Playing in the Just Intonation
The Just Intonation is said to be the most aurally intuitive intonation where 'consonances' are concerned. Whereas 'consonances' and 'dissonances' can be subjective, i'm inclined to the view that the fundamental intervallic components making up the basic 4-note jazz harmony(maj/min 3rds) are consonant intervals. Further, i should add that the perfect unison/octave and fifth are also widely accepted to be intervals of consonances. It is in this light that i wish to discuss, albeit in a limited fashion, the ways of achieving a Just Intonation in the playing of an ensemble. My discussion should apply to most instruments in the orchestra, except the piano and the harp. However, via my limited knowledge, i've often extrapolated my deductions from the humble flute. Also bear in mind that i'm not formally trained in music and so the arguments may not be tight, from the academic point of view. Nevertheless, i present the findings that i've made during the course of my playing and i stand by their truth as perceived with my aural abilities.
The presence of overtones is more apparent in lower instruments than in higher ones. However, insruments such as the oboe have rich overtones that are easily detected especially during the low notes. In addition, the characteristic odd partials of a clarinet can also be easily heard. Hence, a method applicable for these instruments is to use these overtones as tuning anchors. Recall that the overtone series are in fixed mathematical ratios corresponding to the just intonation. In my opinion, it is impractical to attach a number to the relative intervals. For example, saying that a certain interval should be 'x cents flat' does not directly enable a player to execute that 'x cents flat' phenomenon quickly enough, as the player is inclined to play at the Equal Temperament before making the necessary adjustments. This method of overtonal tuning reduces the difficult task of playing in Just Intonation to that of playing in unision with the overtones. I believe that daily practices facilitated by chorales(esp by Bach) facilitate playing in the Just Intonation.
However, the above method is rather restrictive. As the pitches become higher, the overtones become less audible, even for the lowest instruments. There comes a time when it becomes impractical trying to pick out an effectively non-present overtone. In addition, the overtone series become increasingly crowded. Mathematically speaking, they converge, according to the Dirichlet test. That is to say, if the intervallic distance is great(spanning about 4 octaves), a player may find it hard to find the desired overtone to tune to(if he can hear it in the first place) because there are too many overtones that are within the vicinity of the desired overtone. In this light, i recommend what i call the composite tuning method.
The composite method is so named because it utilises the method discussed above(albeit applied in a slightly different fashion) and superimposes the method with aural perception. I shall first discuss the latter.
It has been experimentally verified that the human ear is conditioned to accept Just Intervals as the most pleasant interval(as compared to other kinds of intonation). This aural perception will facilitate(in fact, it should be pivotal) the player to execute a Just Interval. However, the player must have already achieved a good degree of aural finesse in order to be able fully utilise the method. The best way to achieve this is via singing the intervals themselves and adjusting the voice in minute pitch adjustments to abolish the beats/noise heard in an imperfect interval. One will find that at the onset of the disappearance of the beats/noise, that interval will be Justly tuned. One should be cautioned that only close harmony should used for this training purposes.
Having achieved the aural facility required for Just Intonation, the player can then apply this skill to open harmonies by using the overtones that allow them to close the harmony. For instance, if a tubist is playing a low C, and the flutist is playing a fifth space(treble clef) E, the flutist can use the tuba's overtone that occurs at the 3rd space C on the treble clef. Effectively, the flutist's task is reduced to playing in Just Intonation in a close harmony, because he will be effectively tuning a pure and Just major 3rd.
The composite method will only manifest itself as a excellent method via good aural training. If utilised by the rough ear, the method will seek to destroy the very hopes that it wishes to achieve. It is expedient to be unwaveringly critical of one's hearing in order to achieve a pure, clean harmony.
The presence of overtones is more apparent in lower instruments than in higher ones. However, insruments such as the oboe have rich overtones that are easily detected especially during the low notes. In addition, the characteristic odd partials of a clarinet can also be easily heard. Hence, a method applicable for these instruments is to use these overtones as tuning anchors. Recall that the overtone series are in fixed mathematical ratios corresponding to the just intonation. In my opinion, it is impractical to attach a number to the relative intervals. For example, saying that a certain interval should be 'x cents flat' does not directly enable a player to execute that 'x cents flat' phenomenon quickly enough, as the player is inclined to play at the Equal Temperament before making the necessary adjustments. This method of overtonal tuning reduces the difficult task of playing in Just Intonation to that of playing in unision with the overtones. I believe that daily practices facilitated by chorales(esp by Bach) facilitate playing in the Just Intonation.
However, the above method is rather restrictive. As the pitches become higher, the overtones become less audible, even for the lowest instruments. There comes a time when it becomes impractical trying to pick out an effectively non-present overtone. In addition, the overtone series become increasingly crowded. Mathematically speaking, they converge, according to the Dirichlet test. That is to say, if the intervallic distance is great(spanning about 4 octaves), a player may find it hard to find the desired overtone to tune to(if he can hear it in the first place) because there are too many overtones that are within the vicinity of the desired overtone. In this light, i recommend what i call the composite tuning method.
The composite method is so named because it utilises the method discussed above(albeit applied in a slightly different fashion) and superimposes the method with aural perception. I shall first discuss the latter.
It has been experimentally verified that the human ear is conditioned to accept Just Intervals as the most pleasant interval(as compared to other kinds of intonation). This aural perception will facilitate(in fact, it should be pivotal) the player to execute a Just Interval. However, the player must have already achieved a good degree of aural finesse in order to be able fully utilise the method. The best way to achieve this is via singing the intervals themselves and adjusting the voice in minute pitch adjustments to abolish the beats/noise heard in an imperfect interval. One will find that at the onset of the disappearance of the beats/noise, that interval will be Justly tuned. One should be cautioned that only close harmony should used for this training purposes.
Having achieved the aural facility required for Just Intonation, the player can then apply this skill to open harmonies by using the overtones that allow them to close the harmony. For instance, if a tubist is playing a low C, and the flutist is playing a fifth space(treble clef) E, the flutist can use the tuba's overtone that occurs at the 3rd space C on the treble clef. Effectively, the flutist's task is reduced to playing in Just Intonation in a close harmony, because he will be effectively tuning a pure and Just major 3rd.
The composite method will only manifest itself as a excellent method via good aural training. If utilised by the rough ear, the method will seek to destroy the very hopes that it wishes to achieve. It is expedient to be unwaveringly critical of one's hearing in order to achieve a pure, clean harmony.
posted by Simon at 1:17 PM
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