Pentatonic

Eastern Pentatonic - Yo

R M2 P4 P5 M6 R
 w  +  w  w  +

This scale is very similar to the major pentatonic scale; however, it uses a P4 instead of M3. It does have a slightly Eastern feel to it, but it fits in nicely with Western music. It is actually a mode of the common minor and major pentatonic scales.

Eastern Pentatonic - In

R m2 P4 P5 m6 R
 h  *  w  h  *

Take the above scale and flat the 2nd and 6th. It has a similar feel to the Phrygian mode, containing a subset of its notes. Yet the M3 jumps really emphasize an exotic feel.

Egyptian/Suspended Pentatonic

R M2 P4 P5 m7 R
 w  +  w  +  w

Pentatonic - Minor Blues

R m3 P4 m6 m7 R
 +  w  +  w  w

Heptatonic

Double Harmonic

R m2 M3 P4 P5 m6 M7 R
 h  +  h  w  h  +  h

This is called the double harmonic scale due to its dual harmonic tetrachords (h + h). It has a very exotic feel due to the augmented 2nds, as well as containing both the m2 and M7 notes around the root. It is most easily arrived at by flattening the 2nd of the Harmonic Major scale. It is also a mode of Hungarian Minor.

Hungarian Minor

R M2 m3 a4 P5 m6 M7 R
 w  h  +  h  h  +  h

Has 2 augmented 2nds and 2 consecutive half-steps for a very exotic feel. It's most easily derived by sharping the perfect 4th of the Harmonic Minor scale. All its half-steps make its tonality ambiguous. It is also known as the Gypsy Minor scale, traditionally popular in Eastern Europe. It works well over minor and minor/major 7th chords. It is also a mode of the Double Harmonic scale.

Its diatonic chords are i, II7♭5, III+, V, ♭VITemplate:Maj7, vii6.

Octatonic

Whole-Half

R M2 m3 P4 d5 m6 M6 M7 R
 w  h  w  h  w  h  w  h

Consists simply of alternating whole and half steps, repeating 4 times before returing to the root note. There is no clear tonality here - it is a symmetric scale. You can change the root note of the scale to every other note and get the same exact notes and step-sequence. This is often referred to as the diminished scale, due to its inclusion of the m3, d5, and d7 intervals (M6 = d7), which make up the fully diminished chord.

Half-Whole

R m2 m3 d4 d5 P5 M6 m7
 h  w  h  w  h  w  h  w

Hexatonic

Whole Tone

R M2 M3 a4 a5 a6    =  R M2 M3 d5 m6 m7
 w  w  w  w  w  w

Augmented

R m3 M3 a5 m6 M7
 +  h  +  h  +  h

Prometheus

R M2 M3 tt M6 m7
 w  w  w  +  h  w

Tritone

R m2 m3 a4 P5 m7
 h  w  +  h  +  w

Chromatic

R m2 M2 m3 M3 P4 d5 P5 m6 M6 m7 M7
 h  h  h  h  h  h  h  h  h  h  h  h

Chopin
Petrucci

Symmetric Scales

Symmetric Scales are scales that divide an octave into 2 or more equal parts. In other words, the whole/half pattern of notes for each piece will be identical and there are no leftover notes. Here is an example of a symmetric scale I am just inventing:

R m2 P4 d5 m6 M7
 h  *  h  h  *  h

We can divide this into two equal parts:

R  m2 P4 d5
d5 m6 M7 R
  h  *  h

The most symmetric scale is the chromatic scale:

R m2 M2 m3 M3 P4 d5 P5 m6 M6 m7 M7 R
 h  h  h  h  h  h  h  h  h  h  h  h

Which can be represented as follows:

R  m2 M2 m3 M3 P4 d5
d5 P5 m6 M6 m7 M7 R
  h  h  h  h  h  h

R  m2 M2 m3 M3
M3 P4 d5 P5 m6
m6 M6 m7 M7 R
  h  h  h  h

R  m2 M2 m3 
m3 M3 P4 d5
d5 P5 m6 M6
M6 m7 M7 R
  h  h  h

R  m2 M2
M2 m3 M3
M3 P4 d5
d5 P5 m6
m6 M6 m7
m7 M7 R
  h  h

R  m2
m2 M2
M2 m3
m3 M3
M3 P4
P4 d5
d5 P5
P5 m6
m6 M6
M6 m7
m7 M7
M7 R
  h

If the scale is symmetric by dividing the octave into halves, it must have the a4/tt/d5 note.
Pentatonic and Hexatonic scales cannot be symmetric as 5 and 7 are prime numbers that cannot be subdivided into 2 or more groups of equal notes

Common symmetric scales include:

Whole Tone
Octatonic (Whole-Half and Half-Whole)
Chromatic
Augmented

Synthetic Scales

Synthetic Scales are formed by lowering or raising a single note of an existing scale by a half-step.

Exotic Scales

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