Viotar/Quantifying the signal

The signal that we want from the string, somehow will have to be read out by the instrument. No matter how this is done, some sensor will provide a signal, in which the vibration we want from the string should be recognised. This recognising has to be done on a reliable, quantitative basis. More specifically, there has to be some kind of scalar quantity that gives us how far we really are from the ideal trajectory in the bow speed-force space, so a feedback loop can be made to let the system find this trajectory for itself. For this, an experiment will be done, and it's results will be analysed thoroughly.

Experiment plan

- Is the computer model of the bowed string accurate?

- Where does the "pleasant" sound come from that you hear when you stand next to the instrument when it's bowed? Is it mainly the vibration of the body that you hear? In that case it would origin mainly from the pressure variances of the string on the bridge, which translate into the body. On the other hand, it could be mainly the vibration of the string that you hear. In that case, the transversal wave as described by the computer model and measured by a laser sensor is dominant. The outcome of this will be important in the choice of what the capture and amplify exactly, when the instrument is done.

- What does the vibration we want (Helmholtz) look like in the transversal wave of one point of the string?

- What does the vibration we want (Helmholtz) look like in the pressure variances of the string on the piëzo element?

A measurement will be done for the low E-string and the high e-string, on the open string and the 1st, 12th and 13th fret. The open string and 1st fret measurements are needed to "shift" the signal in the frequency domain. Everything that shifts up according to the fret change is part of the vibration we want to measure, the rest is noise. With this principle we are hoping to be able to cancel the noise from the measurements. The 12th and 13th fret are done so that the same can be done for a much higher position (one octave up), because the waveform may have a different character there.

Analysing the results

The first goal was to cancel the noise from the measurements using the method explained in the previous paragraph. This proved to be impossible. The power spectrum of a measurement may be split up in two components: the 'noise' component, which stays the same when a higher note is played, and the 'harmonic' component, which shifts up when a higher note is played.

Probaby, Helmholtz is the only harmonic vibration that you can get from a string when you bow it. With a bow you can never get a normal standing wave as when you would pluck the string. Because of this, it is not necessary to quantify "how much" the measured vibration is the specific Helmholtz waveform. It may suffit to merely quantify how harmonic the measured vibration is. This can be done by detecting the fundamental frequency in the fft of the signal, and looking looking how many multiplications of this frequency are still in the signal. The more overtones, the sharper the Helmholtz, and therefore the better the tone.