Dr. Ross W. Duffin

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A New Approach

     Ensemble music from the Renaissance (as well as from the later Middle Ages) and less complex later music can work in Just intonation and is much enhanced by its use. And even if the exact theoretical ratios are not achieved, it is still possible for performers to make conscious adjustments that will help to “justify” the tuning and make the music sound better acoustically and closer to a Renaissance ideal. Most performers, however, have no idea how to begin. As may have been evident in my discussion of the problematic passages cited by Blackwood, the theory that I have developed over the last few years is that the practice of Just intonation is based on the prevailing mode of the music. I have elsewhere written at length about the theory behind it.Fn35 What modern performers need to understand first of all, is that notes have certain placement tendencies in each of the modal centers: F, C, G, D, and A/E (I consider the latter pair of finals together since, in my experience, they seem to use an almost identical scale). In order to approach Just intonation, then, performers need to gain a fair idea of where the notes are likely to be found in each mode, and how to find alternatives when problems arise, or when the modal center shifts within a section or passage.

     It’s easy enough to look at an individual chord and say, “Oh yes, these intervals need to be pure.” The difficulty comes in figuring out how a perfectly tuned chord is approached and succeeded by other perfectly tuned chords. For example, is the major 3rd of some triad pure because the third is low, or because the root is high? Both solutions can work but each requires a microtonally distinct interval of approach and departure for the root and third of the chord, and one solution is usually better than another depending on the mode and the context. At the point of making the choice between possible solutions, the vertical/harmonic puzzle of Just intonation becomes a horizontal/melodic one for the individual performer. This is the crux of the issue. Notes in Just intonation are certainly not found along the Equal Tempered scale, and they are not always in the same place. Thus, the precise placement of the pitches and the various sizes of melodic intervals are not always predictable, especially to someone reading a single musical line. Performers need to develop the ability to use different sizes of the same written interval, along with a sense of melodic tendencies in each mode that can help them make choices depending on the harmonic and melodic context. Low sharps, high flats, and wide leading tones are a good place to start, but there is more to it than that.

     Refining the different sizes of semitone is the most difficult part of Just intonation for performers, although in practice the semitones are mostly 112 cents (0 up to +1, or -1 up to 0, as in typical leading tones) or 92 cents (0 up to -1, or +1 up to 0, as in typical chromatic alterations of a note). The largest and smallest semitones do occur in chromatic passages, however. Practice in recognizing and differentiating the different sizes of whole tone and semitone is crucial to achieving Just intonation.

     To enable performers to explore the harmonic and melodic requirements of performing in Just intonation, and to learn this skill by practice, I composed five Just tuning exercises which accompany this discussion. The point of these exercises is to familiarize musicians with the kinds of adjustments necessary to sing or play in Just intonation, and to help them to recognize similar situations in the music they perform. The exercises are sometimes highly chromatic, but in a way that reflects harmonies and progressions found in music from the later 16th and early 17th centuries. (Students of the era will no doubt enjoy tracing the echoes of familiar passages in the various progressions.) Performers who can negotiate Just tuning in the complicated progressions given here should have little problem with most ensemble music in these modes!

     The exercises were composed originally in the year 2000 for the use of the Early Music Singers at Case Western Reserve University. The sound is organ-like, with a blendable timbre and stable pitch (although the computer clearly wrestles with playing dissonant cross relations, suspensions, and even second inversions, despite the Just tuning). Performers can practice the exercises by playing or singing along with all voices at once, with a single voice part alone, or in a “music minus one” situation with the computer omitting one part. Three different speeds can be selected (M.M. = 30, 55, or 80). To listen to the individual exercises, follow the Exercises link at left, or click here.

     Mastery of these exercises has proven effective in teaching performers

  1. to be aware of pure intervals in the harmony
    2. to make informed guesses as to where to place the notes melodically
    3. how to make conscious adjustments so the tuning will be better

     These are significant achievements for the members of any ensemble performing Renaissance music. Moreover, returning to the exercises again and again, and wrestling with their problems, can deepen the understanding and improve these skills still further.



Theoretical Background

Benedetti’s Puzzles

Problematic Passages

Is Just Tuning Possible?

A New Approach

The Exercises

 Problem Spots

 Rehearsal Usage



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35. For a detailed explanation of how Just intonation works in late-medieval polyphony, see my chapter, “Tuning,” in A Performer’s Guide to Medieval Music, ed. Ross W. Duffin (Bloomington, 2000), 545-62.


Page last modified: February 2, 2017