The Wonderful World of Enharmonic Spellings
Now that the National Spelling Bee is over for another year I
felt compelled to address one of those odd little topics that makes
life interesting if you’ve been a crazy musician all of your life
and see whether I could take the rest of you along for the ride. If
you’ve been wondering what that B-sharp was doing in your perfectly
nice piece of piano music when they could have used a C-natural and
spared you a little ‘metric conversion’ you’ll soon find out why.
Let’s take a trip through the strange world of enharmonic spellings.
For indeed, as practiced by composers who know what they are doing,
the term 'enharmonics' has everything to do with a kind of musical
spelling.
The concept seems simple enough—the term enharmonic
equivalent means there is more than one way to refer to the
same note. An F natural can also be 'spelled' as an E-sharp. Or a
C-flat could be simply a B-natural--or an A double sharp! Under the
right conditions, namely if your mind is wired that way, you may
enjoy the fact that life sends you another opportunity to escape
from the dull routine of having to refer to the same piano key under
the same name all the time in perpetuity, but then again, and this
probably accounts for the majority of us, you may find it needlessly
confusing. The English language is bad enough with its silent gh and
its p sounds like f when it comes before h and I before e except
after c and on and on until it takes some truly exceptional talents
like the kids at the spelling bee to keep track of all the rules and
show us all how to do it right. What ever happened to an E is an E
is an E, period? Can’t music be the simple language?
It can, and it depends who is using it. In the mists of the past,
there were only seven notes to worry about, A through G. An F was an
F; there was no such thing as an E-sharp. In those days, if you
wanted to 'sharp' something it was a fairly big deal, and wasn’t done
willy-nilly with every note in the system (actually, for a while,
you could only alter the note ‘B’). Gradually, though, things got
more complicated. Although Medieval Music Theory wasn't all that
simple to begin with, the necessity of finding a logical way to
'spell' notes came when different systems began to use the same
notes for different purposes. At first, a G# wasn't really that same
thing as an A-flat--it was actually a different pitch. Then people
began tuning things differently, and pretty soon they were in fact
the same pitch (more or less--more if you have a piano, and less if
you have a non keyboard instrument!) However, that didn't make them
the same in other ways, any more than the words 'to', 'two' and
'too' are the same. They sound the same but function differently.
Enharmonic pitches can be thought of as musical homophones
(they sound the same but look different and mean something different
as well). Basically, making the distinction between two notes that
can have several different spellings requires knowledge about the
musical context, taking into account (1) the overall system in use
(the key), (2) the harmonic grouping within that system, and/or (3)
the function of a particular note with regard to where it came from
and where it is leading. I'm doing my best not to make this sound
terribly complicated, though it obviously takes more than five
minutes to understand, and, since I have a rash passion for
thoroughness, I'm going to take you for a little digression into
'scale creation' to explain the first of those three points: how
understanding the key contributes to whether or not to call
something an f-sharp or a g-flat. This will be followed by a couple
of musical examples to explain the last two points.
Musicians are aware that those seven original
notes are not the same distance apart. While most of them are a
‘whole step’ away from each other, there are two places where the
notes are only half as far apart, between b and c and again between
e and f. On a piano that is easy to see because there are no black
keys in between the white notes in these places. Violinists just
have to imagine it, poor blokes!
(By the way, if you’re wondered what makes notes a certain
distance apart, that has to do with the number of times per second
that the sound produces a wave. The higher notes vibrate faster than
the lower ones. While they’ve all got numbers (the pitch A above
middle c vibrate 440,000 or so times a second, for example) we
musicians can’t handle all that math so we simply measure the
distance between the notes and leave their actual numerical identity
to the piano tuner!)
The fact that those notes are not all at an equal distance apart
has given musicians some interesting ways to go about making music.
For quite a long time in the ancient world, there were a number of
different systems called modes. Basically the way these things
worked is that each mode had its own pattern of half-steps and
whole-steps in different places in its scale. Tunes that used each
mode would sound quite different from one another because the
relationship between the notes, largely based on the unequal
distances between them, would be different for each mode. It is
likely that each town or region had its own mode, and vigorously
opposed the others, until eventually, through trade and war,
musicians became aware of other modes and increased their melodic
vocabulary by trying these wild innovations. By the later centuries
folks like Plato complained that we didn’t need all those modes, and
really ought to confine ourselves to only two.
He got his wish, eventually. Though the modes persisted through
the middle ages (and have actually made quite a comeback in our own
two centuries), musicians after about 1600 settled on just two
patterns for about 300 years: major and minor. You’ve heard of them!
Now if music had simply eliminated those other modes things would
have been easy. Using the white keys alone, one can already play in
major and minor, using exactly one pitch as the starting point for
the system of notes that makes up each key each time: C major and A
minor. The trouble comes in when you want to begin your system on a
different note. Suppose C major isn’t exactly your key. You can’t
reach the high note without making people leave the room. Or the low
note sounds like dry dessert air coming out of your larynx. You’d
like to move things up a note or two.
We can do that. The problem is that we now have to add in those
‘extra’ notes—the piano’s black keys (which, incidentally were white
when they were first introduced; the white notes were black)—those
additional ‘sharps’ and ‘flats’ will help us to preserve the same
pattern of half-steps and whole-steps that we had in the key of C,
now starting on any note we like (including the black keys). Each
major key, for instance, works like this: There are eight notes, and
the distance between each note is a whole step, with the exception
of the distance between the 3rd and 4th note
and the 7th and final note. In C major this is easy. If
you use all the white keys from C to C the distance between the 3rd
and 4th note (E to F) and the 7th and final
note (B to C) is the distance to the very next key on the piano,
with no intervening key of either color in between, the very
definition of a half-step (if you are using a piano!) But for the
key of D you have to make some adjustments to get this same pattern.
Instead of preceeding from C to C, we are moving from D to D, using
every note in between. In order to get the same pattern of notes in
relation to each other (in other words, to make the thing sound like
a major scale) two of the notes have to be ‘sharped’:

Altering those two notes (the ones with the #s in front of them)
means we can sing the standard do-re-mi-fa-sol-la-ti-do the same way
we could beginning on C and it will sound just as nice. Doing the
same thing for the other notes would require more sharps, or flats,
as needed. Now we have a situation were, in trying to simplify
things by reducing them to only one pattern, we’re actually made
them rather complicated, which is pretty much how life is!
It is at this point where, although knowledge of the pattern
should enable one to create any scale for him or herself, without
recourse to an answer key, for purposes of this article we will skip
over the ‘phonics’ method of ‘sounding out’ each scale, and give you
the ‘whole word’ approach, namely, showing you how each major scale
is spelled. Note that there is exactly one of each letter of the
musical alphabet in each scale (besides the top note, which is a repetition
of the bottom). It may be modified by being sharped or flatted, but
it will only exist in one incarnation in any scale:
C major:
c-d-e-f-g-a-b-c
|
C# major / c#-d#-e#-f#-g#-a#-b#c#
D-flat major /
db-eb-f-gb-ab-bb-c-db
|
D major:
d-e-f#-g-a-b-c#-d
|
E-b major:
Eb-f-g-ab-bb-c-d-eb
|
E major:
e-f#-g#-a-b-c#-d#-e
|
F major:
f-g-a-bb-c-d-e-f
|
F# major / f#-g#-a#-b-c#-d#-e#-f#
Gb major /
gb-ab-bb-cb-db-eb-f-gb
|
G major:
g-a-b-c-d-e-f#-g
|
Ab major:
ab-bb-c-db-eb-f-g-ab
|
|
|
|
A major:
a-b-c#-d-e-f#-g#-a
|
B-flat major:
bb-c-d-eb-f-g-a-bb
|
B major / b-c#-d#-e-f#-g#-a#-b
C-flat major /
cb-db-eb-fb-gb-ab-bb-cb
|
While that might seem like a lot of information (and curiously
resemble gene mapping) it is based on a few simple principles, which
is terrific if you enjoy simplifying mounds of data with a few
sweeping rules to illustrate how it all works. Unfortunately,
musician’s minds don’t usually work that way, but here goes anyway:
Each key is a system of notes. No system can have both sharps and
flats in it (if you are wondering why, I'll have to save that for
another time), so custom and logic have chosen one or the other. For
instance, a Gb scale consists only of flatted notes (and one natural
one). This is to make things consistent and predictable. I could
spell the word "spell" five other ways too, you know, (speghl,
spehll, spael, cpewl, ssppel) and by one or another rules of
pronunciation, justify the relation between its written
representation and the way it is supposed to sound, but custom has
agreed on only one. (If you are wondering, the 'gh' is silent in the
first one, as in 'light', the 'c' sounds like 's' in the fourth one,
as in ceiling, etc.) The idea here is to make things simple and
uniform, but the English language has had so many imports from other
languages and difference of opinion from various influential persons
over how to present it on paper, not to mention a long history and
evolution of usage that things have gotten—well, a bit confused.
Relatively speaking, music is much better regulated. Relatively, I
said.
There are a couple of cases where the starting note of the scale
itself can be interpreted enharmonically (i.e., C#/Db, and B/Cb,
which is why I gave two scales on the same line. They are the same
notes, spelled differently) There aren’t as many cases of this as
you would think (only 3, actually). This is because, in order for a
scale to work, it must employ one note of each letter name (and only
one), and, can only have a sharp, a flat, or a natural version of
that letter-named note. Suppose you wanted the re-spell the key of
E-flat as D#. In order to preserve the pattern of whole and half
steps, the scale would be spelled d#-e#-f-double sharp---whooops!
Now as a note f-double sharp is certainly allowed. But in a key
signature, something that sets the rules for which pitches are
altered at the beginning of the piece, some kind soul determined a
while back that double sharps and double flats just weren't welcome.
So we can’t have one of those in there. This key will have to go. It
is just too darned complicated. Sorry. This is probably a
victory for simplicity, or at least, it keeps complexity from
getting totally out of hand. Double flats don’t work in
key-signatures, either (or aren't allowed), though they are
perfectly acceptable out in the wild (i.e., as accidentals). There
are good reasons for having these little miscreants, but they are
sufficiently troublesome that their use has been kept to a dull roar
(though 19th century French composers seem to love them
to death).
And so we are left with the scales listed above. 15 possible
major scales, with their standard spellings. If you are a musician
of any seriousness, it is not really that hard to memorize them. You
will be stuck with them your entire life.
While the concept of taking a note like C and calling it a
D-double flat just because you feel like it seems simple enough
(although I don’t know anybody who would do that since it
unnecessarily complicates things) when you are writing an actual
piece of music you have larger things to consider. This is what
students haven’t grasped when they look at a C-flat in a piece of
music and wonder why the heck it isn’t just a B-natural.
If you are in the key of G-flat, for instance, the note C-flat
belongs to the key, but the note B does not. Intentionally writing a
B in place of a C-flat tells a musician who knows something about
theory that we are probably not being governed by the rules of the
key of G-flat major at the moment. Maybe we’ve left Kansas
altogether, or we’re just on a temporary vacation, but one way or
another it’s news. If the composer intends to ‘go someplace else’
this is perfectly justifiable, but it not, they’ve just given out
false information! Even a musician who doesn’t know anything about
theory will probably find things more confusing if the composer
‘spells’ the notes wrong, since, in a lot of cases, things will look
more complicated on the page.
Except that sometimes they don’t. In cases where an f-double
sharp is required as the leading tone to a G-sharp minor
chord, or some other difficult bit of musical spelling, students who
aren’t familiar with how the system works tend to get a little upset
because they are not thinking within the system in use by the
composer (the key) but only of the limited vocabulary they know
(which does not include things like f-double sharp!). Why do things
get so complicated?
As I’ve tried to indicate, if you understand the way spelling
rules operate in music you will actually find correctly spelled
notes a blessing, even in cases where you have to read things like
f-flat and g-double sharp, because the logic of the system actually
makes it easier to understand that way, but since ‘musical grammar’
is so little known even among practicing musicians, concepts like
these get lost on most of us.
But if you’ve made it this far into the article, I want to leave
you with a couple of musical examples.
The first is from a Mr. Frederic Chopin, whose harmonic
progressions are often quite arresting, and original, and not
obvious. But Fred knew what he had in mind, and he knew how to spell
what he put on paper to make that clear. The little Mazurka (a type
of Polish dance) from which I’m about to quote includes several
B-double flats in them in the strain before the one you’re going to
see. They lead, quite appropriately to A-flats in each case, in the
key of Db, which has need of them. Generally speaking, a double flat
will always lead down to the next note, and a double sharp will lead
up. Since neither is part of the key itself (and not included in the
scale) the context is rather important to those little devils. They
don’t want to be wrong.
But the place I have in mind is a little transition away from the
key of Db back to the key in which he started the piece, f minor.
Now Chopin gets us there smoothly by changing only one note, then
another, and slowly coaxing us into a new harmonic world with
minimal shake-up. In the first of the four measures below is a
D-flat chord. All of its notes are accounted for in the key
signature, so we don’t need any accidentals.

Next he is going to change it to a D-flat minor chord. This
usually causes our spirits to depress a little, but with Chopin you
have to enjoy a little melancholy. A D-flat minor chord happens to
have an f-flat in it, not an E natural, for just as scales have a
standard spelling, so do the chords that come from the scales. Even
though the key of f minor (scale: f, g, ab, bb, c, d, e, f,
melodically speaking) has an E in it, and not an F - flat, the chord
Chopin is using (Db minor), and the key he has not quite left yet ,
requires him to make it a F - flat. As it happens, reading those
notes in the context of the key he is in, I find it much easier with
an F - flat in it, because my mind can quickly realize that I am
looking at a D-flat minor harmony, and instead of four apparently
disconnected individual notes, they all belong to one group. If he'd
put an E in there, I would have to figure out how that fit in with
the rest of the notes and it would take a little more brain function
just to get over the discomfort.
However, in the next bar, Chopin shows us that is he going back
to f minor by changing that one note from an F - flat to an E
natural. You won’t hear anything change regarding that
note. It is the same lever on the piano. But now we are to think of
it differently. You see, the bass note has also changed. It is now a
C instead of a D-flat. This means we are now on a C-chord, and
that is spelled with an E in it, not an F - flat, thank heaven.
E also happens to be the 7th tone of the f minor scale,
commonly known as the leading tone, since it is there to lead us up
to the F, which is what we are getting ready for in the measure that
follows this example. The harmony in the third measure is a little
confusing anyway, because Chopin leaves the A-flat in for one more
measure. It is there to keep up the tension, and is known as a
suspension. Since the A-flat relates to what came before, and
the E relates to what is coming up, there is a mixture of different
spellings in this measure, but nothing we can't handle!
Incidentally, that 'suspension' belongs to a family of items known
as 'non-harmonic' tones (not belonging to the current chord) and one
of its cousins, the 'appoggiatura' (or leaning tone) was the winning
word at the National Spelling Bee a few years ago. (no kidding!)
At last we are ready for F - minor, and if your page turner
doesn’t get the page turned fast enough you can guess at it anyway,
for the way Chopin has spelled his notes gives us enough of a clue
as to what is happening musically that a literate musician knows and
can predict what is likely to happen next.
If you’re feeling somewhat dizzy now, take heart. For every
person whose mind loves the harmonia that comes from a system
of organization that accounts meticulously for every detail, and
which prescribes the correct choice of expression for each member of
the group, there are some who are not that interested, and they
usually include in their number some persons who are famous, and
even known for their intellect. The prospect of having a smart,
respected person tell us that we should all give our brains a break
is a real treat for those of us whose brains bruise easily.
My exemplar of such a stance was an outsider, not trained at a
conservatory, and with little patience for those who were. Erik
Satie liked to flaunt rules and customs, but it didn’t always result
in a greater simplicity, even for people who think a C is always
easier to read than a B#, no matter what the context. Satie’s idea
of musical spelling included a little sarcasm which caused him to
take a simplicity like a C chord and make a monstrously complex
thing out of it:
A C-Major chord the way it is
normally spelled: |
A C-Major chord the way Erik Satie might spell it: |
 |
 |
It takes a little computation to realize that the chord on the
left and the chord on the right sound the same. As for the second
one, not only does it not make sense in any likely musical context
(and Satie would have made sure it didn’t) but it makes reading a
simple chord progression exceedingly difficult. So difficult that
one of his most famous pieces defies memorization by the most
learned musicians. The oft-repeated observation of those who have
played the composer’s Vexations, a short work that is repeated 840
times for upwards of 24 hours, is that even after playing the work
through hundreds of times, nobody can memorize the piece. Nor can
the musician ever get comfortable with it, since the strangely
spelled harmonies require constant concentration to ‘translate’ them
into more comprehensible patterns. Sometimes the same chord is
spelled three different ways to facilitate this abstraction.
Satie wasn’t doing this through ignorance, though the results
might have been somewhat similar if he had been (with the exception
of his imaginatively spelled C chord, surely!). Probably he was
poking fun at what he thought was a stuffy and arcane bunch of
rules, and, considering the double-sharp- and double-flat-happy
culture that surrounded him, it is not hard to feel sympathy for his
position.
The results, however are of a different order entirely. They even
manage to do for this professional musician, schooled in the most
difficult classical repertoire, what the very idea of enharmonic
spellings does for musicians who have not become acquainted with the
concept or learned to understand it, when confronted with an example
like Chopin’s, or innumerable others which feature B#s or A-double
flats on the basis of correct theory or spelling—it gives me a
headache!