• Subharmonics

Here's a link about the Theramin, which also uses this property. Of course, the Theramin is an electronic device and the violin is acoustic, but the underlying process applies to both.

something else about violins- they have a bass bar inside the top plate on the side of the lower pitched strings, to accentuate the lower notes, and the sound post on the other side emphasizes the higher frequencies. Little two-way system in there.

The players must have good ears for tuning, so that their intervals ring (as the barbershop guys say), that is, tune to exactly Pythagorean intervals... those that are NOT of the tempered scale of the piano, where each semitone is a 12th root of 2, but instead, whole number ratios (Pythagorean tuning). This is the tuning that sounds correct to the ear.

For example, a C major chord is composed of the notes C, E, and G. If we assign a low note C as the frequency of X, then a C an octave higher would be 2X. An octave above that would be 4X. An octave above that would be a C whose frequency is 8X.

The other notes would have other whole note ratios. The G between the C (=4X) and C (-8X) would have a frequency of 6X.

The note E would have a frequency of 5X.

So, these three notes of the C major chord would be C (4X), E (5X), and G (6X). The difference frequency between the C and E would be 5X - 4X = 1X. That 1X is a C two octaves down. This is IF the notes are played in tune such that they "ring".

The difference between the G and the E would be 6X - 5X = 1X, again, reinforcing that low C, 1X.

The difference between the G and the C would be 6X - 4X = 2X. That would be a C one octave below the C (4X). So, with all these notes beating together, you produce two subharmonics, which are both harmonically related to the root of the chord (C, 4X), one and two octaves below the root.

So, when this chord is played well in tune, to whole number ratios (Pythagorean tuning), the chord can obtain great depth to the overall sound.

Did I lose anyone?

The E

www.saxontheweb.net

And you can find a link to my articles, including a series on arranging / orchestration at:

http://www.saxontheweb.net/Coats/

Paul Coats

• http://www.saxontheweb.net

Interestingly, the shape of the violin is not just style, with the cutouts on each side, and the "f" shaped slots on each side. There is a reason for the contour of the violin, and all of the curves. There have also been some interesting measurements of the vibrational characteristics of the wood and varnish of the Stradivarius instruments. They have been able to duplicate the tonal effects.

Dr. Arthur Benade did acoustical research into reed instruments, mostly the clarinet. It was easier to model, with its cylindrical bore. In place of the mouthpiece and reed, he used a driver not unlike a horn driver. There were also many observations that to me, appear to be similar to what we observe with horn speakers.

There is a link to saxophone acoustics:

http://www.phys.unsw.edu.au/~jw/saxacoustics.html

And if you hunt around on that site, you can find acoustical treatises on other instruments.

• http://www.phys.unsw.edu.au/STAFF/ACADEMIC/wolfe.html

I get sort of tired of the papers written about loudspeakers because they all look pretty much the same. Each tends to put a spin towards the hoped for conclusion, but they all say the same thing - It's a pretty simple field. So it's nice to see things coming at you from a slightly different angle. Familiar enough to be comfortable with the concepts but different enough to be refreshing and enlightening.

I've been playing violin for a few years and am constantly amazed at how complex and amazing it is acoustically.

http://www.saxontheweb.net/Coats/OrchSax4.html

This is the 4th in the series... start reading at:

http://www.saxontheweb.net/Coats/OrchSax1.html

• http://www.saxontheweb.net/Coats/OrchSax1.html

What I thought would interest you was the way he applied the math, and the similarity of his analysis to horn speaker technology.

For those wondering what this is about... Dr. Arthur Benade was a physicist and clarinetist, who did much acoustical research into wind instruments.

But here are some links I have:

http://www-ccrma.stanford.edu/marl/

http://ccrma-www.stanford.edu/marl/Benade/BenadeHome.html

http://www.phys.unsw.edu.au/~jw/saxacoustics.html

Paul