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Survey and research on just intonation

Dear members or ChoralNet:

I am interested in the subject of just intonation in a cappella choral singing, especially in the aspect of practical application. Since this is a major issue for the choral community, I have developed a survey, which I would appreciate your answering. I would also be grateful for your overall viewpoint on the topic. Naturally, I guarantee that your answers will be kept in the strictest confidence, and I will inform you about the global results of the research.

My e-mail is: joyapublica(a)

1) Do you, or the group or groups you know, in your (or their) rehearsals or a cappella live performances, usually look for pure harmonic intervals of fifth and third, by approaching simple ratios (2:3, greater than the tempered fifth; 4:5, smaller than the tempered major third)? Do you think that habitual use of equal temperament hinders or prevents the achievement of these pure intervals?

2) Do you (or they) normally use— consciously and systematically, or to any extent—, the sounds and intervals of just intonation (Zarlino’s or justly tuned scale, minor and major tones, different types of semitones, syntonic comma, duplication of the second degree of the major scale, different intonation of the notes according to the key...) or other specific tuning system? Or is the achievement of pure harmonic intervals the result of a desire to sing in tune intuitively by listening to the voices and following a heuristic method?

3) Is the use of just intonation, or the tendency to pure intervals, limited to the predominantly homophonic textures? Do you (or they) use any conscious intonational strategy in contexts of polyphonic texture or where the melody is predominant: Zarlino’s or justly tuned scale, Pythagorean scale, equal temperament scale...?

4) In case of using pure intervals, how do you (or they) solve the problems caused by the contradiction between the horizontal trends (leading ascending notes) and vertical ones (major third smaller than the tempered one), for example in the dominant chord?

5) How do you (or they) solve the problem of pitch drift, e.g. in links between second and fifth scale degrees (Dm - GM chords) or in fragments with modulations? Do you (or they) consciously perform adjustments of syntonic comma in some of the voices in the required places? Or do you (or they) rather use auditory memory of important scale degrees —tonic and dominant— to keep the pitch steady and try to make pure intervals if possible?

6) From the point of view of a correct intonation, how do you (or they) deal with works with a great deal of chromaticism and frequent modulations? Do you use just intonation in this type of work, or some form of temperament or other specific model?

7) Do you (or they) modify intonation consciously or unconsciously when you (or they) sing a cappella rather than when accompanied by piano or other instruments tuned in the equal temperament system?

8) In your experience in choral singing, do you think that performing pure harmonic intervals is the natural tuning to which choirs tend, perhaps guided by overtones of the other voices or by avoiding beats? How and to what extent does our habituation to equal temperament interfere with this natural tendency (if it exists)?

9) Do you know of other individuals or groups who are interested in just intonation or who perform in just intonation?

10) Any other comments or observations on the subject of intonation that you consider interesting or important.

I would like to thank you in advance for your cooperation.

Yours sincerely.

José García Illa

Replies (5): Threaded | Chronological
on February 6, 2015 3:37am
I apologize for the late reply to this interesting set of questions.   
1) well, sure, tuning by ear helps tuning better by ear
2) yes, all the time.  But please remember just intonation is not a temperament, it CHANGES.   The second scale step, especially, goes back and forth constantly by a comma higher or lower (22 cents difference)
3) no, not at all
4) you resolve in favor of the vertical tuning.   the third of a dominant seventh chord is (should be) as pure as the third of a tonic chord.   the seventh of the dominant seventh should be prepared by the fourth degree of the scale, and precisely in tune with it.   'Expressive intonation', tuning leading tones higher and sevenths lower is only for unaccompanied melody, if at all (I'd say, never -- though anything out of tune can be expressive in the right environment.
5) pitch drift: PLAN IT as a composer; as a performer, identify it.   See the William Byrd "Ave Verum Corpus" analysis at  where it is posited that the pitch drift was intentional (and intentionally corrected in the course of the piece).  I've written elsewhere about Tallis, "If Ye Love Me", where (imo) the pitch drift is unintentional and not corrected. 
6) as a composer, PLAN it.    See the chromatic fugue in just intonation (score referenced at link):
7) yes -- composers/arrangers might do well to apply far less doubling of the voice with an equal tempered instrument
8) yes; in my experience choir directors who are organists have the most difficulty with hearing just intonation.
9) I compose in just intonation, and have attempted to show that it is not simply applying a temperament: it requires constant attention to make sure your just intervals are possible.
on February 6, 2015 10:39am
William, would you elaborate on the subject and place of singers' vibrato?  Is it necessary for singers to avoid vibrato in order to maintain pure intervals (seems so to me)?  Can vibrato be added to certain notes or intervals as a color?  Is there any evidence that singers' vibrato was added (historically) to camouflage the pitch adjustments necessary in tempered tunings?  Over the years, I find myself preferring less and less--even no--vibrato by singers.  Is there any consensus among top choirs and conductors, that certain repertoire should not be sung with vibrato, or are these decisions for or against considered legitimate personal and interpretive choices ?
on February 12, 2015 2:04pm
Bart, basically: I don't know.  I've argued from time to time that vocal vibrato is an amplitude thing, not changing pitch.  But then I listen to some elderly sopranos and the pitch is all over the place.      Generally I'd vote for a small vibrato for singers, but this is a wide and deep subject on which others may have better perspective.
on February 13, 2015 7:23am
This gets more and more fascinating, musicologically.  No response expected, but my mind is rambling on to:  Were (are) there different schools of vibrato--amplitude vs. pitch?  Would variations in vocal anatomy and physiology have affected how different influential singers and teachers produced and taught vibrato?  I'm also thinking of parallel situations: the few clarinet players like Reginald Kell who played with vibrato instead of the accepted straight tone; the differences in tone color between French and German bassoon playing; or bagpiper Padruig Og MacCrimmon throwing out what he considered excessive gracenotes in the 16th century (since the sound cannot be interrupted on the Scottish bagpipe, pipers use combinations of gracenotes to articulate between notes.  Apparently there developed a cult of virtuosity, with some pipers playing a dozen or more gracenotes before major melody notes.  MacCrimmon, by virtue of his position as the most influential piper of his day, reduced this to "only" eight.)
on February 16, 2015 9:31am
Dear José Garcia Illa,
I've been away and am now reviewing Choral Net questions that especially interest me. I am absolutely delighted to read your thoughts and application. Recently Ross Duffin, a good friend and colleague has written with great clarity his knowledge and application of Just Intonation with choirs - please see his article in Early Music America, Winter 2014, Volume 20, Number 4. The article is entitled, "Cracking a Centuries-Old Tradition"
In sum - singing with Just Intonation, as you know, means to tune the pure intervals of the overtone series: pure octave (2:1), pure fifth (3:2), pure major 3rd (5:4), pure 4ths (4:3), and pure minor 3rds (6:5). (I find tuning the pure minor 3rd takes time). Teaching students at first to hear overtones, contrasting them with piano equal temperament or having the choral bass section (for example) sing an excellent unison on a low G or A (for example) and hearing the resultant pure 8ve, 5th, 3rd above, is a marvelous educational experience for choral singers. They are very motivated to want to reproduce that beauty of sound, and they quickly learn to "lock in" those intervals at important cadences. It really opens their ears to contrast piano equal temperament with hearing pure 5ths and especially major 3rds, that are so very narrow to "piano major 3rds"
The problem of course is "accommodating the 'comma". Vertically at cadences my choirs learn to teach themselves to sing pure 5ths and especially 3rds. Hearing "smaller" 4ths and "wider" minor 3rds in vertical sonorities is not easy. I tend to use the net results of applying many precepts of Just Intonation to horizontal lines. Without doubt, singing major and minor 2nds slightly high  to "piano intervals" in ascending scales improves overall intonation; conversely tuning major and minor 2nds slightly narrow to "piano intervals" in descending scales improves overall intonation greatly.
I have always tuned my choirs (mostly large ones) at all important cadences (no matter the style) to perfect 5ths and 3rds, and consistently ask for wider 2nds ascending and narrow 2nds descending (with continous reinforcement in warmups with melodic formuli), and the results bring good intonation. I have a chart of 21 melodic formuli of variants of minor/major 2nds and min/major 3rds ascending/descending that produce flat pitch ("Three Blind Mice" - "blind" is always flat, for example).
Singing with little (or occasional) vibrato (narrow that reinforces warmth yet consistent clarity of unison pitch within each section) is very important. Major 3rds, 6ths, and 7ths are low to piano/equal pitch. For example the dissonance of a major 7th is made beautiful (and clear!) by producing a more narrow interval than piano pitch - it is gorgeous, with overtones flapping everywhere. Minor intervals conversely are wider - a pure minor 2nd is a thing of beauty - I always make it wide. Tuning the vowels - ie matching the vowels is also a pre-requisite for singing in tune, especially at cadences.
Many of your thoughts/questions are touched upon in my thoughts above, and I think many can be applied directly to them.  Generally in rehearsals I do mention Just Intonation and Pythagorean Tuning and point out how they are conflictual. In my thoughts above on scale-singing, I include the "most in-tune" intervals by borrowing from both temperaments, though primarily Just Intonation. Some thoughts on your questions are below:
4) Scale motion (ascending/descending) I follow my methods above. I tend not to hear "leading tones" as high. If in a G Major chord for example when the 3rd (B) is in the sopranos and the chord leads to an important (especially) final cadence to the tonic (C), I ask the sopranos to sing a wide interval from B to C, to accommodate their "low B".
5) Pitch drift: - wow - we all work on that problem with our choirs:
     a) I always place my choirs in quartet seating, typically - S T A B - they learn better to be independent of their own part (ie. a good tenor does not sit next to a flat tenor), and they learn to listen - which is the key to all choral efforts to sing in tune. I teach the choir (through my methods above) to teach themselves how to sing in tune. When there are not enough tenors, we sit in trios: S A B, and then just duets": S A. There is some controversy about singing in mixed positions. However, in my experience, I think intonation, balance, and expressivity in mixed positions are heightened, and that is also true in polyphonic/contrapuntal textures. We sang all major works of Bach, Handel, Mozart, Haydn, Beethoven, Brahms, Stravinsky, etc. in mixed quartets. Because the clarity of each vocal part was quite good, counterpoint and polyphony was easily projected, and the beauty of the sound (at their best) was warm, clear, and highly communicative.
     b) Typically with a cappella compositions I change keys after the choir has learned a piece quite well. In learning new pieces singers acquire some faulty ear/voice coordination. They learn in unconscious "associated pitch problems" when they learn a new piece - I call it "hunting & gathering" - ie. initially sliding and/or continuously not singing the pitch "square on". Changing keys changes the physiological assocations with the old key and frees singers from their unconsciously formed imprecise ear/voice coordination problems.
     c) Notorious keys for flatting are the major keys (and associate minor keys): F, Bb, Eb, Ab; C, G, D. I tend to shift these keys from F to F#; Bb to B; Eb to E; Ab to A; C to C# or B; G to F#; D to C#. I don't always do that when the choir stays in tune in the home key, though that very rarely happens on F. Learning while singing the notes in e minor (Jesu meine Freude for example) and singing it a cappella on eb minor (baroque pitch!) sounds exquisite. Learning a work with orchestra like Schubert's G major mass - changing it early on to F# and then the week before the concert bringing it up to G, was great!
7) When singing with piano and especially with orchestra, oddly I do not find it to be a problem. Often we have sung major works like Bach's B Minor Mass with period instruments that tend to duplicate our pitch. In many cases with modern instruments I sometimes ask the orchestra at cadences to hear our intonation and duplicate it. With piano, at cadences, because the piano sound is not sustained, I do not find pure 3rds a real problem
8) I think our "habitation" to equal temperament definitely leads to faulty choral intonation. I hear equal temperament as being quite out of tune. In tuning pure 5ths and especially 3rds vertically at cadences, my choirs do too.
9) I would contact Ross Duffin at Case Western Reserve in Ohio and also read his wonderful book: "Who Equal Temperament Ruined Harmony, and why you should care" - Norton, 2007. And especially read his article in the Winter edition of Early Music Amerca - the title of his article is "Cracking a Centuiries-Old Tradition.
     Also, very important scholar/performer with vast knowledge of Just Intonation is Richard Sparks at North Texas State University.
I hope some of these ideas have helped. I have a lot of written materials on Intonation that I am happy to share with you also.
Jim (Jameson) Marvin
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