Pianotech

I seem to remember this topic years ago, on the old listserver, but finding it would be difficult, at best. So, I would like to pose the question again. 

String scaling predicts that string tension varies somewhere around 90lbs and 120lbs per string, depending. Is it possible to predict the change in string tension in relation to a change in pitch?

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Geoff Sykes, RPT
Los Angeles CA
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Yes, you can use the equation for the frequency of a vibrating string: f = 1/(2*L) * sqrt(T/mu). The important part is that frequency (f) is proportional to the square root of the tension (T). Or turn that around, and tension is proportional to the square of frequency.

So if you change pitch from, say, 440 to 442hz, then tension changes by the square of that: (442/440)^2 = 1.0091, or an increase of 0.91%. So 100lbs would become 100.91lbs. 

If you increase by one half-step (twelfth root of 2 = 1.0594), then tension changes by a factor of (1.0594)^2 = 1.1225, or an increase of 12.25%. 

And so on...

These pitch and tension ratios apply the same across the whole scale (roughly ... inharmonicity also changes with tension, though not by much within the normal ranges), so when doing a pitch raise, the total tension also changes by the same percentage.

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Frank Chemotti
Seattle WA
206-331-7495
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Original Message:
Sent: 06-14-2017 13:16
From: Geoff Sykes
Subject: string tension vs pitch

I seem to remember this topic years ago, on the old listserver, but finding it would be difficult, at best. So, I would like to pose the question again. 

String scaling predicts that string tension varies somewhere around 90lbs and 120lbs per string, depending. Is it possible to predict the change in string tension in relation to a change in pitch?

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

So there is really only about 1 Lb change in tension for every 1 Hz in frequency change. A pitch raise from 440 to 442 would increase the overall tension in the piano by about 220 Lbs. Not nearly as much as I expected, but then I didn't know what to expect. This is good to know. 

Thanks --

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Geoff Sykes, RPT
Los Angeles CA
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Original Message:
Sent: 06-14-2017 23:16
From: Frank Chemotti
Subject: string tension vs pitch

Yes, you can use the equation for the frequency of a vibrating string: f = 1/(2*L) * sqrt(T/mu). The important part is that frequency (f) is proportional to the square root of the tension (T). Or turn that around, and tension is proportional to the square of frequency.

So if you change pitch from, say, 440 to 442hz, then tension changes by the square of that: (442/440)^2 = 1.0091, or an increase of 0.91%. So 100lbs would become 100.91lbs. 

If you increase by one half-step (twelfth root of 2 = 1.0594), then tension changes by a factor of (1.0594)^2 = 1.1225, or an increase of 12.25%. 

And so on...

These pitch and tension ratios apply the same across the whole scale (roughly ... inharmonicity also changes with tension, though not by much within the normal ranges), so when doing a pitch raise, the total tension also changes by the same percentage.

------------------------------
Frank Chemotti
Seattle WA
206-331-7495
------------------------------

Original Message:
Sent: 06-14-2017 13:16
From: Geoff Sykes
Subject: string tension vs pitch

I seem to remember this topic years ago, on the old listserver, but finding it would be difficult, at best. So, I would like to pose the question again. 

String scaling predicts that string tension varies somewhere around 90lbs and 120lbs per string, depending. Is it possible to predict the change in string tension in relation to a change in pitch?

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Original Message------

So there is really only about 1 Lb change in tension for every 1 Hz in frequency change. A pitch raise from 440 to 442 would increase the overall tension in the piano by about 220 Lbs. Not nearly as much as I expected, but then I didn't know what to expect. This is good to know. 

Thanks --

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Geoff Sykes, RPT
Los Angeles CA
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Sorry. I meant to say 1/2 Lb change in tension for every 1 Hz change. At least that's what I'm getting out of the formula without actually putting pencil to paper to test the math. I wasn't looking for an exact amount so much as I was looking for something to satisfy my own curiosity and share with the occasional curious customer should they ask.

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Geoff Sykes, RPT
Los Angeles CA
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Original Message:
Sent: 06-20-2017 20:06
From: Mark Schecter
Subject: string tension vs pitch

Geoff,

Using your numbers, 2hz = 2lbs per string, x 220 strings = about 440 lbs. increased tension. Is that more like what you expected?  

Mark Schecter

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Original Message------

Geoff,

Using your numbers, 2hz = 2lbs per string, x 220 strings = about 440 lbs. increased tension. Is that more like what you expected?  

Mark Schecter

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Well I do have a couple of harpsichords I tune, but, no. Unless I have remembered it incorrectly, I thought that normal string tension in a normal piano varies from 90 Lbs to 120 Lbs per string. The reason for the difference being the result of scaling. When you start with a given string size on the left side of a trichord the tension winds up being about 90 Lbs to get it the correct pitch. As you go higher in the scale, with each higher note you wind up increasing the tension in order to get that string up to the correct higher pitch. Eventually, after four to six or so notes, you begin to approach the breaking point of that gauge string and you switch to a little thinner string. Once again, at correct pitch, a tension of about 90 Lbs occurs for that first string until it reaches about 120 Lbs per string, and then the process repeats, again. 

Averaging 100 Lbs per string, times approx 220 strings is 22,000 Lbs of tension. That's 11 Tons. Even discounting the extreme lower number of strings, I can't imagine anything remotely close to that in a harpsichord. But with a cast iron plate, I can imagine that in a piano. 

PLEASE correct me if I'm wrong.

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Geoff Sykes, RPT
Los Angeles CA
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Original Message:
Sent: 06-20-2017 21:24
From: Chris Chernobieff
Subject: string tension vs pitch

I'm still confused by the 90 - 120 lbs. Are you tuning harpsichords and fortepianos Geoff?

Original Message------

Well I do have a couple of harpsichords I tune, but, no. Unless I have remembered it incorrectly, I thought that normal string tension in a normal piano varies from 90 Lbs to 120 Lbs per string. The reason for the difference being the result of scaling. When you start with a given string size on the left side of a trichord the tension winds up being about 90 Lbs to get it the correct pitch. As you go higher in the scale, with each higher note you wind up increasing the tension in order to get that string up to the correct higher pitch. Eventually, after four to six or so notes, you begin to approach the breaking point of that gauge string and you switch to a little thinner string. Once again, at correct pitch, a tension of about 90 Lbs occurs for that first string until it reaches about 120 Lbs per string, and then the process repeats, again. 

Averaging 100 Lbs per string, times approx 220 strings is 22,000 Lbs of tension. That's 11 Tons. Even discounting the extreme lower number of strings, I can't imagine anything remotely close to that in a harpsichord. But with a cast iron plate, I can imagine that in a piano. 

PLEASE correct me if I'm wrong.

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Geoff Sykes, RPT
Los Angeles CA
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