The Oban Times, 18 December, 1915
The Bagpipe Scale
Braehead Villa, Catheart, 13 December, 1915
Sir,–The scale of the bagpipe is clearly taken from the earliest form of the musical scale set down by Pythagoras about the end of the sixth century B.C. The scale is as follows:–
(s) l t d¹ r¹ m¹ f¹ s¹ l¹
Guido, a monk of Arezzo, at the beginning of the eleventh century A.D. added the note given in brackets. There were two octaves in the original Greek scale, the lower for male voices and the upper for female. The pipe scale is therefore the soprano half of the scale of Pythagoras with the added note by Guido. The notes of this first scale were named in order of the first seven letters. That is why we have still A as the Diapason Normal in all countries.
There are only three different pitches that are of any account,–the scientific pitch fixed at Stuttgart in 1837 (A 440), the French Normal Diapason (A 435), and the Philosophical pitch (A 430). The first is preferable because there are no fractions in the vibrations of the middle octave and upwards. As there is only the difference of one-third of a semi-tone between the highest and the lowest of these three pitches, it is of little consequence which is taken as the standard for the bagpipe. If the instrument is to accord with other instruments it should be tuned to A 440, and the tuning should be in equal temperament.
The Greek scale was corrected later by Ptolemy, when the major and minor tones were identified and the semi-tones were given their proper also. This led up to the true scale, which is now taken from the harmonics of the string. The notes of the major scale are found in their order between the 24th of the 48th harmonics thus:
d r m f s l t d¹
Harmonic 24 27 30 32 36 40 43 48
These multiplied by 11, the root of the series, give the vibrations of the middle octave C to high C. This is the true scale and the one which every instrument should come as near to as possible. The human voice, the instruments of the violin family, and the trombone can give a rendering of the true scale; the others are a mere approximation.
The scale of the bagpipe consists of nine notes and does not admit of any transition whatever. If variation lies in the use of the Greek modes, and it has 14 of these to operate upon. It can therefore modulate, but it cannot make a transition from one key to another, seeing it has no chromatic scale. There is only one full major scale in the scale of the pipes and that is in the natural key of C. It is a modulation to change from the major to the relative minor–that is, from C major to A minor–or from the mode of Doh to that of Lah, but to change from A minor to A major involves a transition of three removes and necessitates the use of three notes that are foreign to the scale of the bagpipe. It is more likely that your correspondents who think they are playing and A major are really playing in A minor or in the mode of Lah. It will be a bad day for the bagpipe when it is made to do service as a chromatic instrument.
Let the pipers insist upon a standard pitch, which should be A 440, and keep the bagpipe in its ancient form with its ancient modes. It would be the work of a vandal to modernise such a relic of ancient times, and let the composer of music for the pipes right in the modes and all will be well.
I give, as under, the vibrational ratios of the true and the tempered scale in so far as these relate to the bagpipe, A being 440:–
I am, etc.,