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!