Working Sustainer Circuit

Turning up the gain by the 50 kΩ variable resistor in the gain stage excites the tine and sustains the oscillations. Amplitude depends on gain setting. It works!

Moving the driver closer to the pickup (and end of the tine) shortens time to full amplitude when starting from rest. Other frequencies are amplified and vibrate the tine also, not sure where these are coming from yet. Removing the entire tine/tonebar assembly and turning up the gain shows resonant frequencies of pickup/driver feedback loop - the frequency increases with a decrease in distance between driver and pickup (about 900 Hz with 1 cm separation). Also, Frequency decreases with an increase in gain. Removing the capacitor in the gain stage makes higher frequencies appear at lower gain setting. There appears to be a boundary level in the gain below which these resonant frequencies aren't present.

Les was wondering if the voltage-to-current converter (output stage) would be able to drive a complex load. Loaded with a 10 Ω resistor (same DC resistance as driver) gives a clean output (observed on oscilloscope) but loaded with the driver inductor gives garbage. Maybe need to use a regular power amp?

I'm also wondering about sensing vibrations with piezo pickup to amplify and feed back into the tine in order to avoid the magnetic coupling between driver and pickup in the feedback loop.

ALSO looking for recommendations for free circuit-drawing software...

Frequency Spectrum of Tine -> Pickup Signal

118 Hz fundamental, plucked

275 Hz fundamental, plucked

118 Hz fundamental, struck

275 Hz fundamental, struck

118 Hz fundamental, plucked (zoomed in)

(Click to enlarge!)

These spectra come from 4096 point FFTs of the signal generated by the tine vibrating in front of the pickup. The samples were taken during the steady state portion of the oscillation (after the attack/decay portion) and each plot is an average of 25 trials or more. The spectra are of two different tines, one lower with a fundamental frequency of 118 Hz (B-flat 2), the other higher with a fundamental at 275 Hz (D-flat 4). These frequencies appear as peaks on the graphs and can be verified aurally. There are two plots for each tine, one where I plucked the end of the tine with my finger, and one where I struck the tine with a steel bolt.

The first thing to note is the appearance of harmonic overtones (integer multiples of the fundamental). These are added by the pickup and do not reflect the motion of the tine which has a second natural frequency at around 6.27 times the fundamental [Whitney, 1999]. The 6.27 ratio is for a specific case in the Whitney paper and I haven't figured out how this might vary with cantilever beams of different size, mass, etc. The important thing is that the second overtone is certainly not two times the fundamental.

The spectrum of the longer tine looks similar to that of a guitar string oscillating perpendicularly across the axis of a guitar pickup (instead of along the axis) where even harmonics are much more present than the odd harmonics [Horton, 2008 - Fig. 16, plot labeled "Horizontal"]. Indeed, the motion of the tine is (mostly) in this perpendicular plane.

The spectrum from the shorter tine does not exhibit the same attenuated odd harmonics, and I wonder if the effect is caused by wider deflection of the tine from the pickup axis (deflection is greater with lower frequency tines).

The struck tine spectra have much more high frequency content than the plucked tines. The fundamental anti-node of the tine is at its free end, so plucking it at the end adds energy at the fundamental frequency. A strike is similar to an impulse (equal energy across all frequencies) so it makes sense that we see more energy at higher frequencies and not just at the fundamental. I'm not able to explain why clusters appear where they do in the higher frequency range for the struck tine plots. I also don't totally understand where the small peaks immediately adjacent to the harmonics come from, though Matt suggested I look into sum and difference tones as a possible explanation. This is on my list of things to do.

Early Apparatus

Experimental apparatus with tine, tone bar, pickup and driver coil mount

#1 is the steel tine, #2 is the tone bar, the two together act as a tuning fork. The tine swings back and fourth in front of #3, a passive magnetic pickup. The hammer and felt damper are not part of this apparatus.

#4 is a plastic sewing machine bobbin on the end of a steel bolt. This has since been wound with approximately 600 turns of 30 AWG copper wire and serves as the magnetic actuator. Indeed, when supplied with DC, the coil generates a magnetic field and attracts ferromagnetic tine. Driven with a weak sine wave directly from a function generator, the tine vibrates slightly.

McPherson's Magnetic Resonator Piano uses a feedback loop in which magnetic actuators are driven by a single piezo pickup that senses the summed string vibrations on the soundboard. High-order bandpass filters precede each actuator in the signal path, with each filter tuned to the individual note. Each note is isolated at the source in the Rhodes piano with a dedicated pickup for each tine, but the close proximity of the magnetic actuator and magnetic pickup may be problematic.

In anticipation of a pickup/actuator proximity problem, a piezo film vibration sensor is taped to the end of the tone bar (#5) to test its effectiveness as a replacement for the magnetic pickup. It produced a very weak signal, and I suspect the tone bar vibrates at a different frequency as the tine.

Brief Description of Rhodes Piano

73-key stage piano

The Rhodes piano is an electromechanical instrument that uses a steel cantilever beam (the tine) as its primary tone source. There is one tine per note on the piano. The free end of the tine swings back and fourth in front of a passive magnetic pickup (again, one per note) generating an electrical signal. The sum of these signals is present at the output jack of the instrument for amplification. Similar to an acoustic piano, the tine is struck by a hammer and damped by a felt pad. A small wire (the tuning spring) wrapped around the free end of the tine adds mass and is nudged back and fourth to tune the fundamental vibrating frequency. According to the original Rhodes service manual, the tine is one leg of an asymmetrical tuning fork. The other leg (the tone bar) is longer and much more massive.

Tuning fork comparison

Introductions

This blog is something of an experiment, serving both as a digital lab book for documenting my research and as a means of communication with my advisors and collaborators. I'm currently somewhere in my third year of a master's program in Media Arts & Technology (MAT) at UC Santa Barbara and the research presented here will be for my master's project.

The project is an attempt to electromagnetically actuate the tines of a Fender Rhodes piano, leaving the key/hammer mechanism intact, and controlling the actuators with the existing keyboard interface by sensing continuous key position or aftertouch pressure. Inspiration comes predominantly from Andrew McPherson's Magnetic Resonator Piano (impressive demonstration video) with electromagnetically actuated strings and acoustic amplification through the soundboard. My goals are similar, but designing such a system for an electromechanical piano will present a different set of challenges.

Finally, the title Formant Informant is derived from an old MAT rock band, Former Informer, featuring Pablo Colapinto, Phil Popp, Mariano Mora, and Anil Camci. I always liked their clever band name and am pleased with my spin on it.