"Ooh that dulcimer has a mean tone!"

Jerry says above that "it is not always possible to have on fret go across the fingerboard," but many luthiers are recognizing that and are making "true tempered" fretboards that look real funky:

You can find out more at True Temperament Fretting System .

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Dusty T., Northern California
Site Moderator

As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie

As Dusty Turtle say, this is NOT a dumb question!! It is a question which opens up many doors, and once you start opening the doors, you will have more and more questions. This is basically the large field of "Tunings and Temperaments" or sometimes referred to as "Microtunings" or "microtonality" -- basically all pointing to the whole idea of notes in between the keys of a piano (or smaller than a half-step).

There is some great discussion here, and many of you seem to have a good handle on the overall, general ideas of where frets might go. I particularly resonate with the single string stretched across a board of some sort, where you map out the divisions of the string - which will give you the harmonic series. If you get the harmonic series: dividing a string into 2 (2nd harmonic), 3 (3rd harmonic), 4 (4th harmonic), 5 (5th harmonic), 6 (6th harmonic), 7 (7th harmonic), and so on----then you can see how easy it is to build a just-intonation scale based on VERY simple small-integer ratios:

1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1

These would correspond to the frequency ratios of C - D - E - F - G - A - B - C ---- if you want fret spacing for your dulcimer's bass string (this is for 6+ fret only here - computing the normal 6th fret is another ballgame), you would use the inverse of these (frequency is inversely proportional to string length), remembering that the string length is the distance from each fret to the Bridge. To get your distance from the nut to a fret, just subtract that from the open nut-to-bridge V.S.L.

Another very important thing to remember on the dulcimer is that -- in C - G - G (1 - 5 - 5 Ionian) Tuning, the middle and melody strings will NOT go up EXACTLY as the bass string, because they are tuned to the 5th of the scale (so you start from 3/2 at the nut on these strings, and this time you will have the natural 6th fret and NOT the 6+). So, I'm basically saying here that it is not possible ALWAYS to have one fret go all across the fingerboard like they do on guitars, banjos, and modern dulcimers.

The wikipedia entry on just intonation is superb on deriving all this:

just intonation

I really need to get around to making some sort of an adjustable-fret dulcimer -- individually adjustable frets for each string. Of course one way around this is to use bagpipe tuning 1 - 8 - 8 (I know this works well for just tuning because my 1966 Jethro Amburgey is pretty close to just tuning and bagpipe tuning ROCKS on this!). Sorry about all the detail and ratios, but it really comes down to this kind of stuff, and there are many, many worthwhile web sites to help you get it.

I may be able to answer your questions, or at least I may be able to point the way to some good web resources. Thanks for the great thread!! BTW, I'm a major fan of Equal Temperament, mostly because I play a lot of chords and want to be in tune with keyboard synthesizers.

And by the way, this is not a "dumb question" at all but in fact a very complicated one that involves mathematics, acoustics, and other sciences about which most musicians (including wannabees like myself) are entirely ignorant.

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Dusty T., Northern California
Site Moderator

As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie

James, the conversation that Strumelia links to will indeed help you understand the difference between mean tone and equal temperament as they pertain to the dulcimer, and Peter's explanation also offers more than I can.

But let me just explain the problem that these two fretting systems try to address. It is sometimes said that G-d invented the octave and the fifth and humans invented all the other notes. Imagine a string tightened over a soundbox with no frets. Obviously, if you stop the vibration exactly half way along the string, you will get an octave of the open string. But between that open string and the octave, how many notes should there be? Different cultures answer that question differently. Some have 5 notes, for example. In western music, a chromatic scale has 12 notes and a diatonic scale has 7 notes. But where along that open string would you put them? It turns out that placing those notes along the string is not as simple as it seems, and exactly where they go would actually depend upon the note they are tuned in relation to. That is why in John's discussion Robin talks about placing frets not in relation to the open string, but in relation to the fretted tonic note.

So if you were fretting an instrument to be played in only one key, you could do a great job of placing those frets so that the notes would all sound great in relation to one another. But if you tried to play in a different key, they would sound off. Equal temperament tuning tries to basically split the difference and create note placements that are equally off in all keys, but hopefully close enough so that most of us can't hear the dissonance.

Here is a mathematical explanation of all of this: http://mathforum.org/library/drmath/view/52470.html . The first response by Dr. Toby might be all you need, but the conversation there goes on for some length.

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Dusty T., Northern California
Site Moderator

As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie

Hi James,

I just stumbled upon an older blog post by John Henry that discusses mean tone fretting, it might help explain!:

http://mountaindulcimer.ning.com/profiles/blogs/mean-tone-fretting

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Site Owner

Those irritated by grain of sand best avoid beach.
-Strumelia proverb c.1990

I have a dumb question but exactly what is mean tone, and how does it relate to the dulcimer? I know the sound is different and that is about all I know. Best,

updated by @james-phillips: 03/02/19 04:52:42PM