Octo:)er 9, 1962 Dear Chorus: 'Looks Mr'. Hunter was terribly happy with our rehearsal last evening. like the sectionals plus some work at home are beginning to pay off in a big way. 1Don1 t know whether you could get the effect of the Tallis as I did, but you can be sure it is going to be something special. and Some years back Mr. Shaw sent you a letter dealing with intonation, it seemed to me that a repeat appearance of Aspects of Intonation wouldn't be such a bad idea. Here it is: "O.f all the possible disfigurements of beauty in music the most disturbing may be faulty intonation. We say of a person who manages to sing in tune that he has a "true" voice, and quite unthinkingly reflect the strangely moral judgement which most of us excercise with regard to intonation. Somehow, it seems, singing out of tune is a violation of truth, and cotmter to an inherent, intuitive conscience of hearing. This reaction should not surprise us, for it would seem to be the psychological counterpart to natural law in the physics of sotmd itself. We note that the exhaust of the passing truck causes the window to vibrat e. We reflect that one vibrating object sets other independent objects to vibrating "sympathetically." During vocal warm-up sessions of our Monday rehearsals we hear certain well-tuned unison sounds produce "over-tones'• of the octave and a fifth above, vibrations so firm that it sounds as though a full section of our Chorus must be singing these 11sympathetic" sounds. It is no secret to anyone who has passed through high school physics that sympathetic vibrations exist not only in a ratio of 1 to 1, but (with mathematical exactitude and order) in ratios of 2 to 1, 3 to 2, 4 to 3, 5 to h, etc. (For instance, the octave above any specific pitch has always exact l y twice the vibrations per second of that pitch. It's ratio is thus 2:1.) The vibrating object -- be it surface, string, or column of air: be it tympani, violin or voice -- vibrates not only its fundamental frequency, but to lesser and varying degrees, a series of fractional vibrations, identified as partial s , harmonics or over-tones. It is these harmonics which, in variety and distribution, determine what we call tone quality. A violin may play the same fundamental pitch as an oboe, but it will generate in itself and the air around it its own characteri stic set of over-tones, which distinguish it from other instruments capable of sounding the same basic pitch. From any given tone, then, it is theoretically possible to derive a complete scale simply through these fr act io nal relati onship s. For i nst a0c e , th e intervals of the major scale stand in the following propor t ions:
-2-
The The The The The The The The The The The
act.ave is 2:1 perfect fifth is 3:2 perfect fourth is 4:3 major third is 5 :4 minor third is 6:5 major second is 9:8 minor second is 16:15 major sixth is 5:3 minor sixth is 8:5 major seventh is 15:8 minor seventh is 7:4
The rub, so far as musical variety and richness is concerned, is that any pitches thus derived are substantially limited in their use to the specific scale of the generating tone. If -we want ·to move from one key to another -- a technique which presumably is accomplished by pivoting on a tone commonto both keys -- we would face an almost completely new set of relationships. That is, we could arbitrarily state that 11x 11 is commonto both keys, but the entire remainder of the two musical alphabets would be strangers to each other • . For · instance:
If A equals 440 vibrations then C-sharp and F-natural and G-natural
per second
(5:4) equals 550
(8:5) equals 704 (7:4) equals 770
But:
If C-sharp equals 550 then E-sharp/F-natural (5:4) equals 687.5 And if E-sharp equals 687.5 then G-double sharp/A-natural (5:4) equals 859.375 or 429.6875 (octave lower) And if G-natural equals 770 then F-natural (7:4) equals 1347.5 or 673.75 (octave lower) Thus, without ever going very far afield, F1 equals 704 2
F equals 687.5 F3 equals
and
673. 75
A1 equals 440
A2 equal s 429G6875, as viewed from different reference
points.
we have:
-3The the field nece~sary of other
basic accounstical (physical) problem in into~ation, then, is in of function. Solution lies in selection of the truest a".ld:rr.ost relationship, that which is most productive and least disruptiv 0 relationships.
''What is the function of this note I have next to sing? Do I define it in terms of the note which precedes it, or with reference to something occurring in another voice or instrument? 11 You will understand, I am sure, that if one determines intonation solely by reference to notes immediately preceding, the least little error in the beginning will be magnified beyond all recognition some hundreds of intervals later. One can end up miles from his home-key by an astounding series of melodic half-truths and harmonic improprieties. Since the voice is capable of any gradation of pitch, the problem of unaccompanied group singing is that of providing at any given instant an accurate and true 11picture'' of harmonic relationships (ftmction); and, in the face of modulation (which is change in function) seeking pivot points closest to the original tonality, which promise easiest and safest return. The greatest historical tradition of unaccompanied singing does not indulge, and with great wisdom, in modulatory orgies. Accompanied singing does not absolve us from these responsibilities. It simply means that since modulations are likely to be more plentiful, diverse and distant, our watchfulness must be increased. While recognizing the practicality and flexibility instruments, it still will be possible for us to ''bend" little closer to true and natural function. Most of the It is tne natural thing the orchestra 11bendn similarly.
of equa.l tempered a such rigidity instruments in to do.
This is the hopeful side of problems of intonation. Just as physica .l law is established on the harmonic series of fractional proportion, so there is a correlary in the "laws 11 of human hearing. By nature, free and unearned) our inner ear is to be trusted. We should whet and intensify our attention, we should remove obstacles of voice production, bad enumciation, bad posture, etc., etc., -- but all this is only in the line of doin I what comes natural. 11 R. S.
ANNOUNCEMENTS: We have new parking stickers this year, therefore, if you have not made application for this new sticker please do so this coming Sunday or Mondayv Please do try to avoid absences. By and large attendance has been good, BUT - - - - l 1Nuff said for now.
at rehea r~aJ.s
Sunday, November 14, all women at 3:00 p.m. Monday, November 15, everyone at 8:00 p.m. E. B,.