Only 2048 Possible Scales In Music

Musicians Highly Overestimate How Many Scales There Are In Music.

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Many years ago, in one of my first semesters in Berklee College of Music, I read the book “Innumeracy”.

Written by famous mathematician, John Allen Paulos, the book was required reading for one of the audio engineering classes at Berklee.
The gist of the book, is that we make lots of assumptions and carry many unfounded beliefs that we base on an incompetence with numbers.

An example of this would be the surprised look people sometimes have, when they find out they share your birthday.
People sometimes act like it is so amazing that you have the same birthday, like this is the most amazing thing, and unbelievably rare.
Well… it isn’t!
There’s only 365 days in a year and there are 7 billion people.
The alternative would be really frigging weird. (If you never met someone who shares your birthday)

In my family: we share 4 birthdays in 2 consecutive days.
My dad and I have our birthday the 14th of June, my mom and my son have their birthday the 15th of June.
Even that is mathematically probably really not as improbable as one might think.

Now… based on innumeracy (illiteracy with numbers), I have never gotten anything but a mathematically completely unrealistic answer to the question: “How many scales are there in music?”
I like my music and guitar students to know, because it helps them put things in the right perspective.

We Use 12 Notes In Music.

I precede the question “How many scales are there in music” with the question: “How many notes do we use in music?”
After it’s been established, that we use 12 notes in music, I point out that you can’t figure out how many scales there are in music without first knowing how many notes there are.

The notes are:
C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B

There are 2 names for the notes that fall in between 2 letters. The note between C and D for example can be called C# or Db.
The letters (without # or b) are the white keys on a piano. The letters with # or b added to the letter, are the black keys of the piano.

The Definition of A Scale.

In order to understand the question, “how many scales are there in music”, you need to first know what a scale is.

A scale is: a series of notes.
The smallest series you can have: is a 1-note series.

If I decide to play a G note for the next 3 minutes, and call it a song: I wrote a song using a 1-note scale. It’s in the key of G.
If I had chosen that note to be A, that would have been the same 1-note scale, but in a different key. (The key of A instead of G)

The largest series you can have, is a 12-note scale, which is also called the chromatic scale.
If I write a song using up all 12 notes that exist in music, I wrote a song with a 12-note scale.
If I started it on a G note, the song and scale would be in the key of G.
If I started on a Bb note, the song and scale would be in the key of Bb.
Same 12-note scale, different keys.

All 2-Note Scales.

So there is only one 1-note scale, and there is only one 12-note scale.
Both can be played from 12 different starting points. These starting points are called “keys”.

Since we are working with a 12-note system, that means that we can only have eleven 2-note scales.
The math behind this throws most people off, who usually swear there must be twelve 2-note combinations in a 12-note system.
No easier way to understand this, than to write it all out.
If I start everything from the note A, then the eleven 2-note scales are:

  1. A – Bb
  2. A – B
  3. A – C
  4. A – C#
  5. A – D
  6. A – D#
  7. A – E
  8. A – F
  9. A – F#
  10. A – G
  11. A – G#

The reason there are eleven, and not twelve 2-note combinations, is that A – A is not a 2-note combination, that is just a 1-note scale (as discussed earlier) in which you hit the same note twice.

2-note combinations are also called “intervals”. An interval is a distance between 2 notes.
The above 2-note scales (intervals) are all in the key of A.
If I start all them on C (C-Db, C-D, C-D#, etc…); they’re then all in the key of C.
“C – Db” is exactly the same 2-note scale as “A – Bb”, just in 2 different keys. (The key of C and the key of A).

The difference between a 2-note scale and 2-note intervals as taught in the study of harmony, is that you can have an octave or unison “interval” (doubling of the same note), but you can not play the same note twice in a row and count it as a 2-note scale.
No matter how many times you play an A note, it is still only 1 note. You need 2 different notes in order to have a 2-note scale.

Scales Are Arpeggiated Chords, Chords Are Strummed Scales.

Of course: there are many more 3-note scales than there are 2-note scales. There are even more 4 note scales.
The 3 and 4-note scales also include all the 3 and 4-note chords that exist in music
After all: what is a chord but a scale in which you hit all the notes at the same time?
Or looking at it from the other angle: a scale can be thought of as a chord in which you separate all the notes and play them one after another.

If I am playing the notes C, E and G, I am playing a 3-note scale. If I hit these 3 notes at the same time, I’m playing a C chord.

If I play those notes together as a C chord, I can create different inversions of C chords with these notes.
You can make 6 different configurations with the notes C, E and G.

In closed position:

CEG is root position C chord
EGC is a first inversion C chord
GCE is a 2nd inversion C chord

In open voicings:

CGE is a root position C chord
GEC is a 2nd inversion C chord
ECG is a 1st inversion C chord

No matter in what order I organize these 3 notes, they always sound like a C chord.

Some of The Reasons Why We Badly Overestimate The Number of Note Combinations.

If you point this out to a student, that the number of scales you are looking for also includes all the chords that exist in music, the number significantly grows outside of proportion in that student’s mind and perception.
The reasoning is: if the number we are looking for includes all the chords in addition to all the scales, then there definitely must be at least “millions” of note combinations.

However: given that chords can be looked at as “scales in which you play the notes together”, and scales can be looked at as “chords in which you play the notes one after another”, then the scale and the chord formula are one and the same thing.
The chord formulas are also the scale formulas, and the scale formulas are also the chord formulas.

As an example:
The scale formula 135 in the key of C, gives the notes CEG, which form a C chord when played together, and which are at the same time some kind of 3-note C scale if you play the notes separately.

The notes CEG always form a C chord no matter how you rearrange the notes, but these 3 notes can in 1 given/chosen key, also only be 1 specific scale. What this means is that against a C chord (which establishes the key as being centered on C), the notes C, E and G are going to sound like a 3-note scale in the key of C, regardless of the order in which you play the notes.
If I am hitting an E note first, then I play a G note, then a C note, that is going to sound like a 135 formula in the key of C, even though I hit the 3 first, then the 5 and then the 1.

So part of the reason why people tend to think there are way more scales than there only are, is that they fail to separate the concept “scale” from the concept “key”.

Following example explains this clearly.

It’s a mistake to think that the notes CEG can be 3 different scales (in the same key), as in following faulty reasoning:

CEG = 135
EGC = 1b36
GCE = 146

The faulty reasoning in the above is that the “3 different formulas” (135, 1b36 and 146) you get when rearranging the 3 notes C, E and G, get equated with being “3 different possible scales” in 1 key.
However: These aren’t 3 different C scales, but scales in 3 different keys.
The part of this that is confusing for many music students, is that they forget to consider the fact that these are now 3 different keys.
Remember: a “key” is a starting note, and you can start any scale from 12 different starting notes.

When C is 1 (meaning: “the first note in a series of notes”), it is a C scale, when E is 1, it is an E scale, when G is 1, it is a G scale.
If you change the starting note that you attach to the number “1”, then you’re in a different key.
Explaining this yet another way:
The above shows 135 in the key of C, 1b36 in the key of E and 146 in the key of G.

Sure these are 3 different scales, but it is hard to keep things organized this way because each of of these 3 different scales, is also in a different key each time.

The following example however, is a more accurate and more organized approach to figuring out how many scales there are in music.
The 135, 1b36 and 145 formulas are all starting from a C note as the first note.
If the key of C is kept as the constant 1, then these scale formulas would give following scales:

135 = CEG
1b36 = CEbA
146 = CFA

Point being made: figuring out how many scales there are in music, gets very confusing when you make the mistake of mixing scales over different keys. It is much easier to keep track of and to organize all the possible scale formulas if you keep the starting note a constant.
The task of figuring out how many scales there are in music, gets very disorganized if you don’t stick to 1 key only from where you figure everything out.
A disorganized approach, usually results in lots of undetected mistakes being made.

Another way of looking at this: a major scale structure, played starting from any of the 12 notes that exist in music, doesn’t give you 12 different scales. It gives you 1 scale, called the major scale, which structurally sounds the same 12 times in a row, just from different starting notes.

All that being said…

Conclusion: There Aren’t “Millions” of Scales in Music

The answers I typically get from students, vary from 144, to the much more common answers: “ten-thousands”, “millions” or even “unlimited”.
9 out of 10 times, the answer is either 144 or a ridiculously huge number, as in “millions”.

Which leads us back to… Innumeracy.
A system with 12 notes gives a very limited number of possible note combinations.
That is right: in a 12-note system, you can only have 2048, or 2 to the 11th power, number of note combinations.
There you have it: the magic number is 2048

While this might seem like a hell of a lot of scales to learn, it is still infinitely better than the number of scales most people think exist in music.

This includes every chord that exists, and everything from Middle-Eastern scales, to scales used in Indian music, to Gypsy music scales, to African, Polynesian, to Arabic scales, to diminished scales, all pentatonic scales, and anything you can think off. All scales from ALL cultures are all included in the listing of 2048 existing scales in music.

So next time you hear someone say things like: “Let’s come up with our own scale” or “I want to write music with scales I make up”, you can tell that person that all scales already exist. He/she just doesn’t know them all yet. 🙂

Be on the look out for more blogs about everything guitar, music, songwriting and music education.

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  1. Fabio Fiano Says:

    Great job!

    June 6th, 2020 at 9:47 pm