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Equal beating tuning
#2987109 06/02/20 04:40 PM
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Has anyone ever tried the equal beating division system proposed by Dr. A. Leigh Silver in the 1950s?
He was an honourary member of the I.M.I.T then and wrote extensively on different tunings.
The one he proposed (Acoustic Society America) vol 29 no.4 April 1957) suggested that at A=440 that beat rate would be 1.003 per second, effectively one beat per second (A comes out at 438.6 to achieve exactly one beat per second).
So all fourths and all fifths beat at this rate. So the fifths in the sequence increase in size as they ascend.
It seems completely acceptable to the ear and it does produce a balanced resonance as the beat ratios are reinforced throughout the range.
There is also a little colour between related keys which might keep the just/mean types happy....

It's an interesting and simple tuning though I've never put it onto a client's piano.

Has anyone?

Nick


Nick, ageing piano technician
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Re: Equal beating tuning
N W #2987149 06/02/20 06:34 PM
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Got a link to his method? What you wrote just doesn't work:

So all fourths and all fifths beat at this rate. So the fifths in the sequence increase in size as they ascend.

If the 5th increase in size as they ascend (thereby staying at the same rate) the 4ths must also increase in size (thereby beating faster and faster). Therefore all the 4ths and 5ths would not beat at the same rate.


Jeff Deutschle
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Re: Equal beating tuning
N W #2987211 06/02/20 10:46 PM
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Sounds VERY similar (if not identical) to what Raymond Feaster expounded on in: "The Dynamic Scale". Time period is close too.

Pwg


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Re: Equal beating tuning
UnrightTooner #2987291 06/03/20 07:16 AM
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Originally Posted by UnrightTooner
Got a link to his method? What you wrote just doesn't work:

So all fourths and all fifths beat at this rate. So the fifths in the sequence increase in size as they ascend.

If the 5th increase in size as they ascend (thereby staying at the same rate) the 4ths must also increase in size (thereby beating faster and faster). Therefore all the 4ths and 5ths would not beat at the same rate.
I have probably misrepresented it.
Jeff, I haven't tried a complete tuning of it just a scale and oct each side.
I learned about it from a lecture by Dr. A. Leigh Silver around 1964. I have a hard copy, no idea where it would exist in the cloud unfortunately. Published by the Institute of Musical Instrument Technology. This institute was a brilliant source of interesting lectures and publishings in those days.
This particular lecture is quite hard going with alot of diagrams so hard to talk about in depth here. There are gamograms etc.
The fifths in sequence increase in size as they ascend from 699.3 to 700.6 cents.
Maybe there's more info connected to Feaster as mentioned by Peter.
Unless there's something on the net relating to Acoustic Society of America? Where he published a full account in 1957, which I haven't read.
Nick


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Re: Equal beating tuning
N W #2987330 06/03/20 09:35 AM
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Gamogram? Can't find a definition.

For a 5th to beat the same speed, it's tempering would have to double each octave going down and halve each octave going up. For contiguous 5ths, That's about 2/3 cent for each 5th, additive as you go up, subtractive as you go down. So the figures you gave "699.3 to 700.6 cents" (with the note between being 700.0 cents) would hold true for only two contiguous 5ths.


Jeff Deutschle
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Who taught the first chicken how to peck?
Re: Equal beating tuning
N W #2987351 06/03/20 10:30 AM
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Well I know he was continuing a train of thought started by Alexander Ellis in an article in "Musical Times" 1st October 1879!
Ellis stated, or rather suggested, a simple method for approximating equal temperament which is very useful as a first step for learners (before we had electronics of course).
The apparatus was a seconds watch or two small pendulums set to beat at 1 and 1.5 seconds.
Starting on middle C (I'm old!) Tune up a fifth beat is one per second. Then down fourth to D, beat 1.5 seconds.
You end up with the last fourth (fc) which is tuned to take up the error.
Ellis claimed the approximation was excellent, though it's difficult in reality to check as the chain is broken so accumulated errors can't be checked without it all getting complicated again....
Silver was trying to simplify even that I think. All very good for the pupil to get a feeling for tuning.

I raised it because I wondered if anyone had ever been brave enough to try it out on a musician.
Gamogram is a form of dot notation. It must be such an unused word now I suppose.
So in this context he draws perfect fifths as horizontal lines (between dots) and thirds as vertical lines.
The results of all this is that varying types of scale tuning can be compared as diagrams which is very useful and clear.

I suppose electronics have made all this redundant, it's only of historical interest now maybe.

Have sympathy for those who had to learn without electronics and the magnificent aid that they represent.

Nick

Last edited by N W; 06/03/20 10:31 AM.

Nick, ageing piano technician

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