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Thread: IMO - Why red spruce is the loudest top wood

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    Default IMO - Why red spruce is the loudest top wood

    Achieving a loud mandolin top is simple physics. Given the same dimensions, bracing and the same strings, force of picking, a similarly stiff top with the least mass will produce the highest volume. The role of mass is obvious, the ratio of the mass of the moving string to the mass of the sound board determines volume. Stiffness is required in order to keep the vibrations of the string from immediately dissipating.

    Spruce in general is remarkably stiff for its mass. That is why it was used to build airplanes a century ago. A slightly softer, less dense, less stiff, piece of spruce can sound very close to a harder, heavier, stiffer piece. If the former is carved thicker, then the two pieces can be similar in overall mass and stiffness.

    Red spruce is fundamentally different from Engelman, Sitka, etc because it has alternate white and red, summer and winter, softer and harder, lighter and denser, less and more stiff rings. The hard red grain acts as little stiffening braces so that the vertical span of the top can achieve a given stiffness with less mass. The wider the grain and the darker the red rings, the less mass is required to achieve a given stiffness. While all spruce may have this property to some extent, the red grain in red spruce is the stiffest of any spruce. Lightness and darkness seem to indicate the density / degree of stiffness.

    Now this property also means that the horizontal stiffness is not inherently as great as the vertical stiffness. However, given the shorter span, more pronounced arch, and the reinforcing bridge plate near the widest horizontal point the width of the top seems certain to be stiffer overall than the length, even with red spruce.

    So red spruce = less mass = more volume. Wider, darker red grain = even less mass = even more volume. The equation loudness = tone is beyond the scope of this post.

    After Barry Kratzer told me that he swears by wider grain red spruce last night I did some research and think I see the reason why.
    Last edited by Greg P. Stone; Jul-14-2019 at 8:39am.
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  2. #2

    Default Re: IMO - Why red spruce is the loudest top wood

    Per Gilchrist:
    Red Spruce Picea rubens,..., is the hardest of its species and a good choice for soundboards where clarity is important when playing with other loud instruments. Needing a little more time to play-in than softer spruces, it has the potential of developing into the clearest most powerful tone with strong mid-range projection

    This also explains why so many luthiers state that red spruce is the stiffest / loudest despite wood databases showing similar hardness to other spruces. Red spruce may have the same average hardness, but its widest disparity between softer white and harder red rings makes it the stiffest for soundboard purposes.
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    Default Re: IMO - Why red spruce is the loudest top wood

    From my experience working with red spruce, it make a powerful mandolin. The red spruce I have is from my good friend Ken Ratcliff. It was cut 100 years ago. It is dry. It is very light and responsive. I'm graduating a top that has fairly even, close grain and it is so noisy when handling it. It will make a great mandolin like all the rest have been when using this spruce.

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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by Greg P. Stone View Post
    Achieving a loud mandolin top is simple physics. Given the same dimensions, bracing and the same strings, force of picking, a similarly stiff top with the least mass will produce the highest volume. The role of mass is obvious, the ratio of the mass of the moving string to the mass of the sound board determines volume. Stiffness is required in order to keep the vibrations of the string from immediately dissipating.
    Writing as a physicist, achieving a loud mandolin is certainly a matter of physics, but I cannot agree that it is a matter of "simple" physics. In fact, I only wish it were that simple. Alas, it is not!

    For a given stiffness, the resonant frequencies of the top (that is, the set of vibrational modes, which can be revealed by Chladni sand patterns or infrared vibrometry, etc.) will be higher for a less massive top. These resonant frequencies are roughly proportional to the square root of the stiffness, and inversely proportional to the square root of the mass-per-unit area. But having a higher set of resonance frequencies does not necessarily make for a louder mandolin.

    The loudness is a matter of how efficiently the fixed, vibrational energy of a plucked string (imparted by picking and releasing) is transduced into vibrations of the top, and then re-radiated into the air. The physics of this transduction is extremely complicated, and there exists no simple formula to describe it. This stands in sharp contrast to the resonant frequencies (modes), which can be measured, or also found numerically, even for a complex shapes, by fairly involved computer simulations. The loudness will depend on how well the acoustic impedance of the string is matched to the saddle and bridge, and then matched from the bridge to the top, and then from the top into the surrounding air. The sound field of a mandolin is not uniform, as we all know: many mandolins, especially those with f-holes, tend to project more sound forward than sideways or rearward. These acoustic impedance matches are related to things like the shape/geometry, the fit of the parts (think about adjusting the bridge to fit the top), the flexure of the top (related to its thickness and graduations, of course, but ALSO to the flexibility of the unit at the rim, due to things like the recurve), the string downbearing forces, and a whole lot more.

    As if that weren't complicated enough, there is an important third variable at play here, in addition to the quantities of mass and stiffness, and that variable is the damping. This quantity refers to how the various parts of the mandolin can dissipate the string energy in ways that do not result in vibrating the surrounding air. Mostly, this energy appears as a tiny amount of heat being generated (but not enough to feel with your body). The heat is quite small because it takes an enormous amount of mechanical energy to raise the temperature by much (Joule discovered this in 1843). So the mandolin can lose sonic energy due to the internal damping of the top, back, and side wood, and to damping at the instrument at all points of flexure (joints, recurves, bridges, etc), and so on. Different types of wood will display different amounts of intrinsic damping, in addition to different types of density (mass) and stiffness (flexure). This is an important consideration, too. Instruments with more damping have less energy going into sound and more into heat. Things like the type and thickness of the finish can affect the damping strongly, by the way, without changing the stiffness or the mass appreciably.

    Unfortunately, these three physical quantities (density, stiffness, and damping) are not related in any simple way to any obvious property, like the wood grain width, nor to its color (e.g. darker red), nor to the alternation of wider and shorter growth rings, nor any other easily observed attribute. We can only wish it were that easy! Alas, it's not.

    I'm afraid that your theory is more of a "Just So" story that merely rationalizes your assumed conclusion that red spruce is somehow louder than other alternative woods. It's not.

    In a quest for volume, the famous modern luthier Joseph Curtin has even experimented with a cleverly laminated violin top made entirely from -- amazingly! -- balsa wood. It produced the loudest violin that he'd ever tested. Significantly louder than red spruce. So it's not just about the grain or rings or color or the siffness, per se. I'd say it's complex physics, not simple physics.
    Last edited by sblock; Jul-14-2019 at 11:55am.

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    Default Re: IMO - Why red spruce is the loudest top wood

    When I took physics we started with the ancient Greeks and what I learned is that simpler systems work and are useful despite not being as accurate. "density, stiffness and damping" is exactly what I was talking about. You add a bunch of design options which I excluded by stipulating that the comparison was between two tops of the same dimensions which makes me wonder if you even read my post. Of course I'm going to simplify to examine the difference of a single element. You go ahead and tell Stephen Gilchrist that he is engaged in a "just so" story when he reports his conclusions based on a lifetime of experimentation.
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    Default Re: IMO - Why red spruce is the loudest top wood

    And sometimes you have to hold your tongue just right to produce the best result, even with red spruce.

    As someone who has spent a fair amount of time and effort looking for "the" or "a" magic relationship (in a completely unrelated field except that it involved physical properties of biological materials), I have to say that sblock's response makes a lot of sense to me.

    Which is not to say that you can't make a loud mandolin using red spruce for the top.
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    Default Re: IMO - Why red spruce is the loudest top wood

    The plural of anecdote is not data, even for Steven Gilchrist.
    Play it like you mean it.

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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by Greg P. Stone View Post
    When I took physics we started with the ancient Greeks and what I learned is that simpler systems work and are useful despite not being as accurate. "density, stiffness and damping" is exactly what I was talking about. You add a bunch of design options which I excluded by stipulating that the comparison was between two tops of the same dimensions which makes me wonder if you even read my post. Of course I'm going to simplify to examine the difference of a single element. You go ahead and tell Stephen Gilchrist that he is engaged in a "just so" story when he reports his conclusions based on a lifetime of experimentation.
    Of course I read your post. And of course physics embraces simple models that tend to capture the essence of more complex phenomena. But writing as a professional physicist, your model does not capture that essence.

    Actually, in all fairness, you never mentioned damping at all -- just mass and stiffness. Damping is critically important part of the physics of wooden instruments, especially where loudness is concerned, and you left it out entirely. In addition, I rather tend to doubt that Steve Gilchrist would agree with your simplistic theory about alternating red and white rings, as formulated earlier. Yes, he likes to build with red spruce (many luthiers do: it's a fine choice), and he has long experience with it, but he doesn't rationalize his preference in the way that you do. So please, don't speak for him. I repeat: you have managed to come up with a "Just So" story.

    Also, no one here is saying that a red spruce top cannot make for a loud mandolin. Of course it can. Hey, it's a great top wood! But so are some other woods. Quite loud mandolins can also be made with well-chosen pieces of Sitka, Engelman, and other spruce varieties. Loud mandolins can be also made with cedar and redwood, too. Loud mandolins can, and have, been made with hardwood tops, as well. Yes, it's about getting just the right combination of stiffness, damping, and density for the top wood -- in addition to all the rest (shape/geometry, graduations, string downbearing, bridge mass and fit, finish, etc, etc.). And not all red spruce will fit the bill, any more than some different wood. Proper wood selection for a mandolin top is a complex issue, and over-simplifying it to a quest for alternating red and white rings of certain sizes in Adirondack spruce just misses too much. I doubt that many professional luthiers would subscribe to your simplistic theory -- even those that prefer to build with red spruce.

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    Default Re: IMO - Why red spruce is the loudest top wood

    On average, red spruce is said to have the highest stiffness to density ratio of spruce species. That does not mean the every piece of red spruce is stiffer than every piece of Euro, Engelmann, white, sitka, blue, or any other spruce species. I'll take a light, stiff piece of sitka over an heavy, not-stiff piece of red spruce any day.

    One of the main things that makes a mandolin loud is good coupling. That has very little (if anything) to do with the species of spruce used for the top.
    Yep, it is a complex system, an though I have not heard Steve Gilchrist or any other maker make simplistic general statements about the performance of various spruce species in tops, I don't mind saying they are wrong if they are wrong, regardless of how much more money they are able to get for their mandolins than I am able to.

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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by sblock View Post
    In a quest for volume, the famous modern luthier Joseph Curtin has even experimented with a cleverly laminated violin top made entirely from -- amazingly! -- balsa wood. It produced the loudest violin that he'd ever tested. Significantly louder than red spruce. So it's not just about the grain or rings or color or the siffness, per se. I'd say it's complex physics, not simple physics.
    As a group, there were guitars which had an enormous dynamic range on tap, and monster sustain available. They had soundboards made of thin balsa wood, sandwiched between thin carbon skins. The soundholes were moved to the upper bout so as to leave a larger plane uninterrupted. The soundboard was mounted at the edges on what I think was called a "dynamic suspension" instead of being stiffly attached to the top, preventing energy loss from the damping introduced by requiring the stiff soundboard to flex at the edges when hard attached. The later Ovation Adamas guitars never achieved the same volume and sustain as the originals.

    I know that most bluegrass mandolin players actually rely on the high frequency roll-off inherent in the standard BG mandolin, leading to the lack of enthusiasm for construction types which reproduce the full frequency range of the strings. However, I always found that even design changes like moving the soundholes away from the center of the board (like in Tacoma mandolins) will increase volume.

    I've always been curious about taking such designs, and then adding selective dampening, as found in the enormously woody-sounding Composite Acoustic Legacy-model carbon fiber guitars, to get back the woody thunk and chop desired by traditionalists. For me the curiosity is purely academic though, as I prefer having the full frequency range available in the first place, instead of having the filtering built in.

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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by sunburst View Post
    On average, red spruce is said to have the highest stiffness to density ratio of spruce species. That does not mean the every piece of red spruce is stiffer than every piece of Euro, Engelmann, white, sitka, blue, or any other spruce species. I'll take a light, stiff piece of sitka over an heavy, not-stiff piece of red spruce any day.
    Agreed.

    The last time I bumped into John Arnold, and he said he had just cut a couple of red spruce trees, which had yielded several hundred tops. Here's the rest of the conversation:

    Me: Was any of it any good?
    John: Yeah, about 40 of them were very good. I kept them. I sold the rest to [major manufacturer's name].

    Instrument construction is an art, not a science. And no two pieces of wood are exactly the same, even if they are from the same tree.

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    Default Re: IMO - Why red spruce is the loudest top wood

    I share the opinion that red spruce is among the best, if the best top wood for mandolins, and probably guitars too. That's from years of playing guitars and mandolins and figuring out what I like to hear. If someone else prefers a different wood, that's fine with me.

    The theory of why posed above is off a bit I think. The OP appears to be attributing characteristics to the wood based on what he sees. We all do that to some extent, and oftentimes we're correct. Sometimes not though. In this case all spruces have both late and early (hard and soft wood) but it is sometimes more prominent in red spruce. That's not always true though. We do see it a lot in the currently harvested red spruce, especially examples with prominent compression grain. Again though, what we can see doesn't tell the whole story.

    It was incorrectly stated that red spruce is the lightest and stiffest spruce. It's typically heavy, but also stiff. That means a good builder can make it thinner and get the same strength, but it's not inherently lighter. Since John Arnold was brought up, here's a quote from him - related to guitar tops, but the spruce comments are applicable regardless.

    A quick synopsis:
    Red spruce = heavy and stiff
    Sitka = heavy and less stiff
    Euro = light and stiff
    Engelmann = light and less stiff

    On paper, Euro spruce beats everything. But just because something is theoretically the best does not necessarily mean it produces the most pleasing result.
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    Default Re: IMO - Why red spruce is the loudest top wood

    Here's where I mention dampening: "Stiffness is required in order to keep the vibrations of the string from immediately dissipating."

    Now you obviously have a lot to say that is worthwhile. But it would be far more effective if you would avoid infantilizing those you address. Now you and Bill may feel that no amount of experience gives anyone any insight into wood choices but you are demeaning and dismissing a vast amount of practical experience and knowledge. You are attacking most luthiers and most mandolin players as having worthless opinions. Well as someone new to this forum and mandolins my opinion may have little value; that's why the first thing in the title is "IMO". But guess what? I have every right to express it without being belittled and mocked.
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    Default Re: IMO - Why red spruce is the loudest top wood

    I’m just stating the experience is not science. There’s no controlled, reproducible data generated that way.

    Can’t see that statement as demeaning to anyone.
    Play it like you mean it.

  19. #15

    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by Bill McCall View Post
    I’m just stating the experience is not science. There’s no controlled, reproducible data generated that way.

    Can’t see that statement as demeaning to anyone.
    You communicated much more effectively this time. Even so I would submit to you that every mandolin built is a controlled experiment that produces a result. Those luthiers who are successful over a long period necessarily draw valid conclusions from experiments to enact continual improvement.

    The first time you wrote that Steve Gilchrist and all those of similar dedication and experience have nothing to offer but anecdotes. On reflection I think you will conclude that the two messages are vastly different in tone and substance.
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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by Greg P. Stone View Post
    Here's where I mention dampening: "Stiffness is required in order to keep the vibrations of the string from immediately dissipating."

    Now you obviously have a lot to say that is worthwhile. But it would be far more effective if you would avoid infantilizing those you address. Now you and Bill may feel that no amount of experience gives anyone any insight into wood choices but you are demeaning and dismissing a vast amount of practical experience and knowledge. You are attacking most luthiers and most mandolin players as having worthless opinions. Well as someone new to this forum and mandolins my opinion may have little value; that's why the first thing in the title is "IMO". But guess what? I have every right to express it without being belittled and mocked.
    My goodness. No one here is infantilizing, belittling, or mocking you, so please get over that. No one is demeaning experience, either. This is a serious forum and our responses have been appropriately serious and science-based. I just happen to think you are entirely wrong, and that your "simple explanation" doesn't explain the facts, at least as we currently understand them. Furthermore, no one here is saying that loud tops (even the best tops) can't be made from red spruce. But we are saying that your theory for the reason why red spruce is a good choice is overly simplistic, and unlikely to be valid. Not all of the loudest mandolins out there are made from red spruce, after all, so other choices can clearly work well, too. Furthermore, NO ONE is "attacking most luthiers and mandolin players as having worthless opinions." No credible reading of anything written in this thread would reveal any attacks on the opinions of "most luthiers and mandolin players." My goodness, no! Many players and luthiers hold the opinion that red spruce is an excellent choice for a topwood (and so do I). There is no argument about that. But I (and others) disagree with your entirely conjectural theory about why red spruce is a good choice. You seem to be confusing these two very different things. You also seem to be interpreting any disagreement with your theory as a personal attack. It is not.

    Finally, you wrote that "Stiffness is required in order to keep the vibrations of the string from immediately dissipating." And you claimed that this is where you mentioned "damping." Huh? There is no mention of damping. And stiffness (or lack thereof) does not cause dissipation, sorry. What you wrote is wrong from a physics perspective. You have confused high stiffness with low damping. It is true that a lot of stiffer woods also tend to have less internal damping, so these quantities can be correlated, but they are intrinsically different (and measured using different units), and they lead to very different physical consequences. In general, having more stiffness does NOT necessarily result in having less dissipation, so what you wrote was technically wrong (sorry). Less damping results in less dissipation. The ring-down time of a string (sustain) is a function of the rate of energy loss. That loss takes two main forms: (1) energy radiated as sound (loudness) into the surrounding air, and (2) energy dissipated as heat inside the instrument (with no associated sound production). Key sources of dissipation are joints and gaps in the structure, and losses through friction in the flexure of the wood or finish, due to conducting vibrations. Again, this is not about stiffness. Stiffness and mass alone lead to what physicists call a "conservative force," i.e., one where a return to the original position (say, after a single cycle of vibration) results in the same energy as before. Conservative forces will never cause a note to ring down. Damping, on the other hand, is an non-conservative effect that will definitely cause a note to lose energy. And so will radiating the energy into the air, as sound.

    Honestly, I am trying to give you a serious answer here, so please don't interpret this response as an ad hominem attack. It isn't. Just because I don't approve of your theory doesn't mean I don't (or won't) like you. We've not met, after all. And I have found a lot to like in most mandolin players!
    Last edited by sblock; Jul-14-2019 at 3:42pm.

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  22. #17

    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by Greg P. Stone View Post
    You communicated much more effectively this time. Even so I would submit to you that every mandolin built is a controlled experiment that produces a result. Those luthiers who are successful over a long period necessarily draw valid conclusions from experiments to enact continual improvement.

    The first time you wrote that Steve Gilchrist and all those of similar dedication and experience have nothing to offer but anecdotes. On reflection I think you will conclude that the two messages are vastly different in tone and substance.
    The tone of those two posts may be different, but the substance was supposed to be the same, anecdotes are not data points. Further, an event is not the same as an experiment.

    But for data, 'Technical Bulletin #158, Comparative Strength Strength Properties for Woods Grown in the United States" is quite interesting. Table 1, page 12, shows comparative numbers for Engelmann (often a choice for luthiers), red and sitka spruce. The stiffness of sitka is slightly greater than red spruce, with Engelmann significantly less stiff. I recognize this is not a tone wood experiment, but discussing the characteristics of wood on their strength, weight and stiffness characteristics can easily be done with actual data.

    I have no doubt that red spruce is an excellent tone wood, and so is sitka spruce. Engelmann spruce, cedar and redwood are also fine tone woods. I have instruments made from different tone woods, I attribute the sonic differences to the skill and design of the maker.
    As noted above, how that wood is used in an instrument is subject to wide variabllity.
    Play it like you mean it.

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    Default Re: IMO - Why red spruce is the loudest top wood

    In the violin-making world, these types of discussions have been going on in various forms for a couple hundred years now. Lots of money involved, lots of bright people, lots of skilled craftsmen, a number of pretty good scientists. Interesting reading on the violin makers forums.
    -Dave
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    Default Re: IMO - Why red spruce is the loudest top wood

    All that I know is that a great builder can make great mandolins with a variety of woods for the soundboards. I don't prejudge based on the type of wood used, but judge a mandolin based on how it sounds. And I know that a Collings with an Adi top or an Italian spruce top will sound more like a Collings than a Gibson, which will sound more like a Gibson with Adi or sitka, or an Ellis with any type of spruce, or a Gil, or a Kelly, or... and we all respond differently to those voices. Viva la difference!

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    Default Re: IMO - Why red spruce is the loudest top wood

    I think one thing is missing in this discussion and that is what do you mean by "loud". Is it the amount of energy in the sound waves radiated by the mandolin (the physics view) or is it how we can hear the mandolin in a noisy environment. The latter does not necessarily match the former because the frequency content and the perceptions of our auditory system comes into consideration for the latter. Most of us would consider the latter to be of most relevance, but it is also by far the most complicated. My experience mirrors that of Gilchrist. Red Spruce tends to produce the most powerful instruments, and I think that is because it tends to produce mandolins that have higher clarity in the sound that cuts through the noise of other instruments. The obvious question now is how do you define clarity in physics terms. I dunno, I just hear it, I have not measured it. Has anyone done FFT analysis of mandolins that have great clarity and those that don't? Measuring the modes of vibration is not going to give you the answer, nor is it going to tell you how to make mandolins that have great clarity in sound.
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    Default Re: IMO - Why red spruce is the loudest top wood

    There is a lot of science that goes into getting volume from a mandolin, but not much of that science is known or well understood.
    I think it is agreed that for the wood top, low specific gravity and high stiffness is important for volume.
    Since luthiers build their mandolins differently, other factors will also have a significant and uncontrolled impact.
    As an estimate based on the following table, it appears that other factors being equal, Red and Sitka Spruce have the highest ratio, and should be the best for volume.

    Wood (Sp Gr) (Mod of Elasticity MPa) Ratio
    Black Spruce 0.46 11100 24130
    Engelmann Spruce 0.35 8900 25429
    Red Spruce 0.4 11100 27750
    Sitka Spruce 0.36 9900 27500
    White Spruce 0.4 9200 23000
    Silver maple 0.47 7900 16809
    Red Maple 0.54 11300 20926
    Balsa 0.16 3400 21250
    From Mechanical Properties of Wood, David W. Green, Jerrold E. Winandy, and David E. Kretschmann

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    Default Re: IMO - Why red spruce is the loudest top wood


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    Default Re: IMO - Why red spruce is the loudest top wood

    I'm neither a physicist nor a long-time mandolinist; just an average guy who is learning his way around a new (to me) instrument. But I have been a musician going on 50 years and I like to think I have what my grandma used to call "a grain of common sense."

    In essence we're talking about taking a piece of what was once a living organism, crafting it by the hand of another living organism, using primarily techniques derived by years of trial-and-error, and evaluating the results by the most subjective means possible; i.e., aesthetics. Then we're trying to compare that subjective evaluation to other subjective evaluations made by other people, of other instruments crafted by individual craftsmen from other pieces of once-living organisms, and trying to draw some type of general conclusions as to what makes one instrument sound like/different from another one.

    All that to say that while scientific inquiry is a good thing even in music, and anything which advances the art and science of lutherie is a good thing, trying to definitively answer some of the questions surrounding musical instruments is probably like trying to understand why your Uncle Ned fell in love with your Aunt Bessie and calls her "Beautiful" when the rest of the family all agree that her face could stop a clock and her singing has been known to attract loved-starved bull moose.
    -- Johnson MA-100 Mando
    -- Eastman MDO-305 OM
    -- 3 Seagull Merlin dulcimers (2GDG, 1DAD)
    -- 1952 Harmony Roy Smeck guitar
    -- Ortega Lizzie Ubass
    -- Pfretzschner violin
    -- Glaesel viola
    -- Ibanez acoustic/electric
    -- Misc: cello, cigarbox guitars, charango, lots of stuff on wish list.

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  33. #24
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    Default Re: IMO - Why red spruce is the loudest top wood

    Not a luthier but Bill McCall's "The plural of anecdote is not data" is one of the best things I have ever read on the Cafe.

  34. #25
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    Default Re: IMO - Why red spruce is the loudest top wood

    Quote Originally Posted by JimKo View Post
    Not a luthier but Bill McCall's "The plural of anecdote is not data" is one of the best things I have ever read on the Cafe.
    That expression is certainly one of my favorites, and it's a popular one, but it wasn't coined by Bill McCall. Interestingly, it says the exact opposite of the original quote, due to Raymond Wolfinger in 1969, to the effect that "the plural of anecdote is data." See http://blog.danwin.com/don-t-forget-...cdote-is-data/, for example, for a bit of history on this. But most of us scientists feel that Wolfinger had it the wrong way around! A bunch of anecdotes, usually collected under very different circumstances, do not constitute a trustworthy data set. The saying that "the plural of anecdote is NOT data" has more validity, and these days, you can even buy a T-shirt that says it:

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