Sabbath delight: Angela Hewitt interviewed on Bach, the Well-Tempered Clavier, and… baby hippos?!

Possibly Canada’s greatest living treasure in the realm of classical music is pianist Angela Hewitt. She has a huge and musically diverse repertoire (her recent recordings of Scarlatti sonatas are quite scrumptious), but is best known for her complete recordings of J. S. Bach’s keyboard works.

Here she is in Hong Kong in late 2018, giving a quite delightful interview to a local music professor for about an hour:

She talks about her background (her father was a British-born organist and choir director at a cathedral in Ottawa, her mother a pianist), about playing Bach on the piano, why she uses Fazioli pianos exclusively now, about her favorite preludes and fugues from the Well-Tempered Clavier (I’m not surprised C#m book 1, Bbm book 1, and F#m book 2 are among them). A few amusing as well as enlightening nuggets:

  • Because both Canadian and Bach, a comparison to Glenn Gould is inevitable. But she recalls seeing him on TV as a child, and asking her parents, “who is this kook?” Later on, she decided that, without detracting from Gould’s (staggering) musical talents, her vision of Bach wasn’t his, and that in particular Gould’s tempo choices were too eccentric and counter-intuitive for her taste. (It’s also hard not to notice that she’s as outgoing as Gould was introverted. She even once answered a fan note from yours truly :))
  • Her taking ballet lessons as a child helped shape her approach to rhythm in Bach, particularly the degree to which the rhythms of French courtly dances (quite explicit in the French suites, the orchestral suites, and the French Overture) come through in Bach’s preludes. The dance steps required notes inégales, rhythms that are more or less subtly syncopated even when written as equal notes. (Cf. “swing” and “boogie-woogie” in American popular music.)]
  • Similarly, being in a choir (her father’s?) since childhood gave her an appreciation of phrasing and articulation that you would not normally acquire from playing Bach on a piano (or other keyboard instrument) in isolation.
  • Her realizing during preparing for her then-current Bach concert tour (after a long spell of focusing on other repertoire), “there’s no bulls–t [sic] at all in Bach’s music”. By [bovine scatology], she means redundant notes or passages, “fluff”, “filler”. (As I understand it, a piece by Liszt, for example, will contain quite a bit of ornaments, flash-bang, musical “foley effects” that can be ad-libbed or simplified while still basically retaining the same piece. In contrast, everything in Bach is “just so”.[*])
  • How she was taught Bach (starting at age 3) by her parents in the same sequence she recommends for learners now: first the Anna Magdalena Notebook and the Little Preludes, then the Two-Part Inventions, then the Three-Part, then the French Suites, and only then the Well-Tempered Clavier.
  • How an important factor in deciding tempi for the preludes is “harmonic tempo” (her interviewer’s term), i.e., the frequency at which chords change. For example, the (in)famous First Prelude in C she takes comparatively fast as it only changes chords one to the bar (and she’d otherwise “be asleep by the time it’s over”), while the Fm prelude with many changes to the bar she plays more slowly and more expressively than many pianists.
  • My LOL moment: One of her favorite fugues is the long, ponderous, organ-like A minor from WTC book I, which she calls “my little hippopotamus fugue” [sic]. This is actually a reference to a Victorian musicologist named Ebenezer Prout, who, as a mnemonic device for the required articulation, put all sorts of droll lyrics to the fugue themes. A full list can be found here. For the A minor from Book One, it was : “On a bank of mud in the river Nile, upon a summer morning, a little hippopotamus was eating bread and jam.

Glenn Gould (whose correspondence is replete with musical jokes) clearly missed that joke, and instead played the fugue at a brisk tempo that is “rushing” for Angela’s taste, but brings out the relentless motorics of the piece. Here (via commenter “riverstun”) Gould discusses how he spliced together the final recording from two takes (out of eight) at the same high tempo, one of which he labeled the articulation as “pompous” and the other as “skittish”.

Sadly I could not find Angela’s performance of the same fugue on YouTube: suffice to say that in my iTunes music library, her recording runs for 5:33, compared to just 3:27 for Gould! (The great Tatiana Nikolayeva’s version, part of a single track with the prelude, I timed at 4:30.)

It is a marvel of the modern age that not only can we pull these contrasting performances up at the touch of a button, but we can even hear the performers explaining their artistic decisions. This is a luxury Bach himself (I nearly wrote Bach Himself, but that would be idolatry) could not have dreamed of in his lifetime, but would have been quite delighted with.


[*] exceptions that prove the rule are pieces like the 2nd movement of the 3rd Brandenburg, where Bach leaves a space for an improvised keyboard cadenza, or sections of the Chromatic Fantasy where performers are given sequences of chords to arpeggiate to their own taste.

Sabbath delight: Tatiana Nikolayeva plays J. S. Bach’s entire Well-Tempered Clavier

I had no idea who this fabulous Russian pianist was until I heard her performance of J. S. Bach’s Art of the Fugue on the Hyperion label — and was blown away by its combination of sensitivity and contrapuntal clarity. I treasure that recording above all others in my collection—if I could only take away one to a deserted island, that would be the one.
Sadly, shortly after that recording, she was felled by a stroke during a concert in San Francisco, and passed away days later, never having regained consciousness.
She had a very broad repertoire, most of it recorded in the former (thank G-d) USSR and (until recently, at least) only available on CDs with doubtful source audio provenance. (Vinyl rips? Analog studio tapes?)
But her first and last love was Bach. After she won the Bach Competition in Leipzig (then in the DDR) in 1950 with her Well-Tempered Clavier performance, the composer Shostakovich was so impressed by her voice-leading ability that he wrote his own 24 Preludes and Fugues, Op. 87 especially for her.

Until recently, all I had heard of her earlier output were lo-fi Youtube rips off vinyl recordings — with lots of hiss and distortion I had great trouble listening past. Now somebody uploaded a high-resolution digitization of the CDs. Below is the video for your enjoyment; I managed to locate a legal download for the source and promptly bought it. [Book I; Book II] You will wish to do the same if you like the recording. (I thought nothing could surpass Glenn Gould’s or Angela Hewitt’s for me, but this is something specia. )
“Perhaps not all musicians believe in G-d, but they all believe in Bach.” (Mauricio Kagel)

J. S. Bach (Tatiana Nikolayeva, piano): WTC Books I & II (complete)

As a bonus, here follows the complete performance by another great Russian pianist, Sviatoslav Richter. Enjoy!

J. S. Bach (Sviatoslav Richter, piano): WTC Books I & II (complete)

Saturday musical delight: Well-Tempered Clavier in MuseScore animation

Via YouTube channel “gerubach”, which has been presenting “scrolling score” youtube videos of musical compositions for many years, I stumbled upon the following gem of a playlist:

All of Book I of Bach’s Well-Tempered Clavier is being rendered there in MuseScore animation: as you hear the audio, not only do you see the score on screen (two systems at a time) and a pointer scrolling across the notes being played, but at the bottom of the screen, you see the notes currently sounding displayed on a piano keyboard.

Especially in combination with YouTube’s ability to play back videos at reduced speed without altering the pitch, this is a marvelous self-tutoring tool for keyboard playing as well as music theory.

The audio is taken from the performance by pianist (and former competitive weight lifter!) Kimiko Ishizaka [official website]. The MuseScore team could legally do so as the (IMHO excellent) performance was released in the public domain (!)

The onetime child prodigy pre-funds her recordings through Kickstarter campaigns (most recently, she ran one for a “Libre”recording of Bach’s The Art of Fugue), then releases them online under PD or Creative Commons licenses. The word “Libre” she uses has some currency in the open source software developer community: It refers to one of the two words in French (and other Romance languages) that correspond to the English “free”, namely libre (without restrictions, “free as in speech”) vs. gratis (without cost, “free as in lunch”).  She does not work gratis, but on what I have been calling a “massively distributed commissioning” model, and what is becoming known as a “threshold pledge” model: she sets a funding goal, solicits pledges from patrons on Kickstarter, and if her threshold is met, the work is performed and the money collected. For her last campaign, the threshold she set was 20,000 Euro, and the minimum pledge was 10 Euro — the price of an album at a CD store (remember those). Larger pledge amounts (20 Euro, 50 Euro, 100 Euro) get various extra goodies, such as live recordings from recent concerts, a physical CD of the music, and admission to one of three “meatspace” live concerts.

D. Jason Fleming has been talking a lot about the “Open Culture Movement”. I believe this is an interesting example, and may actually point a way toward the future for classical performers. The big losers here, of course, are the classical music labels, who in this model are about as profitable as illegal CD bootleggers….


Closing the circle and ending the spiral: of well-temperament and equal temperament

I’ve been struggling for a while with how to present this in an accessible way. Stumbling upon this video below made me want to try: let’s have a go at this.

“Circle of fifths” or “spiral of fifths”?

It’s been well-known since the days of the ancient Greeks that the musical intervals we perceive as “purest” are the ones where the frequencies are simple fractions.
• octave: 2:1
• perfect fifth: 3:2   (and its inversion the perfect fourth, 4:3)
• pure major third: 5:4 (and its inversion the minor sixth, 8:5)
Less consonant are smaller ratios such as:
• pure minor third: 6:5 (and its inversion the major sixth, 5:3)
• greater whole tone, 9:8 (and its inversion the minor seventh, 16:9)
Now if you have a continuous-pitch instrument such as the violin or the human voice, you can just sing/play the intervals perfect (in “just intonation“) and be done with it. But what about fixed-pitch instruments such as guitars/lutes or pianos/harpsichords?
Big deal, you say: just stack up pure fifths, thus build the circle of fifths, and we can span a whole scale. Twelve fifths up and seven octaves down, and you should be where you started.
Sounds good in theory, except: the circle of pure fifths isn’t — it’s really a spiral of fifths. (3/2)^12 divided by 2^7 works out to 1.013643265…, almost a quarter of a semitone too wide. This small interval 531,441/524,288 is known as the Pythagorean comma.
Big deal, you say, if it doesn’t close: at least our fifths are pure. But what about the thirds?
Okay, let’s stack up four fifths, C-G-D-A-E, and drop two octaves down. We get… ((3/2)^4)/4=81/64, a Pythagorean third which is considerably wider than the pure major third. The ratio between them, (81:64)/(5:4)=81:80, which is known as the syntonic comma (or just plain “comma”). It’s just slightly (2% of a semitone) flat of the Pythagorean comma.
Even to an untrained listener, Pythagorean thirds sound unpleasantly sour. There is no way to fix this without either detuning the fifths or adding microtones to the scale.
So what if instead we start stacking up major thirds? Well, let’s see: C-E-G#-B#=C. That’s (5:4)x(5:4)x(5:4)=125:64, or 3:64 short of an octave!
In short: pure octaves, fifths, thirds: pick two.
The octave is the one interval nobody wants to mess with. (Well, there are “xenharmonic” scales, but nobody outside academia has even heard of them.)

Pythagorean intonation: pure fifths at all cost

You may effectively say: I must have the fifths (and hence fourths) pure, and if that means the thirds are sour, I’ll treat them as dissonant.
This is exactly what happened in Western music until the Renaissance.
Since all intervals in Pythagorean tuning are rational fractions that have no prime factors larger than 3, Pythagorean is also known as “3-limit rational tuning”.  [According to the same classification, “just intonation” as practiced by a cappella vocal ensembles is also known as “5-limit rational tuning”, since the largest prime involved is five (e.g., in the major third 5:4, the minor third 6:5).]
String instruments naturally lend themselves to Pythagorean tuning: anybody with musical hearing can tune pure fifths (or their inverses, fourths) by ear, just by tweaking until the “beats” stop. Violins are tuned in fifths; bass guitars, and the lowest four strings of a guitar in standard tuning, are tuned in fourths.

Quarter-comma meantone: pure major thirds at all cost

Alternatively, we can sacrifice the pure fifth in such a way as to restore the pure major third. The simplest way to do this is to narrow all fifths down by one-quarter of a Pythagorean comma, such that four narrowed fifths minus two octaves come out exactly a pure major third, 5:4. Such a fifth would be 5^(1/4)=1.495348781… (This quarter-comma meantone temperament was first proposed by a Spanish monk of Jewish origin named Pietro Aaron.)
Fifths in 1/4CM do “beat” (they are flat by about 1/20th of a semitone), but one can get used to them. The trouble: twelve fifths now stack up to three perfect major thirds (5:4)^3,  which we’ve seen above work out to 125:64, or 3:64 short of an octave. If you like: where Pythagorean tuning creates an expanding spiral of fifths, quarter-comma meantone gives rise to a contracting spiral of fifths.
Thus, you end up somewhere with one last fifth that is really bad, a so-called “wolf fifth” wide by two-fifths of a semitone. Since there are twelve possible places to start tuning, you can pick one such that the wolf fifth does not appear in the most frequently used keys. (Typically, it is put on G#—D#.) There are also several “wolf thirds” in the most remote keys.
Quarter-comma meantone was the prevalent tuning for much of the Renaissance. If one stays in the “safe” keys (with no more than two sharps or flats, say) and does not modulate to the more “remote” ones, it is quite tolerable. But don’t even think of playing in F# or Db on a keyboard tuned in quarter-comma meantone.

A first compromise: sixth-comma meantone

Musicians soon started experimenting with different meantone tunings.
In sixth-comma meantone [Ed.: a.k.a. Silbermann temperament], the wolf fifth can be reduced to about one-sixth of a semitone, at the expense of making the thirds just a little bit wide. This tuning still enjoys some popularity among “authentic Baroque practice” performers. Twelve fifths are now 1/5 semitone short of seven octaves.
Eleventh-comma or twelfth-comma meantone are nearly impossible to tune by ear, but are actually as close as makes no difference to equal temperament (see below).

Well-temperaments: closing the circle

As the Renaissance morphed into the Baroque era, composers started becoming ever more adventurous with modulations, and solutions that retained playability (to a greater or lesser extent) for all twelve major and all twelve minor keys were sought.
This led to the family of so-called “well-temperaments”, in which the Pythagorean comma is spread out over all twelve fifths, (at least) initially in an unequal fashion. Such temperaments are also called “circular”, in that twelve fifths now stack up to exactly seven octaves.
The term “well-tempered” (wohltemperiert) was originally coined in 1691 by the German organist and music theorist Andreas Werckmeister. He himself proposed several well-temperaments, one of which (Werckmeister III) is still in some use today among the HIP (historically informed performance) community.
In Werckmeister III, six of the fifths are tuned a quarter-comma flat (F-C, D-A-E, F#-C#-G#) while the remote G#–D#, to compensate, is made sharp by a quarter-comma and the remainder are tuned pure.
Another example is Vallotti temperament, in which the six diatonic fifths F-C-G-D-A-E-B are all tuned 1/6 of a comma flat and the rest are tuned pure. Young temperament, developed by the physicist and polymath Thomas Young, is based on the same pattern except cycled by one fifth to C-G-D-A-E-B-F#. There are many others: Kirnberger (advocated by a pupil of J. S. Bach), “tempérament ordinaire”,…
Common characteristics of all these well-temperaments include the following:
• all keys are at worst tolerable
• “nearer” keys approach just intonation
• “remote” keys approach Pythagorean intonation with its sharp thirds
Some of these are easier to realize by ear (i.e., without a digital tuner or other assistive device) than others.

Equal temperament: nothing perfect, everything equally imperfect

Mathematicians like Simon Stevin and Marin Mersenne in the West (and independently, Zhu Zaiyu in China) had proposed a more radical solution: to simply divide the octave into twelve equal parts, 2^(1/12)=1.059463094…, which is equivalent to narrowing all twelve fifths by one-twelfth of a Pythagorean comma to 2^(7/2)=1.498307077…
This is known as “equal temperament”, specifically “12-tone equal temperament” (12-TET). It is a special case of well-temperaments, and arguably the only “unbiased” or “universal” one. It is actually equivalent to tempering all fifths by 1/12th of a Pythagorean comma, and as close as makes no effective difference to tempering all fifths by 1/12 of the (slightly smaller) syntonic comma. So 1/11 comma meantone is functionally equivalent, and 1/12 Pythagorean comma meantone exactly so.
The luthier Vincenzo Galilei (father of Galileo) was perhaps the first to actually apply an approximate ET12 in instrument building, when he calculated fret spacings based on the ratio 18/17=1.058823529…, a fairly decent rational approximation to 2^(1/12)=1.059463094.
Ears used to the clean major thirds of quarter-comma meantone balked at first: also, 12-TET is not so easy to tune correctly with the naked ear. Despite the common misconception that everybody since Bach used equal temperament, other forms of well-temperament did not leave common practice until well into the 19th Century, but eventually 12-TET did become the Western standard for fixed-pitch instruments. Other well-temperaments have seen a modest revival in the HIP (“historically informed performance”) movement, particularly for harpsichord and organ tunings.
People with relative pitch may claim that in 12-TET, keys lose their “character”. To people with absolute pitch, they still have distinct sounds — though I have often asked myself a “cicken or egg” question here. For example, do I think of D minor as a “pensive, cerebral key” because it sounds like that (to someone with absolute pitch), or because I’ll forever associate it with Bach’s Art of Fugue BWV1080?

How ‘Well-Tempered’ was Bach’s Clavier?

Many people mistakenly assume J. S. Bach invented 12-TET. Of course he did not, nor was he even the first to write a composition exploiting it — that would have been Johann Caspar Fischer . Bach was however the first to write a major cyclical work, of transcendent musical value no less, that absolutely requires some form of well-temperament — and in doing so certainly hastened its adoption.
There is a scholarly consensus nowadays that Bach used not 12-TET but one or more well-temperaments, though it is not clear which. Bradley Lehman, in an article in Early Music, claimed that the ornament of the title page of the Well-Tempered Clavier actually encoded Bach’s own favored well-temperament [ and ], while a harpsichordist has recently argued [] that the temperament was in fact just the tempérament ordinaire described in Diderot’s Encyclopédie.

Equal temperament: blessing or curse?

Paraphrasing Winston Churchill about democracy: 12-TET is the worst possible solution for tuning fixed-pitch instruments…. except for all the others that have been tried.
On modern electronic instruments, when performing tonal music that also goes easy on modulation, one could in principle play in bespoke temperaments for each key. However, 12-TET is at this point so ingrained that people with fine musical hearing may actually consider just intonation or a favorably located well-temperament as ‘off’, even though it is objectively more in tune! Yet, unequal temperaments pop up in the strangest places — such as some guitarists slightly tuning down their B string in order to get just-intoned major thirds.
Allow me to end this post with one of my favorite Bach preludes played in two different temperaments on the same piano: the first time in Young temperament, the second time in modern 12-TET. Enjoy!