. The two times, in this view, might be said to be `in harmony', the simplest possible."
Electronic studio music had not been invented yet, although the Theremin was widely known before the publication of Cowell's book (Leon Theremin and Henry Cowell were acquaintances, as we shall see). But Cowell still managed to gain the insight about rhythmic impulses which can merge into an audio stream at fast enough rates, from observations of the steam-driven siren:
"There is a well-known acoustical instrument [Joscelyn Godwin's note points out that this is a siren] which produces a sound broken by silences. When the silences between the sound occur not too rapidly, the result is a rhythm. When the breaks between the sound are speeded, however, they produce a new pitch in themselves, which is regulated by the rapidity of the successive silences between the sounds."([p. 50])
Cowell has discovered harmonically-related layers of polyrhythm:
"Referring back to our chart, we find that the familiar interval of a fifth represents a vibration ratio of 2:3. Translating this into time, we might have a measure of three equal notes set over another in two. A slight complication is now added. Corresponding to the tone interval of a major third would be a time-ratio of five against four notes; the minor third would be represented by a ratio of six against five notes, and so on. If we were to combine melodies in two (or four) beats, three beats, and five beats to the measure, we should then have three parallel time-systems corresponding to the vibration speeds of a simple consonant harmony..... The conductor of such a trio, by giving one beat to a measure, could lead all the voices together; for the measure, no matter what time divisions it included, would begin and end at the same instant." ([p. 51])
He mentions more complicated variations, which would include units of the time-scheme that shift from one voice to another, and that the complete rhythmic harmony could shift at will, like a succession of different chords (the collection of interval-relationships) like in tonal harmony. (he has already discovered the "metric modulation" principle) Still further variations on polyrhythms would include sub-dividing the overall measure -- if a measure with three beats in it were sub-divided into halves, each half would take one and one-half beats. But this could be reconciled by going to a smaller sub-unit, i.e. one beat is now 2/6, so one and one-half is 3/6, in a matter which is "another application of the principle of the dotted note".
If eleven notes were to the measure and a "lower octave" was desired, that would make five and one-half beats to the measure, but this would be written using tied eleventh-notes, i.e. each of the five would be 2 11th's long, and the one-half would be 1-11th long.
"These finer rhythmical distinctions [i.e. 11th-notes, etc.] open up a new field for investigation. Not only do nearly all Oriental and primitive peoples use such shades of rhythm, but also our own virtuosi, who, instead of playing the notes just as written, often add subtle deviations of their own."([p. 55 ])
Cowell has also discovered the quantitative time variability of the human performer. The experiment he mentions here concerns multiple performers interpreting one constant passage of music, while Stockhausen proposes a different experiment involving the same performer interpreting differently-notated versions of the same passage, since presumably Stockhausen was already well aware of the variations that exist among different musicians:
"Professor Hornbusel, of Berlin [a note by Joscelyn Godwin suggests that this is a mis-spelling of Hornbostel, who apparently Cowell was expecting to study with in 1931, shortly after publication of the book], has made the experiment of recording the time-values of a passage, as actually played by a capable musician. He found that the lengths of notes as played were quite irregular; for example, the first of the first two eight-notes was almost twice as short as the second, while the quarter-note following was not twice as long as either of the eighth-notes."[p. 55 - Cowell's example #8 shows four 2/4 measures, with a pickup bar of 2 eighth notes, a bar of one quarter and 2 eights, another quarter and 2 eights, and a final ending of 2 eighths.]
We recall the disagreement among Stockhausen, Backus, and H. Davies over the difficulty of performing certain fragments of very precise, fast sub-divided time units, in which Backus cast aspersions on the calibre of Stockhausen's musicians. Here is Cowell's suggestion that performers learn cross-rhythms by simply practicing them a lot. Stockhausen's situation was even more difficult, because he was not referring to a steady stream of notes, which are easier to understand and practice systematically, than his fragmentary figures, which will presumably be different in each instance.
"An argument against the development of more diversified rhythms might be their difficulty of performance. It is true that the average performer finds cross-rhythms hard to play accurately; but how much time does the average performer spend in practising them? Cross-rhythms are difficult and must be familiar before proficiency can be obtained in performing them; but if even a few minutes a day are seriously devoted to mastering them, surprising results are obtained. Surely they are as well worth learning as the scales, which students sometimes practise hours a day for years. By experiment we have observed that such rhythms as five against six against eight or nine, and other combinations of three rhythms together, can be quite accurately performed by the devotion of about fifteen minutes a day for about six months. Some of the rhythms developed through the present acoustical investigation could not be played by any living performer; but these highly engrossing rhythmical complexities could easily be cut on a player-piano roll......" ([p.64])
Now we examine Cowell's call for a new rhythmical music instrument (eventually built by Theremin):
"It is highly probably that an instrument could be devised which would mechanically produce a rhythmic ratio, but which would be controlled by hand and would therefore not be over-mechanical. For example, suppose we could have a keyboard on which when C was struck; a rhythm of eight would be sounded; when D was struck, a rhythm of nine; when E was struck, a rhythm of ten. By playing the keys with the fingers, the human element of personal expression might be retained if desired. It is heartily proposed tht such an instrument to play the scale of time-values given at the end of this chapter be constructed. On such a keyboard one might make many variations, such as playing a rhythmic chord as an arpeggio, which would result in starting the rhythmical units canonically." ([p. 64])
Strictly speaking, this instrument produces different tempi on each key, in synchronized equal-length polyrythmic measures. Presumably notes in the given tempo would continue to sound repeatedly as long as one's finger held down the key for that tempo. The entire instrument would have to be tuned to a fundamental unit tempo, and all the keys would be fixed ratios measured from the fundamental.
Note that the scale Cowell proposes (rhythms of eight to a bar, of nine, ten, etc. and presumably he is just glossing over the accidentals in between C, D, and E!) is the same as the chromatic one that Stockhausen derived from division of a largest unit duration.
In our previous section, we listed this scale as Column 2 of Table 1, and we showed that it was equivalent to multiplying the largest unit by the reciprocal of the chromatic scale degree. Assuming that Cowell really means to set out keys in numerical order, so that key #1 plays 1 beat in a period, key #2 plays 2 beats in the same period, etc., we found that if the overall period had a duration of 1 second, that scale degree #n would have a duration of 1/n seconds; more generally, with a fundamental largest duration of M, the duration of scale degree N would be N/M.
Stockhausen, on the other hand, calls for two new musical instruments to be built. The first is a duration keyboard. Only one tone would be sounded for a single strike of a key. Instead of repeated notes at a given tempo, the single tone would sound for the given duration assigned to that key. The pitch of the note would vary according to how much pressure was brought to bear on the key.
Nowadays one could design instruments combining features of both Cowell's tempo instrument and Stockhausen's duration instrument. A single strike of a key could produce variable results according to the configuration. At one extreme setting, a keystroke could initiate an event of fixed duration as in Stockhausen's design. Variations could be available in which this single event could be subdivided according to various considerations of tempo, polyrythms, or additive rhythms (groups of events could be triggered according to various group-formation criteria). Or the event could be variable length, continuing to the release of the initiating key. A fixed tempo could be generated, as in Cowell's instrument, or other variations could be controlled by other variables such as pressure, location, and alternate actions.
With today's flexible sound modules and controllers such as Buchla's Thunder ([Buchla1990]), such instrumental setups are now possible to design and save as preset configurations, enabling the same basic hardware to support multiple instrument philosophies and layouts.
Stockhausen's call for a second instrument, which would be capable of continuously variable pitch and timbre, and continuously variable frequency bandwidth between white noise and definite pitch, is a little more tricky, but an approximation could still be set up on a Buchla Thunder with the right kind of software running on a computer that is listening to the MIDI output from the Thunder controller. Variable parameters of synthesis algorithms could be made available for continuous control with finger pressure or location on the various Thunder keys, if only the synthesis system was general-purpose enough to support such uses.
In Cowell's book, after his call for the tempo instrument, he considers metre, which he takes as "the result of rhythmically regular accent". He uses one unit, the quarter note, for reference, and considers different metres like "3/4 time", "4/4 time", "5/4 time" i.e. where the overall length of the measure is additive based on the number of units contained within (unlike the previous investigation of time where the overall length was constant and the ratio of the sub-divisions to the whole were what varied, i.e. half-notes, half-triplets, quarter notes, quarter triplets, eights, etc.). He also uses the 2/4 measure as a basis, since one could take his previous tone of C = 16 cps, transpose it down 3 octaves, and obtain 2 cps, or 2/4 metre where a measure takes up one second of duration...
In this system of metres, his overtone series gives the chart (from his [p. 68])
Serial Tone Intervals Metre on 2/4 Base Number (Read up) 6 G Minor third 12/4 (6/4,3/4,6/8) 5 E Major third 10/4 (10/8, 5/4) 4 C Fourth 8/4 (4/4, 2/4) 3 G Fifth 6/4 (6/8, 3/4) 2 C Octave 4/4 (4/8, 2/2) 1 C Fundamental 2/4
Joscelyn Godwin's note, p. 154, points out that "whereas the entities of rhythmic organization on the level of `rhythm' become smaller in proportion to the upward movement of the harmonic series, those of `metre' become progressively greater. The unity of the system breaks down at this point." For example, one would not be able to superimpose several partials within the period of one fundamental unit, because higher partials actually cover longer timespans than lower partials do. The duration of the fundamental metrical unit in this system is actually the shortest duration; the first harmonic covers twice as many beats, hence twice as much time, as the fundamental.
The bracketed metrical equivalents (i.e. 6/4, 3/4, 6/8 for 12/4) are given for changing the octave-register in order to combine better with other tones, or metres in this case....the chromatic version of this scale is given at the end of the chapter.
Cowell discusses metrical modulation and bemoans "metrical monotony" on p. 69, in a foreshadowing of the total serialist desire to avoid repetition and introduce continual change:
"The simplest way of using metrical rhythms on the analogy of musical tones is to keep shifting the metrical units in successive measures. If the changes be made, as is often done in the work of Stravinsky, in all the parts at the same time, the result is analogous to a simple melody in tone. To some persons, even so slight a change as this seems unrhythmical and abstruse.... If in lieu of a melody the same note were to be repeated for an entire work, it would be considered absurd; yet this endless repetition is just what is expected in metre, in which hundreds of the same metrical units, such as measures of 3/4, etc., follow one another without change."
He points out examples of composers who wrote irregularly-accented phrases of uneven lengths which lay unevenly across the even metrical bar-lines, yet who never tried writing with changing bar lengths instead. Beethoven's "famous use of sforzando on the weak beats of the measure" is one example, and the syncopation of jazz music is another (in Cowell's day, jazz was basically just what we now call Dixieland).
"What is required to re-create interest in metre is not to do away with so powerful a musical element, nor to keep the bar-lines always the same and then negate them by accents; because accents within the measure are never felt to be the same as first beats in the measure. Neither is it necessary to make of metre a sort of skeleton-in-the-closet, as though it were an evil thing, essential to preserve, but so unlovely that it must be covered by almost any accenting of phrase which will disguise the metrical foundation. All of these devices are interesting in music, but it does not seem amiss to get at the root of the trouble and bring the possibilities of metrical variety up to the same standards now applied to other branches. When metres change frequently, or when harmonies are formed from them, they give pleasure, and it is again of interest to hear them clearly defined, instead of disguised."([p.70])
Cowell eventually considers tempo, the third aspect of musical rhythm, and treats it with harmonic overtone series too. Here, taking MM=24 as a base fundamental, then MM=48 would be the octave, MM=96 the next octave, etc. The interval (ratio) of a fifth is MM=72 against the octave MM=48, the interval of a third is MM=120 against 96, etc. He notes that the base, 24 in this case, is better taken as a very low number, lower than the usual metronome range of 40-208 beats per minute, because that allows higher partials to be used without getting into too high absolute numerical values. MM=24 was taken as the base fundamental just for ease in avoiding fractions in the tempo scale.
This corresponds once again to Stockhausen's example of the construction of a scale of durations by division of the largest unit, because multiplication of metronome tempi corresponds to division of frequency, or duration if the numbers are normalized relative to 1 second, so the scale is shown in our Column 2 of Table 1 in our last section.
Recalling Stockhausen's criticism of the practice, on the part of serial composers, to work with modulations of the base unit of their "subharmonic scales of proportion" in order to avoid excessively long durations that otherwise result from higher duration scale degrees, we note the following from Cowell which describes the practice that Stockhausen described as "inappropriate" in serial music. (Of course, Cowell is no serialist, although he has heard of Arnold Schoenberg's twelve-tone method).
"In this way the key tone of the whole time or metric system can be changed at will, and many simplifications of practice can be made. If, for instance, the rhythmic chord of C (in the ratio of 4:5:6) has been struck, and it is desired to strikc the chord of F, this can be done in the key of C only by the use of three-sixteenth notes against three-twentieths notes against eight-notes. If, however, the tempo be changed from MM=96 to MM=64, the chord of F can be expressed by quarter-notes against fifth-notes against sixth-notes, since by means of the change of tempo the key will have been changed to that of F." ([p. 98])
We now consider a final example, Cowell's construction of a chromatic scale with equivalents in metrical length, duration, and tempo. To form rhythmical scales out of the simplest possible ratios, he has to choose small-number overtone ratios to approximate the semitones of a 12-note octave. Here we combine information from his charts found on p. 99, 101, 105, 106, 107 of his book. We are unsure why his C:C octave deviates from the style of the others in that its metrical ratio length is not expressed as a ratio of reciprocals.....also note that in the metrical ratios the fundamental measure is of unspecified variable metre, because otherwise the calculations would get too complicated. That is, since the quantities he is expressing are ratios, they can be given in various equivalent forms (as 1:2 is equivalent to 2:4, 3:6, 11.9:23.8, etc. and the most convenient values for a given situation can be picked from the equivalence classes making up the ratio).
Chromatic Intervals Ratios Metrical Ratio Correspondin
Equivalen Alterna
Tones From C Length (Quarter g Time Value t
M.M. te MM.
Notes)
Nos. Nos.
C:C Unison =1:1 2 = 1-2/4 4th note
48 60
measure:1-2/4
C:Csharp Augmented = 14:15 210 = 14-15/4 7/30ths note
51 3/7 64 2/7
Unis. m.:15-14/4
C:D Major second = 8:9 72 = 8-9/4 meas.: 2/9ths note
54 67 1/2
9-8/4
C:Eflat Minor third = 5:6 30 = 5-6/4 meas.: 5/24ths note
57 2/5 72
6-5/4
C:E Major third = 4:5 20 = 4-5/4 meas.: 5th note
60 75
5-4/4
C:F Perfect fourth = 3:4 12 = 3-4/4 meas.: 3/16ths note
64 80
4-3/4
C:Gflat Diminished = 5:7 35 = 5-7/4 meas.: 5/28ths note
67 1/5 84
fifth 7-5/4
C:G Perfect fifth = 2:3 6 = 2-3/4 meas.: 6th note
72 90
3-2/4
C:Aflat Minor sixth = 5:8 40 = 5-8/4 meas.: 5/32nds note
76 4/5 96
8-5/4
C:A Major sixth = 3:5 15 = 3-5/4 meas.: 3/20ths note
80 100
5-3/4
C:Bflat Minor seventh = 4:7 28 = 4-7/4 meas.: 7th note
84 105
7-4/4
C:B Major seventh = 8:15 120=8-15/4 215ths note
90 112 1/2
meas.:15-8/4
C:C Perfect octave = 1:2 4 = 1-4/4 meas.: 8th note
96 120
2-2/4
He notes that in the duration column, if the fundamental were allowed to vary with the ratio being expressed instead of always being a quarter note, the numbers would be simpler in some cases (i.e. he has done this in the metrical column, but not in the duration column).
For example, if he held the metrical foundation constant to a 2/4 metre measure, then to express the interval C:Csharp, the ratio would be fourteen measures of 2/4, set against fifteen measures of (2-1/7)/(49-255ths) metre.
"This is a metre of 2-1/7, since an accented note will be followed by one and one-seventh unaccented notes. One measure of such metre will contain two 49-225ths notes plus one 7-225ths note, the latter kind of note being one-seventh the length of the former; and the length of time of the whole measure is such that it is contained two and one-seventh times in a measure of 2/4 metre. Both the kind of metre and the length of the measure, then, express the fraction two and one-seventh, which is the correct expression of C sharp, if C equals the number 2....
"The almost insurmountable complexity of this procedure is now sufficiently evident. It would be interesting, though, to hear such rhythms cut on a player-piano roll...." ([p.103])
In the charts, two alternate scales of metronome markings are given, one starting at MM = 48 and the other at MM = 60. The scale starting from 48 yields more fractions as values (for Csharp, Eflat, Gflat, Aflat) than the scale from MM = 60, but the fractions in the MM = 48 scale fall on the "less-used chromatic tones" while the fractions in the MM = 60 scale (Csharp, D, B) include the frequently used notes D (major second) and B (leading tone).
We recall Stockhausen's emphasis, early in his article, on maintaining the fundamental unit of duration constant, in order to make the various ratios among different durations perceptible. We wonder whether Cowell's metrical ratios, with their shifting numerators and denominators, would be possible to implement in actual compositions, and whether they would be perceivable as a harmonic series even if they were composed and performed.
For example, suppose we wanted to perform a "major triad" in his metrical harmony. This would mean three pairs of metres, or six total. Somehow the three individual ratios have to be interpreted, but their collective relationship as a "chord" also has to be expressed.Their lengths are uneven. If they all began simultaneously, some would go on longer than others. We wonder if this is not just an exercise in numerology, just as Backus accused Stockhausen of.
First, for the fundamental, we would need one 2/4 measure set against another 2/4 measure. For the major third, four 5/4 measures are set against five 4/4 measures. For the fifth, two 3/4 measures would be set against three 2/4 measures.
Cowell invoked influences from previous composers to justify his new ideas:
"Although the rhythmical values suggested in the foregoing scales are for the most part new, simpler cross-rhythms, more particularly those formed by different note-durations, have of course been used by many composers. Chopin in notating his rubato improvisations hit on some extraordinary combinations; Brahms developed individual forms of syncopation; Scriabin carried a Chopinesque variety of cross-rhythm a step further than Chopin; Stravinsky utilized irregular metres and cross-accents.
Charles Ives, however, has gone furthest in weaving webs of counter-rhythms. Chords of rhythm are suggested in his works, and he builds up musical moods which rely on musical subtleties to an even greater extent than on tonal elements for their effect." ([p. 108])
To close this paper, we provide anecdotes about Cowell's instrument, the "Rhythmicon", from ([Mead1981]).
Henry Cowell had discussed the possibility of building a rhythm instrument with his friend Henry Varian in 1915-1916, who actually drew up some plans but never finished it. Eventually Leon Theremin built the Rhythmicon. Theremin charged Cowell only $200 to build it, even though he was being offered up to $10,000 from Hollywood studios to build more Theremins, because, according to Mrs. Cowell, "he always enjoyed Cowell and was glad to help him."
The Rhythmicon produced different rhythms which were partials in an overtone series on a rhythmic fundamental (duration), and the pitches produced at each rhythm were the corresponding partials of a pitch series on an audio frequency fundamental. Rhythms of 2 against 1 would sound in an octave, rhythms of 3 against 2 would sound in perfect fifths, etc.
Cowell had written a concerto, called the Rhythmicona, which was to be premiered by Nicolas Slonimsky in Paris in February 1932 but was cancelled and never performed. The instrument was too fragile and difficult to transport to Paris. Charles Ives was financing it, and was also paying for a second one which was to be more like an "instrument" rather than a "machine", as it would have levers and pedals to control the rhythms (one could infer from this that the first instrument was too inflexible in its design to be very musically useful). The second Rhythmicon was never built, however.
The first Rhythmicon was demonstrated at the New School for Social Research in New York on January 19, 1932, along with the Theremin, but most people were more excited by the Rhythmicon because they had already seen the Theremin numerous times before.
Reviewers complained about the limitation in which "one is constrained to represent a single rhythm always upon the same repeated note and without deviation from the regular beat...." (Marc Blitzstein, writing in "Modern Music").
Then it was demonstrated again in San Francisco on May 15, 1932 and was better accepted on the West Coast. But Alfred Metzger, writing in the San Francisco Chronicle, described the rhythmicon's sound as "a cross between a grunt and a snort in the low `tones' and like an Indian war whoop in the high-tones"...
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