#04 An Analysis of the Tailpiece or How To Choose The Right Material

The choice of setting up a tailpiece on a cello gives very different results in the sound. It can affect the balance or richness of tone, as well as the ease of sound emission.

Understanding the contribution of the tailpiece to the overall tone is the first goal of this study, and as a result, it helps the luthier in his choice of set-up, and to optimize the instrument.

 We compared several set-up, changing only the wood of the tailpiece. After a qualitative study of the perception of the sound of the instrument, we looked for a link with acoustic measurements.

 The recording of a scale for each tailpiece set-up allowed the study of the time envelope, the sound spectrum of the instrument, and the spectrum of the tailpiece vibrations.

  Finally, the modal analysis of each tailpiece made it possible to specify the mechanical behavior of their own resonances, as well as the values ​​of the dynamic markers which are the modulus of elasticity and the Quality factor linked to sound damping.

Correlations appeared between the perceptual sound classification of these assemblies, and the mechanical qualities of the wood species used.

 The choice of the tailpiece, made by the luthier, can thus be guided by using the preliminary study of its properties.

Click here to watch and download the full study in pdf

Introduction

 A Perceptional study of 8 successive tailpiece set-up, on a Mittenwald Cello, allows us to discover sound differences, due only to the change in the species used for the tailpiece.

The action of the string by the bow is first communicated to the bridge, whose feet transmit vibrations to the body of the instrument. The body and the front will then emit an audible sound.

The vibration of the strings is also communicated to the body of the instrument through the bottom nut, passing through the tailpiece. The size of the latter is insufficient to emit a sound, but it will filter the vibrations transmitted, and thus contribute to the overall sound of the instrument.

In the acoustic study presented here, each set-up was recorded on two channels:

• one recording by a microphone, showing the sound perceived by our ears,

• and a second one, by an accelerometer placed on the tailpiece, which recorded the vibrations which goes through it.

The temporal envelope is the amplitude curve of the notes of a scale played. It shows an inequality of sound amplitudes from one note to the next in the same set-up, but also other inequalities, for the same note, from one tailpiece set-up to another.

When listening, these differences are not perceived as variations in power, but as changes in tone.

  Spectrographic analysis allows each note to be split into its harmonic components,

- with the sonogram,

- then the spectrogram.

The study of the aerial sound recording, by the microphone, does not show many differences between the different assemblies

We were particularly interested in the other way recorded with the accelerometer, that of tailpiece vibrations.

Indeed, over the entire spectrum played, the curves highlight almost blank frequency bands, and other bands with boosted amplitude.

Some set-up have very uneven bands, other tailpieces are much more regular.

The breadth, and the number of these bands is correlated with the perceived sound quality of the instrument: the more "blank" bands there are, the less set-up of this tailpiece is appreciated.

The "boosted" frequencies are often the same for the whole range of a given set-up, and suggest their coupling (a sympathetic resonance) with resonance modes proper to the cello body, but also to the tailpiece. We therefore studied the possible influence of these modes on the tone.

Modal Analysis

Any object,… here the tailpiece, reacts to preferential resonant frequencies, it has its own modal signature. It can resonate in sympathy when a corresponding note is played, and interact with it.

Thus, the vibratory transmission between two objects, as here between the tailpiece and the resonance chamber, can be filtered, altered or amplified by this coupling.

For each set-up studied, we determined the resonance modes of each tailpiece in three situations: as an individual object (Free-free), then as a connected object, in tension as on a silent cello, on a "dead rig", ( devoid of sound box, and finally, set-up on the cello studied.

We see that the first resonance peaks of a tailpiece correspond to the same reinforced frequency bands on the sonogram and on the spectrogram. Conversely, the amplitude troughs between these resonance peaks correspond to diminished vibration bands of the spectrogram.

There is therefore a correlation between the natural frequencies of the tailpiece, and the tone result.

 The more powerful and well separated the resonance peaks of the tailpiece, the more uneven the sound emission spectrum will be (frequent example : the boxwood tailpiece).

 The more the peaks of the tailpiece are numerous, doubled, unequal, less powerful, the more the sound emission spectrum will be regular, and appreciated .

  This study can be a starting point for other projects :

 -What material for a tailpiece? What are the ideal qualities required for this acoustic filter.

 -What is the influence of the assembly: length, type and geometry of the tailgut materials, which also modify the vibratory qualities transmitted by the tailpiece.

 -Can we better understand the historical evolution of this accessory, during organological and technological modifications, and the evolution of musical tastes?

If you want to know more: Click here to watch and download the full study in pdf