hey, welcome to 12tone! you know that Bach piece? the one that goes (bang) if you've
ever taken piano lessons, or lived with someone taking piano lessons, or just been near a
piano in a public space, you've probably heard it hundreds of times, but there's a pretty
good chance you've never heard it played correctly. and I don't just mean the people playing it
weren't very good.
I don't know that.
I don't know your life.
but even if you've heard it played by some truly incredible pianists, it's likely that,
at a deep, fundamental level, what they were trying to play wasn't what Bach wrote.
why?
let's go back in time.
(tick, tick, tick, tick, tock)
this video is sponsored by CuriosityStream!
ok, so let's start with a little history.
that piece is the beginning of the Prelude in C major from book 1 of Bach's Well-Tempered
Clavier, written in 1722. in the Well-Tempered Clavier, Bach challenged himself to write
a prelude and a fugue in every key, both major and minor, for 24 total pairs.
20 years later, in 1742, he decided to do it again.
together, these two collections are among the most significant of Bach's surviving works,
and they remain an important part of the classical piano repertoire to this day.
this is especially true for the Prelude In C, whose simple arpeggio structure has made
it one of the most popular instruction pieces for new piano students.
because we're so used to hearing these pieces performed by modern musicians, on modern instruments,
it's easy to assume that's how they've always sounded, but in the words of L.P. Hartley,
“The past is a foreign country; they do things differently there.”
music has changed a lot in the roughly 300 years since Bach wrote his first Clavier,
and many of those changes make it hard for modern audiences to experience or even imagine
the pieces as they would have been played at the time.
for starters, you've most likely heard it played on a piano, but when Bach wrote Book
1, he'd probably never even seen a piano.
I mean, they did exist, sort of: the fortepiano, an early model, was developed around the turn
of the 18th century by Florentine instrument-maker Bartolomeo Christofori.
unlike other contemporary keyboard instruments like the harpsichord, the fortepiano worked
not by plucking the strings, but by striking them with a little hammer. this allowed the
instrument to respond to the performer's touch, playing notes louder or softer depending on
how hard they struck the keys. in fact, the name fortepiano literally translates to loud-soft,
to emphasize the instrument's dynamic range.
but while Christofori's invention was decades old by the time Bach wrote the Clavier, it
wasn't very popular, and its use was mostly confined to Italy.
it wouldn't be introduced to German-speaking countries until about a decade later by another
instrument-maker, Gottfried Silbermann, and when it was, it was criticized for its weak
sound and heavy touch by none other than Johann Sebastian Bach. the piano wouldn't really
come into its own until the late 18th and early 19th century, so, yeah, he probably
wasn't writing with that instrument in mind.
that said, I'm not sure this is a huge deal.
technically speaking, the name "Clavier" simply means keyboard, and could apply to any keyed
instrument.
historically speaking, it seems likely he was thinking of the harpsichord, but by calling
for simply a clavier, he left the door open for things like the clavichord and even the
organ.
besides, instruments were still exclusively handmade, so they weren't standardized in
the way modern production practices require.
even if he did specifically mean harpsichords, he would have been aware of many different
kinds of harpsichords, with different ranges, actions, and designs.
at the time, it was common to compose keyboard music in such a way that it would work perfectly
well on whatever instrument it happened to be played on, so while he almost certainly
never considered playing it on a piano, especially not a modern one, there's not a lot of evidence
that suggests he would have minded it.
modern performances also mostly play it in the wrong key.
these days, most Western instruments are tuned pretty much the same way.
we pick a note, called concert A, and just define that as 440 hertz, or cycles per second,
then tune the rest of the notes to match.
if you go to your piano and play the A above middle C, you should hear exactly that frequency,
and if you don't, it's probably out of tune.
but as we go back in time, we see two trends: first, concert A gets lower, and second, it
becomes less standardized.
there simply wasn't a need to coordinate tunings across different communities, so people didn't.
before the 18th century, for church music, most musicians simply tuned their instruments
to align with whatever the local pipe organ did, because it's really hard to retune a
pipe organ, and even outside the church, music didn't tend to travel very far, so it didn't
really matter if your German harpsichord would sound in harmony with some British bard's
lute. you were never gonna hear them together.
so how did Bach tune his concert A?
well, it's hard to say.
we don't have a direct record.
the best we've got is that in 1880, musicologist Alexander Ellis did a detailed survey of various
tunings across Europe, including working out that Mozart's concert A was most likely 421.6
hertz.
unfortunately, he didn't get a similar reference for Bach, but we can make some educated guesses.
Book 1 of the Clavier was written while Bach was working in Köthen in 1722, and while
Ellis doesn't have any reference pitch for Köthen, he does have one from an organ in
Dresden, Germany, about a hundred miles away, also in 1722.
that organ had a concert A of 415.5 hertz, almost exactly a modern G#, so if you really
want to hear what Bach's Prelude In C would've sounded like to him, it might be better to
play it in B. maybe.
again, it's hard to say with certainty, but that's probably about the right range.
unless you have perfect pitch, though, this is unlikely to matter.
the more relevant difference, and the one this video is actually about, is the tuning
system.
these days, any piano you've ever heard is probably using a system called equal temperament,
which means that every half-step is the exact same size.
this allows for easy transitions between different keys, and considering Bach's Clavier uses
every key, it was assumed for a long time that this was the system he intended.
the point was to show the equivalence of the various keys in equal temperament.
this theory was supported by 19th century musicologists like Philip Spitta, and it makes
sense: it wasn't the most popular system in Bach's time, but equal temperament was a thing.
musicians were talking about it, and he was probably aware of those discussions.
but while some modern scholars still support it, others no longer believe this was Bach's
intent.
after all, he didn't call it the Equal-Tempered Clavier, he called it the Well-Tempered Clavier,
and well temperament was a thing too.
now, it wouldn't be accurate to call well temperament a tuning system: it's more like
a family of systems, all built on a shared philosophy of compromise.
they allowed composers to write and play in all 12 keys like equal temperament did, but
with more respect for just intonation.
just intonation was a popular idea in baroque-era European music that claimed the ideal sound
for any given interval was a specific, simple frequency ratio.
each interval has one or, in some cases, multiple defined ratios, but for our purposes we only
really care about the octave, which is a 1:2 ratio, the perfect 5th, with 2:3, and the
major 3rd, or 4:5. these are the three primary intervals in Western music, but unfortunately
they don't play nicely together: you can't build any of these three intervals just by
using the other two, so a tuning system can only consistently use one of them.
musicians in Europe pretty universally agreed that the octave was the most important, so
they were left with the problem of how to make the 3rds and 5ths as good as possible.
the most common solution in Bach's day was meantone tuning, which made all its fifths
slightly flat.
not enough to sound out of tune, but enough to give you a bunch of nice, pure major 3rds.
those smaller fifths don't quite wrap around to make an octave, though, so in order to
make the system work, you have to include what's called a wolf fifth.
this is one fifth that's sharp enough to compensate for all the flatness of the other 11.
it sounds nasty, but you can just hide it between two notes that weren't likely to be
played together, most often G# and Eb. this meant that meantone instruments were locked
into a couple specific keys: you could wander a little in either direction, but if you went
too far you'd run into the wolf.
well-tempered systems, on the other hand, used careful arrangements of pure, flat, and
occasionally even sharp 5ths in order to balance the detuning of the intervals across the entire
spectrum of notes, so that no particular 3rd or 5th sounded wildly wrong.
this allowed for instruments that could play in every key, but importantly, each key was
different.
in 1784, composer Christian Schubart wrote a book on musical aesthetics in which he described
the emotional colors of the various keys.
G major was rustic and idyllic, B minor was the key of patience, and most famously, D
minor was said to represent melancholy womanliness.
...yeah.
now, these characteristics aren't just about the tuning: the keys also had specific cultural
and historical connotations that informed Schubart and others' interpretations of them.
for instance, you'd probably recognize the claim that D minor is the saddest key, even
though in equal temperament, that doesn't actually mean anything.
but the point is that, to Bach, the idea that different keys had their own unique characters,
informed in part by specific interval structures derived from their tunings, would probably
have been a familiar one, and it likely informed his composition of the Clavier.
so which specific well-tempered system did Bach use? the short answer is… we don't
know.
if he wrote it down, it's been lost.
more likely, though, the answer simply seemed obvious to him and he didn't feel the need
to specify, much like modern composers don't specify when their work is intended to be
played in equal temperament.
it's just not necessary.
some scholars theorize that he probably intended to use some kind of Werckmeister tuning, a
family of systems proposed by Andreas Werckmeister.
the most common of these, called Werckmeister I, uses four slightly flat fifths, placed
between C and G, G and D, D and A, and B and F#. the rest are pure. this does a pretty
good job of spreading out the detuning, but it still has some extremely sharp 3rds, like
the one from F# to A#, so there's a couple keys that don't sound great.
there's a more advanced system, called Werckmeister III, which uses five flat fifths and then
a sharp fifth, resulting in only one bad 3rd, which is also a possible candidate.
these tunings were fairly well-known in Germany at the time, so it would make sense if this
is what he meant.
many of the other common well-temperaments, like Valloti and Kirnberger, came out too
late to be real candidates for Bach's use, but there is still another possibility: he
simply invented his own tuning system.
in fact, we have good reason to believe this might be the case: Johann Forkel, who wrote
the first biography of Bach in the late 18th century, claimed "Nobody could install the
quill-plectrums of his harpsichord to his satisfaction; he always did it himself.
He also tuned both his harpsichord and his clavichord himself, and was so practiced in
the operation that it never cost him above a quarter of an hour."
so clearly, Bach cared deeply about the precise tuning of his instruments, and wasn't happy
with how other people did it.
but does that mean he invented a whole new system, or was he just really picky?
it's impossible to say for sure, but if he did invent a system, he may have left us a
clue. on the original cover page of the Well-Tempered Clavier, Bach hand-drew a doodle that looked
something like this, and music theorist Bradley Lehman argues that this is the key to unlocking
the mystery of his tuning system.
this requires a bit of decoding, so to start with, let's flip it upside-down.
great.
now, let's assume each of these loops represents a perfect 5th. this first one is F to C, then
C to G, G to D, and so on.
if we can use the doodle to work out the size of each of these 5ths, we'll have enough information
to tune our clavier, and while it may not be immediately obvious, there does seem to
be a way to do that.
we'll start at the left.
this first loop has a double-loop inside it, which we're going to interpret as meaning
a slightly flat fifth.
specifically, it's lowered by one sixth of a pythagorean comma, which…
ok, quick aside about commas.
remember how I said you can't make any of our primary intervals out of the other ones?
well, commas are how we measure that.
basically, if you go up 12 perfect 5ths, then down 7 octaves, you'd expect to wind up right
back where you started, but in just intonation, you don't.
you wind up about a quarter of a half-step sharp.
that small difference between those two distances is the pythagorean comma, and it's the thing
we're trying to remove by tempering out our intervals.
it's why all this tuning stuff is so difficult in the first place.
in order to get our system to work, we have to successfully hide the entire pythagorean
comma without creating any obvious wolf intervals.
that's the challenge.
anyway, the first five fifths all have this same double-loop notation, giving us most
of the C major scale, and we've already hidden five sixths of our comma.
so far so good.
when we go from E to B, though, the loop is empty, which means no deformation at all.
this is a pure, just 2:3 ratio.
we can't do too many of those in a row, though, because of our other main problem, the syntonic
comma. this is like the pythagorean one, but instead of being about the relationship between
5ths and octaves, it's between 5ths and 3rds. if we stack four 5ths in a row, then drop
down two octaves, we're supposed to get a major 3rd, but in practice it's really sharp,
so we always want to get at least some flatness in any run of four 5ths to smooth it out.
as such, Bach only does three empty loops, then the last three each have a single smaller
loop inside.
what does that mean?
well, if empty means pure and a double-loop means 1/6th of a comma, then it seems reasonable
to assume that a single loop is half that, for 1/12th, which as it turns out is exactly
the 5th we use in equal temperament. this leaves us with a little extra flatness at
the end.
we've hidden our entire comma and then some. to compensate, the final 5th, from Bb back
to F at the start of our diagram, is a little sharp, but not so sharp that it feels like
a wolf.
it may seem fairly technical, but this system wouldn't be too difficult to tune by ear,
and it sounds pretty good.
Lehman has uploaded a couple videos of him playing pieces from the Clavier in this tuning,
link in the description, and they definitely work.
there's no wolf intervals, no wildly sharp 3rds, nothing that would inhibit the performance
of music in all 12 keys.
but just because it's pretty doesn't mean it's what he did. and that's important to
keep in mind: Lehman's model is great in theory, but it's not supported by all that much direct
evidence.
David Schulenberg points out that, if the doodles were meant to communicate important
information about the intended tuning, Bach likely would've told his students, and yet,
in their reproductions of the Clavier, the loops are often drawn differently, if they
bother including them at all.
so while it's a compelling theory, it remains just that: a theory.
that doesn't mean it's wrong, but we also shouldn't assume it's right.
and that's the trouble with history: there's never as much evidence as we'd like.
but does that matter?
why should you care? should you care?
well, that depends what you're trying to do.
if you're a new piano student trying to work out the fingerings for the Prelude In C, then
no, none of this matters.
just keep doing what you're doing.
if you're a casual listener, it may not be relevant either: artistic intent isn't the
end-all of musical experience.
there's nothing wrong with enjoying modern takes on the Clavier.
Bach's dead.
he doesn't care.
but if you're trying to understand the music and culture of the Baroque period, or just
expand your understanding of how music is allowed to work, then these questions of historically-informed
performance become incredibly relevant.
playing it on an equal-tempered piano just 'cause it's the easiest thing to do is missing
the point.
you're giving up all sorts of historical context by not engaging with the complexities of Bach's
musical world, and your understanding of what's going on in the piece will suffer for it.
you'll lose sight of the nuances that informed his decisions.
maybe he wanted Werckmeister tuning.
maybe he had his own system, communicated through cryptic doodles.
maybe he just meant standard meantone and some of the pieces were supposed to sound
like s***. or maybe he did mean equal temperament after all: some theorists do consider it a
member of the well-tempered family.
it could even be a combination of those: remember, the two books of the Clavier were written
20 years apart.
his preferred system could easily have changed in that time.
each of these possibilities implies different things about the work and his approach to
it, and we can try to work out which one is most likely based on other choices he made,
but until we can go back in time and ask him, we'll never know for sure.
it's a mystery, and it probably always will be.
but that's ok. the answer is just an answer.
the fun part is asking the questions.
as it turns out, asking questions about music is also the entire point of my podcast, Ghost
Notes! did I mention I have a podcast?
well, I do.
it's a collaboration with Noah from Polyphonic, who knows way more about music than I do,
and each episode we try to get to the bottom of some big music question.
we just released an episode about what makes a good singer, which long-time viewers will
know is actually the thing I have a degree in.
we also have a guest episode with Alex the LowSpecGamer coming out in a couple weeks,
and if you want to hear it as soon as it's released, you should really check out Nebula.
Nebula is a streaming platform built by some of YouTube's top educators, including Adam
Neely, TierZoo, Marques Brownlee, and Extra Credits.
Nebula produces lots of awesome Original content, including Ghost Notes, so new episodes are
exclusively available there.
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again, link in the description.
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