Wednesday, August 5, 2015

Don't believe what you read in the papers

A few days ago one of my commentators drew my attention to a Tom Service piece in The Guardian about the Leif Ove Andsnes complete cycle of the Beethoven piano concertos with the Mahler Chamber Orchestra. Andsnes not only played the piano part, he also conducted the orchestra as would have been done during Beethoven's life. Sounded like an excellent project, excellently delivered. The problem came with Tom Service's coverage of the event. He manages to get some pretty fundamental things wrong while blathering on about some more obscure things. Go read the article first: "What would Beethoven have thought of Leif Ove Andsnes's take on his piano concertos?"

I think that he goes astray in a few places. First of all, that quote from Beethoven. He says "It appears in William Kinderman’s 1814 essay on Beethoven’s piano music in the Cambridge Companion to Beethoven" which makes it sound as if Bill Kinderman wrote an essay in 1814. Not so! Bill is a musicologist working today, and probably the leading authority on Beethoven. He and I used to teach together at the University of Victoria. I also think that Tom Service's interpretation of the quote goes astray. Beethoven is likely talking about the new style of piano playing that was coming into favor around then, exemplified by figures like Hummel and Dussek. Far more about finger-virtuosity than the likely more musically profound improvisations of someone like Mozart (whom Beethoven may have had in mind) or Beethoven himself, for that matter.

The other big error is in what he says about equal temperament: "Beethoven would have heard Andsnes’s instrument as being crazily out of tune." No, he wouldn't. The big shift in temperament from Pythagorean or meantone to equal temperament, that we use today, took place in the 17th and first half of the 18th centuries. By the time of Bach, it had largely been completed. Between meantone and equal temperament were a variety of compromises, many of them the work of a theorist named Andreas Werckmeister who published some works in the 1680s and 90s in which he argued for a kind of well-tempered tuning that would do away with most of the unpleasantness of the meantone system. Bach's Well-Tempered Clavier is an obvious reference to Werckmeister. This work, often cited as being the first example of equal temperament, was probably not intended to be played in our modern system, but in one of the ones worked out by Werckmeister. But it was close to our modern equal-tempered tuning because all of the keys were usable.

Beethoven, of course, coming well after this, and using all the keys with equal freedom, wrote for equal temperament. Oddly, one thing that Tom mentions completely disproves his case: "the distance between the C minor of the first movement and E major of the slow movement is a shocking shift from one world of feeling to another, which he then makes a joke of at the start of the third movement, translating G sharp to A flat." G sharp and A flat are the same note only in the equal tempered system. Tom is completely confusing the distance between C minor (three flats) and E major (four sharps) in the circle of fifths with the difference between G sharp and A flat in Pythagorean tuning: it is called the Pythagorean comma and it is why the use of remote keys like A flat is only possible in equal temperament or something close to it.

It is bad enough when writers in the mass media--or even in program notes--try to completely avoid any technical discussion of music theory, but it is even worse when they get it wrong.

Now let's listen to Beethoven's Piano Concerto No. 2 in B flat major, op. 19, which was actually composed before the No. 1. This is Steven Lubin, fortepiano, with the Academy of Ancient Music directed by Christopher Hogwood. Brace yourself, because the instrument is one from Beethoven's time so it sounds quite different from a modern piano.


Ken Fasano said...

Beethoven's tuning would not have been either Werckmeister well-temperament (too early) or modern equal temperament (too late). (Kirnberger, who was a student of JS Bach, had his own well temperament). Beethoven's would have been something like Young well-temperament (Thomas Young, not LaMonte!), where each key is playable, but sounds different. C major would not sound quite like C# major. It would not have been until Wagner's time that ET would be available (?); according to the following article, by Kyle Gann (who DOES know what he is talking about when it comes to tuning), it is not until the early 20th century that ET becomes practical:

A.C. Douglas said...

Helluva post!, Bryan. Love it.


Bryan Townsend said...

Thanks, A. C.!

There is considerable debate about the history of temperaments, but I think that we can agree that whatever tuning Beethoven used, it was one that was close enough to equal temperament to make all the keys usable. Beethoven would not have heard equal temperament as being radically different from what he was used to. That was my main point.

Yes, Kyle Gann does seem to know a lot about the history of temperament. At least if we accept Owen Jorgensen's book as the be-all and end-all of the discussion. Does anyone else have a comment? And does anyone know of any recordings of Beethoven on historical instruments that use historical temperaments?

Nathaniel Garbutt said...

I'm in agreement with Ken.

Equal temperament didn't didn't become ubiquitous until the early 20th cent when technology became available to reliably tune it.
ET was discussed and tested as early as the 16th cent - It was also quickly dismissed as a bad solution due to the impracticalities in tuning it reliably and the horribly sharp thirds making unsuitable for the time.

There is actually a pretty pronounced difference between ET and the well temperaments used during the late 18th/ early 19th cent. The differences become even more pronounced in modulations and Abrupt key changes between movements (Beethoven certainly would have noticed). ET has no difference between the any intervals i.e. all fifths/thirds etc are the same no matter of the key. The Mean tone temperaments also exhibit this quality as all generating fifths are the same distance. The well temperaments, including Werkmeister's, Kirnbrger's and Young's all vary the generator from fifth to fifth. This results in the fact that there will be thirds of different sizes (and all other intervals for that matter) and thus each key is noticeably different...some more stable than others.

Both Beethoven and Chopin used these temperaments to great effect and really their musical language for the paino depends on them. Beethoven's abrupt changes of key between movement has a much more pronounced effect when the keys are actually different in tuning and not just pitch.

The thing to rememeber with Beethoven though is that he was showing strong signs of hearing loss by about 1800 so he probably had lost the ability to distinguish between the earlier temperaments of Werkmeister and Kirnberger and the newer Young I and II which appeared around 1800 (from memory) much less internalise them and bring them into his inner ear.

Vallotti is another possibilty for Beethoven.

The most recent research regarding the Well-Tempered clavier seems to suggest a modified 1/6 comma meantone. This is very much inline with other documented evidence of how Bach liked to tune his keyboards with slightly wide thirds as well as the possibility that the design on the title page is an enigmatic tuning puzzle which can be deciphered as such.


Bryan Townsend said...

Thanks to you both for the clarifications and additions. I have read some of the research on Bach's exact temperament, but it was q while ago. Thanks for reminding me of it.

Two comments come to mind: what technology is necessary to tune equal temperament? I'm sure there are some very convenient gadgets available now, but I can recall piano tuners using metronomes to time the beats for the intervals going back a few decades. The metronome is a technology dating back to Beethoven's time and isn't that all the technology you need to tune equal temperament?

The other thought is that are all the people recording Beethoven, Mozart and even Chopin for that matter, using only equal temperament? Is that what Malcolm Bilson is using in his complete recording of the Mozart concertos on fortepiano?

Nathaniel Garbutt said...

Hi Bryan,

Yes, a metronome would have been used. The beats in ET are all fractional (I can't recall specifics but 8.3 springs to mind) so the more reliable the metronome the better. It was always possible to tune it but it is just a hard temperament to tune correctly. There are also a number of peculiarities to tuning a piano...You can't actually tune perfect octaves for instance in the top registers as they end up sounding out of tune so you need to fudge it a bit to make it sound good.

There were some studies done in the early 20th cent. analysing the tuning practice of the best organ/piano tuners in England who believed they were tuning ET but turns out they weren't and actually had a small bias towards making the more common keys more in tune. This is actually still quite common. I've used probably 7-8 different tuners over the last while and they all end up with some slight differences.

ET is very common today. Almost all recordings on a modern piano would be in ET. It usually takes a grand piano a few months and a few re-tunings to settle into a new temperament....So it wouldn't be practical to do it for a single concert of recording...Unless it is the pianists piano. Old instruments are probably not tuned in ET to begin with so the pianist has probably chosen a temperament appropriate to the age of the instrument. There are however, increasingly more and more recordings of the above repertoire recorded on pianos of the time using temperaments of the time. Ronald Brautigam has done quite a lot or recordings of Mozart and Beethoven for instance.

I'm actually unfamiliar with the Malcolm Bilson recordings so I don't really want to answer the question. Having read some articles written by him however, I would speculate that he is not using ET as it "Would serve the music better" to use 1/6 comma mean-tone (more usuable keys as the wolf interval is narrowed by distributing the syntonic comma over 6 fifths instead of 4 as in 1/4 comma mean-tone) or an early well temperament.

Bryan Townsend said...

Hey Nathaniel,

Absolutely fascinating! I realize that I am like the kid with his nose pressed up against the window of the candy store when it comes to all this exotic tuning stuff. Why? Because I'm a guitarist and from what I have read, we and the lutenists have been doing roughly equal-tempered tuning since the 16th century. I guess because of the way the fretboard is put together.

The problem comes to mind, if Malcolm Bilson decided to do his recording of the complete Mozart piano concertos in his favorite well (but not equal) tempered tuning, what is going to happen when he plays with the orchestra? Are there going to be serious intonation discrepancies? You would think so...

Nathaniel Garbutt said...

Hi Bryan,

It depends on the orchestral players. Mozart and other violinists of the time understood and had different fingering positions for say D# and Eb. Leopold Mozart actually wrote an important treatise for violin that demonstrates this. Most HIP violinists would be used to playing a slightly different fingering for the enharmonic notes.

My understanding of the idea is that a whole tone is divided into 9 equal subdivisions (or comma - another one!). A diatonic (major) semi-tone is 5 commas and a chromatic (minor) semitone is 4.


C - Db = 5 commas
C - C# = 4 commas
D - C# = 5 commas
D - Db = 4 commas

This was common across all string instruments. Brass instruments can also "lip" the tuning to accommodate if need be and woodwind instruments can also make subtle modifications with their embouchure (especially earlier a tangent, a lot of early jazz clarinet players prefer the Albert or simple system to the Boehm for greater ability to bend notes).

There is also a Haydn string quartet (I can't remember which one off the top of my head) where Haydn makes an enharmonic modulation and writes a little instruction to one of the players to play the written note as its enharmonic equiv and not the actual written make the modulation smooth.

I was actually thinking of you an other guitar players earlier today with fixed position frets. I saw an HIP performance last night of the Pergolesi Stabat mater which involved a lute. His lute had gut wound frets much like a viola da gamba so easily adjustable. I'm not too familiar with guitar like instruments to be honest so I don't know what was typical, especially with archlutes etc.

Bryan Townsend said...

Thanks, Nathaniel for all the detail! I will have to track down that Haydn quartet and do some research into the fretting on lutes and guitars.

Rickard Dahl said...

While the digital piano sound isn't perfect yet there is a clear advantage (there are several advantages but that's a topic for another day): You can switch the tunings very easily (assuming the digital piano has the function (i.e. is good/expensive enough)).

Rickard Dahl said...

I forgot to mention it in my last comment but the digital piano I use has the following temperaments: Equal, Just (Major), Just (Minor), Arabic, Kirnberger, Meantone, Pythagorean and Wreckmeister.

Nathaniel Garbutt said...

Hi Rickard,

Yes, digital pianos are fantastic for this. I bought a relatively good stage piano that allows custom tunings (this was pivotal to me buying it) so I can input any temperament and modify it to my hearts content. Love it.

Marc Puckett said...

Nicholas Lezard says-- if this is in fact what you all were writing about-- that the Haydn quartet with the manuscript note is op 77, n 2 (in F major, Hob. III:82, from 1799, dedicated to Prince v. Lobkowitz-- this in the parenthesis is from the IMSLP; no note in that printed edition, alas). This is all quite fascinating, however impenetrable it all is still, ha.

"Haydn, in 1802, made an explicit note in the autograph score for his Op 77 No 2 Quartet that a cello's E flat is to be played as if it were a D sharp - more evidence that this was by no means common practice. And when Beethoven started going deaf, was he still hearing his compositions in the old style, or in newfangled ET?"

Bryan Townsend said...

I obviously have to get a fancier digital piano! What model do you have, Nathaniel?

Marc, thanks for tracking down that Haydn quartet.

Nathaniel Garbutt said...

Hi Marc,

That seems to the quartet I was thinking of.

Hi Bryan,

I have a Kawai mp11

It's not as good as playing and acoustic obviously but it still has a pretty good touch and action. Interfaces well through midi, has a kinda clunky mp3 playback but is quite easy to record to both mp3 and midi.

It is also really quite heavy so it needs a good stand so as to not sway and move when playing it.

Bryan Townsend said...

Thanks, Nathaniel. Looks like a very nice high-end model.

Marc Puckett said...

"Between the first and second editions of Woldemar's Méthode, Haydn was in Vienna writing his last complete string quartet: Op 77, no. 2 in F, which he finished in 1799 and published in 1802. The autograph score... survives and contains some striking and highly unusual markings relating to tuning. In the development section of the first movement, in the cello part, he writes "l'istesso tuono" between an E flat and a D sharp. At the same time he indicates a change of finger from the middle to the index finger of the cellist's left hand and also specifies "das leere A" in the first violin, meaning that the first violinist should play the note A on the open second string of the instrument instead of stopping the D string. What does all this mean? It's not entirely clear, but I have a theory.

First of all Haydn's stipulation that E flat and D sharp should be "l'istesso tuono"-- 'the same note'-- in itself confirms that he expected the player would normally play them as different pitches. In ET, of course, they are the same note, so it's only in a system like extended meantone, where they are different, that special indication like this would be required. Since Haydn is about to use what's called an "enharmonic modulation"-- in this case, changing keys by treating the E flat as if it were really a D sharp-- he calls for the pitch to stay the same (in spite of the expected change of finger) in order to enhance the surprise, as it were. That, at any rate, is my explanation of why he did it. The open string A in the first violin then makes a tritone against E flat whereas it would have made a diminished fifth against the D sharp. Both are pure in extended sixth-comma meantone, but it takes a precise placement of the A in order to get the most out of the pure interval and calling for an open string achieves that by removing the possibility of vibrato. It is quite possible, even likely, in my opinion, that Haydn expected the cellist eventually to change the pitch of the D sharp to an actual D sharp from that of the slightly higher E flat, since the note then alternates with the E natural above it, and it would be easy to lower the D sharp once that alternation begins. And Haydn's marking may in fact refer specifically to the first D sharp, since he carefully drew vertical lines beneath the last E flat and the first D sharp....

The special tuning indication was transferred from Haydn's autograph to his copyist's parts and into the first printed edition in 1802."

From locations 839-857, Kindle edition, of Ross Duffin's How Equal Temperament Ruined Harmony.

I will say that my poor head has finally more or less grasped the idea of 'temperament' and how there are different ones. :-)

Bryan Townsend said...

Are all of those two long paragraphs quotes from the Duffin book? Assuming yes, I have a couple of comments. While there are certainly interesting aspects to the history of temperaments, it is possible to go overboard and start claiming that equal temperament "ruined harmony" (when we all know it was actually Arnold Schoenberg!). Go a bit further and pretty soon you wake up in the morning and find you are Harry Partch with his 43-tone octave.

As a matter of fact, most bowed string instruments, such as those that make up the string quartet, do not have frets and therefore are accustomed to shading the tuning depending on the harmonic context. They can adjust the pitch as needed, except on open strings. In the section of the Haydn quartet cited, the preceding passage is in E flat minor, but just towards the end a minor second motif appears: C flat to B flat and F flat to E flat. The first forms part of an augmented 6th chord (spelled as a diminished 7th) and the second is a contrapuntal imitation. But instead of going to A flat, the key implied by that motif, Haydn stops everything and reinterprets the F flat to E flat as E natural to D sharp (though he starts with D sharp). For the harmonic "joke" to work, of course they have to sound like the same note, even though harmonically they are quite different notes. F flat to E flat is the diminished seventh to fifth in A flat while E to D sharp gets us to the root of a viiº7 chord in E minor, which is where he is going, harmonically. I think that Haydn's note to the cellist was cautionary: don't shade the pitch of the D sharp as you might normally do, because the E flat/D sharp is a pivot note and it only pivots properly if it is heard as the same note. Duffin realizes this, of course.

But the fact is that string quartets, string orchestras, choirs, singers generally, all shade the pitch to improve the tuning based on context. They did it then and they do it now. It is even possible on the guitar, when playing chords in higher positions, to shade the pitch slightly. I also believe that wind players typically do some of this as well. But it is nothing so systematized as to call it a temperament as it depends on context, as in the Haydn quartet.

Marc Puckett said...

As I get further into that little Duffin book (which incorporates a series of biographical vignettes of musicians etc who have commented in one way or another on temperament-- which, frankly, probably is as profitable to me personally as the argument itself), the argument ('ruin of harmony') seems to boil down to a) ET wasn't used 'almost universally' in fact until after 1917 more or less and b) it is chiefly a problem (inasmuch as it is a problem) for pianists and organists, who have the fixed keyboards... well, that's as far as I've gotten, two thirds of the way through.

There was a keyboard instrument called a Teliochordon, a kind of fortepiano, liked by Haydn in a letter of 1792, patented by some crazy Englishman called Charles Claggett in 1788, 'where each octave was divided into 39 notes, accessed by means of pedals'. Heavens!

Marc Puckett said...

Claggett was an Irishman who lived in London. I found a site called Xenharmonic [] which looks like it might have everything anyone might want to know about temperament etc.

Am going to finish the Duffin and then forget about temperaments for the time being because I see a great abyss of unprofitable intellectual games-playing over there, and want to avoid it, ha. Unprofitable for me, I mean. Eigenmonzos and octarod commas; good Lord.

Bryan Townsend said...

Marc, I believe you are having an inordinate amount of fun with these temperament disputes! Yes, it really is a fixation for keyboard players, it seems. Oh, and there was a fellow in the Renaissance, whose name I forget, who designed a keyboard dividing the octave into a lot of notes.

Marc Puckett said...

I see, reading through this thread again, that Ken Fasano in the very first comment makes, via the Kyle Gann article (which am only beginning today)-- "it is not until the early 20th century that ET becomes practical"-- a point that is consonant with one of Duffin's bottom line points.

There are YouTube videos/recordings of various pieces of Bach, Mozart, Beethoven, performed in different temperaments....