Scales

A scale is a named set of notes. Here's a CC-major scale.

X:1 L:1/4 K:C C D E F G A B w: c d e f g a b
Sheet Musiccdefgab

The order doesn't matter -- it's just about the notes. Here's a GG-major scale.

X:1 L:1/4 K:C G A B c d e ^f w: g a b c d e f♯
Sheet Musicgabcdef♯

If you compare the two, they have all the same notes except for one. CC-major has an ff where GG-major has an ff\sharp. Why does that turn it into a completely different scale? Well, the names of the scales have two components: the root and the character.

Gundefinedroot majorundefinedcharacter\underbrace{\quad G \quad}_{\text{root}}\quad \underbrace{\text{ major}}_{\text{character}}

The character tells you which intervals belong to the scale, starting from the root. For major scales, the intervals are:

P1,M2,M3,P4,P5,M6,M7{P1, M2, M3, P4, P5, M6, M7}

Here's how we apply this to the GG-major scale:

g+P1=gg+M2=ag+M3=bg+P4=cg+P5=dg+M6=eg+M7=f\begin{aligned} g &+ P1 = &g\\ g &+ M2 = &a\\ g &+ M3 = &b\\ g &+ P4 = &c\\ g &+ P5 = &d\\ g &+ M6 = &e\\ g &+ M7 = &f\sharp \end{aligned}

And to the AA-major scale:

a+P1=aa+M2=ba+M3=ca+P4=da+P5=ea+M6=fa+M7=g\begin{aligned} a &+ P1 = &a\\ a &+ M2 = &b\\ a &+ M3 = &c\sharp\\ a &+ P4 = &d\\ a &+ P5 = &e\\ a &+ M6 = &f\sharp\\ a &+ M7 = &g\sharp \end{aligned}

You can construct the major scale for every one of the 12 notes in this way. You can also build different kinds of scales with the same root but different characters. Minor scales have this set of intervals:

P1,M2,m3,P4,P5,m6,m7{P1, M2, m3, P4, P5, m6, m7}

Applied to a root of gg, we get the GG-minor scale.

g+P1=gg+M2=ag+m3=bg+P4=cg+P5=dg+m6=eg+m7=f\begin{aligned} g &+ P1 = &g\\ g &+ M2 = &a\\ g &+ m3 = &b\flat\\ g &+ P4 = &c\\ g &+ P5 = &d\\ g &+ m6 = &e\flat\\ g &+ m7 = &f \end{aligned}

Here's what GG-minor looks like on a staff:

X:1 L:1/4 K:C G A _B c d _e f w: g a b♭ c d e♭ f
Sheet Musicgab♭cde♭f

Notice that for all the scales I have shown you so far, the set of notes you end up with have exactly one note for each letter -- it may be a \flat or a \sharp, but every letter is represented. There is no golden rule that says this has to be so. There are scales that do not have this property, but many of them do.

Another thing to think about is why we choose to use ee\flat in the GG-minor scale and not dd\sharp. They are the same notes -- is there a reason to pick one over the other?

Well, yes, they are enharmonic equivalents. But the intervals in the pattern bag for minor scales have a P5P5 and a m6m6, so when constructing the scale we have a 'perfect' five-note distance (a P5P5) and a 'small' six-note one distance (the m6m6), not an augmented five-note distance (which does exist). So, we arrive at a dd and an ee\flat. It's nice to have this consistent way of doing things so that our pattern-loving brains can get good at reading sheet music.

As an aside: you can end up with notes with double sharps or flats like a bb\flat\flat, but at that point fortunately most musicians are practical enough to accept the enharmonic equivalent notation of aa.

To finish off this topic, here's a table of four of the most common scales. Note: the minor scale that we mean when we just say 'minor' is formally called the 'natural minor' scale.

NameIntervals
MajorP1,M2,M3,P4,P5,M6,M7{P1, M2, M3, P4, P5, M6, M7}
Natural minorP1,M2,m3,P4,P5,m6,m7{P1, M2, m3, P4, P5, m6, m7}
Harmonic minorP1,M2,m3,P4,P5,m6,M7{P1, M2, m3, P4, P5, m6, M7}
Melodic minorP1,M2,m3,P4,P5,M6,M7{P1, M2, m3, P4, P5, M6, M7}
DorianP1,M2,m3,P4,P5,M6,m7{P1, M2, m3, P4, P5, M6, m7}

It can be helpful to picture a decision tree when thinking about scales. In this mental model the Dorian scale is usually placed in the group of minor scales because it has a minor third, an important characteristic that we will see again when thinking about chords.

m3
M3
m7
M7
m6
M6
m6
M6
Start
Something minor
Major
Natural minor or Dorian
Harmonic or melodic minor
Harmonic minor
Melodic minor
Natural minor
Dorian

That's all for scales for now!