jwilzewske: Was Dallapiccola’s Piano Microtonal or Just-Tuned?

W hy are D-sharp, F-sharp, and G-sharp so horrible?”
— Anonymous.

M any recent composers have come to feel that the compromise of Equal Temperament was a mistake. They feel that the musical logic of moving from any key to any other key became a priority at the expense of music’s sonic sensuousness. Equal temperament chords do have a kind of active ‘buzz’ to them—a level of harmonic excitement and intensity. Equal Temperament could be described as the musical equivalent to eating a lot of red meat and watching violent action films. By contrast, Just intonation intervals are much calmer, more passive. You literally have to slow down to listen to them.”
— Kyle Gann.

After my recent CMT blog post on Dallapiccola’s ‘Quaderno di Annalibera’ I have continued to explore these pieces, especially ‘Simbolo’. The dissonances in them are peculiar, unsettling. And the consonances in them are also peculiar—unsettling in their ‘tentativeness’, a quality that’s hard to put your finger on.

I revisited the late David Lewin’s excellent analysis of Quaderno, in hopes of finding a persuasive explanation of these pieces’ effects on me. But, rather than feeling convinced or reassured, I instead began to feel that Lewin’s erudite analysis may manifest certain ‘assumptions’ that were not acknowledged, namely, the assumption that Dallapiccola’s piano was tuned in the standard, modern way—with Equal Temperament (ET). Lewin’s analysis presumes that the piano was equal-tempered. It’s a natural assumption to make, but is it necessarily true? After all, Quaderno was composed during a period that was for Dallapiccola full of intensive exploring and discovery.

How would the tensions and dramatic consonances and dissonances in Quaderno work if the instrument had been tuned in Just Intonation (JI), I wondered? To find out, I downloaded a script to my MIDI keyboard / synthesizer, to change it to JI tuning.

The result was fascinating. The effective tonal dissonance is markedly different when Simbolo is played in JI tension structure instead of ET. In fact, Dallapiccola’s choice of register for the several lines or voices seems especially congenial in JI. The consonances in JI generally fall in Dallapiccola’s relatively long passages and very often dwell on long, now only mildly dissonant stases. In ET, the consonances are transient, and the stases are pretty strongly dissonant. ‘Violent’, to use Gann’s phrase. In my opinion, the contemplative quality of Dallapiccola’s Quadernos di Annalibera is far better in Just Intonation than in Equal Temperament. The JI has a primitive, crunchy-but-laconic, ‘communitarian’ feel. By contrast, the spectra and timbre of the ET—for the intervals in Simbolo, say—are, to my ear, too urgent.

In ET, it’s hard to keep Simbolo from sounding hurried, judgmental, aspiring, and self-referential. In JI, however, Simbolo exhorts the listener (and the pianist) to a zen-like composure, a stop-and-smell-the-roses alertness, a non-judgmental satisfaction with what one has. The former matches what we know of Dallapiccola’s politics; the latter matches what a father (Luigi) might reasonably express to his young daughter (Annalibera).

Modern composers using Just Temperament include Carola Anderson, Bill Alves, David Canright, Jon Catler, John Chalmers, David Doty, Tom Doughterty, Dean Drummond, Dudley Duncan, Adriaan Fokker, Glenn Frantz, Kyle Gann, Denny Genovese, Philip Glass, Eivind Groven, Lou Harrison and Michael Harrison, Norman Henry, Ralph Hill, Jim Horton, Ben Johnston, Joan LaBarbara, Anne LeBaron, Janis Mattox, David Mitros, Norbert Oldani, Harry Partch, P.Q. Phan, Larry Polansky, James Pugiliese, Robert Rich, Eric Ridgway, Terry Riley, Gino Robair, Daniel Schmidt, Carter Scholz, Bill Sethares, Jules Siegel, James Tenney, Toby Twining, Erling Wold, and La Monte Young.

But, so far as I can tell, there’s no documentation that Luigi Dallapiccola used JI when composing Quaderno. Nonetheless, the emotionally coherent effect that JI imparts to these pieces makes the JI conjecture at least plausible.

We have no way of knowing in mm. 2-3 whether the G-flat—A-flat—D is an order-segment of an emerging tone-row. We don’t know in ET, and we don’t know in JI. So we don’t hear the trichord { G-flat, A-flat, D } in mm. 2-3 as yet bound to an intervallic ‘context’ when we hear { G, D-flat, F } in m. 4. We are only ‘situated’ in-context later on. And yet… and yet in JI the ‘context’ looms in a more immediate, more rapidly apprehended, more hospitable and inviting way.

The sense of tension in this music is, I suggest, fundamentally linked to the temperament (and its timbre and spectrum, to use Sethares’s language) in which the music is played. The JI tuning is far less tense overall. Most of the tritones in Simbolo are less disturbing in JI than they are in ET. Often these JI tritones are more consonant than the thirds and the sixths—because of the particular positions of the intervals [see spreadsheet, below] used in Simbolo. (But, conversely, in JI some of the Major sixths are off by a whopping 32 cents. Even some of the Perfect fifths are as much as 24 cents out of tune.)

In other words, JI neutralizes some of the tensions that were present when the pieces that comprise Quaderno are performed in ET and simultaneously gives wolfish dissonances in intervals that would otherwise be warm and consonant. Rather than feeling disoriented, we are oriented in new and dramatically different ways. It is as though I am hearing Simbolo for the first time—and maybe understanding it for the first time? Did David Lewin ever think about this?

Lewin once wrote that the marking ‘oscuro’ in m. 33 is a hint that ‘something large’ should happen in mm. 34-36: a tone-row might appear; a new configuration may appear, or a new variation; or the piece may just end (which it does, soon afterward). Lewin maintained that the enigmatic effect of the writing here is not just due to a ‘stimmung’ but rather is due to an ‘incompleteness’—a withdrawing or withholding of the hoped-for tone-row.

Instead, I now think it plausible that Simbolo may have been intended to be played on a JI-tuned piano. Why? In part, I think this because then nothing ‘large’ is expected and frustrated in mm. 34-36; nothing so red-meatlike happens earlier in the piece as occurs in ET. Some of the gestural ‘questions’ and ‘problems’ that Lewin worries about are, in JI, not so puzzling or enigmatic. Instead, in JI we get the calm equanimity that Kyle Gann alludes to. It is a seductive conceit. It may be right or it may be wrong. But based on these little MIDI keyboard experiments it is now intriguing enough to make me want to look for evidence, talk to Annalibera.

And, while JI may be the best possibility, it is not necessarily the only alternative. For example, I think I will also try the temperament put forward by Giuseppe Zarlino, the Maetre de Chapelle of San Marco in Venice. In 1560 Zarlino proposed inverting the Major and Minor tones of the upper group in Aristoxenus’s classical scale. This gave him these intervals:

C	D	E	F	G	A	B	C
0	204	386	498	702	884	1088	1200	cents

He then reduced every fifth by 2/7ths of a comma to minimize the comma between the rest of the intervals. This was basically a Meantone (MT) temperament. The MT scheme redistributes the intervals such that the principal ones, such as fourths and fifths are uniformly near-perfect in most keys and other intervals are re-tuned so that they still fulfill their traditional intervallic role within the scale. The most common way of doing this involves flatting the first four fifths (C-G, G-D, D-A, and A-E), reducing them enough to give a true third.

This also eliminates the difference between the Major and Minor tones, producing a ‘Mean’ whole tone between the two, hence, the MT name. The major thirds and the minor sixths are then true, but most of the fifths are slightly flat. It enabled safe modulation from key to key but it left problematic intervals like the fifth G#-D# (viz, the Anonymous remark at the top of this post). The interval’s way too sharp, and its inversion (the perfect fourth) is severely flat.

This is known historically as a wolf tone, so called because the effect is like howling of wolves. There are other wolf tones, but this one is the worst. Apart from readability, the wolf tones are one reason why composers historically have tended to avoid using keys with a large number of sharps or flats.

Here is a spreadsheet you can download by clicking on the screenshot. The spreadsheet enables you to see the sensitivity of deviations from ET to scale position, for JI and for a variety of other historical temperaments, including Zarlino.

Spreadsheet with Temperaments and Intervals calculated

Interestingly, Mozart avoided C# (D-flat), F# (G-flat), G# (A-flat), and B Major. Correspondingly, he also avoided A# (D-flat) minor, D# (E-flat) minor, F minor, and G# (A-flat) minor, respectively. These keys display prominent wolf tones. Mozart also avoided F# (G-flat) minor and B minor. The latter is odd when you consider that one of his favorite keys was the relative D Major. And if you totalize across the various historical temperaments, both D Major and B minor are about as ‘wolfish’ as the more famously wolfish keys.

Major	Minor
C-sharp (D-flat)	A-sharp (B-flat)
D-sharp (E-flat)	C
F-sharp (G-flat)	D-sharp (E-flat)
G-sharp (A-flat)	F
A-sharp (B-flat)	G
B	G-sharp (A-flat)

Here is a spreadsheet you can download by clicking on the screenshot.

Spreadsheet tabulating Mozart keyboards works’ keys

I think I should take an inventory of Dallapiccola’s works, to see what patterns appear and to see whether any of it sheds light on the Quaderno, either corroborating or discorroborating the ideas about JI vs. ET. I’d be very grateful for comments from any of you Dallapiccola scholars out there ...

jwilzewske

Wednesday, April 2, 2008

Was Dallapiccola’s Piano Microtonal or Just-Tuned?

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