Why do we start with pitch and notes? Because there is a strong
argument that it was where music started, at least historically, in the
West. Admittedly, the case could be made for the origins of music in rhythm, though,
and I wouldn't want to get into that argument, so we will deal with that
next. We have to start somewhere.
1
Some lower ranges, down to 4 Hz, can be felt rather than heard. We do
not generally perceive them as notes. Nor are the extremely high ranges
so perceived, although both may be part of the ambience of an otherwise
musical piece.
2
It is the relative positioning that makes us hear groups of them as a
melody. Modern English speaking music culture generally recognizes 440
Hz as the standard a out from which the rest of the notes are measured,
but this has not always been true, and is not universally recognized
today (The rest of Europe is a little higher, for example). But even if
a = 400, as long as the relative relationship of the notes is more or
less stable, most people do not notice the difference, and virtually all
would still consider it music. See my discussion in the
Waveforms and Harmony
page.
3
Occasionally, you will see a keyboard with different colors, or with the
black and white reversed. It is the layout of the keys, not the colors,
that makes it a standard keyboard.
Pitch just means sound waves that are isolated enough and stable enough
that we can identify a dominant wave form. Since it is a subcategory of
sound, it is also audible. We cannot know whether animals perceive music
as music (we can know they hear it), we must include
only what is audible to humans. This further limits us to the range between
20 Hz (12 in laboratory conditions) and 20 kHz, but the more extreme
ranges are rarely perceived as musical.1 All of this is
obviously on a continuum, and some music makes use of that, but as a
whole we subdivide the total into standard divisions (which vary by
culture) that we call 'notes.' In the West this stabilized at 12
subdivisions of the octave.2
Other cultures have other divisions, and other senses of what is
harmonic, but it is not the purpose of these pages to
analyze all music theories worldwide.
Piano keyboard octave with note names
At the right is a single octave on the piano. You will notice that there
are seven notes bearing a single letter (i.e. without
♯ or ♭ signs. They are lettered
a–g, although convention has them start on
c, go to g, and then start over at a.
This is one version of a seven note subset of the full 12 note
collection. The black keys are the other five, bringing us to 12. The
black keys receive their names relative to the adjacent white keys,
3 so each has two names one from the key to the left (making it
x♯), and the other from the key to the right (making
it y♭). Of course, the note to the right of the
b in this image would be another c.
4
By 'full' piano keyboard, I mean a standard sized piano. Many electric
pianos have only 77 keys, and some have less than that.
The full piano keyboard has 88 keys=notes4 and has become the
range that sets the standard for most western music. We name the octaves
in sets from c to b based on the piano range.
Piano keyboard with octave labels
The bottom notes would be a0–b0; the d above
middle c is d4, and so forth. The organ can go lower than the piano
as well as higher; obviously electronic instruments can produce notes well out of
this range—they can keep going in both directions beyond the range of human
hearing. Those notes are represented in the same way (sometimes even outside of the human hearing
range).
There are no sharps and flats, which is why it is all white keys. The
major scale is the one you hear most often in Western music, and
particularly in modern pop music. The scale steps themselves are
numbered. In the case of C major, c can be called
1, but is usually just named the root or the
tonic. The 2, or the second, is d, e
is 3 or the third, and so forth up to the next c,
which is both 8 (the octave) for this scale and the root for
the next one. Note that I try to use italics when I use numbers for
scale steps. I also try to use lower case for notes and upper case for
scales (and chords, on a later page).
If you look at the piano again, you should notice something right away.
Not all white keys have black keys between them. When there is a black
key between the whites, the distance between the two white-key notes is
called a whole step. When there is no black key that
interval is called a half step. An 'interval' is the
distance between any two notes, not just notes that happen to be next to
each other. Since the white keys together make up a major scale you can
observe that the third and fourth notes are a half step apart, and so
are the seventh and eighth (the octave). All others are a whole step
apart.
White keys starting from G
If the audio button is screwed up, try the MIDI
This is the pattern for all major scales. Try starting on g
and playing only white notes. What you notice (particularly if you play
it) is that the interval between the seventh and the octave is a whole
step, so it doesn't sound like a major scale (not necessarily a bad
scale, just not major). In order to fix this, when you are playing the
G scale, you have to add an accidental (sharp or
flat-in—this case, a sharp). If, instead of playing the
f♮ (natural=white key) you instead play
f♯ the scale will sound right. This is what the
G major scale looks like:
G major scale
If the audio button is screwed up, try the MIDI
In fact, each key (scale based on some tonic) has a different set of
sharps or flats (but not both, as we will see) to make its major scale.
D has two sharps (f♯ &
c♯), A has three (d♯,
c♯ & g♯), etc. Do you see a pattern?
Each time I added a key, it included all the sharps from the previous
key and added one more. In fact, the extra sharp was always on the
seventh of the new key. This is a consistent pattern, but
the trick is to remember the order in which the keys get added (you
probably noticed that they were not alphabetical). That happens to be
(starting with 0 sharps) C, G, D,
A, E, B, F♯, &
C♯. I don't know of a good mnemonic for that; e-mail
me if you do, or think of one. There is a nice mnemonic for the order of
the sharps as they get added, though: Father
Charles Goes Down
And Ends Battle. If
that does not seem all that cool to you, you may change your mind when
we talk about the flat keys, which will be right now.
OK, you probably noticed that didn't cover all the keys. Noticeably
missing was every guitarist's nightmare key (which, ironically, seems to
be every pianist's favorite), E♭. I am sure you
thought of several others. So, going in the other direction the order of
flat keys is F, B♭, E♭,
A♭, D♭, G♭, &
C♭. Only F does not have a flat tonic. What
makes it a flat key is that it is created by adding one flat to the scale—b
becomes b♭. After that they pile up like the sharps,
except they add the fourth of the key each time rather than the seventh.
So, B♭ has two flats (b♭, &
e♭), E♭ flat has three
(b♭, e♭, and a♭)
and so forth. The order of the flats as they get added has the mnemonic
Battle Ends And
Down Goes Charles'
Father. You probably noticed that this is the last
mnemonic backwards. Conveniently, it makes a (sort of) sentence in
either direction.
As an aside at this point, did you see that when the accidental appears
with a letter, it is written after. If it is with a note on a score, it
is written before. As we will see later, when notes (or chords) are
written as numbers and require accidentals, the accidental usually, as with
score notes, precedes the number (although I have seen it both ways).
If you start on (the key of) G♭ and go backwards
through the flats until you hit C (0 flats/sharps), then
continue going forward through the sharps until you hit
F♯, you will have circled through every possible major
key with each step moving you to the fifth of the previous key. This is
called the circle of fifths. Diagrammatically, it appears this
way:6
Note that C (the relative major) begins on the third step of
the Am scale, and the reverse is that Am (the
relative minor) begins on the sixth step of the C scale (=down
a third). This is a consistent pattern for all relative majors and
minors. You probably also noticed that what I called Am is
simply called 'a' (lower case) in the chart. This is a common
variation which you will see in some theoretical analyses of music for
scales, chords, and intervals.9
A common feature of melodies in western music is use of what is called
the leading tone. This is always the half step before the tonic, and
gets its name from the fact that it creates some tension, or at least a
feeling of incompleteness. The listener usually wants it to resolve that
tension by moving to the tonic, so it is said to 'lead' the listener
back to the beginning. That note is a normal part of a major key, but in
the natural minor scale the seventh is a full step below the tonic, so
the scale lacks a leading tone. To address this, there are two
modifications to the minor scale that are often made. The first is
called the harmonic minor scale. It solves the problem with the brute
force method, just adjusting the seventh up a half step:
10
Not authentic Oriental (i.e. South or East Asian), but it is the sound that
Western composers have used to create that impression among Western
listeners.
A harmonic minor scale
If the audio button is screwed up, try the MIDI
This provides a leading tone, but gives the scale a sort of Oriental
feel10 that comes from the fact that you no longer have a
smooth transition between the sixth and seventh steps (it now jumps up
three half steps, rather than the normal one or two, between
notes). Still it works for chords: with this scale you get to play an
E (major) chord as part of an Am key. Lady Gaga
uses a lot of this in "
The other approach is to keep the melody smoother by raising the sixth
step as well when the melody is moving up towards the tonic, but have
the scale revert to the natural minor when it is moving down (since in
those circumstances a leading tone is not needed). This is the approach
taken in the melodic minor scale:
A melodic minor scale
If the audio button is screwed up, try the MIDI
All these minor keys, of course, work the same way as the major keys in
the sense that distribution of whole and half steps are consistent
across keys.
13
Heinrich Glarean coined the term 'Hyperaeolian' ('above Aeolian') for
this scale in his Dodecachordon (1547), and wrote, or
commissioned, a couple pieces to demonstrate it, but even then he did
not include it in his larger system.
You may have noticed that there was one missing. What do you get if you
start and end on b using only white keys? The simple reason is that this
mode was not used in the medieval period. The root chord is built on a
tritone, which was dissonant to their ears.13 The Greeks had
used a mode they named 'Locrian,' so in the 19th c.
that term was adopted to cover this 'mode.' It has been used
occasionally, and sometimes serves as a backbone for modern lead riffs.
Like the other modes, it is obviously transposable.
C Locrian mode
If the audio button is screwed up, try the MIDI
The trick with modes is to be able to hear the proper resolution. We are
so programmed to hear the majors and minors that the modes often don't
feel right. But some, like the Dorian, have undergone a revival in
pop.
14
By 'atonal' I mean music that tends to shy away from what most people in
the West have come to regard as harmonious: a sort of musical version of
the same experimentation that lead to abstract expressionism in the
graphic arts.
15
'Diatonic' (lit. through the notes) is a term for music based on the seven
note scales I have been talking about, and usually specifically major or
minor.
Other scales are possible, and I may get around to doing a page on them,
but 20th c. academic music (which some people call 'serious' music,
others 'modern classical') was often dominated by the chromatic scale.
This scale consists of all twelve notes. It is obviously an important
part of atonal music,14 but in tonal music chromatic
embellishments are still frequently used in and around
diatonic15 scales to add interest.
Moving in the opposite direction, popular music, lead parts in
particular, have a strong tendency to reduce the scale to a five note
subset called the pentatonic scale. With some variation this is also
called the 'blues scale.' These scales are important enough that I will
reserve them for a fuller discussion later.
Intervals
Intervals between notes are categorized in a way similar to the way we
described the position of a note in the scale. They are classified by
distance. A note that is two scale steps away from some other
note (regardless of whether those were half steps or whole) is said to
be a third away. When the melody jumps up from the lower of these two
notes to the higher we say it has moved up a third, if the other
direction that would, sort of obviously, it would be called 'down a
third.' The idea is that if you count the first note as one and move
through all the scale notes to the second note (counting as you go) you
will be on three when you get there. Similarly, if you count scale steps
to five, the interval between the first and last notes is said to be a
fifth.
You quickly discover, though, that not all intervals of the same numeric
size sound the same (a to c is a third, but so is
a to c♯). Four of the intervals
(2nds, 3rds, 6ths, & 7ths)
are said to have minor and major versions. In all four cases the
relation between minor and major is the same: the major is one half step
higher than the minor. As it happens, all but the second correspond to
the major and minor keys. A major key contains the major third, sixth
and seventh; the minor key contains minor versions of all three. Neither
contains a minor second; among the modes, only the Phrygian mode does.
In point of fact, using this method, the Phrygian appears to be a more
natural minor key than the Aeolian.
Minor second:
If the audio button is screwed up, try the MIDI Major second:
If the audio button is screwed up, try the MIDI Minor third:
If the audio button is screwed up, try the MIDI Major third:
If the audio button is screwed up, try the MIDI Perfect fourth:
If the audio button is screwed up, try the MIDI Tritone:*
If the audio button is screwed up, try the MIDI Perfect fifth:
If the audio button is screwed up, try the MIDI Minor sixth:
If the audio button is screwed up, try the MIDI Major sixth:
If the audio button is screwed up, try the MIDI Minor seventh:
If the audio button is screwed up, try the MIDI Major seventh:
If the audio button is screwed up, try the MIDI Perfect Octave:
If the audio button is screwed up, try the MIDI
In these intervals, it is the first two of every three note set that represents the interval in
question. The interval between the second and third notes is the inverse, discussed below (under
"Interval inversion").
The fourth and fifth are called 'perfect' intervals (there is no minor
or major fifth). The note in between them, sometimes called the
tritone, is considered either a diminished fifth
(5) or an augmented fourth
(4).
16
Outside of the equal tempered scale, f♯ &
g♭ are not identical. There is a barely audible, but
real, difference between the notes in the Pythagorean scale, for
example.
Other intervals can be said to be diminished or augmented when they move
into the space of another note. A diminished second is the same as a
unison (two instances of the same note); an augmented third is the same
as a fourth. They may have different theoretical functions, but in equal
tempered scale, they are the same pitch. Any time you have two notes (or
scales) that are functionally the same but have different names, we call
them enharmonic equivalents (e.g., f♯ &
g♭).16
By the way, the scale steps have names. We have already seen that the
root can be called the tonic. Here are the rest.
Second
Supertonic
Third
Mediant
Fourth
Subdominant
Fifth
Dominant
Sixth
Submediant
Seventh
Subtonic
Eighth
Octave
Most modern theoreticians will add leading tone to this list
for the major seventh, and will also call the minor seventh the
subdominant (also known as the dominant seventh).
These are useful terms, and as you know, I have already made use of the
term 'leading tone,' but it is not originally part of this system, as
the lack of a Latin name may suggest (this distinction in theory dates
from the early 20th century). It also upsets the consistency of
major-minor inversions discussed two paragraph hence.
These terms do not at all contribute to your understanding of music
theory, but they are standards in music lingo. If you are not familiar
with them, you may be confident that you will be embarrassed at some
point.
Interval inversion and compounds
17
Unless you want to call the octave the inverse of the unison.
Every interval in the chromatic scale (and any of the scales we have talked about) has an
inverse, with the exception of unison (same note).17 Up a second always gets you to
the same note as down a seventh, except that the latter is an
octave lower. Up a third is the same note as down a sixth. In both these
cases, the major-minor aspect must be reversed. Up a major third, for
example, is the same as down a minor sixth. And the reverse is true.
This principle holds for seconds and sixths as well. This is, to some
extent, reflected in the names in the last table. The mediant inverts
the submediant; the supertonic inverts the subtonic, etc.
Patterns of intervals:
minor 2nd inverts to major 7th
major 2nd inverts to minor 7th
minor 3rd inverts to major 6th
major 3rd inverts to minor 6th
perfect 4th inverts to perfect 5th
tritone inverts to tritone *(augmented forth inverts to the diminished fifth). See the next paragraph.
perfect 5th inverts to perfect 4th
minor 6th inverts to major 3rd
major 6th inverts to minor 3rd
minor 7th inverts to major 2nd
major 7th inverts to minor 2nd
The two 'perfect' notes, the dominant and the subdominant (fifth and
fourth) have the same relationship, without the major/minor
qualification. The tritone, like the tonic, always inverts to itself,
although I suppose some theoretical purists would insist that the
diminished fifth must invert to the augmented fourth (its enharmonic
equivalent).
Compound intervals are intervals greater than an octave. The
relationship to the in-octave intervals we have talked about so far is
that you need to add seven to the one to get the other. Using this
method, an octave + a second is called a ninth; an octave + a fifth is a
twelfth, etc.
Intervals and scale steps
Do not confuse intervals and scale steps. They are similar concepts, but
the first describes the distance between any two notes, while the second
describes the function of any given note in the scale. The latter
happens to be the same as the distance between the next lower tonic and
the note in question, but they are nevertheless fundamentally different
concepts.
18
By the way, if you are trying to be able to hear, or sing, intervals,
the first two notes of "My Bonnie" are an excellent example of a major
sixth—one of the more difficult intervals to just get in your head when
you are first starting.
This first phrase from the Scottish folk-tune "My Bonnie" illustrates this
difference. The numbers along the bottom line are the scale steps. The
red letters/numbers are the intervals between notes in the
melody.18 I have used upper case 'M' for major and lower case
'm' for minor. This is a common practice that you will see frequently.
Musicianship
Ear training
19
Right at the beginning of my first semester studying music theory, the
instructor asked us, among various other theory related things, to pull
out a sheet of music paper and write down the tune to "America the
beautiful." It was not that he was a patriot; he just wanted to see how
much we were bringing, skill-wise, to the class. After an hour I was
still there. He concluded that the three of us that were left must
either really know what we were doing, or be totally clueless. I, of
course, fell into the latter category.
20
Start with "Frère Jacques" or "Row, Row, Row your boat," then move to
something a little more complicated. Do not start with to "America the
beautiful."
21
The syllables were originally notes in a familiar hymn (perhaps the
Sound of Music's "Do, Re, Mi" serves that function now). The original
tonic was ut, but was changed to do in 16th
c. Italy so that all syllables would be open. A syllable for the
seventh, si, was added at the same time. The change to
ti was made in 19th century England (by Sarah
Glover) so that each note interval would have a different initial
consonant. Solfège was originally accompanied by note shapes and hand
signals.
One of the best things you can do for yourself is train your ear to hear
and identify intervals.19 Take an easy song,20 and without picking it out on
your instrument, try to imagine what the intervals are. You will notice
I did not say 'notes.' You are welcome to try to develop perfect pitch
(the ability to recognize or produce an exact note on demand) if you
want, but that is not as important as hearing the relationship between
the notes. This is called relative pitch. Once you have it, you will be
able to hear a tune in your head and just write it down. No need to go
running to your guitar or piano. No need to carry a tape recorder with
you everywhere you go so you can embarrass yourself singing into it
while you are riding the subway, because that happens to be where you
got the tune idea.
If you were actually in a college class learning this stuff, I can
guarantee you that you would be expected to develop both this, and the
next skill. The reason is that the professional musicians who run those
classes know how important it is to your musicianship.
Sight singing
Along with ear training, you should be learning to sight sing. This
internalizes the connection between the written notes and the actual
pitches better than much anything else you can do. If you don't read
music for your instrument, you should do the same kinds of exercises
developing that skill as well.
Many students find the use of solfège to be a useful tool in
learning this skill. Each scale step is given a separate syllable, which
aides in the learning by name association. The system was first designed
in the eleventh century, and has undergone refinement over the
years.21 In English speaking countries the syllables are
1=do, 2=re, 3=me,
4=fa, 5=sol, 6=la,
and 7=ti. More advanced solfège adds modified
syllables to handle accidentals within a scale. The more complicated
version looks like this:
Major scale
Root (1)
Do
diminished 5
Se
minor 2
Ra
Perfect 5
Sol
Major 2
Re
minor 6
Le
minor 3
Ma
Major 6
La
Major 3
Mi
minor 7
Ta
Perfect 4
Fa
Major 7
Ti
In reality, it can get even more complicated than this, because it has
various other names for enharmonic equivalents (there is a separate
augmented 4, for example). Minor keys are either simply
transposed (the tonic stays as do) or treated as a type of the
major so that the tonic is sung as la.
The reason people find solfège helpful is that the better way to read to
sight sing is not about identifying the relationship between notes and
dots, but about learning to recognize the intervals between them, and
their place in the current scale. Solfège reinforces this, but it is
hardly necessary.
If Latin syllables seem weird to you, you could always substitute scale
steps. "My bonnie" would be 1,6,5,4,5,4,2,1,6. If you were particularly
into it, you could use French (or some other language) for the accidentals.
But you don't really need a crutch like this; it's just that some people
find it helps.
Moving on
We are not done talking about melody, but we are going to move on for
now to the second major component in music, rhythm.
