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Beginner here. So far, I have understood that a scale is an ordered subset of the twelve main notes. Consequently, a scale can be described by a pattern of half steps and whole steps along with a tonic note.

I am interested in counting scales corresponding to the so called modes of the major scale. I am only interested by musically different scales so one scale with two different writing count as one in this context.

We know there are seven modes so seven patterns to begin with. Each of them can be played with twelve tonic notes so there are up to eighty-four scales to consider.

I guess the real number is lower as some of those scales might be identical. So here is the question: How many different scales based on the modes are there?

As a bonus question: Along those scales, is there some of them that are not "musically interesting"? If so, how many and why?

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Counting Scales

Consider these two scales:

  • a C major scale starting on the second degree: D-E-F-G-A-B-C
  • a C major scale starting on the third degree: E-F-G-A-B-C-E

They contain the same group of notes, but they start on different roots. If you count these as two different scales, then there are a total of 84 distinct scales, with no overlap.1 However, it's possible to say that both of these are the same scale--C major. With that sort of counting, there are only 12 different scales: C maj, Db maj, D maj, Eb maj, E maj, F maj, Gb maj, G maj, Ab maj, A maj, Bb maj, and B maj.

As stated previously, if you count the two scales above as being different, then there are 84 distinct scales, and none of these 84 are the same. To see why there isn't any overlap among the 84, consider the two columns below.

  ROOT      QUALITY
  C         Ionian
  Db        Dorian
  D         Phrygian
  Eb        Lydian
  E         Mixolydian
  F         Aeolian
  Gb        Locrian
  G         
  Ab        
  A         
  Bb        
  B         

Each scale is formed by choosing one root note and one quality. Let's take C Ionian as an example. If you change just the root note (say, to Db Ionian), then you have changed to a different scale. If you change just the quality (say, to C Dorian), again have changed to a different scale. This illustrates that every unique root + quality combination forms a different scale.

Another way to put it: it's impossible for a C scale (any C scale) to be the same as a Db scale (any Db scale) because the two scales have different roots. For each root, there is a family of scales which will not overlap with any other family of scales. The C family of scales contains 7 different qualities, and so does the Db family of scales. For each of the 12 roots, there are 7 different scale qualities. So the number of different scales is 12 x 7 = 84.

Uses

Every one of the 7 modes has a useful function that you do hear in jazz. I'll stick with a C major scale as my example:

SCALE/MODE       ASSOCIATED CHORD(S)
C Ionian         Cmaj, Cmaj6, Cmaj7
D Dorian         Dmin, Dmin6, Dmin7
E Phrygian       E7alt, Emin♭9, E7#9sus
F Lydian         Fmaj#11
G Mixolydian     G7
A Aeolian        Amin, Amin♭13
B Locrian        Bø7

The chords listed are not comprehensive. For example, there are few chords with upper extensions written. Not all of these scales/modes are as widely as others. For example, B Locrian is not the only choice for a Bø7 chord--one could also play B Locrian ♮2. The Locrian ♮2 mode comes from a different parent scale from the major scale. It comes from the melodic minor parent scale.

Other Parent Scales

The major scale (e.g., C-D-E-F-G-A-B) is not the only scale from which you can form distinct modes. Here are the most common parent scales from which to build modes:

C major:            C   D   E   F   G   A   B
C melodic minor:    C   D   Eb  F   G   A   B
C harmonic minor:   C   D   Eb  F   G   Ab  B
C harmonic major:   C   D   E   F   G   Ab  B

There are distinct parent scales. There are two ways to understand what it means that they are all distinct:

  • you can choose any two parent scales in any roots and there will be no overlap
  • if you choose one parent scale, its modes will not match the notes of other parent scale

So these parent scales--and the modes coming from them--are all distinct from each other. For a list of the modes for these other parent scales, check out my answer here.

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Each major scale has 7 modes, which use exactly the same notes as each major scale, but have a different root each. So, you can say each one is the same, or each is different, depending on how you view the concept.

Then the minor scales each have modes, worked off each note contained in each scale. bear in mind with three minor scales, only the harmonic and melodic minors will give different modes - those of the natural minor are exactly those of the relative major. In fact, the natural minor is called the Aeolian mode.

From a technical point of view, any scale is purely a set of notes. Consider the chromatic, diminished and the whole tone scales. They are not key-centric - they can't be. Harmonic minor is another. Modes, however, are also scales - sets of notes (dis)played in order - but belong to certain parent scales. As in E Phrygian mode has a parent scale/key of C major. That makes something like A harmonic minor a scale, but not a mode. In fact, it has its own set of modes!

Probably the least used from major modes is the Locrian, which produces some triads which hardly seem to resolve.

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We know there are seven modes so seven patterns to begin with. Each of them can be played with twelve tonic notes so there are up to eighty-four scales to consider.

Right, 84 different scales

I guess the real number is lower as some of those scales might be identical.

No, none of the 84 are identical when considering absolute pitch classes. To explain my meaning by example: D Dorian and Eb Dorian have the same relative interval relationships but use different absolute pitches and so we will count them as 2 scales. By that criteria you get 84 modal scales. Otherwise, in relative terms there are only the 7 modes.

In practical terms all these 84 scales are necessary. If some music was in D Ionian and then changed to D Dorian, C# Dorian is not identical to D Dorian and not acceptable as a substitute. No other scales would be identical. Only D Dorian would fill the need. All 84 are unique and necessary.

...is there some of them that are not "musically interesting"?

Except for some arbitrary, subjective opinion like "I think C Ionian is uninteresting," none of the 84 scale is more or less interesting than the others. Ionian (considered as the major scale) certainly ranks as very important in western music. It's used very frequently. But, that doesn't mean the other scales and modes are 'uninteresting' or 'unimportant.'

An analogy may help. In cooking pepper is used sparingly compared to other ingredients. That doesn't mean pepper isn't important. With the spice the food is bland. Quantity or frequency alone does not determine something's importance. Along these lines Ionian is very common, but it doesn't mean the other modes and scales are not important.

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