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Andreas Preuss

How important is the overtone range to the sound of a violin?

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1 hour ago, Michael Darnton said:

One of the methods I use to help prospective buyers sort out instruments is the presence of absence of these components. Some violins just want to change pitch with vibrato and not too much else. With better instruments you wouldn't even care if the pitch change were there or not, because it's the harmonic envelope of the note that's doing most of the pulsation. When you learn to listen for it, it's a dramatic difference that better violins have.

This doesn't imply that the better violin has more overtones; I think it means that the  superior system is more fragile to tiny changes where the cheaper just wants to plow on doing the absolute minimum. That's one of my arguments against things like plate tuning and making instruments to "sound like Strads", since that kind of building is all about locking in behavior, not facilitating variability. I think it's better to have an instrument that's able to respond differently to every twitch that's thrown at it, not one that gives what it's been programmed to give, regardless of input. Appreciation of this is directly related to the player's control, and control is directly a product of competence, which I believe accounts for the widespread acceptance of reliably monochromatic instruments in preference to exciting ones.

I have mentioned it before,  but it is worth repeating.   Scientific American magazine had an article many years ago about a very old trumpet which had been hammered out on a wooden mandrel.  It had lots of irregularites and dents.

Players found that the tone was "more flexible" then with a modern trumpet.  Maybe violin makers try to be too precise   (????)

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Re: Guitars, at least the steel string variety. The cost of Martins from the 30's or Gibsons from the earlier 40's as well as the tone produced by folks like Tony Rice [30's Martin] or Russ Barrenburg [40's Gibson] would suggest that "wearing out" is not the case.

Classical Guitars "may" be different, but I suspect not.

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4 hours ago, David Beard said:

So the octaves of the fundamental are the powers of two:

2^0 = 1  The fundamental of a series.

2^1 =  2  the octave

2^2 =  4  the second octave

2^3 =  8  The third octave

2^4 =   16 The fourth octave

2^5 =   32 the fifth octave 

etc.

 

Mr. Beard, as much as I admire the quality and thought-provoking nature of most of your posts, what you have asserted above is seriously flawed. The harmonic series starts out as the fundamental frequency times two (an octave), but doesn't continue as single-digit multiples of the fundamental frequency. Instead, it quickly subdivides into fifths. thirds, and into intervals which are less than a half-step apart.

In other words,  when you go high enough in the harmonic spectrum, there is little that aligns with a comfy chord any more, or Western intonation. If anyone wants to go to the trouble of trying to assign note names to all the frequencies displayed on Don's graph, that will be readily apparent. Not that what are traditionally perceived as non-harmonic structures can't be useful. A little dissonance in the harmonic structure can often be perceived as better articulation and projection.

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24 minutes ago, Johnmasters said:

Today,  I hear a lot of "viola-like" sound in the lower registers of many players.  I don't recall  this in old LP's from the 50's and 60's.  Do you believe that this has occurred?  (the overplaying of the famous old instruments)  

I hear a lot of this, but I do think that there is a different reason for it. I *think* that it is due to changes in setups.  I think that we may have all gone with the flow on some of these things without trying to find out where they are taking us.

Martin guitars have been mentioned, and most guitarists know that the 70s were a bleak time regarding Martin desirability, Likewise in the same period for Steinway, and maybe for US cars as well. I'm starting to get that feeling about 1970s violin setup standards, too, so you might consider that instead of tonal attrition. Remember, Vuillaume predicted that Strads would wear out and his violins would continue to improve and be recognized as better in 100 years, and he was definitely wrong in that prediction.

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20 minutes ago, David Burgess said:

Mr. Beard, as much as I admire the quality and thought-provoking nature of most of your posts, what you have asserted above is seriously flawed. The harmonic series starts out as the fundamental frequency times two, but doesn't continue as single-digit multiples of the fundamental frequency.

In other words,  when you go high enough in the harmonic spectrum, there is little that aligns with a comfy chord any more, or Western intonation. Not that this can't be useful. A little dissonance in the harmonic structure can often be perceived as better articulation and projection.

???? Refer to every source back to pythagoras.  The mathematical harmonics are simple integer multiples of the fundamental. Theoretically all are present.

However, in practice we often remove the extra octaves when discussing musical intervals.

There are various was to compound intervals to getting a particular scale tempering, but some if the basic materials are:

Unison interval multiple is 1

Octave interval's multiplier is 2

Adjusting to a range between these, the rest of the intervals are tempered by compounding these harmonic intervals:

The perfect fifth multiplier is based on 3, it's first occurence in the series.  Adjusting for the octave this gives 3/2, or 1.5

The harmonic major third is based on 5. 5/4 = 1.25

And the harmonic minor 7th is based on 7, first occurring in 7th position of a series (assuming you count from the fundamental as 1).   This gives  7/4 = 1.75.

All other intervals of pure temper compounds of these.  If you add two intervals, you get the new multiplier by multiplying.  If you subtract intervals, you get the new multiplier bt dividing.

So, re of s major scale is generally taken as the fifth of a fifth reduced to the right octave.  Thus (3×3)/8 = 1.125.

 Etc.

Many conflicting ways to complete the scale by slightly different interval ratios gave rise to all the Renaissance machinations over tempering.

Brass players will bend the 11 and 13 partials to match scale tones at times, but these partials aren't really significant in the scale systems.

 

 

 

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The overtone series, harmonic series goes:  fundamental, octave above that, P5, P4, M3, m3, m3 out of tune, M2, then the next octave starts and is mostly M2 and smaller.  So for example C, C, G, C,E, G, Bb, C or if the fundamental, the note you are fingering, was G,  G, G, D, G, B, D, F, G.

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This chart may help:
https://en.wikipedia.org/wiki/File:Harmonic_Series.png

he interesting point to notice is that line of + and - numbers--that's the distance in cents of each harmonic from the true pitch of the note it has been notated as on the scale. The thing to draw from this is a D Burgess noted is that the higher harmonics are essentially trash inasmuch as they aren't tuned to any particular note except when the increasingly-scarce octave note pops up.

Note that David Beard calls the fundamental the first harmonic.
David Burgess calls the partial above that the first harmonic
Both are correct--there isn't agreement among musicologists regarding this particular point of terminology. I think that the confusion beyond that is because D Beard's mathematical rendition in his post wasn't a complete harmonic sequence, but rather only the included octaves, leaving out all the fun stuff.

 

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Yes.  Be prepared to hear someone call the fundamental the first harmonic.  In music the series is taught as stacked intervals though, not a formula.  And only the first octave, since the relationship to the fundamental break down (and they are weak).

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I know, but the sequential multiplication of the fundamental frequency, 100, 200, 300, 400, 500, 600, etc. gives another handle for visualization, makes it more readily understandable why the higher you go the greater the number of harmonics piling up between octaves and makes it clear why past a certain point there's more trash frequencies than music (between 100 and 200, none, between 800 and 1600 are 900, 1000, 1100, 1200, 1300, 1400, 1500, and the next octave is twice as bad). If you rely on musical note descriptions of tidy intervals, you run out of names and sensible intervals in the region under discussion.

 

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The harmonic series is not a sequence of powers of two. It is a sequence of integers times the base frequency. Using an open A440 as an example:

1x440 = 440 The fundamental of the series

2x440 = 880 The first overtone of the series and also the first octave

3x440 = 1320 The second overtone of the series, but not an octave

4x440 = 1760 The third overtone of the series and also the second octave

etc

So there are many overtones of the harmonic series that are not octaves of the fundamental frequency.

As Don spectral plot proves experimentally, the violin overtones, for all practical purposes, are integer multiples of the base frequency. So experiment and theory match.

I would take technical exception with Michael Darnton's observations about "computed" FFT frequencies. FFT does not actually compute frequencies. Rather, it computes the contribution of each frequency across a large and detailed frequency spectrum that depends on the sampling rate (how many times per second the analog tone is captured as number) and the time span of the entire sample.

If you convert a violin tone into a digital signal using a high sampling rate for several seconds, then the FFT algorithm can accurately compute the contribution to the signal of all frequencies in the spectrum range down to a very fine frequency resolution.

Inharmonicity is the deviation of overtone frequencies from integer multiples of the fundamental. Effectively, this does not happen for a "well bowed" violin tone. If it does occur, a well sampled tone would display peaks at frequencies that are not integer multiples of the frequency of the first peak.

It is possible that tones can sound "false" if the violin does a poor job of reproducing the fundamental and some of the lower octave overtones, or does a much better job reproducing the higher overtones than the lower ones. The overtone frequencies are accurate, they are just not very strong.

I think what you are looking for is some general observation on what the strength of each overtone should be relative to the fundamental. Call this the overtone profile.

I studied this a few years ago by sampling tones from various recordings of highly regarded violins. The note needs to be sustained for a second or so and played with no vibrato. Where the violin bow point was relative to the bridge affected the profile. The profiles of a good G string were quite different than that of a good E string.

When comparing similar plots made of bad violins, I could usually tell why a bad violin sounded bad, but could not deduce any reliable rule as the why a good violin sounded good.

Even if one could come up with a set of overtone profiles that many could agree gave a beautiful violin tone, it is not obvious to me how one can translate that into practical rules for making a violin.

 

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12 minutes ago, ctanzio said:

I would take technical exception with Michael Darnton's observations about "computed" FFT frequencies.

Just to be clear, those weren't my observations; they were the comments made to me by several people who'd written commercial programs related to piano tuning and were made in response to my question about the harmonics being all tidily stated in their programs where we knew the situation was different. As one told me, "it wouldn't matter to us because we can't adjust it anyway". One other source has commented to me that FFTs are much less accurate than the people using them suspect, mainly because we don't have infinite computing power,  so shortcuts are written into the programs to make them work on real equipment, if I understood correctly. You might take the real-time music and stretch it out so you can do miniscule analysis, but I don't think that's going to avoid the inherent compromises that he indicated live in the technology. Unless you are writing your own FFT right from scratch, I guess...... maybe you are doing that?

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** The harmonic series consist of every frequency that is an integer multiple of the fundamental.

** Yes, some people count from the first partial above the fundamental.  However, intrinsically every partial is linked to an integer. Just divide the harmomic by the fundamental.  This gives the natural count I used.  The math is much prettier this way.

** The series contains all octaves of the fundamental, these are the powers of 2 that I highlighted.  The series also contains a partial for every integer between the octaves, which is the point I was trying to clarify. 

** To be clear, the cents deviations shown in the wiki article are in relation to modern equal temper.  From an historical music theory perspective, those are mostly showing how far out of tune the modern compromise equal temper is from a pure temper, not the other way around.  However, the 11th and 13th, and many of partials higher than that are not actually in either the modern equal tempered scale, nor the historical more natural tempers either.

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19 minutes ago, ctanzio said:

Even if one could come up with a set of overtone profiles that many could agree gave a beautiful violin tone, it is not obvious to me how one can translate that into practical rules for making a violin.

Lots of physical measurements of violins and lots of corresponding frequency graphs training a machine learning program could probably eventually spit out physical dimensions to carve to get a given graph.

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1 hour ago, David Beard said:

???? Refer to every source back to pythagoras.  The mathematical harmonics are simple integer multiples of the fundamental. Theoretically all are presen

That's true. What I meant to point out is that these simple multiples are not necessarily  octaves, contrary to what you claimed. Middle C times 3 is not a C, but a G. Middle C times 9 is pretty close to a D. When one goes high enough in the series, it gets even more bizarre. with multiple "notes" between half-steps.

So when a violin puts out enough of these high harmonics, it starts to include many (arguably) "dissonant" tones, and some people aren't going to like that.

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9 minutes ago, David Burgess said:

That's true. What I meant to point out is that these simple multiples are not necessarily  octaves, contrary to what you claimed. Middle C times 3 is not a C, but a G. Middle C times 9 is pretty close to a D. When one goes high enough in the series, it gets even more bizarre. with multiple "notes" between half-steps.

So when a violin puts out enough of these high harmonics, it arguably starts to include many "dissonant" tones, and some people aren't going to like that.

This makes a lot of sense.

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57 minutes ago, David Burgess said:

That's true. What I meant to point out is that these simple multiples are not necessarily  octaves, contrary to what you claimed. Middle C times 3 is not a C, but a G. Middle C times 9 is pretty close to a D. When one goes high enough in the series, it gets even more bizarre. with multiple "notes" between half-steps.

So when a violin puts out enough of these high harmonics, it starts to include many (arguably) "dissonant" tones, and some people aren't going to like that.

Guess you didn't read what I wrote.  Doesn't matter. 

 

I only said powers of 2 give octaves.

 

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3 hours ago, Michael Darnton said:

:)You can always have that "nice" sound if you do a consistent well-placed bowing position, pressure and speed to a good violin, but what, as I said to one person, if the music demands harsh, or a dusty foggy sound, and all your violin will do is it's usual one thing? Then you become the person in the section the conductor glares at, and maybe delivers a frustrated rebuke to.

"How?" It's something that I have been working on for quite a while, with varied success. Part of it is the realization that the early makers had neither the same tools nor the same attitudes about their work as we do. For a start, throw away your fancy post-Industrial Revolution era caliper.

Like!

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7 hours ago, Michael Darnton said:

This doesn't imply that the better violin has more overtones...

Look at the chart of the open G string I posted earlier.  Every  overtone shows up, out to 14,000 Hz.  I don't think it''s a question of overtones being there, but it's all about the relative amplitude of them, which is related to the frequency response of the body.  

In my observation, good violins tend to have a response with minimal dropouts and peaks, which translates into a full spectrum of overtones, without some dominating the sound.  I think it corresponds to what a violinist would call "colors"... if there's a dropout, there are colors missing.  Peaks, and there is unevenness and too colored of a sound.

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On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

Since a feays now I am trying to put in words what is going around in my head. And no matter how I try to formulate it, it looks like half missing the point. 

Anyway.

So, what do overtones do to the sound? 

They make it sound nice or nasty.

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

Are overtones the only important factor for the so called projection? 

Well our hearing and our nervous sytem are attuned to the screech factor. It gets our attention and summons our emotions. Usually fear, but fear and excitement are so closely related aren't they?

 

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

Or is it rather a certain 'mixture' of overtones which makes the sound stick out? 

I suppose so

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

And then how does it relate to details in the making process? 

Some things make an instrument screech too much, others not enough but we can't agree what they are. I could go on about the varnish again but....

...on another note, is low density spruce just a fad?

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

Comparing instruments with Strad arching to instruments with Stainer arching makes clear that arching shape has a fundamental influence on the the timbre.

Stainer maybe had more trouble getting to sleep when cats in heat were a courting of a summer's night. And no sooner had he nodded off when the dawn chrorus of birds drove him half crazy? So he resolved to make violins which projected without screeching.

I don't know if Stainer's sound (™) could be described as more dulcet tones? But I am sure that it's just not fashionable to wax lyrical about Stainer just as it wasn't for Strad at the end of the 18th century. But Strad some make low arch violins in the 1680s and some high archings in the 1720s and 30s. So it this 'Golden Period' concept based on tone or was his own aim to satisfy customer demand in the fashion of the times? And the fashion in the early 18th century was for perhaps low arching? Anyway, I'm absolutely in awe of his amazing output.

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

.Second there is the string angle which regulates the vertical force on the top. However does a smaller angle (less than 180) make more overtones? Or eventually overtones in the wrong frequency range?

I think too small a string break angle produces more power, but at the expense of balance. The instrument is harder to control, perhaps less nuanced?

On ‎4‎/‎13‎/‎2019 at 4:53 PM, Andreas Preuss said:

Then, maybe the material itself. If we would use another material the violin wouldn't sound the same.

But you could use skilfull marketing to sell 'superior sounding' plastic moulded violins.

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On 4/13/2019 at 11:53 AM, Andreas Preuss said:

Second there is the string angle which regulates the vertical force on the top. However does a smaller angle (less than 180) make more overtones? Or eventually overtones in the wrong frequency range?

In my experiments, using a device which raised and lowered the height of the "virtual saddle" within several seconds, without even relaxing the string tension, my impression was that less downforce reduced the strength of the higher harmonics. However, I was unable to lower the virtual saddle below the height of the violin's real saddle, so I wasn't able to explore what greater downforce than what the violin originally had would have done.

I should add that less downforce attenuating the higher frequencies was only my impression, and I did not confirm this with FFTs. Sometimes, an FFT has revealed things which were quite different from what I thought I was hearing.

D. Beard, apologies if I misinterpreted what you had written.

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10 hours ago, Don Noon said:

Look at the chart of the open G string I posted earlier. 

Actually, that didn't answer the question I asked earlier. As an example of what I was interested in, could you (for example) show spectra not only of the open G, but also of every successive G across all positions and strings? I think it would be interesting to see if there were any departures from harmonicity in higher positions for example.

I could do this myself, but I'm on holiday at the moment :)

 

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8 minutes ago, David Burgess said:

In my experiments, using a device which raised and lowered the height of the "virtual saddle" within several seconds, without even relaxing the string tension, my impression was that less downforce reduced the strength of the higher harmonics. However, I was unable to lower the virtual saddle below the height of the violin's real saddle, so I wasn't able to explore what greater downforce than what the violin originally had would have done.

I should add that less downforce attenuating the higher frequencies was only my impression, and I did not confirm this with FFTs. Sometimes, an FFT has revealed things which were quite different from what I thought I was hearing.

Interesting experiment, David. Did you make a saddle like a bridge lifter?

I just have an scientific non approved believe that one of the major points in getting a full and 'fat' sounding overtone spectrum comes from the balance between bridge downforce and resistance to it from the top. This means as well that the balance between treble and bass side bridge foot is important. And I think it can explain why a fraction of more or less tension made by the sound post can alter the sound on sensitive instruments quite dramatically.

 

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1 hour ago, JohnCockburn said:

Actually, that didn't answer the question I asked earlier. As an example of what I was interested in, could you (for example) show spectra not only of the open G, but also of every successive G across all positions and strings? I think it would be interesting to see if there were any departures from harmonicity in higher positions for example.

I could do this myself, but I'm on holiday at the moment :)

 

I only used that one note to confirm what is pretty solid theory.  If you think about the Helmholtz motion, the "kink" which periodically whacks the bridge is constrained to the fundamental period.  It is the impact-like force of the kink that produces all of the overtones, and since the kink is forced to a specific period, then all of the overtones are likewise constrained to multiples of that period.  It just can't do otherwise, unless you lift the bow off of the string, or have something other than the Helmholtz motion.

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On 4/13/2019 at 1:19 PM, JohnCockburn said:

Can you define what you mean by "overtones"?

Today is Monday.  I'll try to spend the next four or five days playing and report back Friday/Saturday morning.   I have a few fiddles that come alive with overtones while being played. 

I'll just have to make an opinionated determination of do these overtone/harmonics sounds get in the way while trying to make music or do they keep a person going because they sound so well?  Not having the chance to hold or play a fiddle in the last three days I have to say I have no answer or opinion/thought for the overtone range question.

Hmm, maybe I'll forget to come back. 

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59 minutes ago, Andreas Preuss said:

Interesting experiment, David. Did you make a saddle like a bridge lifter?

I just have an scientific non approved believe that one of the major points in getting a full and 'fat' sounding overtone spectrum comes from the balance between bridge downforce and resistance to it from the top. This means as well that the balance between treble and bass side bridge foot is important. And I think it can explain why a fraction of more or less tension made by the sound post can alter the sound on sensitive instruments quite dramatically.

 

Sound post tweaking causing significant sound alteration? Hmmm, I'm wary of this belief and others like it. It's so easy to fool oneself.

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