Tuning aluminum bars part2

Bob and Denny and Tuningphiles,

I have just finished experimenting with tuning a bar as per my last email.
The goal was to get the 2nd partial into a 3/1 ratio.

Here are the results on a 1/4 inch aluminum bar 30 cm long

I mounted the bar at the nodes of the 1st partial (.22) and then cut a
progressively deeper groove at the node of the second partial (.50). The
groove is only 1 mm wide and only on one side of the bar. I use a magnetic
pickup to amplify the vibrations of the bar and the bar has a small
magnetic armature at one end to accomplish this.

I measured the partials by ear using the frequency generator and counter.

Partials(hertz)
Action 1 2 Interval (approx)
no groove 349 964 11/4+ (+ meaning slightly sharp)
1mm deep 345 966 7/5
almost 1/2 329 966 11/9-
slightly more 317 966 64/21
end grind 319 970

So you can see that I went slightly to far. This may be able to be
corrected by grinding from the end, although my first attempt increased the
2nd partial at about the same rate. The second partial can be flattened by
cutting a groove at its node, although this will probably also effect the
first partial. Ideally, one would not go to far when cutting the .50
groove.

I believe that the ancient HP analog frequency generator is starting to
have a shift problem, as I found it very difficult to get a consistent
measurement. The counter would sometimes shift as much as 3 or 4 hertz
over 30 seconds or so.

The amplitude of the third partial is insignificant, so I am ignoring it,
and it will probably be even more attenuated by future dampers.

Darren Burgess
South East Just Intonation Society
Gainesville, FL

i have a question for Darren Burgess:

i have a question for Darren Burgess:

Exactly how did you mount the aluminum bar for testing??

When you refer to using salt or sugar, I can see how that the node can
be detected by the area where sugar still remains, but again, how do you
mount the par to preform such a test??

thanx alot----Anson Antriasian

Antriasian@aol.com wrote:

>
>
> i have a question for Darren Burgess:

This was my comments not Darrens!

> Exactly how did you mount the aluminum bar for testing??
>
> When you refer to using salt or sugar, I can see how that the node can
> be detected by the area where sugar still remains, but again, how do you
> mount the par to preform such a test??

I just place the bar on some foam near the modes by eye. Just guess. you can
always reset the foam strip if you want. You end up with a line through the
bar! This is the Harry Partch method! An empiricist at heart!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Just for reference:

a bar, rod or tube of perfectly uniform shape, free at both ends will have
the following first three modes of vibration:

Mode freq nodes antinodes
1 f1 22.4% 50%
2 2.756f1 13.2%, 50% 31.6%
3 5.404 9.4%, 35.6% 22.5%, 50%

Darren Burgess has chosen to lower mode one so that modes 1 and 2 will be
in a 3/1 ratio. In the golden age of US marimba making, the ideal was to
widen this to a 4/1 ratio and least in the lower octaves.

In traditional marimba or vibraphone bars, which have the advantage of a
stronger amplitude in the 1st node, lateral modes in the bars often
interfere, as do twists in the grain of wooden bars. These can be adjusted
through notching at an angle in the middle of the bar or by reducing the
width of the bar.

I'm not certain about this at all, but I believe that the problem with
square bars is that the lateral vibrations are so close to those of the
playing surface that phase interference occurs.

>
> i have a question for Darren Burgess:
>
> Exactly how did you mount the aluminum bar for testing??
>
> When you refer to using salt or sugar, I can see how that the node
can
> be detected by the area where sugar still remains, but again, how do
you
> mount the par to preform such a test??
>
> thanx alot----Anson Antriasian
>

Dear Anson,

I don't use salt to test where the node is. It is very reliably found at
.225 of the total length of the bar, from each end. Slight variations
don't make much difference. I just calculate the point, drill two holes
and it works.

The mount of the bars is fairly complex, so I don't care to describe it by
email. When the instrument is complete I will post pics on a website.

Darren Burgess

>
> I'm not certain about this at all, but I believe that the problem with
> square bars is that the lateral vibrations are so close to those of the
> playing surface that phase interference occurs.
>

Daniel,

That sounds like a very plausible explanation. Well, the interesting thing
is that the test bar I just created didn't have any phase problem (it's
1/4" square). Perhaps it is a better machined metal than other stock I
have used. In addition the manner in which these bars are mounted helps to
dampen the lateral vibrations. (according to the patents).

By the way, the patents I have are as follows, with a number and brief
review of each. They illustrate very well the history of technological
advances in the art/science of metal bar tuning. Patents can be obtained
through www.uspto.gov for $3 a copy. Abstract are found at a decent
library, in my case the U. of FL. Internet info on these is nill as they
are too early--no internet info prior to 1976. They are wonderful
documents for those of us who haven't become addicted to the convenience of
synthesizers, tuning tables, and samplers. ;-)

3048071 Excellent info on getting the first four partials into octave
relationship. Includes a really cool chart that plots the variation of
frequency of the partials given the location of grooves along the length of
the bar. (Describes the 5 octave carillon I am restoring/retuning)
2655069 Earlier patent where points on the bar are ground to flatten
partials or crimped perpendicular to the plane of vibration to stiffen the
bar and sharpen the partial.
2606474 Extensively describes the construction and engineering behind a
flemish bell tone instument (I also have 5 octaves of this instrument)
Lots of info in this one. This instument is quite complex and integrates
several earlier techniques.
2413062 Bell instument that has variable amlitude and frequency control of
the "hum" tone
2703504 Round bar tuning method that involves bending the ends and cutting
grooves
2588295 Ditto
2273333 complex method of bar tuning that involves alot of grooves
throughout the length of the bar. This one has almost no detailed
information or measurements, so it is only historically useful.
1632751 A patent referenced by patent 2703504, I don't have this one but
it should be useful.

Perhaps more information (ie hard data and greater detail) can be obtained
on these patents. Anybody have any ideas?

Darren Burgess
SEJIS-Gainesville, FL