sustain

[John Bertotti]

Keeping in mind I'm counting in my head and picking with my right hand not a finely calibrated tool with exact pick strength every time. Octave mandola strung up five courses as follows lowest G rung between 16 and 18 seconds same for D and A. The E rang for almost 23 seconds and the highest currently tuned to B rang for the least at about 12 to 13 seconds on average. These are what I come up with every time.

1) Now does this give me some idea as to most dominant note of the instrument with that E sustaining the longest?

2) Would the correct term be wolf note? It doesn't woof or have any beats just rings on and on and on.

3) Is it normal for one string to out sustain the others?

4) Is there a way to build to balance this?
Thanks all John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/rock.gif

[Dave Cohen]

John, you have just opened up a can of worms, so to speak.

Generally speaking, a string plucked at a given note will sustain longer if there are no body modes at nearby frequencies to steal energy from it. That is a double-edged sword, however, b/c the body modes are necessary to excite the air modes in order to get efficient sound radiation. The strings, owing to their dimensions, don't radiate sound with anywhere near the efficiency of a soundhole or a plate.

Most often, just plucking the open strings and measuring "sustain" doesn't tell the whole story. You should do the same for each fretted note up to the 6th fret on each string as well. Another problem is the way you are measuring "sustain". Physicists use the "characteristic time", which is defined as the time it takes for the sound pressure level to decay to 1/e of its largest amplitude. The number "e" is the base of the natural logarithm, and has the value e = 2.7183..., so 1/e has a value of about 0.368. In other words, the characteristic time is the time it takes for the sound pressure level of a plucked note to decay to about 37% of its highest value. One way to do that would be to use the mic and sound card in your computer. You will get something that looks like a tornado on its side. Strictly speaking, you should take the absolute value of that data and then smooth the peak values, then find the characteristic time from the graph. For your purpose though, you could dispense with the absolute value business and just look for the 37% value on your graph.

What you are looking at is not a "wolf note". Wolf notes in plucked string instruments are notes which decay especially fast, i.e., the opposite of what you are dealing with. In bowed string instruments, a wolf note is a loud and harmonically unpleasaant note produced by some nonlinear phenomena.

What can you do in building to avoid your problem? Good question. I'll let you know if I live long enough to figure it out in the lab. The intuitive type luthiers will probably tell you to keep building, keep track of your results, etc. To really delineate your problem, you need to giv dimensions such as scale length, frequencies of body modes, etc.

[John Bertotti]

Thanks Dave, I actually understood every word. I knew I should of went fishing instead.

Actually I remember a thread a couple years ago where someone was using a hacklinger gage to measure tops and backs. What they discovered of one maker in particular was that certain spots on the top were left thicker. Could this be an individuals approach to working with these issues? By the way I have no idea off the top of my head who was doing the measuring or who the builder was.

Thanks John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/mandosmiley.gif

[Dave Cohen]

I think that the "lumpiness" seen in some builders' plates could be one of two things. It is either the result of their tapping and listening process, i.e., when they feel that the plate is "there", they just stop graduating, lumps or no, or else it is just sloppiness. I don't know which, but I do know that physics has a slightly different take. Tom Rossing has a paper in 1981 or thereabouts in the short-lived Journal of Guitar Acoustics. In it, as a result of a combination of simulations and modal analysis, he concluded something to the effect that 'it doesn't matter how you make it stiff, only how stiff you make it'. In other words, where the lumps, braces, etc., are doesn't matter as much as the overall stiffness, and maybe ratio of longitudinal to lateral stiffness, of the plates

[John Bertotti]

Thanks Dave, funny how dispelling some myths in the end will probably save some time. John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[Martin Jonas]

John,

Another thing to consider when measuring sustain from course to course is that you won't get a reliable measurement unless the two strings of each course are in perfect unison. #Even a very slight difference in tuning between the strings leads to destructive interference and greatly accelerates note decay. #The differences between the course that you've noticed may be indicative of the instrument, they may also reflect minute deviations from perfect unison.

Martin

[Dave Cohen]

Martin, I think that you might want to revisit the fundamentals regarding your post.

(1) Small differences in frequency between the two strings in a course will result in beats, and the overall decay envelope will be a decreasing exponential, very similar to what would be seen if the two strings in the course were exactly in tune. Beats are a lot different from (totally) destructive interference.

(2) Getting the two strings in a course exactly in tune is a near impossibility. What happens is that you get 'em close, then they start exchanging energy via the bridge.

(3) Phase is another problem, though it does not apparently lead to destructive interference. The two strings start out in phase, or nearly so, then at some point get out of phase, and the decay changes. Gabriel Weinreich had a paper on this back in 1977. The reference follows:

Weinreich, G. (1977) "Coupled Piano Strings", J. Acoust. Soc. Am. 62 1474-1484.

The contents of that paper will definitely surprise you, as there is not cancellation as you suggested.

[Martin Jonas]

Dave,

I'll have to check that paper. "Destructive interference" was a sloppy term for me to use; what you get for not-quite-in-unison strings is two waves of slightly different frequency which go in out and out of phase, i.e. alternating constructive and destructive interference (in other words, a beat). However, I would have thought that the extent to which the strings are in unison should affect the overall decay envelope. My thinking is that the wave function decays as a result of energy dissipation from the string through the bridge and the instrument. I haven't analysed the dynamics of string energy dissipation (not really my field of physics) but is energy dissipation really linear to wave amplitude? My expectation would be (possibily erroneously) that doubling the amplitude more than doubles the rate of energy dissipation. If so, then the presence (and magnitude) of a beat should accelerate the overall rate of energy dissipation: during the periods of constructive interference the rate of energy loss is greater than during those of destructive interference, and if I'm right on the non-linearity, the average energy dissipation for beating strings should be greater than for strings that are more closely in unison, i.e. a faster decay and a shorter sustain. Am I coming at this from the wrong angle? As I said, it's not my field of physics, and I know you've studied these questions in great detail, so I wouldn't doubt what you say on this; I'm just surprised.

Martin

[Dave Cohen]

Yep, read Weinreich's paper. Or you can catch a very abbreviated digest of it in the Fletcher & Rossing text, "The Physics of Musical Instruments" (2nd Edition) pp 385-6 (chapter 12), Springer, 1998.

[Larry Simonson]

This thread brings to mind my interest in a data base of objective properies of mandolins. Would a well chosen set of sustain-time-constants for a particular instrument be instructive, perhaps not by itself but relative to another instrument?

[Dave Cohen]

The bigger question is "What constitutes a representative set of characteristic times for a given instrument?" If you measure the characteristic times for each open string and each fretted note up to the 6th fret on each string and the 7th fret on the E string (i.e., every half-step from the 196 Hz G up to the 880 Hz A), you will find not just variation, but variation by more than an order of magnitude. On an f-hole archtop mandolin, the body modes start at anywhere from 270 Hz to 330 Hz The lowest note on the mandolin is the 196 Hz open G, which will have a fairly long characteristic time. As the notes get closer to the frequency of the lowest body mode, the characteristic times will get shorter. Since the body modes are pretty evenly distributed in mandolins, there are really no gaps which will allow for notes with longer characteristic times. So every note above the frequency where the body modes kick in has a vastly shorter characteristic time than is the case for the notes below the body mode frequencies. I did that exercise for a couple of Neapolitan mandolins. In those things, nothing happens in the body until 500 Hz or higher. So starting at about 450 Hz, the characteristic times dropped off rapidly. By about 500 Hz, the characteristic times were shorter by at least a factor of ten than those below 450 Hz, and they remained short up to 880 Hz (and presumably beyond). The moral is that to assemble meaningful data for comparisons between mandolins, you would have to measure characteristic times for every note on each instrument to be comnpared, and do the comparisons note by note.