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Will get you measurements on my Swanson–actually measured it last night, but left them at home. Do note that you may find unusual differences in the F-G distance depending on how people measure. Some, maybe most, pedal harps “fan” out in the last 2-3 strings to get a little more room for fingers, and a little more straight pull on the sound board. Mine is several mm closer near the action than near the soundboard.
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.
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.
As a recovering engineer, how would you approach measuring from where the string is tangent to the groove in the stationary nut to where it touches the lower disc prong?
Yes. Carl, Biagio and I have all touched on that, but all the mentions are buried in the middle of some long posts.
Reading back, several things were left unsaid, because we knew that Carl is one of the finest harp technicians in the US, and a former pedal harp manufacturer. He also wrote The Book on harp maintenance for harpists. We knew he was just asking for the math parts.
Measuring and comparing sounds like a good idea. The hard part is measuring accurately enough.
Wow–1/4 step flat! I was thinking you were talking 8-10 cents when you said it was really off. No wonder you want to find a way to fix it!
Think about the math for two semi-tones this way: each semi-tone divides the starting length by 12th root of 2, which I called “k” above for easy reference. So two semi-tones divides starting length by k, and that result divided by k again. Or, length divided by k^2 (squared), which is also 6th root of 2, which is also the square root of the cube root of 2.
In the formula you referred to, you can use k^2 in place of k everywhere to calculate for whole tone lengths. 6th root of 2 is 1.122462048. 1.1225 should be plenty close enough. It will be hard to measure even to 4 significant digits (that would take measuring accurately to 1/128″ in fractions or 1/5mm in metric), so the inaccuracy in measuring will be the largest error.
I was thinking on how to measure nut to prong or prong to prong accurately enough. Best I’ve thought of is using a depth mic, if you’ve one long enough. Should get pretty close with a dial caliper also, though. That will get you readings in thousandths, which will work in the math a lot easier than handling the fractions from a ruler. Working all in metric would be even easier if you’ve a tape or rule long enough for the strings.
Take care with Henri coming.
I’ll take a stab at the algebra—
Let k = 12th root of 2, let l = total length from nut to soundboard, let f = length from nut to lower prong of natural disk.
f = l – [length from lower prong to soundboard]
or
f = l-(l/k)multiply every term by k gives:
kf = kl -l = (k-1)ldivide both sides by (k-1):
kf / (k-1) = l(in words): multiply the length from nut to lower prong of natural by k (12th root of 2), then divide by k-1, giving the total string length nut to soundboard.
The same equation can work for natural to sharp: just use the lower prong natural to soundboard length for the nut to board length, and the natural to sharp prong length is what is measured.
It will take careful measurement. Any error is multiplied by about 20 times in the whole string length.
Carl, you (and Biagio, and others) know this, but for anyone who may search and find this in the future, remember that the length to the soundboard is the length _after_ the soundboard has “bellied” up. And as you point out, Carl, the prong contact points need to leave the pitch slightly flat, so that the increased string tension from their grip will pull the string on up to pitch.
Maybe you have an easier method by comparing with a harp that will regulate. Measure the ratios of lengths (nut to natural, natural to sharp, sharp to soundboard) on several notes of a harp that regulates well, then keep those ratios the same on the harp you’re modifying. The “good” harp will have already accounted for soundboard pull-up and disc grip in each register of strings, so there is no guessing about that.
Carl, assuming you’re saying “reduce the length at a constant diameter and density”, which is what you would need for mounting levers, but not for calculating a whole stringing, divide the length of the longer string by 1.059463094 1.0595 ought to be close enough. If you want to multiply, the number would be 0.943874313 or about 0.94387.
The number is the 12th root of 2, because if you take a string length, and multiply it by the 12th root of 2 twelve times (one for each semitone) you arrive at a length exactly twice the original length, and a pitch exactly one octave lower. 2^(1/12) = 1.059463094.
Does that help?
Organbuilders would express that as “12th halving” because the number halves every 12 notes.
@wil-weten is right: regardless of cleaning, the headjoint must be movable to tune. Typical position for standard pitch is usually set at pulled out 2-3 mm, else if the room were cold, one would never be able to move sharp to match continuo instruments.
A wood recorder needs to be swabbed thoroughly, including the block–every time it is played. Leaving it wet might mean a cracked block over time; unless the instrument is at least semi-pro level, that repair would probably equal its value. It is challenging to properly access the block to swab it with the body attached.
If you are in the USA, suggest you contact David Green at Antique Sound Workshop. They have a website. And they have a huge amount of information on the website in the information bulletins section. They can also recommend the proper lubricant. I use a regular woodwind grease, which is much more solid than petroleum jelly.
If you need the string/harp, there is no reason not to shim the pin you have, use it for a month, and then put the replacement in when it arrives. (or the next time you restring)
You can unwind the gut 5A and rewind it on the new pin without damaging the string.
Shimming a pin is very common to get the fit just right–even on new harps.
Those look like silicone rubber tubing wrapped with leather. The tubing is available in many sizes and wall thicknesses. Looks like they took the tubing, wrapped it with suede leather, glued it down, and cut to length. Some other makers use rubber also for a padding layer.
You could probably find a combination of tubing and leather that would work on your harp. You _will_ have to regulate afterward.
It will wear (as does felt) and go out of regulation, and you’ll still have to regulate when you replace it. Can’t replace felts without regulating also, and you have to have the base off to correct the under/over motion at every regulation, so I don’t really see what one is gaining. A little savings in waiting for glue to dry, maybe. On a Camac, with their cable system, it may make things simpler.
And Biagio, doesn’t that look like a crack in the soundboard about one octave above the bass end–cross-grain, far side of the harp, right about where the edge of a string rib under the soundboard would be?
Zooming in on the photo, sure looks like about a 4 inch long crack to me.
No need for custom pin. Send the photos to L&H. I think all L&H pins are Morse taper, which is common worldwide.
I would use a stiff tubing brush (nylon or brass) in the hole, or at least blow out with compressed air. Do not ream or alter the hole.
After cleaning, and before ordering a pin, that pin projection looks borderline for just shimming–and you can try that without harming the harp.
Obtain a piece of fine wet or dry silicon carbide sandpaper, something like P320 or P400. Cut a piece nearly as wide as the neck is thick. Trim the piece so that it will roll up and slip into the hole–WITHOUT OVERLAPPING. The piece will not be rectangular, because it rolls up into a taper shape. The ends do not have to meet, but they shouldn’t overlap, at least at first. Roll the paper WITH THE ABRASIVE OUT–toward the neck, and the paper backing toward the pin. Slip into the hole, and get it seated, then put the pin in.
If the pin does not go in far enough to string on the other side, remove the pin, and the paper, trim the paper down, and try again. The paper should be nearly from one side of the neck to the other, but not visible. The pin will seat a little deeper after it is tuned a few times, so leave it a little short of where you want it to end up.
If that works, you don’t need a new pin, and it will be fine for years. If not, you might try some overlap on the paper, which might help, or might not hold the pin firmly. In any case you won’t hurt anything if you orient the abrasive toward the wood, and don’t glue anything.
The backing on that paper is pretty tough stuff, much more so than any regular paper, and the fine abrasive on the outside keeps the shim in place so the pin turns inside the neck/shim.
If that doesn’t work, take a picture of the pin with it firmly seated as if it were holding string tension, and send to L&H. They can determine what pin is needed. Pins come in 1/4 inch length increments, and in Morse Taper sizes usually #4 and #5, with some #3 and #6. Going to a larger taper will make a LOT of difference. I’m guessing much more difference that the little bit of extra length you are showing.
If you search “serial number” on the forums here, you can read quite a few posts about the fire and early L&H serial numbers.
I saw in-person #128 a few years ago, dated to 1894 supposedly. Carl Swanson has posted that he thinks his harp #300 dates to 1898-1900.
In the US, lever harps would be pretty uncommon before the 1960s or even 1970s, so the harp would need to have been built after then-unless the original owner might have come from a country with a harp playing tradition.
You also said inexpensive which would make me think of nylon strings, and at typical inexpensive lever harp tensions, I’m not sure there would be very many broken at all.
In an attic, with huge ranges of both temperature and humidity, you might have wood damage, or not. You probably would have to finish on the wood crazed or sticky or messed up in some way, and with an ocean climate I’d expect all the tuning pins rusty perhaps beyond use, and the brass parts of the levers corroded green.
But I’m making a lot of assumptions. The biggest problem I see with the harp as you laid it out, depends on when the story is set. We’re only 50 years now from the earliest time when a 34 nylon string harp might have been built. nylon strong
