jwilzewske: simbolo

Showing posts with label simbolo. Show all posts

Wednesday, April 2, 2008

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 ...

Wednesday, March 19, 2008

Dallapiccola on Children’s Rights and Duties: Quaderno di Annalibera

Luigi Dallapiccola was was 48 years old when Quaderno was composed, nominally as a gift for the eponymous Annalibera, his daughter, on the occasion of her eighth birthday. [Annalibera Dallapiccola was born on the day of the liberation of Italy, whence the ‘libera’. Prof. Annalibera Dallapiccola is now a scholar in Asian and Indian art and is an Honorary Professor of Fine Arts at University of Pennsylvania and the University of Edinburgh. Formerly she was Professor of Art History, South Asian Institute, Heidelberg University.] The Quaderno is composed of eleven variations on a twelve-tone sequence based on the name B-A-C-H (the pitches B-flat, A, C, and B).

Surely we can wonder whether Luigi meant Quaderno as a veiled criticism of government: projecting children as analogous to the general public (under Mussolini, or under subsequent regimes). After all, other of Luigi’s compositions were famously political.

But there is plenty of evidence that we should take Quaderno at face value—as a collection of etudes addressed by father to daughter. For one thing, the title ‘Quaderno’ recalls Johann Sebastian Bach’s ‘Notebook’ for his daughter, Anna Magdalena. Other correspondences include Dallapiccola’s recapitulation of Bach’s contrapunctus subtitles for movements in strict canon, as in Art of the Fugue.

Quaderno’s movement titles are (in English) as follows:

Symbol;
Accents;
First Counterpoint;
Lines;
Second Counterpoint (Canon in contrary motion);
Friezes;
Andantino amoroso and Third Counterpoint (Canon cancrizans);
Rhythms;
Colors;
Shadows; and
Quatrain.

These movements are lovingly didactic in a fatherly way—their names and their playful, thematically-expansive musical content are difficult to construe as covert political polemic.

Some 15 years ago David Lewin published a detailed transformational analysis of the Simbolo movement. Simbolo is marked ‘Quasi lento, misterioso’ and fully lives up to the misterioso. Regarding Simbolo, Lewin said: “The group [of transformations] is not a list of immediate aural intuitions or intentions ... Rather than trying to make our transformations denote phenomenological presences in a blow-by-blow narrative, we can more comfortably regard them as ways of structuring an abstract space ... through which the piece moves” (Lewin, p. 34).

If Dallapiccola wrote that the tone row in Simbolo isn’t meant to be perceptible to the listener, then we should take him at his word. He was, at the ripe age of 48, in a period of rapid change and learning—we hear plenty of discovery and exploratory gestures in these ‘etudes’. We can also readily conceive of what the intense, inquisitive Annalibera may have been like at that age—and imagine the motives that may have been at work in the father, trying to create something beautiful and highly symbolic ‘for her’, to be hers. It is one hell of a birthday gift. And, as things go in the Age of Reason—late in childhood and before the onset of adolescence—it was the perfect time for Luigi to make such a gesture. Misterioso—one of the duties of a composer (of a musician; of any artist) is to trade on the novel and non-obvious. Il Luigi ci istruisce così!

There is no reason why music theorists should give undue emphasis to tone-row or other serial compositional methods—giving priority to the ‘system’ seriously mis-represents the compositional process. It does violence to the music and dishonor to the composer! Dallapiccola especially was no slave to the [twelve-tone, serialist] ‘system’.

Even in Quaderno where a tone-row is perceptible, it does not dominate. As the canon or other variations progress, the role of the tone-row becomes less and less clear. Or, more accurately, the force of the ‘system’—the thematic mechanics—begins to cope with the accretion of other equally-legitimate guiding principles, other thematic genera. How like a Bach fugue this is! Once a theme is developed, it is absorbed into layers upon layers, variation upon variation. Futile to analyze a fugue by exhaustively identifying subject, counter-subject, and so on! Dried insects preserved in an entomologist’s collection have more fidelity to nature than this!

Based on the evidence we see in Quaderno, I don’t believe Dallapiccola relied on twelve-tone rows compulsively. There are so many other factors, that present themselves to the ear, that should inform a faithful analysis true to Dallapiccola’s motives and intentions. Above all, analysis should enlighten the performer and the listener.

So my speculation is this: Luigi Dallapiccola created Quaderno not only as a special gift, but also as a way of memorializing his sentiment(ality) about childhood. He was concerned about children as well as other members of society, both before the war and in the post-War period. A highly private man, he maintained a traditional idea that what went on in the family was nobody’s business, least of all government’s. But he was not a traditionalist as concerns the rights and duties of children, from what we can tell in his writings. Poverty and social exclusion may be resistant to solution by public means, but that simply implies that individual families must redouble their efforts. Children, too, have moral standing and therefore have duties commensurate with their rights. The childhood privilege of engaging in fanciful, creative and artistic pursuits carries with it, for example, an obligation to exert effort in good faith, to pay attention—for the children to avail themselves of the opportunities that the parents set before them.

If there is a better way to talk about this than through the notions of ethics and children’s rights, perhaps Luigi Dallapiccola knew such a way. The embarrassingly prevalent and pernicious (U.S.?) ideology—which insists that parents should be like gods to their children and that children are basically property, in a status of utter subjection to the will of the parents; and which defers to some distant time in adolescence any accountability by children for their acts—surely had no place in Luigi’s world-view.

Of course under U.N. and E.U. resolutions, children are emphatically not property, but they are nonetheless ‘extensions’ of the parents’ identities. Emotionally and biologically, this is natural. And, legally, this is true as well. Children progressively acquire autonomy or sovereignty—increasing rights, commensurate with increasing responsibilities and abilities. They discover and progressively grow beyond the parents’ identities. Quaderno is a gentle exhortation, by Luigi to Annalibera, to have serious fun in this process—of finding her own identity, of finding her own voice, of finding the good in the world and in other individuals and other cultures.

In summary, children are by nature ‘becoming’, not yet arrived into the fullness of identity. Of course, all of us are all always still ‘becoming’ no matter how old we may be, but children are more so. To Luigi Dallapiccola, children were persons to be taken seriously, as subjects with moral standing who have complex and evolving interests that merit public concern and complex and evolving duties that require the attention of the children as well as the attention of their parents and of society. Etudes are at this boundary: they are emblems of the social duty to give (parents’ and society’s duty of care), and they are emblems of a complementary duty to receive (the child’s duty of care). In a way, Quaderno is a meditation on ‘children as children’ and ‘parents as parents’ instead of as proto-adults and gods, respectively.