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"Tuning & Intonation" Part 1

Joseph Butkevicius

The art of playing "in-tune" is perhaps the most overlooked aspect in music education and performance today. There are many factors that influence the ability of a performer to play with proper intonation. Instrument scaling, combinations of instruments, knowledge of theory, and tone production, must all be considered to play "in-tune" in any given musical situation. This ability is accomplished through consistent individual and group practice. For the individual, understanding of the basic pitch tendencies and tuning procedures for their instrument, combined with the ability to alter these natural tendencies and maintain excellent tone production are essential abilities. For the group, understanding the scale tendencies of the instruments that are playing, and working together to "tune" chords and create a group "tonal center", all contribute to the promotion of "in-tune" performances. Understanding of all these aspects integrated into daily practice, will ultimately improve intonation and foster a natural part of learning to play your instrument in tune in any situation.

Understanding the Concepts & Tools

Understanding the concepts (and terminology) that must be put into practice is crucial. Knowledge of how all the aspects work together will facilitate execution of proper intonation. The tools, (tone production, scales, and chords), are the means to realize the concepts through practice. Understanding "tonal center", general scale tendencies, and functions of scale degrees within chords, give purpose and a course of practice for which the tools can be applied.

Tonal center is continuously focused through tone studies. Establishing a strong fundamental in tone production is an essential starting point. Achieving tone, with subjective descriptions such as "warm" and "dark", are desirable and facilitate the task of playing in tune with other instruments. A strong fundamental is rich in upper partials that influence the procedures of adjusting pitch. A good example of control over this manipulation can be found in piano design and equal tempered tuning. Piano designers work to produce even tonal results throughout the range of the piano through many design aspects beyond the scope of our discussion here. Since a pitch cannot be altered during a performance on piano, piano tuners must, through setting an even temperament, adjust pitches (and their subsequent overtones) to conform to their temperament standard. A poor piano design, where the natural string partials and soundboard resonance are in conflict, make the task of the piano tuner a more difficult one. So too, this will occur with two players trying to tune together while producing poor tone. Upper partials reinforce the fundamental tone. A strong fundamental tone containing many upper partials provides more aural reference points to fine tune intonation. This realization implies other factors to consider with regards to intonation. Adjusting intonation while playing with "fixed" pitch instruments (i.e. piano, marimba, harpsichord, etc.), will be different than adjusting to instruments where their pitch can be adjusted during performance (i.e. woodwinds, brass, strings, etc.). Wind instrument players must be able to vary their pitch slightly while maintaining a strong fundamental tone. This is necessary to overcome natural pitch deficiencies inherent in instrument design and make pitch adjustments in the context of ensemble playing. Finding and practicing this" tonal center" makes pitch adjustments to either side of the center easier. An instrument with excellent scaling obviously facilitates the whole procedure.

Thus we are led to ask the question: what defines the tonal center? In light of our discussion so far, two answers come to mind. In the case of fixed pitch instruments, the tonal center is defined by the skill of the piano tuner or instrument maker under the standards of equal temperament. This is the easier answer of the two. The second is defined by the laws of music theory and the ears of the performer. Playing with another instrument where pitch is alterable is more difficult since the "reference tones" are subject to alteration. A piano pitch cannot be changed during a performance and provides an unchanging reference for intonation. Since the tonal center of a piano is set, playing together in tune with a piano is simply a matter of matching a given tonal center. A problem arises given that, equal tempered tuning is naturally out of tune by definition. Equal temperament is a compromise. It is basically comprised of intervals where fifths are condensed, fourths are expanded, and consequently all major thirds are progressively sharpened as the frequency (e.g. Hz) increases. But, as has already been said, these pitches are fixed and act as a reference for tuning. What then is the reference for instruments that are not "fixed"?

Establishing the tonal center for adjustable pitch instruments can be found in part through musical theory. Since there exists no fixed restriction as in a defined equal tempered tuning, the player must establish a tonal center based upon the natural tendencies of the notes themselves. This suggests that different tuning possibilities exist and are dependent on the instrumentation of the ensemble. If fixed pitch instruments utilizing equal temperament are used in an ensemble, then equal tempered tuning will govern the tuning with all players conforming to its standard tuning references. Without a fixed pitch reference instrument in an ensemble, the tuning approach can be more subjective and demands greater awareness and adjusting from the performers. The starting point for establishing a tonal center is found through the practice of scales (for the individual) and chords (for the ensemble).

Scales, when practiced for intonation, are the building blocks of proper intonation within chord structure. Once a strong fundamental tone throughout the range of an instrument is established, its application to scales and chord functions form the basis of proper intonation. For purposes of discussion, the diatonic major scale will be our sample topic. Diatonic scale degrees exhibit natural tendencies. One must consider this for the purpose of establishing a tonal center for a given scale degree. The two strongest tendencies involve the two natural half steps in the diatonic major scale. These are movement between the third and fourth scale degree and the seventh and eighth degrees. The fourth and seventh degrees exhibit the strongest movement by half step to resolution in the form of establishing a tonic. They are naturally unstable as the interval is a tri-tone, (the only one of its kind), as it exists in the diatonic major scale. These intervals (and their subsequent resolution) imply the two basic chords minimally necessary to establish tonic (i.e. V7 - I) in a progression. Understanding the importance of scale degree tendencies and its relevance provides a commonality for establishing a tonal center through tonality. When one considers that a scale degree tendency is consistent regardless of pitch or selected tonic, a basis for determining intonation can be established. This also stipulates that a given pitch will be slightly different depending on its scale degree designation in different tonalities. For example, the note Bb is the fourth scale degree in the key of F major. Its natural tendency is lower (relatively) since its tendency is towards resolution to A (4-3). This can be more readily experienced through the V7 - I chord progression in F major where Bb (fourth scale degree) functions as the flat seventh in the C7 chord resolving to A, the third scale degree of F major. In B major, the enharmonic counterpart of Bb, namely A#, is the seventh scale degree and is consequently relatively higher since its natural tendency is to resolve the half step upward (7-8). The relative pitch of enharmonic tones is governed by the context of tonality. For this reason A# and Bb, while enharmonic notes, are very different in function and relative pitch. The scale degree determines the relativity of pitch, and by definition is consistent. Since pitches function as different scale degrees for given tonalities, the relative pitch is determined by the tonality and its subsequent scale degree designation. Our efforts towards executing proper intonation must be concentrated through proper scale degree placement and the chordal structure that is its extension. The context of scale degree and subsequent chord structure provides us the only consistent basis from which the formulation of proper intonation may be derived. It may also be noted that these rules do not apply when playing with fixed pitch equal tempered instruments. (i.e. the pitch of A# and Bb are identical since they are predetermined by equal temperament).

Tuning the perfect intervals (fourths, fifths, unisons, and octaves) within chord structures sets the framework for positioning a tonal center for the remaining scale degrees. It is imperative that these intervals be played pure, without beats. It is near impossible to position the third, if the root and fifth of the chord are badly out of tune. The third scale degree has a subjective placement. Our ears "allow" it to be somewhat sharp due to equal temperament.

We must rely on perfect intervals, therefore, as a consistent basis for solid intonation. The tonal center of a given pitch has a dual function. The first, as we have discussed, is its scale degree tendency as defined by the tonality. The second is its function as a chord degree. For example, in C major, E is the third scale degree. The vi chord in C major is A minor, where E functions as the fifth of the chord (a perfect interval from vii chord's root). This demonstrates that any note will also have a secondary tendency as it functions within a chord. The intonation for the chromatic notes (accidentals) can now be demonstrated. Although they do not appear naturally in a given tonality, their tonal centers can be determined from their secondary chord degree functions. Accidentals follow their function by creating resolutions by half step. Sharps create leading tones resolving up and flats create half steps resolving down. The relative pitch of these accidentals is synonymous with their function.

Intonation Practice Routines

Given this basic, yet complex, understanding of the theory, what practical practice techniques can be formulated for playing in tune? The answer must be applied in two area: individual practice and group practice.

For the individual, tone studies are the first starting point. Knowledge of an instrument's inherent scaling inaccuracies must be taken into account. Practicing these "problem" notes with strong consistent fundamental tone and the ability to alter the pitch while maintaining consistent tone is a worthy practice effort. There are as many techniques as there are instruments and your private instructor can help you identify and practice these techniques. Embouchure and breathing are important issues for all instruments. Remember, dynamics play a role in tone production and intonation and any individual practice efforts must incorporate all dynamic levels. Scale practice for intonation can be accomplished by practicing each scale degree in reference to the tonic:

C-D, C-E, C-F, C-G, C-A, C-B, C-High C....High C-B, High C-A, etc......

At first I would recommend using a tone generator set to the tonic so that each interval may be tuned correctly and to prevent the tonic pitch from drifting. At this stage the ultimate importance of ear training and pitch memory are revealed. Listening to and removing "beats" by adjusting the pitch are the purpose of this exercise. Eventually, when the reference tone is removed and pitch memory can be established, our scale is finally formulated. Extending this concept up and down throughout the registers and in all keys provides a lifetime practice routine. A favorite practice routine of mine involves the practice of arpeggios. Find a room with tremendous echo acoustics. (Big churches, bathrooms, and solid wall, floor, ceiling rooms, devoid of furniture are excellent prospects). Playing arpeggios in these spaces produce chords in the resultant echoes and provide and excellent reference for tuning the perfect intervals.

Group practice routines begin with duets. The ability for two players to "match" pitch (and tone) to the extent that the individual players tone is indistinguishable is the object of this exercise. Have one person pick a note, establish it, and have the other person match this sustained pitch. The first player must NOT alter the pitch. Later reverse roles, so your partner can practice matching the tone. The next exercise is practice for the perfect intervals (fourths, fifths, and octaves). After matching a pitch, the leader changes notes a perfect interval in any direction while the other player sustains the unchanging reference tone. When the leader has established this tone, player two must then match it. When this is accomplished the leader can then move on to another perfect interval. The person who changes notes is responsible for tuning their tone, while the other person sustains the reference. For example:

Player 1 (leader) C----------------G-----------------------D------------------------A-----------------------------
Player 2...........................C---------------------G------------------------D-----------------------A----------------

Later, switch roles, so player 2 can have a turn at tuning the interval. This is perhaps my favorite tuning exercise since tuning of intervals and matching unisons are both practiced.

In ensembles of three or more, the same techniques apply. Players assigned notes consisting of perfect intervals must tune their notes first. Our knowledge of chord structure can help us determine whether or not our assigned note is part of a perfect interval or not. The idea of "tuning from the bottom" is relevant here. The chord is tuned from the root and the reference tone is established by the instrument assigned to this note. If our individual practice has been successful, other players will have an easier time adjusting to this note. Non-perfect intervals and/or non-chord tones can be placed relative to their scale degree tendencies. This assumes that the performers are aware of each part for adjusting their individual intonation. This process is very dynamic. It also stands to reason that as more parts and individuals are added, the process of proper intonation becomes more difficult.

As we have demonstrated, there are practical techniques for achieving in-tune performances and that these can be derived from the structure of the notes themselves. Control over your instrument and flexibility of pitch is required. Situations vary depending on the instrumentation and one must consider the presence or absence of fixed pitch instruments. In part 2 of this article, we will be discussing particular intonation tendencies for individual woodwind instruments. These will include tuning techniques, instrument misconceptions, and instrument scaling.

If you have any questions and/or comments, send an e--mail.

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