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.

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Dear Richard,


First let me say I'm a  total BP newbie, so I know nothig about BP's. I also want to say that I do not disbelieve anything you;ve said above. My question is though, if your theory is correct, then how do so many psalteries exist which are built in a manner contrary to your above specs which people seem to be very happy with?

I tend to belive your theory based on my experience with the BP I've just purchased (see my posts about repeatedly breaking strings and the inability to get the thing tuned up to pitch). That being said, are there not many happy BP owners who don't experience this but their BP's are built with evenly-spaced hitch pins? And if so, how can this be in light of the math you've described?

I hope you understand that I'm not being argumentative by any means--I'm truly interesed in how this all works. Also trying to figure out if I've purchased a lemon.

First, it's not my theory or my opinion, it is simple truth. Look at the fretboard of a guitar, the frets are closer together as you move toward the body. Look at a harp, the long sweeping curve of the neck is to allow each string to be proportionately longer than the one before it. Both guitar and harp makers understand that as you move from high notes to lower note the vibrating length must increase in a logarithmic progression. You ask if what I have posted is true, then why are so many Psalteries build with equidistant pin spacing? A better question to ask is; "have builder of equidistant spaced Psalteries studied string theory?" Why would a Psaltery be different from other stringed instruments? The same laws of Physics apply to all of them.  

Please Richard, share as much as you can with us!  The more we understand the more we can do to improve our psalteries and our playing. I don't build but I want to understand. 

I don't think poor Madelyn should have to make drastic alterations to her psaltery, I think the builder should take it back. Just my opinion. 

My first psaltery and probably my favorite (which could simply be because it was my first) was built by Eric Meier of Phantasy Psaltery. Eric is no longer building and I think that is a great loss. He made a fantastic psaltery. When shopping for a psaltery early on I noticed the comments made by Richard and Eric about staggered hitch pin spacing and correct sound. Off hand I think that only Omega (Richard) and Phantasy build psalteries with staggered spacing. It was a consideration and part of my reasoning for choosing that psaltery. The other considerations were wound strings for lower tones, note range, weight and of course cost. 

Physics is physics (aren't I profound ), you can't argue with it. However my guess is that builders believe there is an acceptable range they can work within producing a nice sound if not the very best sound and keeping cost and complexity of building down. It probably works in many cases for many players, and than again doesn't work for some others. The longer I play the more nuances I pick up listening to various psalteries and the more my "taste" develops. 

I would LOVE to get my hands on a Omega Strings psaltery. I had an opportunity one time, but only a few minutes. From my brief encounter I will tell you it was a GORGEOUS piece of instrument, the woodworking was fantastic. It had a strong voice but it wasn't the right time or place for me to really play it. I'm hoping another opportunity will present itself. 

I can't help myself but I've got to add my two cents worth regarding this discussion on hitch pin spacing and string breakage.

I would agree with Donna's comment below regarding Eric Meier's design of the bowed psaltery utilizing uneven spacing of the hitch pins. The first psaltery I built was accomplished using Eric's Psimple Saltery plans that I found on the internet. His explanation of the theory is one of the best explanations I've encountered and I now build all my psalteries using this technique. Hopefully, this document can still be found at "www.apsimplepsaltery.com/gauges.htm"

I found that Eric's basic design is flexible enough that additional strings could be added to the standard, 2 octave, 24 stringed instrument. In fact, I have the second psaltery I built two years ago and it has a total of 31 strings on it and it is equipped with wirewound PB strings so it is now a tenor. The reason for the 31 strings rather than the traditional 30 was to cover the range of a song I couldn't play with 30 strings.

Perhaps I was lucky in selecting the correct diameter strings for this conversion but the end result is a very playable instrument. If strings are breaking on your psaltery, either there is a design defect, a poor choice of strings or a physical flaw in a pin. Did you know that there is sometimes a burr left in the hole on the tuning pegs? I noticed this while I was stringing one of my psalteries when the string was catching on something as I pushed it through the pin. T burr at this location can easily create a weak spot in the string as it makes a 90+ degree bend on he tuning peg. I now run a drill bit through the hitch pin and tuning pin holes to make sure they are smooth.

Attention to detail is very important !

I seem to recall one of our members mentioned that the string was coming out of the tuning peg. This could be caused by not having enough wraps around the peg. I like between three and four wraps but I also put a short 90 degree bend on the end of the string which firmly secures it to the peg.

First let me clarify one thing. I use only solid piano wire, so everything I say in this discussion will be limited to that wire. Wound strings are very different and must be treated accordingly. I build harps and well as BP's so I am very familiar with wound strings and I can get into wound strings, but that is for another discussion.  


String weight  actually is a constant in some regards. Some folks think that if you are breaking strings you can install a larger diameter string and all will be well. Not so. (a full explanation is lengthy so it will have to wait for String Theory 102) If you are breaking the same string often then the vibrating length for that string is too long which forces you to put too much tension on it to bring it up to pitch and the only cure is to shorten the vibration length, Increasing the string size doesn't change the % of breaking point which is constant for any size string at a given vibrating length and tuned to the same note. So in short if your vibrating length is breaking a .010" strings that vibrating length will also break a .012".


Donna is right, if you bought a Psaltery that breaks the same string before you can get it up to pitch it is a very poor design and the builder should take it back and give you a refund.



Maybe it's just late and I am tired but I really don't understand your last post.

You wrote:

Do you have evidence of a number of instruments sharing this fault to back your case, Richard?

What "Fault" are you referring to?

You wrote:

"I'd hate this site to become the home of a makers' war."

So would I. I promise you that won't happen, I will stop posting first. All I am trying to do is share some simple laws of Physics, not opinions.

You wrote:

"I think you need more than one, or possibly two, instruments which have had questions to start making such suggestions."

Could you please rephrase this. I am not sure what "questions" your are referring to or what "suggestions" you think I made.

You wrote:

"if a heavier string allows you to cut the vibrating length"

I don't think I said that. But I will say that the weight of a the string has no bearing on the vibrating length. Vibrating length for a given note is the same regardless of the gauge of  wire used.

There is a lot more math to cover in ST-102 which will cover this and a lot more...if and when I cover it. If people don't want to hear any of this then I will drop the whole thing. I didn't intend to stir up a hornets nest. And remember, none of what I have said is my opinion, it is all verifiable facts.

I don't think Richard said anything out of line or anything that might start a builders war. The reality is that there is something wrong with Madelyn's psaltery and I wouldn't want any potential bowed psaltery enthusiast to give up on the instrument due to such a frustrating experience. Is hers a lemon? Possibly. Is the one I purchased a lemon? Possibly. However, the builder is doing the right thing and taking it back to try to understand the problem. 

I want to add that both of our psalteries are lovely instruments and it is in the best interest of all, including the builder, if he identifies any design flaws or material flaws and corrects them. If other customers have experienced similar issues and have no other exposure to the bowed psaltery they probably have the perception that the psaltery is a high maintenance and fussy instrument when it's not.  

Richard, please don't be discouraged from String Theory 102. Too few people share this type of hands on experience. I know many people are interested for a variety of reasons. A friend of mine was reading your post when the network went down and was soooo frustrated not being able to finish until later.  

Richard, please continue your discussion on String Theory as I find it very interesting.  I have played and own a number of bowed psalteries from various builders.  I have experienced some of the growly and squeaky sounds and would like to experiment with correcting those issues.

Before I go any further with ST-101 let briefly share my vision for the Bowed Psaltery.

The Bowed Psaltery is unique in the music world. The sound it produces is unlike any other stringed instrument. The reason for this is 30+ strings. Because it has no damper each strings continues to vibrate so you can have upwards of 10 to 15 strings vibrating at the same time which produces the "secondary harmonics". The Bowed Psaltery have been in this country since the late 50's or early 60's and by and large it hasn't changed much. It still has mostly equidistant pin spacing and some still have the same gauge wire on all strings. Basically, each new builder copied the one before him so there has been very little "evolution" or innovation. This is why it has gained little respect in the folk music world. The editor of the Autoharp Quarterly in an editorial once called the BP "a screeching arrowhead". Shortly after starting to build BP's I realized that they had the potential to move out of the fringes of folk music and take a respected place in mainstream music. But before that could happen a radical change in design was needed. Having some strings sound better than others is not acceptable with any other stringed instrument; why do Bowed Psaltery players accept it as normal? If some strings can sound really good, then all of them can. The trick was the figure out why the good ones sounded better and apply the principles to all the rest of the strings. It is possible for every maker of Bowed Psalteries to radically improve the sound quality of their instruments if they; first, believe it is possible and secondly, do their homework and learn the principles and then apply those principles to new designs. This is why I started this discussion. I am 66 years old and retired. I am really not interested in building 1000's of BP's. I am willing to share what I have learned with every BP builder on this forum. To goal is simple, I want to see be Bowed Psaltery move ahead and take it's rightful place in mainstream music. I, alone, can't get the job  done, but if a lot of builders catch the vision it will be possible to accomplish the goal in just a few years. I am not "tooting my own horn", trying to start a war, or impress people with my "vast knowledge". I know what I am talking about and I am willing to share that knowledge with anyone who is interested.

That's my vision and my goal. If you are interested in sharing that vision post a reply and we will get the ball rolling.

My goal in building this web site was very much like yours Richard, to promote the bowed psaltery and help the instrument find a place in mainstream music. I think it has a place in folk/traditional music as well as some contemporary and certainly in the "new age" genre.

I don't build so my contribution is to "get it out there". Of course we need to get it out there at it's best. Players and builders have to be adaptable, flexible and open minded. Sometimes that will mean open to constructive criticism. Most instruments we know today have have centuries to evolve, not so with the bowed psaltery. It's a baby, in it's infancy so to speak.

If the goal is to promote and improve the BP, then we must pass on information, share experiences. That's another area I hope Psaltery Strings can help in.

I know that many members are interested in building their own psalteries or improving the ones they have. I hope you will continue to share what you know with the community. It is, in fact, very generous of you. 

We could create a builders group, or take this to the Builders section of the forum.

Richard, you are passionate about your string length theory and I respect that, but whenever one makes outright declarations of the absolute "truth" of their theory in the scientific realm, they are inviting analysis and criticism of that theory.  I believe your "bold statement" regarding pin spacing results from an argument that is flawed in at least two respects.

First, in what I regard a minor error, you introduce "tone" into what was an entirely mathematical argument up to that point.  Although I'll agree with you that tone is a function of string tension, the "acceptability" of any given tone is largely a function of human perception and culture, both very subjective at their best.  I also believe that, even if there is an exact string tension which produces the "best" tone at a given string length, there's not necessarily an extreme dropoff in the tone produced at tensions in a small range on either side of the ideal tension.  Thus, contrary to your argument that string length is the only variable in the string frequency equation as applied to a BP and that all the other factors must be regarded as constants, tension can be regarded as a variable as well, albeit in a small range.  

As a side issue, another factor in tone production which doesn't lend itself well to mathematical analysis is the bow itself.  I have bowed psalteries from five different makers, but I have bows of twelve different designs, including BP, violin and cello bows of varying sizes.  I've found that changing the bow which I use can make a marked change in the tone produced and often use a change in bow on any given BP to create the tone I want for a particular tune.

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.  Although you gave an example of a player unsuccessfully trying to use a string of greater diameter to avoid breakage, any experienced mountain dulcimer or guitar player will know that it's just the opposite direction one must take, i.e., if string breakage is a problem in bringing a string up to pitch, a smaller gauge string is needed. Although the string equation doesn't have a direct variable for string gauge, the gauge is part of the "mass per unit length" variable of the equation.

In conclusion, I believe you're in error in regarding all the factors of the string equation to be constants except for the string length.  I believe that proper pitch and excellent tone can be produced on an equidistant spaced BP by varying the string gauge and, to a much lesser extent, the tension, to match the string length.

Please don't take my comments as disparaging your BP design.  As a matter of fact, I've been trying to justify adding an Omega to my herd for several months, but the funds just haven't been available to match the desire.


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