Question for harp builders??

[carl-swanson]

OK, I took some measurements from a sampling of strings on an older 23(serial number 4300. Original soundboard, not badly pulled up) I used a compass to measure the distances between flat and natural, natural and sharp, and flat and sharp (go to Amazon and look at Toolmaker’s Precision Spring Dividers Calipers Compass. That’s what I used). I took the measurements in inches, and then converted them to centimeters. I’m giving you both measurements here so you can check that I didn’t mess anything up. I measured the distance from flat to the soundboard eyelet with a piece of string and measured that on a tape measure in inches. I’m not including that measurement here. I think my measurements with the calipers are as accurate as anyone is going to get.

Here are the measurements. The first numbers are in inches, then, in parenthesis, centimeters. Also, I tuned each string in flat, then noted how it was off in natural and sharp.

C5 2 cents sharp in natural, 10 cents sharp in sharp
Flat to natural: 2.250 (5.715). Natural to sharp: 2.1875 (5.55625)
Flat to sharp: 4.4375 (11.27125).

B5 2 cents sharp in natural, 3 cents sharp in sharp
Flat to natural: 2.4375 (6.19125). Natural to sharp: 2.250 (5.715).
Flat to sharp: 4.5625 (11.58875).

C6 Flat to natural is OK. Natural to sharp is 5 cent sharp.
Flat to natural: 3″ (7.62). Natural to sharp: 2.7500 (6.985)
Flat to sharp: 5.7500 (14.605)

B6 Flat to natural is OK. Natural to sharp is 3 cents sharp.
Flat to natural: 3.0625 (7.7785). Natural to sharp: 2.8125 (7.14375). Flat to sharp: 5.8125 (14.76375).

A6 Flat to natural is 1 cent sharp. Natural to sharp is 4 cents sharp.
Flat to natural: 3.1250 (7.9375). Natural to sharp: 2.8750 (7.3925).
Flat to sharp:5.8750 (14.9225).

From these measurements, I want to know what the length of the string from the stationary nut (flat position) to the soundboard eyelet should be.I’m very curious to see what the “theoretical” length of each string should be based on the mathematical formula, as opposed to what the actual string length is. Thanks!!

[billooms]

For a given string with a given tension, the frequency*length should be constant (in theory).

On my 85CG (s/n 21594) the C5 string has the following spacings:
Flat to natural: 5.52cm (on pitch)
Natural to sharp: 5.27cm (on pitch)
Flat to sharp: 10.79cm (+03 cents)
Total length (nut to eyelet): 102.7cm

These spacings are a bit less than Carl measured on his model 23, so his total length will probably be longer than mine.

From theory, the total length from these measurements should be 98.4cm (using the flat-to-natural distance) or 98.9cm (using the flat-to-sharp distance). Both are wrong compared to the measured length of 102.7cm by quite a large difference!

The reason is because of the increased string tension from the engaged disks. The frequency*length is really not constant due to the increased tension. On this particular string on my harp:
Natural: frequency*length * 1.00250
Sharp: frequency*length * 1.00453

Applying these corrections for the increased tension, I calculate the correct string length of 102.7cm

If Carl’s C5 string has similar increases in tension from the disks, then I would estimate his C5 string is in the range of 106.3 to 107.3 cm. With similar assumptions, Carl’s B5 will be in the range of 110.3 to 115.1 cm.

Note that the increased tension in lighter (shorter) strings will be quite different than on the heavier (longer) strings — especially on the wire strings. Errors from measuring small numbers (and small changes in assumed tensions) will translate into larger errors in calculating the total length.

So am I close Carl?

[balfour-knight]

Hi, Bill,

It is interesting how harp models vary with regard to string length! One would think that all concert grands would have basically the same scale, since pedal harp strings are considered to be “standard.” I used your length of C5, 102.7 cm to get the equivalent of 40.43″. I then measured that same string on my Camac Atlantide and it is 41.75″. Gregg and I have enjoyed doing this sort of string comparison between his L&H Prelude and my Atlantide. It is all very interesting!

Cheers,
Balfour

[billooms]

Balfour —

Yes, I had thought that all the L&H concert grands would have been very close. Perhaps it’s because of the age of the harps — mine is only a bit over 2 years old and I suspect Carl’s is older.

When I was on the L&H factory tour 2 years ago, they said that all of the professional concert grands (except the Salzedo) had the same sound box and mechanisms. They also said that the mechanisms for Salvi Harps were assembled in the Chicago factory (although perhaps the design dimensions could be different).

[carl-swanson]

Hey Bill,

So nice to hear from you, and to get your feedback. I’ve read your post, but I’m getting ready to do a short “harp”trip tomorrow, so I don’t have time to study it. I’m also waiting for one of the other people here to send me some calculations. So I probably won’t have time to sit and digest all of this until maybe Thursday or Friday.

I do think, as you said, that the increase in tension for a gut or nylon string when the disc is engaged is going to be more than for a wire string, and therefore, the “theoretical” string length will be more off for them than for the wires. My real curiosity is to compare the theoretical, calculated string length to an actual string length that works. My guess is that all of my string lengths will be shorter than the calculations say they should be.

[charles-nix]

I have looked at your measurements, Carl, and written a spreadsheet to play with them. @billooms observation that freq*length is constant is an excellent way to analyze. I think it works out equivalent to looking at calculated ratios of predicted to actual length if the prediction is adjusted for measured mis-regulation.
I am a little confused about what Bill means stating “flat to natural (on pitch), natural to sharp (on pitch), flat to sharp (+03 cents)”.

Caveats, concerns, comments:
1) I worked in inches, because that looks like the original measuring unit.
2) Measurements: for C5 and C6, the Flt/Nat and Nat/Shp distances add up exactly to the Flt/Shp. For B5, B6, and A6 they do not. I’m guessing this is measurement error. For A6, the difference is 1/8″, which will make an overall prediction difference of nearly 2″.
3) From the size of the measurement error (if that is the cause), I am estimating that the calculations have around 2 significant digits. It is good enough for a first guess.
4) I have a column on the spreadsheet marked pitch adjusted length. My thinking is that if the flat to natural or flat to sharp length gives a pitch too sharp, then the length is too long, and predicts a string too long. I confess that I haven’t thought this through as much as I would like, and I may have corrected in the wrong direction.
5) Because the measurements don’t add up, I calculated length both by adding the distances, and by using your reported flat to sharp distance. We can eliminate that if you can determine why they don’t add and eliminate the problem.

A pdf of the spreadsheet is attached. I’ll email the full thing to you (or anyone else) Carl. On the full spreadsheet, I have provided a cell for you to enter the actual length, and then it will also calculate the ratio of predicted to actual. We should be able to take those ratios as a proxy for the effect of the disc tension, and then calculate for the harp you are rebuilding.

Nothing will be perfectly correct: after all, the pitches are a diatonic scale, with two semi-tones, and the rest whole tones. Conversely, the string lengths AND the action distances change along a smooth curve (most actions, anyway). I guess what is really important is to be sure that the whole string is not so short that the vibrating pitch of each interval ends up sharp of desired pitch with the disc closed to the minimum amount.

A separate issue is the effect of increased tension. I think that certainly longer strings are less affected than shorter. But a disc requires a certain angular displacement of the string to effectively prevent any buzzing. A given angular displacement of steel will raise tension (and pitch) much faster than for the same length gut. It is a much less elastic material.

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[billooms]

I was not clear on my earlier post. I should have said:
Flat: on pitch
Natural: on pitch
Sharp: +03 cents

[carl-swanson]

Hi guys,

I just got home from a short regulation trip. I’ll try to read all this again tomorrow morning. Charles- thank you for your highly analytical approach and organized thinking on this. I really appreciate it. I’ll read your post 4 or 5 times before I respond to it, just to make sure I understand it as well as this brain can!

I agree with you. The flat to natural distance added to the natural to sharp distance, should add up exactly to the flat to sharp distance. Let me look at all the numbers again and see where the problem is.

I think my end goal is to try to figure out what effect the tension of the discs on the string has, and how much compensation should be allowed for that. In other words, I suspect that figuring out the string lengths from the numbers I gave you, using the formulas that were discussed previously, will add up to a total string length that is longer than the actual string length on the instrument. I’m guessing that the actual string length needs to be somewhat shorter than what the math says it should be, in order to accommodate the disc tension. So if that is true, my final question would be: Can we come up with a formula for figuring out the total length of a string on a harp that will give us that shorter actual length. My concern is almost entirely with the strings that use a stationary nut, i.e., C5 to E7.

[charles-nix]

Carl, I think looking at the ratio of predicted/actual on several of the strings on your 23s (or maybe even several harps) will give you a good idea. I suspect there will be some scatter in the numbers that we can reduce with improved measurements. I would also suspect there will be a break in the ratios right at e/f and b/c because the measurements, soundboard, and action change lengths along a smooth curve, and the pitches suddenly move only half as much right there.

Part of that suspicion you might already be able to confirm: when regulating, do you frequently need a bit more (or less) disc grip on F6 than E7, C6 than B6, and on F5 than E4? It would absolutely be more noticeable in the wires than higher up because of non-adjustable nuts and single size discs. Amount of grip is the only adjustment available, to the extent to which even that can be changed. I’ve not regulated enough harps to have a good estimate if that is common.

When you replace the soundboard, what will be available to change? you mentioned the height of the column? Changing the neck shape couldn’t alter anything except reserve length could it? That will change the lower wires more than the upper wires, but we could drop the proposed new lengths into the same spreadsheet in the actual length column, and see if the ratios come up near to what you see on your 23s.

[balfour-knight]

Good questions, Charles! If I were Carl, I would set this up as a “lab experiment,” with the actual strings stretched out on a board with tuning pin, end holder of some kind, i.e. hitch pin, and moveable “bridges.” You could check out the mathematical formulas this way. Then you would need some sort of way to apply the forks of the discs to the strings and hold them that way, to sound out the actual pitches and make sure they work, since the action of the disc makes the pitch rise somewhat. It would be terrible to just rely on the math and rebuild the harp to the wrong dimensions!

Best of luck, Carl,
Balfour

[billooms]

Attached are measurements for strings C5 to E7 on my L&H 85CG. Measurements are to the center of the lower prong of the disk (or the center of the fixed nut). I measured the strings with a flexible tape measure in metric and the accuracy is estimated to be +/-1mm. I converted the metric measurement to inches since it looks like that’s the preferred dimension for those following this topic.

Strings C5, B5, A5 were measured from the top of the plastic grommet on the sound board. The rest of the strings had no raised grommet.

I did not list the specific accuracy of the tuning of each string. The distances are fixed independent of whether it sounds a few cents sharp or flat.

The last 3 columns of the spreadsheet are what Carl probably needs — the ratio of total string length to the nut-to-disk-prong distance (or disk prong to disk prong). Plotting them versus string gives almost a “straight” line for the wire strings. The gut strings don’t quite follow the straight line.

• This reply was modified 3 years, 9 months ago by billooms.
• This reply was modified 3 years, 9 months ago by billooms.

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[balfour-knight]

Hi, Bill,

That is a wonderful chart of string specifications/measurements! Incidentally, I wondered what is the sounding length of your longest string, 7C on the 85 CG? L&H used to be so proud of their long bass strings!

Best wishes,
Balfour

[billooms]

C7 is about 62.25 inches.

[balfour-knight]

Thanks, Bill! On my Atlantide, C7 is 61″ even though this harp stands 74.25″ tall. It is a full, beautiful Low C, with good placement on the soundboard!

Cheers,
Balfour

[balfour-knight]

Carl, just wondering how this project is going, if you are willing to update us. Hope you are doing well.

Cheers,
Balfour

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