Cowell took his system through the 16th harmonic. Though the harmonic series does not correspond to the Western equal tempered scale, a fact that Cowell recognized, the first 17 tones can be roughly approximated on a traditional keyboard. Intervals between harmonics beyond the 17th are narrower than a semitone. He suggests that theoretically there is no reason not to go beyond the 16th harmonic if the means to produce the tones are available. I have extended the concept up through the 24th harmonic.

After a few "proof of concept" studies, the virtual rhythmicon initially conceived and executed using the Kyma system expanded into a complex virtual rhythmicon environment involving control over far more parameters than pitch and tempo that, finally, exploded into a set of 25 omni-related rhythmicons.

The sounds of the original "basic rhythmicon" recur throughout the 24 Rhythmiconic Sections. Analysis of its rhythmic structure and internal harmonic relationships provided the tools for my compositional approach to the rhythmicon environment. The fundamental pitch (first harmonic) of the basic rhythmicon is 65.406 hz, two octaves below middle C, which was the lowest pitch of Theremin's rhythmicon. The pitches of the remaining 23 harmonics are whole number multiples of the fundamental.

Sample 1: Virtual Rhythmicon, all harmonics

RealAudio: 0:32

To explore the sounds of the rhythmicon further, visit Nick Didkovsky's Online Rhythmicon. Didkovsky has created an interactive site for Minnesota Public Radio using the Java Music Specification Language. The online rhythmicon requires the JSYN plugin, available at the site. His realization uses 24 harmonics, as described here, rather than the original 16 harmonics version. Users can choose from among several waveforms for a variety of sounds and are allowed to record the results of their experimentations. In 2006, Innova Recordings released a CD compilation of works created with Didkovsky's virtual rhythmicon.

The basic rhythmicon in my work consists of three blocks of harmonics: H1 - H8, H9 - H16, and H17 - H24. So that the rhythmic layers don't disintegrate into sonic mush, the sounds are simple and clear. Each block has its characteristic timbre. The tones of the first block, H1 - H8, consist of a pulse layered with a sine wave. The release of the pulse is slightly faster than the sine which gives these tones, especially the lowest three, a buzzy attack and smooth fade. The tones of the second block, H9 - H16, consist of three layered square wave oscillators. These are slightly detuned from one another. The resulting phase effects vary the timbre of this middle block over time. The third block, H17 - H24, consists of two sine wave oscillators linked as an FM sound in a 1:1 ratio. The volume level of the modulator is about two thirds that of the carrier. This gives the high tones a nice metallic sting.

Sample 2: Lowest 3 harmonics, middle 3, then highest 3.

RealAudio: 0:32

Cowell's objections to the rigidity of Theremin's rhythmicon are easily overcome with present day tools of computer music. Similarly to Leland Smith's use of SCORE to realize the rhythmicon part of Cowell's Rhythmicana, I used the scripting capability in Kyma, which allows me to set the frequency of the fundamental and tempo of the basic rhythmicon along with other variables. Changing the value of these variables in the script changes the relative frequency and tempo of all 24 harmonics as well as a number of other parameters.

After creating the basic rhythmicon, I developed additional timbres and means of control during the course of composing Rhythmiconic Sections which vary considerably from the original clear and clean approach. In addition, development of the ability to sustain the harmonics as constant tones varying in volume relative to the intensity of beats--to the extend that the beats can be completely submerged--introduced a new conceptual dimension to the virtual rhythmicon environment. The use of sustained tones is especially evident in Section 19. Another development was the capability of enveloping the beats of a rhythmicon of quick tempo to form beating-beats of a slow meta-rhythmicon which can be heard in Section 23. The most extreme timbral variation was the use of spectral analysis on spoken text and the subsequent splitting of the spoken words into beating layers. This can be heard in Section 4.

Other timbres which can be heard throughout the pieces include synthesized gong/bell sounds, waveform sounds in which MIDI controllers let me shift among a variety of waveforms to vary timbre, various sustained tones for low harmonics, amplitude modulation sounds with real time control of the pitch of the modulators for timbre shifts, layered waveforms with real time detuning control, and samples. Short samples play through during each beat of the harmonic(s) to which they are assigned with appropriate time and pitch shifting. Long samples which sustain perhaps over many beats are enveloped, allowing them to be heard when triggered. These techniques and means of control have continued to be refined in works completed subsequently to Rhythmiconic Sections.

Thus in addition to the basic pitch and tempo settings of Theremin's electromechanical rhythmicon, the following parameters and aspects of the rhythmicon are controllable in the virtual rhythmicon environment developed in Kyma for Rhythmiconic Sections:

Attack-Decay-Sustain-Release (ADSR):

ADSR envelopes control the beating of the harmonics. The ability to vary these parameters in real time controls the expressive quality of the rhythmicon and can also affect the timbre of the sound of the rhythmicon as a whole. Generally I confine envelope parameters to the length of the beat of the harmonic, but when needed, the release parameter can extend beyond the beat for any desired length of time.

 

Volume:

All harmonics of the basic rhythmicon are "on" all the time. A separate MIDI controller determines the volume level of each harmonic and thus which sound at what level at any given moment.

 

Pan (stereo position):

Another set of controllers determines the stereo position of each harmonic, although in most cases a default set of fixed values was used in Rhythmiconic Sections. The ADSR parameters, volume, and pan are controlled with MIDI controllers via sequencing software, MIDI faders or Kyma scripting.

 

Staccato/Sostenuto:

All harmonics can be set individually at any point along a continuum between clearly separated beats and non-beating sustained tones. This control is separate from the ADSR controls, thus, for example, sharply articulated beats can occur partly or largely submerged in sustained tones, or conversely, beats can rise like smooth bubbles on the surface of sustained tones.

 

Timbre shifting:

The timbre of a number of the sounds can be shifted in real time using MIDI controllers. The combination of timbre shifting, ADSR shifts and shifts in the balance of sustained tones to beats, not to mention panning and relative volume, provides a complex and fascinating compositional environment.

 

The Kitchen Sink:

I toss in other non-rhythmicon sounds as needed.