I have been building Bowed Psalteries for about 20 years and shortly after I started I saw the need to understand why a string does what it does. I did my homework and studied string theory until I understood the math. All of music can be expressed mathematically; the playing of music is art but music itself in all math.
So with that said, I will try to explain why a string does what it does.
The tone a string produces when it is bowed has nothing to do with the note it is tuned to. If you want to prove this just tune any string down one note. Your tuner will tell you it is vibrating at the proper frequency but it will sound horrible.
Proper tone depends on the amount of tension on the string.
Since the note the string is tuned to is fixed, the only variable to adjust the tension is the vibrating length (this is the length between the hitch pin and the bridge).
There is a perfect vibrating length which will apply the correct tension which will produce the best tone for every note in the scale.
The secret to a sweet sounding Psaltery is having the correct vibrating length on each string.
If you ask most Bowed Psaltery players if their instrument has a "sweet Spot" they will say "yes, it does". The sweet spot is a portion of the range that sounds better than the rest of the range. It is usually somewhere in the center of the range. The longer strings sound course or "gravelly" and the shorter strings sound "tinny" or "screechy". The reason for the difference is the vibrating length of the strings in the sweet spot are correct and the others are not.
I will make a very bold statement. "If your Psaltery has all the pins on the right side the same distance apart then it is impossible the have the correct vibrating length on all strings.
I am in no way being critical of any specific design but what I am saying is true. If you doubt it, then "do the math" for yourself. Math doesn't lie.
There is a lot more to this, such as % of breaking point, tension/length ratio, etc. but that is String Theory 102.
We will see what kind of response this post gets before I go deeper.
"Now, as for the major disagreement I have with your argument, it's your disregard for string diameter as a variable in the string equation."
Some say that if you are breaking a string you substitute a larger string in it’s place.
Ivan, you say that if you are breaking a string you substitute a smaller string in it’s place.
I say that if you are breaking a string the only solution is to shorten the vibrating length, the gauge of the string has no bearing.
It is impossible for all three statements to be correct. We can debate the issue all day and never resolve it. So let’s see what the math says. Math doesn’t lie.
At the moment I’m only concerned with a string that is breaking often and nothing else.
If the string is breaking often you are applying too much tension to bring it up to pitch. I will introduce a term that is familiar to most harp builders; Tensile Strength Ratio. Each gauge of wire has a breaking point expressed in pounds of tension per square inch. At its breaking point it can be said to have a Tensile Strength Ratio of 100%. To calculate the Tensile Strength Ratio for any string use the formula:
Tension / Breaking Point X 100 = TSR
For this example we will use the note C6 and vibrating length of 7 1/4". If we use .012” steel wire the tension will be 19.08 lbs/sq. in. .012 steel wire has a breaking point of 36.757 lbs./sq. in. so using the formula above we can calculate the TSR at 51.908%
Now, let’s see what happens when we substitute a larger wire size of .014”, keeping the pitch and vibrating length the same. The tension will be 25.97 lbs/sq. in. and the breaking point for .014” steel wire is 50.03 lbs/sq. in. Using the same formula the TSR is 51.908%.
Now, let’s see if substituting a smaller wire will be different. If we substitute a .010” wire tuned to the same note with the same vibrating length the tension will be 13.25 lbs/sq. in. The breaking point of .010” steel wire is 25.525 so the TSR is 51.908%
This is the math. Math doesn’t lie. In all three examples the TSR is the same. If you are breaking strings it is because you are applying so much tension that you are approaching 100% TSR and changing the diameter of the string will have no effect. The only solution is to shorten the vibrating length which will reduce the TSR and the string breaking problem will be solved.
Now I have shown you the math and proved my point. If you still disagree, then do as I have done and show me your math.
By all means, Richard, please do go on. While I understand very little of this information ( the "math portion" of my brain is pretty much atrophied) it is information that I need to learn...it all makes sense in a way. My experience with this instrument is only a few months old so I haven't as yet developed an educated ear but the more I play, the more I want to learn.
First, let me say that I'm VERY appreciative of all the info, input, and opinions on this. I must apologize in advance for having to ask this question, though: is there any hope for my psaltery, and if so, what will it take to make it right? If it's not likely that it's fixable, then I would ask the seller to refund me and hope that he is cooperative. If it IS fixable, then I'm happy with that as well, since it is beautiful and had a sound that I found very pleasing. Any hope here?
I have not read anything you may have posted on your BP but I can tell you what wrong with it and how it can be fixed, if possible. All I need to know is the note, the length and the gauge of each string and I will do the math and let you know. If you have pictures posted let me know where if not please email some to firstname.lastname@example.org
OK forget about the gauge just send me the note and vibrating length for each strings.
I've sent the BP back to the seller, so I'm not sure of the notes, and (please excuse my ignorance here) I have no idea what a vibrating length is. Does this just mean the length of that particular string?
I can tell you that it is a 30 string tenor, ranging from F3 as the lowest note to A5, and all of my problems with the strings were with the sharps & flats on the left side starting at the second F# and down from there (down toward the bottom of the psaltery, not down as in lower notes). Those last 8 strings (higher in pitch) were all giving me fits--either snapping or unwinding. I triple and quadruple checked that I was tuning the right pin, to the right note, in the right octave, and I used gentle turns in tiny increments. As soon as I got to within one note or so of pitch,......SNAP! Even the Bb in the middle of the BP that I'd successfully tuned and played previously, quickly flattened itself to A, & when I went to tune it back up, SNAP! Very disheartening.
If you sent the BP back to the maker then the problem is solved. My bet is that the vibrating length (the length from the hitch pin to the bridge) for those strings was too long and the only cure is the shorten the length. Without any specs I can't do the math.
Thanks, Richard. The problem is that I sent it back at his request so that he could troubleshoot it. He intends to then send it back to me. My fear is that it is unsalvagable and I'm looking for input as to whether this situation even sounds salvagable to the experienced BP'ers on this site. If not, I need to ask him to please refund me and hope that he cooperates.
You could ask the builder to give you the information on your BP and post it and I could do the math. Ask for the vibrating length, wire gauge and note of each string.
I have a 30 string (I'm thinking he only makes one style, but I'll check) psaltery by this builder. I will get those measurements and post them this weekend, unless I determine that Madelyn has a different model than I do.