Dwight Brown

It’s a good point, but science requires us to take each variable one at a time. But we are talking about an awful lot of variables! (We haven’t even talked about bows yet!!) like most investigatons you have to start somewhere. I guess you pick the the ones you are the most interested in or you think have the most potential or even the ones you have the equipment and methodology to examine. DLB

Indeed. The ideal instrument and set up is a hugely complex system dependent upon a large set of variables . But to simplify and look at one independent variable at a time would be be the path forward to quantify results. Just a really long path indeed! DLB

I'm sorry if the paper I posted is not readable. My cut and paste skills are not too hot. DLB

Absolutely ! Much better methodology. I think you can only do this stuff for a limited amount of time before everything starts to sound the same to you. I wouldn't have a clue as to a good way to quantify data for real analysis . Maestro Curtin has doen a lot on that working with others. DLB I did find that Kolstein has a an ajustable length bass tailpiece . Another problem is that it takes some time for an instrument to recover from big changes and settle down again (again a subjective observation) . Your mention of the after length on the other side of the string from the nut to the peg brings up a whole other set of ideas! We have a string that is all under tension but divided in one form or another into three pieces. This still does not take into account the tailpiece and tail gut and their vibrations and contributions to the whole system. I have always wondered if the tail pieces Moeniggs used to put on instruments with the large gold oval had an effect other than we all knew where they came from. (when I was a kid it was indeed a status symbol!) DLB

Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden STRING “AFTER-LENGTH” AND THE CELLO TAILPIECE: ACOUSTICS AND PERCEPTION Eric Fouilhé Maker Laboratoire de Mécanique et Génie Civil de Montpellier ericf26@gmail.com ABSTRACT In a long term research on cello tailpieces, we have first identified the vibrating modes of a cello tailpiece mount- ed on a Dead Rig [1], and have worked on the possible influence of the wood on these modes. Among musicians and violin makers, several empirical theories exist about an ideal “after-length”, i.e. the distance of the tailpiece to the bridge which leaves a small length of vibrating string. Here we describe on the parameters involved when varying the “after-length”, and explore the influ- ence of the position of the tailpiece on the modes and on the sound. 1. INTRODUCTION On a modern cello, the tailpiece is where the four strings are attached. The tailpiece (C, fig 1) has one attachment at each end, and the setting is more or less standardized in its 3 lengths.: We call the “after-length” the distance B between the bridge (a) and the tailpiece (C fig.1). On the other side, it is held by the tail-cord (D fig.1) which pass- es around a saddle (d), and fixed by a loop around the cello endpin. Empirical theories declare that the after-length should be 1/6th of the playing length of the string. Our question is whether varying the three lengths B, C and D changes the motion of the tailpiece and the sound of the instrument. We attempt to make connections be- tween acoustic measurements and the perception of sound by sound perception experts when varying the position and length of the cello tailpiece. The three components B, C and D are interdependent in the “tailpiece chain” BCD. In order to isolate the after- length question, we used an adjustable tailpiece to char- acterize the influence of this after-length compared with the influence of the tail cord and of the tailpiece’s length on the tailpieces modes on a Dead Rig and then on the vibration modes of a cello. Anne Houssay Laboratoire de Recherche et de Restauration Musée de la musique Cité de la musique / Paris houssay.a@gmail.com 2. MATERIAL AND METHODS2.1 Material Two modern standard tailpieces in ebony and one adjust- able tailpiece in African blackwood were used: -Tailpiece T.1: ebony (Diospyros), 62 g, length 235 mm. -Tailpiece T.2: ebony (Diospyros), 62 g, length 250 mm. -Tailpiece T.3: African blackwood (Dalbergia), 76 g, 235 mm, with double system of attachment both baroque and modern, two possible after-cords: one of standard length, the other with an extension of 23 mm (“baroque type” attachment) (Figure 2). b a d Figure 1. Profile of (from left to right) a: bridge, B: af- ter-length, C tailpiece length with its stopping nut b, D:tail-cord length, saddle d. (Above, profile of the Stradivari violin “l’Aiglon”. modern attachement baroque attachement Figure 2. Tailpiece T.3, of length 235 mm, with two possible attachments. The attachments are made in com- posite fibers and do not stretch significantly whith 60 kg tension of the cello strings. Copyright: © 2013 First author et al. This is an open-access article dis- tributed under the terms of the Creative Commons Attribution License 3.0 Unported, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 60 Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden The Dead Rig is made of a strong metallic beam with no resonance at the modal frequencies we are studying, see [1]. It holds a string length and a fixed bridge at the same angle as on the cello, and an end attachment with the same dimensions as on the cello. The violoncello is a good student cello made in Mire- court in 1930. As described in our papers on the modal analysis of the cello tailpiece [1], we used a 2g PCB impact hammer, a PCB uniaxial Accelerometer and George Stoppani’s Software. George Stoppani’s modal analysis software, gives the FRF to the hammering of specific points on the tailpiece, amplitude, damping, and an animated visualiza- tion of the mode shapes of the tailpiece and / or the cello. 2.2 Methods On both the Dead Rig and on the cello, we have stretched and tuned cello strings with different after- length configurations of tailpieces. Three different meth- ods were used: modal analysis of the tailpieces under tension, Bridge Admittance measurements on the cello, and sound perception of the cello played three expert listeners: the player and two violin makers. The bridge admittance of the cello was measured by hammering at the treble side of the bridge, the response of the body was measured with the accelerometer at the top bass side of the bridge: it gives an RMS where the A0 air mode and the B1- and B1+ torsion modes of the cello are identified with their frequencies and modes shapes. Repeatability is achieved in the modal analysis of the tailpieces on the Dead Rig with a mean of 300 measure- ments taken, and in the 10 admittance measurements of the cello’s bridge for each tailpiece Set-up. Perception learning by musicians leads to an expert type of listening different from that of non musician [2]. From the point of view of neurosciences, there is a change in cortex that is linked to learning experiences in both visual arts and music [3] and the training of the ear leads to a change in hearing perception and cognition [4] Thus, we argue that musicians but also some instrument makers have developed an expert type of perception, and this leads us to chose relevant experts: a professional cellist and two violin makers. A chromatic scale, extracts of Bach’s suite n°1 in G Major and of Brahms Sonata N°1 in E minor was played. Each expert listener expressed their perception of the instrument’s power, balance, tonal quality, and dynamic range, precision of attack and wolf note. The latest is generally found on most cellos between E and G, on one or more strings. Quantitative appreciation of the qualitative judgments, the semantic diversity of the terms employed by the mu- sician and makers, and the influence of the room used for the test have their importance, and our protocol was cho- sen similar to one used by a violin maker in his work- shop: The musician made her comments first in order to avoid the influence of the listeners. The maker who was not involved in the experiment spoke second. The third expert took notes of the comments and asked for explana- tion to get a more precise idea of what the expert meant to say, each expert being free in which order he reacted about the different parameters, because constraint would have spoiled their first immediate perception. Effectively, perception work has to take into account short and long term sound memory and comparisons two by two with short term perception memory of the experts was privi- leged. 3. RESULTS 3.1 Modal Analysis of the Tailpieces on the Dead Rig : We compare seven different settings (Figure 3) on the Dead Rig giving four different after-lengths: 95, 115, 116, 128 mm (A standard after-length used today for cellos is 115 - 117 mm.) For this, we use - 3 different tailpiece lengths : tailpiece T.1: 62 g, length 235 mm. tailpiece T.2: Ebony, 62 g, length 250 mm,after-length 116 mm. tailpiece T.3 with two possibleafter-lengths. - Six different tail-cord lengths : 51 mm, 39 mm, 30 mm, 28 mm, 18 mm, 10 mm. These Set-ups are summarized in Figure 3. Type of setting After- length Tailpiece Tail cord Set-up 1 116 mm Standard 235mm T.1 Standard 30mm Standard Set-up 2 95 mm Short 250mm T.2 Long 30mm Standard Set-up 3 116mm Standard 235mm Standard T.3 adjustable 51 mm Long Set-up 4 128mm Long 235mm Standard T.3 adjustable 39mm Long Set-up 5 128mm Long 235mm Standard T.3 adjustable 18 mm Short Set-up 6 116 mm Standard 235mm Standard T.3 adjustable 28mm Standard Set-up 7 115mm Standard 250mm T.2 Long 10mm Very short 61 Figure 3. Types of settings for the experiments: colors are used for reading the following curves. 3.1.1 Comparison of Standard and Short After-length T.1 (standard) and T.2 (long) are compared with two different after-lengths: normal (116 mm: Set-up 1) or short (95 mm: Set-up 2) and the same standard tail-cord length. The first modes of the tailpiece on the Dead Rig, in group I and group II (Figure 4) as we have shown in previous articles [1] are rigid Body Modes. On the Dead Rig, we get the same frequencies for a normal Set-up and for a smaller after-length. Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden In group III (the bending and torsion modes), the RMS shows strong differences between #6 (Bending 1) and #7 (Torsion 1): the longer tailpiece has a lower frequency for the flexion and torsion modes (beam modes) indicating a greater flexibility of the tailpiece itself giving them more amplitude. The shorter tailpiece and longer after-lengthhave lower energy in amplitude. Figure 4. Test 1 : Modal analysis of the tailpieces T1 and T2 on Dead Rig, RMS of Set-up 1 (pink) and Set- up 2 (blue). Here, we see that the modal differences are due to the length of the tailpiece, which is less flexible in the shorter tailpiece (Set-up 1) in the bending and torsion modes, rather than effects coming from the after-length modifi- cation. 3.1.2 Comparison of three different tail cord lengths We compare the Set-up 3, 4 and 5 on the same Adjustable Tailpiece T.3monted on the Dead Rig (Figure 5). - Set-up 3: standard after-length, long tail cord. - Set-up 4: long after-length, standard tail cord. - Set-up 5: long after-length, short tail cord. 3.1.2.1 Effects on Swing and Rotating Modes (Group I): For modes #1, #2, #3 (the swing and rotating mode (see [1]) around 57 Hz) we have shown previously that the tailpiece has rigid body modes and that it swings and rotates on its attachments. The three Set-up show the same frequencies. Amplitudes of Set-up 3 with standardafter-length and a long tail cord is significantly above the two others (8.2 dB, 9 dB). 3.1.2.2 Effects on See-saw Modes (Group II): For modes #4, #5, we found previously that the tailpiece on the Dead Rig present see-saw balancing modes around 200 Hz: Here, frequency rises +10% between Set-up 3 and Set-up 4 with a diminution of 23% of the tail cord length. Frequency rises + 25 % for a diminution of 54% of tail cord. The increase in frequency is significant with the diminution of the tail cord. Figure 5. Modal analysis of tailpiece T.3 on Dead- Rig: Long tail cord: Set-up 3 (red), standard tail cord: Set-up 4 (green), short tail cord: Set-up 5 (turquoise). 3.1.2.3 Effects on Bending and Torsion Modes (Group III): Modes #6, #7, #8, of the tailpiece on the Dead Rig were found to be bending and torsion modes just above 450 Hz: Here, frequencies are very similar for Set-ups 3, 4 and 5 of the adjustable tailpiece. Amplitudes are similar for Set-up 3 and Set-up 4, while the amplitude of Set-up 5 is lower in the middle range: the tail cord being very short damps the #7 bending and torsion mode. Thus, it is more the length of the tail cord that affects these modes, and not so much the after-length. When the tail cord is shorter, in Set-up 5, the movement is damped in amplitude but the flexibility of the tailpiece itself is not much affected. 3.2 Modal analyses of the tailpieces on cello Bridge Admittances give us the principal Body Modes of the cello mounted with different Set-up. We compare the effects of two different after-lengths and then of three different after cord lengths on the cello to compare them later with the tailpiece modal analysis on the Dead Rig results. 3.2.1 Comparison of standard and short after-lengths T.1 (standard) and T.2 (long) are compared with two different after-lengths: normal (116 mm) or short (95 mm,) a shortening of 21 mm (-15, 8%) between the two; the same standard tail-cord length is used. We explore the coupling of the tailpiece with the cello Body Modes ex- tracted from Bridge Admittance measurements (Figure 6). 62 Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden Figure 6. Cello Body Modes for standard Set-up 1 (pink) and Set-up 2 (blue) with long tailpiece T2 and shorter after length. Same tail cord length for both. The difference between the standard Set-up and the shorter after-length is very slight: Near A0, two peaks are visible: the lower in frequency is connected with the first modes of the tailpiece (group I figure 4); the second corresponds to the first air mode of this cello A0 which is around ... There is a deep split which corresponds to the coupling of the tailpiece and the cello, and it is similar in both Set-ups. However, when shortening the after-length from Set-up 1 to Set-up 2, i.e. from 116 mm to 95 mm (-15, 8%), the first cello air mode A0 rounded peak on the right is raised only 2% in fre- quency and decreases (-2 dB) in amplitude, while the tailpiece peak on the left is also raised about the same amount with a slightly higher amplitude. Body Cello Mode B1- shows even less difference be- tween the two Set-ups: an increase of 1, 9 % in fre- quency, and similar amplitudes. Body Cello Mode B1+, as the after-length is shortened goes up 2, 5% in frequency and is more separated in three different peaks. The standard Set-up has higher amplitude on B1+. This is the most affected cello Body Mode. 3.2.2 Comparison of three lengths of tail cord The tail cord lengths seem to be of relatively greater importance as we have seen in preceding comparisons (see 3.1.2). We compared the following set ups on the cello (figure 7): - Set-up 4 is the adjustable tailpiece with long tail cord and long after-length. - Set-up 5 is the adjustable tailpiece with shorter tail cord and long after-length. - Set-up 2 is a longer tailpiece with standard tail cord and short after-length. We can see that the cavity mode A0, and the two main Body Modes B1- and B1+ of the cello change with the different settings of the tailpieces. The two normal length tailpieces (Set-up 2 green and 5 turquoise) do not react in the same way, which show the importance of their at- tachments. Figure 7. Cello Body Modes for long tail cord: Set-up 4 (green), standard tail cord: Set-up 5 (turquoise), and short tail cord: Set-up 2 (blue) with long tailpiece T2 and shorter after length. 3.2.2.1 Effects of tail cord length on the Air Mode A0:(92-95 Hz) With Set-up 2, the frequency of mode #3 of the tail- piece itself (around 75 Hz), is distinct from cello A0 frequency (around 92 Hz). The amplitude of A0 lowers very little (-2 dB) when the tail gut is shortened, from Set-up 4 to Set-up, 5. But from a long to a short tail cord, the cello Body Mode A0 peak splits in two, indicating a coupling interaction of the tailpiece mode #3 with the cello mode A0 when shortening the tail cord. The split of A0 is even more striking, and the amplitudes diminish even more (- 8 dB) when the after-length and the tailcord both get smaller with a longer tailpiece in Set-up2. 3.2.2.2 Effects of tail cord length on the cello Body Mode B1-: (169–173 Hz) The B1- peak is split for Set-up 4 (after-length and tail cord longer), a new peak appears at 181 Hz between B1- and B1+ showing a strong effect of the coupling. There, the amplitude is minimum (- 4 dB). Set-up 2 and 5 (after- length and tail cord smaller) have a very clear and strong B1- peak. 3.2.2.3 Effects of tail cord length on thecello Body Mode B1+: (195-199 Hz) B1+ peak is high and clear for Set-up 5 (Turquoise) and Set-up 4 (green) although a little lower in amplitude for the latter. Mode B1+, with Set-up 2 (blue), is loosing a little am- plitude, leaving a main peak with less amplitude and one smaller peak on each side. This indicates the coupling of one or two modes of the tailpiece and a consequence of the split of A0 on A1 (which on cello, is just below B1+). In this Set-up, the tail cord is very small, attaching more firmly the bottom of the tail to the body of the instrument. 63 Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden It seems that while adjusting the Set-up of the tailpiece, the main modes of the cello can be coupled with modes of the tailpiece. This is shown by the split of the peaks into different peaks which lowers the amplitude of the main Body Mode. Set-up 4 with long after-length and long tail cord splits dramatically A0 and B1-. Set-up 5 where the tail cord is very small, attaching more firmly the bottom of the tail to the body of the instrument splits B1+ in three. 3.3 Perception results The cello used for this test is usually qualified as power- ful, open, and slightly more powerful and hollow towards the treble, with a clear sound (in a sense of a lack of roundness). It has a strong wolf note on the F# on the G string. 3.3.1 Tailpiece T.3- adjustable tail cord length:When lengthening the after-length from Set-up 6 to Set- up 5, not much change is noticed. The sound gets a little more precise, the tone nicer, with a little unbalanced treble and a more metallic sound; less dynamic for 3, from small to extra long, the balance between bass and treble is better, treble notes are better and have a larger dynamic range. The whole sounds better, with the basses more open and global resonance also, the precision of attack remaining. However, the wolf note is now strong. The wolf note was reduced with a medium tail cord length. 3.3.2 Tailpiece T.2- Short to Standard After-length:When lengthening the after-length while diminishing the tail cord, from Set-up 2 to Set-up 7, the main sound gets better, from a powerful and metallic character with attack difficulties and unbalanced trebles, towards much better basses and trebles, easy playing and a lesser wolf note. The instrument is more difficult to play but globally has a better tone. 4 SYNTHESIS With three different approaches: modal analysis of tail- pieces under tension on a Dead Rig, comparison of the main Body Modes of the cello obtained from the Bridge Admittance measurements, and musical perception of the instrument, we have tried to isolate the effects of the variability of the after-length. Even though this dimen- sion is linked to that of the tailpiece and of the tail cord, we have isolated this parameter by using artifacts, such as an alternate use of baroque type or modern type of at- tachment on same adjustable tailpiece, and the use of tailpieces of different lengths. The analysis is then ap- proximate, and is getting more precise with other com- plementary tests which are not mentioned in this study, but are included in a PhD in progress. The perceptive analyses remain modest and only qualitative in order to confront dynamic mechanical measurements with percep- tion for each Set-up 4.1 Swing and Rotating Modes (Group I) and A0: Group I is the group of the three first modes of the tail- piece described by Stough [5] and by Fouilhé and al. [1]. They have a strong amplitude around the frequency of the lowest string of the cello (C = 65,4 Hz) and are linked together, however, they do not produce any perceived sound because A0 acts as a filter of lower frequencies. When both the after-length and the tail cord get smaller with a longer tailpiece in Set-up 2, the peak of B1+ is split, which indicate a coupling of some kind. Figure 8: Cello Body Mode A0 (from the Bridge Admittance) for Set-up 3 (red) and Set-up 4 (green). The large red peak of Set-up 3 seen at 82 Hz on the left of the cello’s A0 (93 Hz) (Figure 8) correspond to Tail- piece mode #3 at 75 Hz on the Dead Rig. This can be proved when damping with the hand the vibrations of the head of the tailpiece, then the peak at 83 Hz disappears, leaving a single A0 peak. A0 and #3 could be coupled in some Set-up, for in- stance in Set-up 3 but not in Set-up 4. However, when the after-length or tail cord are varied Group I is not affected in frequency but only slightly in amplitude. As early as 1819, Felix Savart who was working with Vuillaume mentioned the importance of the tuning of A0 with other modes [7]. Carleen Hutchins [8] and Jim Woodhouse [9] confirmed the importance of the tuning of this mode. Recently, Bissinger has shown a correlation between the amplitude of A0 and the tone quality of vio- lins [10]. Thus we have shown that the coupling of the tailpiece with A0 divides the peak of the resonance of the instru- ment, thus sharing the energy between A0 and that mode. This lessens the sound quality especially in the bass reg- ister. It is thus preferable to un-tune the tailpiece from the A0 by means of setting up after-length and tail cord. 64 Proceedings of the Stockholm Music Acoustics Conference 2013, SMAC 2013, Stockholm, Sweden 4.2 Coupling of the Tailpiece’s See-saw Modes (Group II) and the Cello’s Main Body Modes B1- and B1+ Two rigid Body Modes, #4 and #5, belong to group II and have been described by Stough [5] and Fouilhé [1] (Mode #4=Rh), they are see-saw modes. Their frequency is near B1- and B1+ below 200 Hz, in a range where a coupling interaction will influence the tone. Figure 9: Mode #4 of the tailpiece under tension : strong see-saw motion, see [1]. Because of the asymmetric lever which is shorter to- wards the head of the tailpiece (in red Figure 9), because the tailcord firmly holds it on the lower end (in blue), Mode #4 is little affected by the after-length but more by the length of the tail cord. In Set-up 3, 4 and 2, the tail cord gets progressively smaller at each Set-up; the end of the tailpiece is main- tained progressively stiffer near the saddle. The conse- quence is an increase in frequency and lowering ampli- tude of Mode #4 (figure 5). The perception is that the cello’s sound is powerful, richer in harmonics, but more demanding in the emission. In Set-up 4, when the tail cord is at maximum length, if Mode #4 gets below the frequency of B1-, B1+ splits in two peaks (Figure 7). The sound of the instrument is modified, and there is a diminution or even disappearance of the wolf note. The sound is milder, less powerful, less aggressive, lower harmonics are lost, the general tone has less character, and the articulation is less precise under the bow. The tail cord can thus be adjusted between this two ex- tremes but one can expect that it is dependant also on the weight of the tailpiece. 5 CONCLUSIONS The importance of the lengths of the “chain” = after- length + tailpiece length + after cord has been described with modal analysis and related to tonal adjustment. Variations in after-length from standard to smaller af- ter-length do not significantly affect the tailpiece modes frequencies measured on the Dead Rig, nor the Body Modes of the cello on which the Set-ups were tried, ex- cept on the B1+ whose frequency was raised 2,5% with a -15, 8% after-length. The after-length has been found to be more sensitive to diminution than to increase around the standard length. The changes in the standard tailpiece lengths (of 116 mm ± 5 mm) did not affect sensibly the frequencies of the Cello Body Modes nor the perception of the tone, except where the flexibility of the tailpiece itself is involved. It is more in the variations of the tail cord that differences were measured. Frequency rises of + 25 % for a diminu- tion of 54% of tail cord have bee noted. The increase in frequency is significant with the diminution of the tail cord, and these changes were related to perception changes. It is known that the air mode of the cello A0 is impor- tant for the quality of lower tones: The higher in fre- quency and the steeper is the A0 peak, the quicker there is saturation when pushing the string hard with the bow. On the opposite, when the A0 peak is moved and wid- ened towards lower frequencies, the general tone of the instrument is lower, and the bow can be pressed harder. Here, we have found how tailpiece adjustments can be used to move A0 in order to enhance these effects when desirable, as well as how it acts on the wolf note. Other factors are to be associated like weight and wood variations, and have as much importance in the tonal adjustments of the cello. 6 REFERENCES [1] E. Fouilhe, G. Goli, A. Houssay, G. Stoppani, “Vibration modes of the cello tailpiece”, inArchives of Acoustics, 36, 4, 2011, pp.713-726. http://acoustics.ippt.gov.pl/ DOI: 10.2478/v10168- 011-0048-2. [2] Jeremy L. Loebach, Christopher M. Conway, and David B. Pisoni, “Audition: Cognitive influences”, in Bruce Goldstein ed., Encyclopedia of Perception, SAGE, 2010, Volume 1, p.138-141. [3] Andrew J King & Israel Nelken, "Unraveling the principles of auditory cortical processing: can we learn from the visual system?", Nature Neuroscience 12, 698 – 701, 2009. doi:10.1038/nn.2308 [4] Laurel J. Trainor and Andrea Unrau, "Developement of pitch and music perception", in Springer Handbook of Auditory Research: Human Auditory Development, Werner, Lynne; Fay, Richard R.; Popper, Arthur N. (Eds.), Vol. 42, Chapter 8, January 2012. [5] Stough, Bruce. “The lower tailpiece resonances” inCASJ Catgut acoustical society journal 3, N°1 series II, pp.17–25, 1996. [6] Curtin Joseph, “Scent of a violin, the signature modes of Old Italian violins & violas, part 1 “, inThe Strad , June 2009. [7] Savart, Félix, “Mémoire sur la construction des instruments a cordes et a archet”, Paris, 1819, p.135. [8] Hutchins, Carleen M, and Duane Voskuil. “Mode tuning for the violin maker.” in Catgut acoustical society journal Vol. 2 N°4 serie II, 1993. [9] Woodhouse, Jim. 2002. “Body vibration of the violin- What can a maker expect to control ?”, inCatgut acoustical society journal vol 4 N°5, 2002. [10] Bissinger, Bissinger George, “The viocadeas project: Structural acoustics of good and bad violin” in JCASvol 124, 2008, p.1764-1773. 65

I want to say I have seen an adjustable length tail piece some where but I don't remember. DLB

I have tried that on several instruments. When I switched to viola as a kid there was a method book someone gave me and it said that all violas were set up like that. I have never had much luck good or bad trying it but it is sure worth a try. I had a very nice viola that needed a weight under the fingerboard to stop a weird sort of wolf on open A. Nothing to do with the present discussion but I'm sure there are all kinds of tricks and tips that can come to help set up an instrument. I know Manfino uses rather short tail pieces on his violas as he fells the added after length helps the sound. I have always been kind of a slave to the 1/6 thing but I have no imperical evidence . DLB

One could do a pretty subjective experiment with about 16.5" viola and a variety of different tail pieces of different lengths or a viola or cello with fractional size tail pieces. I always understood the rule of thumb to be after length should be 1/6 of vibrating string length but I know for sure in violas it can be all over the place. DLB

I said a thicker string. Should have been a more massive string. They are probably thicker but that is not the correct measurement. DLB

What strings are you using? DLB

But you better do it in metric (SI) units or the ghost of your middle school science teacher with haunt you forever! DLB

https://www.coleparmer.com/i/ohaus-8018-50-dial-type-hanging-spring-scale-with-demonstration-dial-50n-x-2n/1110064?PubID=UX&persist=true&ip=no&gclid=Cj0KCQiAj4biBRC-ARIsAA4WaFi5Rf4PRueyyT2WLABHEdbsogXHFJJiZwdkHy4p4YNvlXxmEBPtm64aAv3sEALw_wcB Something like this with some weights, a 2x4 board a string and some pulleys would get it done maybe. DLB

Snapping Tail Guts...... If that isn't a name for a band I don't know what is! DLB

I think you are right. DLB

Would the tailpiece and the tail gut be part of the same system? If you had the same instrument with shorter or longer tailpieces the length of the whole thing under tension would be the same just more or less afterlength and less tailpiece or less afterlength and more tailpiece. Sorry about my typing, my eyes are really acting up. I go see the surgeon next friday! DLB