One result of this type of tuning is that certain pitches become increasingly high with each ascending octave. Similarly, if the same "F" sharp were to function as the major third of a "D" major chord, performed with an ensemble professing to utilize just intonation (the true mathematical intervallic pitch frequency ratios), the "F" sharp would also sound high, but, in this instance, because of its 14 per cent-too-long intervallic relationship to the tonic "D".
One of the most troublesome types of intonation, from the point of view of the wind/brass instrumentalist, is what Pablo Casals called expressive intonation. In a word, this is the performance practice, most commonly found in string players, involving the often arbitrary and exaggerated use of tuning as a technique in phrase shaping and voice leading (the "melodic implication" concept).
If our "F" sharp were played with violins in the key of "G" major, if it were functioning as the leading tone, it would sound low; however, conversely, if it were notated as "G" flat, proceeding to "F" natural, it would sound high.
All of this is admittedly oversimplified; however, it does prove to illustrate the point that a knowledge of the entire spectrum of the subject of intonation could be an invaluable aid to the serious performer, and further, that no substantive discussion of tuning could occur without such knowledge.
Christopher Leuba, formerly solo hornist of the Chicago Symphony Orchestra, has written a marvellous handbook, A Study of Musical Intonation, which presents the subject in a scientific manner, but with emphasis on how it all relates to the performer.
This publication has become an underground classic among many U.S. musicians, and this writer believes it should be in every performer’s library.
BRASS BULLETIN is to publish it in full in three successive issues, starting with no. 32, November 1980.
Thomas Stevens