The Oban Times, 19 January, 1907
The Scale of the Highland Bagpipe Chanter
Salsburgh, by Holytown
10 January, 1907
Sir,–Major-General Thomason, in his interesting third article on this subject, it appears to have someone altered his opinions with his figures. It seems as if some confusion lurked in his mind regarding absolute and relative pitches.
The pitch of the chanter high G considered only as a tone is its absolute pitch; while, if considered in relation to the other notes, that is relative pitch. It matters not whether Donald Mor MacCrimmon had 100 vibrations in his high G or 800, provided he did not alter its melodic relations. This he did not do. Major-General Thomason draw sweeping conclusions from the high G of the figures he gives for the Dunvegan chanter, seemingly unaware that the upper part of its scale is nearly a full tone out of tune. If properly tuned, with its high G a perfect octave of the low G, the former would have 804 vibrations, as against its present 791. He admits practically that not to have this octave perfect is an error, and yet he draws his main conclusions from a mistuned chanter, in which this very error occurs. This error is due to the chanter being tuned from above downwards in “A Major,” instead of in the natural method of scale formation, from below upwards. Who ever heard of anyone ascending a ladder from the top? Common sense teaches the few pipers to tune upwards from low G–though many do the opposite. We hear a lot anent bad chanters, that is the fault in them?
The oldest chanter–the Drummond–as tested originally by Gen. Thomason, has its scale formed rather under the natural pitch at a level of the first of the three black notes of the piano above the middle C; the others are formed above the natural pitch. What is the natural pitch? The lowest note we can here is C 16. Raise this four octaves, doubling at each octave, and we get C 256 vibrations. But our modern scale is first found in the scale of natural harmonics at the level of G, the 24 partial, that is a fifth or 3-2 above C, which gives G 384 vibrations. All scales lower than that are produced at an artificial pitch. That pitch is treble G.
Major-General Thomason says I rely on illustrations applicable to a state of affairs no longer existent. I do not know what he means. I say the chanter scale is in the old Greek mode five, and in saying so I agree with Mr. Ellis, F.R.S, that the Zalzal is practically the correct scale. I rely solely on the nature of bagpipe music and on the application to Major-General Thomason’s figures of arithmetical ratios drawn from Nature’s scale of harmonics, checked by comparison with a modern major and old Greek scales.
The old Greeks made no difference between the greater and lesser steps of the scale–consequently each major third had 18 commas, each minor had 13, each major 6th had 40 commas, and each minor 6th had only 35. Their diatonic semitone had only 4 commas, as against 5 in ours, while our major 3rd has 17, our minor 3rd 14 commas, our major 6th has 39 commas, and our minor 36 commas. A comma is 81-80ths or the fifth of the semitone. There are 53 in an octave. The old Greek scale have perfect fifths and fourths like ours, as a little thought will prove. Mode five should have good fifths and fourths. I think if we apply the rules of the old Greek mixed with those of the modern scale, and the knowledge of the fact that pipers, owing to the influence of the drones, are satisfied with fairly good fifths and fourths, we overtake all the apparent mystery which has been made to surround the chanter scale. Add to these a large grain of bad tuning, and a certain amount of “mean temperament.”
Major-General Thomason does not appear to realize that in admitting the high G to be a perfect octave of the low G he is admitting the whole of my case. In his first articles he did not say anything about this octave, but his remarks anent the octave of A would then have led one to imagine he took A to be the fundamental note of the chanter scale with a sharp seventh, considering that he flattened this only by a subterfuge. Here I append the ratio table by which his figures can be tested. I give also the ratios of the modern mode at the same level, and also the Zalzal for comparison. Zalzal, meaning even vibration, it is natural to think that this old Arabian word simply refers to a scale, the upper part of which is a replicant of the lower–in plain words, a diatonic scale.
The chanter scale, I believe, has been formed at a lower harmonic level in the past, and in the key has been forced up by the drones. Major-General Thomason mentions bands of pipers in reference to the rise of pitch in the chanter 200 years or so since. I always understood pipe bands to be a modern excrescence, and the drums and outrage. That by the way, but now for the tables. The RAF actions of the chanters, represents commatic differences and does not condemn the scales. Nature does not deal in fractions, but all scales made by man are part nature and part art. This table expresses exactly the relations of the notes in each scale. The modern scale given is, of course, in true intonation, the others are undoubtedly tempered, and the third one is out of tune in part:–
|TABLE OF VIBRATION RATIOS|
|(For full figures see Gen.
Thomason’s Tables IV., V., VI., and VII.)
|Speed of sound taken as 1100 feet per second.|
|(Original G 372)||23,||25,||28,||31,||34,||38,||42,||46,||50|
The table is worked out at the absolute pitch of the G in each scale. The fractions show commatic differences as compared with a major modern scale formed at the same pitch, the fractions in the first not representing the relation to the succeeding note. The table shows, at a glance, the tuning, and proves the Dunvegan chanter to be absolutely discordant in the upper part. Yet this is the chanter on which the foundation of Major-General Thomason’s principal arguments rest. The figures can be tested by means of a chromatic tuning pipe, and a scale of natural harmonics such as can be found in any good book on Acoustics or Musical Statics. That scale will not give fractions, but an estimate can be made from, say, the 18th partial, which is D and the original key of the chanter mode. I make no apology for the table I give, except to the printer, and I trust it will not make him athirst for my blood.
I hope this dissertation will satisfy your courteous correspondent, “F,” and I trust he may not read force in it.
Mr. MacPhedran, in your issue of January 5th, is correct, so far as he goes in his statements, but, like myself, he apparently misunderstands the ultimate trend of Major-General Thomas’s investigations. That appears to be the fixing of a standard of pitch –absolute, not relative pitch. The former may change; the latter has not changed, except at the hands of a band such as Major-General Thomason’s great Ceòl Mòr player was placed in charge of. This player could tune his own chanter correctly, but did not realize that the error was in the chanters of the band, not in his own, and consisted in the sharp instead of the flat seventh.
I imagine “Caber Feidh” played with a sharp seventh. Unfortunately, I have often heard it. It is a reflection of the tinkering with the scale which came into vogue about twenty years ago, and is still found in certain chanters whose makers I dare not name, for I am not yet tired of living. Let pipers begin their tuning at low G, and tune the G, B, D, G; then take A and tune A, E, A, and their chanters will then be almost correct. The chanter scale is all right, if understood. It wants a little nursing. Our greatest players, as a rule, know how to tune. The chanter has evidently always been tuned by great players in fourths, fifths, and octaves. It has suffered most at the hands of those who were not pipers, but musicians of a modern type. Fix its pitch by all means. Use good reeds and common sense in tuning, and the good playing will follow in due course. –I am, etc.,
Charles Bannatyne, M.B., C.M.