The Oban Times, 8 June, 1907
THE BAGPIPE CHANTER SCALE
Salsburgh-by-Holytown,
3 May, 1907
Sir,–One of your correspondents on this subject quotes from Dr. Fraser’s recent work
anent the evils of tampering with the ancient scale of the bagpipe. I am prepared to allow that it is not advisable to take liberties with any scale. At the same time it is fair to state, after a close study of General Thomason’s carefully compiled tables of variations, that every pipe-maker appears to have an “ancient scale” of his own. No two chanters, ancient or modern, have scales giving a similar vibration ratio. In plain words, no pipe-maker seems to know what the correct scale is.
The Dunvegan chanter figures were a disappointment to me, but this was cleared up when General Thomason explained at his Edinburgh meeting that the chanter was shortened when being repaired, in order to make a good job of it. A shortening of the sixteenth part of an inch, especially in the upper part, would alter the whole chanter ratios. I append a table giving the vibration numbers of this chanter in the old Greek scale, and also in a similar scale, with an attempt to get away from the very sharp major sevenths of the Greeks without accepting as correct for our purpose the close mathematical ratios of the modern diatonic scale. I have been guided in forming the scale, which I believe is the correct chanter scale, by the ratios of the lower fifth–G to D–of the Dunvegan chanter.
| DUNVEGAN CHANTER | |||||||||
| G | A | B | C † | D | E | F † | G | A | |
| Greek, | |||||||||
| 402 | 452 | 508 | 571 | 603 | 678 | 763 | 804 | 904 | |
| Thomason (observed). | |||||||||
| 402 | 452 | 500 | 557 | 605 | 675 | 770 | 791 | 904 | |
| Mixed Greek and Modern Suggested Standard. | |||||||||
| 402 | 452 | 502 | 557 | 603 | 678 | 753 | 804 | 904 | |
Let it be supposed, for the sake of argument, that Donald MacCrimmon did not lower his high G, but raised his low G from 395 to 402 vibrations. His high interval of G to high A has a ratio of 8-7ths. Let the lower interval be made to correspond. Then the scale would read:–
| G | A | B | C † | D | E | F † | G | A | |
| 395 | 452 | 500 | 557 | 605 | 675 | 770 | 790 | 904 | |
| 8 7 |
21 19 |
19 17 |
13 12 |
19 17 |
8 7 |
71 69 |
8 7 |
The Greek scale in the modern diatonic resemble each other in having fourths and fifths of 22 and 21 commas respectively. The Greeks made no difference between the greater and smaller tones. Each major third had thus 18 commas, as opposed to the 17 of the modern scale; each minor third had only 13 to 14 commas of our scale, and therefore the smallest semitone had only 4 commas to the 5 of our diatonic semitone. Let these facts be applied to the perfect octave A to high A, of the above scale. It is found that the fourth, A to D, has 22 and 7-24ths commas, and is that the fraction sharper than a true fourth, consequently the upper fifth, D two high A must be 17-24ths less than a true fifth. The interval D to F has 18 and 18-24ths commas, and is therefore the fraction more than the true Greek major third. As a result of this, the minor third, F to high A, if the fifth, D to high A, were perfect would contain 12 and 6-24ths commas instead of 13.
But we have seen that the upper fifth is 7-24ths short of being perfect, and therefore the minor third, F to high A, contains only 11 and 23-24ths commas. High G to high A contains 10 and 6-24ths, therefore the interval F to high G has only 1 and 17-24ths commas, and is therefore 17-24ths short of the lower imperfect fourth of the Greek mode fourth, which has 27 commas. C to F has 24 and 21-24ths, while D to high G has 20 and 11-24ths commas. Thus the scale we are studying is made up of modes four and five of the Greeks, superimposed, and partaking of the good and bad points of each.
It is obvious that the Dunvegan chanter is mistuned in its upper part, and a great part of its seeming deficiency there is probably due to the reduction of its length in repairing. The scale I have tested the original figures by is generally called that of Pythagoras, and reached completion 500 years before the completion of the Christian era. On it were found in the old modes on which bagpipe and most all Scottish vocal music, is built. This is admitted by all musicians.
If anyone will take the trouble to build up the Greek scale in mode one, with intervals of G9, A9, B4, C9, D9, E9, F4, G commas, my arguments will be easy to follow. I have marked in the table also, with a cross, the smallest intervals. It was the position in ratios of these in the oldest chanters which guided me to the opinion that the chanter scale had originally been in the old Greek modes of the fourth and fifth, modified by local usage. The next scale given in the table has ratios A 10-9ths, B 10-9ths, C 13-12ths, D 9-8ths, E 10-9ths, F 16-15ths, G 9-8ths, A. This, I am certain, is the correct chanter scale. The Zalzal is a scale midway between that and the Greek scale.
As musicians have always accepted the Greek scale as that on which ancient Scottish music was built, I think the Zalzal may be put out of count. The ratios of the Zalzal are A 9-8ths, be 11-12ths, C 13-12ths, D 9-8ths, E 11-10ths, F 13-12ths, G 9-8ths, A. While Donald MacDonald shows by his chanter that he had a glimmering of the truth, yet he did not arrive at it, and his chanter only allows for an approximate consonants of the A tetrad with the drones. I think the scale committee would be greatly strengthened by the addition to it of such a member as your correspondent of the 10th inst., who signs himself “H. S.” It is true, as he states, the perfect chanter will never appear until the advent of the perfect reed, but if all chanters were made to a standard scale, there would not be so much difficulty in tuning the chanters of, say, a band, consonant. This would give an increased beauty of tone and an absence of the “awful din” of beats now heard in listening to most pipe bands.
The late Mr. Colin Brown’s instrument for measuring vibration numbers is known as “the voice harmonium.” It is mentioned by Ellis, by Curwen, by Harris, and many others, and is considered one of the few perfect instruments for the purpose it was intended. Many of the chanters examined by Brown had scales resembling none known, ancient or modern, and the same may be said of many of those given in figures by General Thomason.
I have always said the chanter scale was all right if understood. Anyone who knows Ceòl Mòr well should be alive to the modal nature of the scale. This is recognised in certain modern books of piobaireachd by signaturing the A tunes with two sharps and a minor symbol, the D tunes by two sharps, and the G tunes by one sharp. The first represents the notes C and F as being sharp and G flat, the second represents C and F as being sharp, while the third represents the F as being sharp. Now, the scale of G to A in the key of D is the one fixed scale which will play tunes so signatured. While for several obvious reasons it would be wrong to make the chanter scale G to A in the key of D of the present diatonic scale, I submit that the next scale given in the above table overcomes the difficulty, retains the peculiarities of the music it is intended to play, and so strikes the balance between old and new ideas. The scale committee may meet and come to a decision, but I am afraid the conservatism of the pipe-makers will prevent the adoption of the scale agreed upon. So, as of yore, we may still have the spectacle of the pipe-makers, ancient and modern, as portrayed by General Thomason tables, each probably seated in his own secret Paradise, playing on his own “ancient” scale.–I am, etc.,
Charles Bannatyne, M.B., C.M.
