CHAPTER 3: History to 1800

3.5 The Baroque, Rococo and Classical Periods 1600-1800

3.5.1 The west

1.1. Popular cultures in the 17th & 18th centuries:

2. Germania

Detailed evidence: 2 of 6: Nierop

[p.116]


fig. 65: from Wis-konstige Musyka,
Rembrantz van Nierop,
Amsterdam 1659

 
The second detailed description of a popular dulcimer is another enigma, for it gives a tuning which the writer says is standard in the Netherlands, yet for which no other evidence was found anywhere. The bridging pattern which would be required for such a tuning exists on no surviving instrument, although it was portrayed once, in the clear engraving of Stimmer (1575, fig.50). The work concerned is Dyrck Rembrantz van Nierop's Wis-konstige Musyka (approx. 'Scientific Music') published as an appendix to the second edition (1659) of his Wiskonstige Rekening (approx. 'Scientific Arithmetic') and discussed by Barbour (1930); it includes a diagram of a Hackebort together with a discussion of the tuning problems and a note about a mathematical approach to determining the positions of the bridges. Rembrantz' first page is reproduced at fig. 65 and in English begins as follows:

'To make a Hackebort and to tune it. A Hackebort which here in this country is usually made as the figure shows, which is put in seven parallel (equally-spaced) singingtones in an octave, of the length of half a string/ where the bridges C.G and B.F after having been adjusted and the strings been tuned (which could not be done by ear without great effort): and although it is a crude and peasant instrument, against the nature of the art of singing (which is not sung on seven parallel singingtones), it has nevertheless often fallen to me to adjust it, so that I was forced to find a way, other than the natural way, to make the bridges sit in their right place ....'

He then continues to show how he derived arithmetical measurements for placing the bridges

"op haer recht plaetse/ dat waneer de snaeren dae over pespannen waren/ de octaven terstont getreft konden worden" 'in their right place, so that whenever the strings are stretched over them the octaves can be struck at once'

His basic problem was that there were two treble bridges, each of which divided a single string into three playing portions, there being no crossing of strings in different planes, as shown in fig. 244 (p.392b of the paper version of this thesis, type 2) . Barbour has described Rembrantz' essay in detail, and shows that the tuning might have been Pythagorean, mean-tone or equal-tempered, but not just-intonation, although adjustments could be made by altering the tension in the various string sections ("men dit door stijver of slapper optrecken der snaeren kan halpen").

Barbour describes how Rembrantz discusses the division of the octave into seven equi-distant tones, producing a scale with second and seventh degree 1/7th tone flat, fourth and fifth degrees fairly accurate, and third and sixth degrees neutral, between major and minor, compared with the scales in use in art music. The mention of neutral tones immediately causes one to wonder if this system was evolved in an effort to produce on a dulcimer a tuning which corresponded more to a locally-current traditional (folk) scale used for vocal music, but Barbour does not consider this possibility; his quotes and translations are not sufficient for this to be ascertained, and it as not possible to obtain a complete copy of the original. If this were the case, it would form a fascinating parallel to Reidar Sevåg's examination of Norwegian folk scales preserved by the fingerboards of a hundred or so old langeleiks (95).

Be all this as it may, by and large a diatonic major scale was certainly the norm, though the extent to which the basic pure fifths across the treble bridge were modified to give one or another temperament was probably minimal, and possibly purely fortuitous. There are certainly players nowadays who 'listen for the beats' as they tune, but it is more commonly a question of finding a compromise which will not offend too many listeners.