Timbre and tuning of clamped oscillators
Now, having some notion of the complexities of vibrational modes in various odontophone settings, we are able to address the issue of timbre and tuning.34 As we have already said clamped rods produce non-intuitive, complex sounds with distinctive timbres. These sounds are difficult to describe. Timbre is especially difficult to describe, in part because it is not a single quality but, as often defined, all of the qualities of a sound other than pitch (frequency), volume (amplitude), and dynamics in time.35 To assist in conveying information about the qualities of sounds produced by odontophones our exposition is based on empirical data: images, audio, video, spectrograms, and real life observations. The audio and video files allow the sounds to speak for themselves, while spectrograms provide a visual representation of the sound(s) in time. Unfortunately, descriptions of sounds are limited by the insufficiencies of language to describe timbre and allow for much ambiguity; we do not have universal terms to describe the nuances of sound perception. We hope that the reader will indulge our poetic and subjective adjectification in attempts to describe the timbral qualities of such complex sonorities, understanding that this is also part of the nature of human perception.36
The Baschets’ explorations and appreciation of the results of experimental structures invited general audiences to enjoy and open their ears. They believed that art allows us to engage with the complexities of life that are difficult to apprehend with reasoning or logic. The Baschets used sound sculpture as a way to appreciate these complexities without indulging in unavailing reasoning and intellectualization. Thus, their explorations in timbre and tuning represent a huge part of their work, and a significant aspect of what we are dealing with, knowing that only the actual sounds give meaning to our explanations.
Within the corpus of the Baschet work with clamped elements we can find three distinct approaches to tuning: intentional tunings (taming complex vibrational modes by adding weights in certain regions or using the first mode of oscillations of short rods to achieve recognizable tunings such as twelve tone equal temperament), found xentonal tunings (allowing tunings to emerge from the structure, exploring tunings other than than twelve tone equal temperament), and timbral gamut design (in which the timbral gamut takes precedence over pitch gamut).
The Baschets developed reliable techniques for tuning their odontophones (within the limitations of each specific system), using weights along the lengths of the rods to tune overtones to create specific pitch gamuts (and to shape timbral qualities).37
One of the biggest challenges with clamped rods (or any instrument) is the difficulty of maintaining consistent timbre over several octaves. As we have seen, if we select a specific order of overtone as the intended pitch to be perceived, and the length of adjacent rods is gradually increased or diminished, other overtones will appear at some point with as much presence as the overtone chosen for the desired dominant pitch voice. In this sense, it is comprehensible to take the strategy of creating gamuts in a range (generally less than two octaves) in which it is possible to maintain the same timbre, to avoid falling into the transitional regions in which a rod becomes multiphonic, obscuring a clear sense of a dominant pitch. In mountings that feature multiphonic rods (rod lengths in transitional regions) there is the possibility of taming the multiple voices of each rod by adding weights along their lengths to retune the frequencies of specific overtones.38 This operation can become compositional in itself, since it is in fact tuning a rod to sound a certain chord or group of pitches.
Even the first sound sculpture by the Baschet brothers, Sound Structure With Bow and Balloon (1955), featured weights along the rods’ lengths, indicating that the entire system was likely tuned to a specific (recognizable) scale. Unfortunately we only know that it was intended to be played with a cello bow, and it was dismantled and its components reused in other sound sculptures.
Intentional tuning is best exemplified by instruments created during the the period of the Lasry-Baschet ensemble (1955-1964) in which a great deal of music was written and performed, blending the diverse interests of the participants, from reinterpretations of classical music to quasi-ambient downtempo abstract new-age music. Further research into the history of the Lasry-Baschet ensemble and its members would be a valuable endeavor. The Baschet Cristal was a significant development in the Baschet instrumentarium during this time. The challenges of accurately tuning the semitones of the Bachet Cristal demanded their attention for a significant period and the potential of the chromatic Baschet Cristal brought them to arrange their music by giving melodic and harmonic roles to the precisely tuned chromatic Cristal. Other instruments using percussive sounds of plates and clamped rods took on roles as accompaniment, generally more timbral than harmonic.39 In these accompaniment instruments tuning was not as important as finding the desired timbre and envelope features to accompany the Baschet Cristal. Thus, these (percussive) odontophones exhibit a degree of ambiguity between the pitch function and the timbral function because of the nature of the clamped rod’s sonority in itself, in contrast with the clear pitch of the Cristal, as heard in recordings such as Sonata Exotique/Structures For Sound (1957-59), Danse du Ressort (1957) doubling the melody of a Cristal Baschet, Mister Blues (1962) accompanying a jazzy clarinet, or Rhapsodie De Budapest (1976), doubling a piano melody. In collaboration with musicians, composers, and performers the Baschet brothers adapted to the specifics of each project. Percussion odontophones, by the nature of their sonorities, were less likely to be chosen for diatonic or 12TET music, but technically it is possible, as we can see in the Baschet Piano presented in our Round Rods examples.
Other examples of intentional tunings can be seen in several plate instruments: In Orgues Xavier De La Salle the Baschets used freely suspended plates tuned to just intonation intervals and, in 5 Crosses, fixed plates tuned, in pairs an octave apart, to a melodious gamut of intervals tuned by ear or by calculations. In any case, the plates in both cases were tuned by grinding material from the edges (to raise the pitch) or grinding in the center (to lower the pitch), a rare instance of destructive procedures used for tuning.40
It can be interesting to note the similarities and differences between the vibrational characteristics of friction and percussion odontophones.41 Clamped rods on a Baschet Cristal are forced to vibrate by friction, creating a standing wave which results in overtones following the harmonic series (instead of the inharmonic overtones of a clamped rod we have come to expect) so the perceived pitch is much clearer. In this regard, the Baschet Cristal displays a markedly different acoustic behaviour because of the activation. The specific proportions to tune a Baschet Cristal to 12 TET is actually quite complex and sensitive to minute changes. The doubly coupled rods have their own natural vibrating modes and wavelengths that can be altered by the positioning of the glass rod. This forces an antinodal region to appear on the threaded rod (which is pushed back and forth at that connection point by the longitudinal vibrations of the glass rod), resulting in a transverse vibration of the threaded rod sustained by the friction.
Adding perpendicular plates at the free end of the rod can help with fine tuning, since the inertia of the whole rod is altered by the added weight, which can be delicately adjusted along the length. Anyway, inharmonic overtones can appear and can be tamed into the harmonic depending on the location and weight of the added tuning masses. In this respect the Baschet experimented a lot and succeeded in achieving stable 12 TET tunings across five octaves. In any case, the harmonic series overtones that result from forced vibrations in a Baschet Cristal generates a clear sensation of pitch, so tuning it is a delicate thing to do, but avoids the challenges of the inharmonic modes inherent in struck clamped rods.
The technique of retuning the inharmonic overtones of a percussion odontophone comes from the sophisticated Baschet Cristal N-fitting mounting system, used without the glass rod, as we can see on the Chromatic Percussion for Marc Antoine Millon and other sound sculptures in our Doubly Clamped Rods examples.
Tuning did not seem to be a major concern of the Baschet brothers (although we are still searching the Baschet archive and new data proving otherwise might still be found in the future), particularly because they conceived of sounds from a perspective that did not necessarily have to do with playing music in a traditional way, but to subvert the roles of what and who can be part of art or culture (and where they exist). For this reason they devoted only a small portion of their efforts to tuning and music theory. Once they mastered certain acoustic knowledge, they dove into the celebration and appreciation of sound for its own sake, without the externally imposed restrictions or preconceived musical scales. François particularly enjoyed allowing people to create their own tunings and mountings, which we can see in his unfinished DIY Kits project. The older they got the less the Baschet brothers were interested in defining a particular style of music or producing it themselves, but preferred to facilitate people making their own unique musics.
Xentonality is a recently coined term, with no standard exhaustive definition, that represents a field that we will not discuss very deeply here.42 For the purposes of our exposition we will use xentonal to refer to any non-conventional tunings, different than twelve tone equal temperament (12 TET).
William Sethares proposes the term xentonal as part of an exquisite theoretical system in his book Tuning Timbre Spectrum and Scale.43 Although Sethares’ amazing theoretical approach allows us to understand, design, and compose with new xentotal tunings there are many tunings that do not come from such analytic (mathematically calculated) approaches. To this end we must qualify our understanding and use of the term in a way that can be better applied to the Baschets’ work: not a calculated xentonality but a found xentonality.44
The presence of such unique (xentonal) tunings in Baschet odontophones does not come from a theory to meticulously divide the octave into equal divisions smaller than the western semitone (as in the work of some microtonal composers and instrument builders). The xentonal tuning in the Baschets’ work comes from the experimental use (and empirical manipulation) of naturally inharmonic oscillating systems: since a clamped rod can produce distinguishable overtones that do not match the harmonic series it is often easier to accept them than attempt to retune them.45 As we have shown in Vibrational Modes of Clamped Oscillators and The Gum and Teeth Behave As A System when several rods are connected these overtones realign themselves by resonance to form (found) xentonal gamuts.
The Baschets never worked deeply on tuning theory: neither on theory about the tunings they found nor making instruments to test tuning theories. In this sense they are far from alternative microtonal tuning theorists such as Harry Partch, Ivor Darreg, or Julian Carrillo. They worked in a way that allowed them to freely discover sets of sounds completely beyond known tuning systems, but cohesive because of the naturally occurring resonances in the complex oscillating systems.
The fact is that in many cases the Baschet showed no interest at all in western tunings but openly searched for new tunings in a personal, intuitive way. In many of their pieces they did not search for any tunings at all, they just wanted to offer a palette of sounds, beyond any consideration of pitch (tuning). Despite the fact that the Baschet’s best known work is the family of the Baschet Cristal, usually diatonically or chromatically tuned, the majority of their work did not use conventional tunings, precisely because they were devoted to the exploration of the possibilities of inharmonic oscillators.Understandably, these clamped elements were a lasting inspiration since their very first experimentations in sound sculpture, both for the building possibilities: modular and easily modifiable and precisely because of the unknown (untapped) potential of their sonic behaviour.
In addition to allowing xentonal tunings to emerge from the complex sound of the clamped oscillators the Baschets also experimented with visual arrangements of rods that resulted in little xentonal universes, never exactly replicated. Let’s consider some of the mountings that create such gamuts.