June 14, 2019

Whole tone hammered dulcimer tuning

This article presents an alternative chromatic tuning of the treble side of the diatonic hammered dulcimer inspired by the cimbalom, without changing any strings.

The most common cimbalom tuning is the Hungarian style, which allows for playing in any key. The Hungarian style uses several different patterns for the different parts of the instrument. But the one that caught my eye is the lowest octave, which is tuned using a whole tone pattern. This, incidentally, resembles another late 19th century Hungarian invention: the Jank√≥ keyboard. So, I decided to tune the dulcimer this way.

In the diagram below the left side shows the traditional treble bridge configuration of the hammered dulcimer. The right side shows the whole tone tuning achieved by shifting the treble bridge to the right, just short of the center of the instrument.



The traditional dulcimer tuning is based on tetrachords, or identical 4 note scale patterns. It splits the major scale in 2 equal parts so that the first half of the major scale can be played on the right side of the bridge and the second part on the left side. It's probably the most compact ordering of the notes of a major scale. (This pattern also appears in the cimbalom starting at middle C). Depending on the size of the dulcimer you can play diatonically in the keys of A, D, G, C, etc ... Two notes from each scale are duplicated in the next scale: the 5th and 6th of each scale (E and F# of A) are repeated as the 2nd and 3rd of the scale above it (E and F# of D). This confers some flexibility as to whether you play a scale horizontally or vertically.

The new tuning is one whole tone scale on the right of the treble bridge, and another whole tone scale on the left. The huge advantage of this system is being able to play and easily transpose to any key. Due to the isometric nature of the layout, patterns hold their shape when moved up and down the bridge. If you need to play a pattern on the opposite side of the bridge you mirror the pattern and adjust for the minor second intervals. There are no repeated notes, so the range of the instrument is expanded.

There are traditional chromatic layouts for the hammered dulcimer, and they also provide an easy way to transpose, but only on those courses tuned consistently a semitone apart. One disadvantage is the longer length of an octave; it is twice as tall as in the whole tone layout. Additionally, the whole tone layout is entirely consistent, without the need of random sharps in the corners of the instrument.

Tension

The numbers on the right of the diagram indicate the semitone changes for each treble string after the new tuning. Although the total semitone change is negative (-4 semitones) the overall tension increases by 2%. The choice for B/A# as the first string was made to keep overall tension changes to a minimum. Initially I tried C#/C for the first string resulting in a 28% overall increase in tension which caused the instrument to bow!

Bridge placement

In the traditional dulcimer tuning the treble bridge creates two notes a 5th apart, or 7 semitones. The ratio of the lower pitch over the higher pitch can be given by 0.5^(7/12) or 0.667. So if the string is 78.8 cm we have two equations:

right + left = 78.8
right / left = 0.667

Which solves to: left = 31.54 cm and right = 47.26 cm.

When the pitches are one semitone apart the ratio is 0.5^(1/12) or 0.94. With this ratio the left side should be 38.26 cm and the right 40.54 cm.