When vocal/choral ensembles attempt to use pure thirds and sixths yet invariably find that the pitch then drops (despite their "in tune" intervals) it is because they have failed to understand the structure of the syntonic scale! The purpose in constructing the arcicembalo, with its 53 notes per octave, was to bring together both the Pythagorean system (with its pure 4ths and 5ths) and the Syntonic (with its pure 3rds and 6ths). Vocal performers who do not understand these differing structures will inevitably fail to avoid inflicting upon their performance what is known as "comma depression" resulting in an inexorable fall in pitch.

The first step is to understand what (to them) is the most puzzling interval: the diatonic semitone (i.e. the "normal" as opposed to the "chromatic" one) must always now be larger than the smaller Pythagorean one. [Musical theorists during the later 15th and early 16th centuries had now reversed the respective sizes of the diatonic and chromatic semitone, making the diatonic "major" and the chromatic "minor" - the opposite of the traditional Pythagorean sizes.] This will ensure (for example) that when the 4th C-F contracts to the pure major 3rd C-E both intervals remain "pure" (because the diatonic semitone E-F is larger than the Pythagorean one by a syntonic comma, meaning that the resulting pitch of E is a comma lower than its Pythagorean equivalent, yielding therefore the narrower 5/4 major 3rd against the C).

The second step is to understand that there are now two sizes for the tone! The first is the normal Pythagorean 9/8 ("major") tone, while the now-new second is the syntonic "minor" tone with the smaller size of 10/9. Continuing with the previously-adduced pitches, if the arrived-at pitch of E (lower than its Pythagorean equivalent, since it forms the narrower pure 3rd with C) is then lowered by a "major" (=Pythagorean) 9/8 tone to D, the resulting D will therefore also be a syntonic comma lower in pitch than is its Pythagorean counterpart. The result of this will mean than if this "syntonic" D is now sounded against the initial F the resulting minor third will produce the wider-than-Pythagorean "pure" 6/5 minor third interval. But the left-over interval between this D and the initial C a tone lower will now be the "minor" 10/9 syntonic tone.

Naturally all these conditions will need to be replicated to other transpositions that might occur during the course of a piece!

Fortunately there are certain rules-of-thumb that can be applied to make the situation less theoretical and more practicable:

a) always make "normal" semitones slightly larger than expected, while making "chromatic" ones (i.e. F-F#, Bb-B, C-C# etc) smaller

b) whenever a pure major 3rd is sounded, it should be the higher note that is always slightly flattened

c) whenever a pure minor 6th is sounded, it should always be the lower note that is slightly flattened

d) if a pure minor 3rd is sounded, it should always be the lower note that is slightly flattened

e) if a pure major 6th is sounded, it should always be the upper note that is slightly flattened

Since all these rules-of-thumb involve understanding how to flatten notes, the only way to ensure pitch stability (and avoid comma depression) is to back up this practice with a clear understanding as to which tones within the system are major, and which minor! It is a very complex business, and we can fully understand therefore why Adrian Willaert (a prime innovator in this field) insisted that each and every one of his singers at St. Marks Venice must attend a weekly private tuition session with the master under his terms of contract - and indeed is known to have sacked one who failed to honour this. No doubt a part of this session was concerned with identifying and annotating all these intervals so that the weekly musical performances ended up being in tune.

Baziron

The difficulty with this performance (and other similar ones) is obvious - vibrato!

Not wishing to open up another controversial pathway, I should say that the "difficulty" I have in mind is simply this: what is the point in trying to arrive at purity of interval/intonation when the performing method adopted by default is one that is designed only to prevent purity of interval and intonation?!! Whenever a pitch applies vibrato the pitch-oscillation that results actually guarantees that the "note" thereby sounded actually fluctuates in pitch (over its duration) by a differential that in itself far far far exceeds a syntonic comma!

If, therefore, a performance of this kind is desired (and I have nothing against it as such, especially in dramatic texts) it seems to me that the whole point of striving for purity of intonation becomes merely a decadent academic exercise.

Trying it completely without the vibrato, however, provides a new opportunity for discovering the finer distinctions between consonance and dissonance.

Baziron

I agree Richard, and only meant that attempting the achievement of a particular quality through the self-defeating adoption of a performance method that actively denied it was "decadent" (in the real sense of the word), and that the academic immaturity of attempting the impossible (in terms of physics and acoustics) was also similarly decadent (again in the literal sense of the word).

It is difficult to know exactly how the performance might have differed had the tuning experiment not been attempted, since it could hardly have been less in-tune than it was. But I think, as an experiment, it was a failure - in terms not merely of its practicality, but also (more disturbingly perhaps) of its concept.

Baziron

It does look very distracting, as do his facial expressions.

Anyway, as I said, the CD recording is a big improvement on that youtube clip (especially since you can't see Mr Curtis!). it still doesn't, however, measure up to the subsequent recordings by La Venexiana (2001 and 2005) or Concerto Italiano (1999).

Tell us more!

Check this out, Kitty (and anyone else), it's a documentary on the American composer Harry Partch, his self-made instruments and ideas on microtonality. It's not Gesualdo of course, by a long chalk.

I think that depends on how you listen (and indeed how you sing).