Scale Intervals
| Major Scale | T | T | S | T | T | T | S |
| Minor Scale | T | S | T | T | S | T | T |
T = Tone
S = Semitone
Mode Intervals
| Aeolian | T | S | T | T | S | T | T |
| Locrian | S | T | T | S | T | T | T |
| Ionian | T | T | S | T | T | T | S |
| Dorian | T | S | T | T | T | S | T |
| Phrygian | S | T | T | T | S | T | T |
| Lydian | T | T | T | S | T | T | S |
| Mixolydian | T | T | S | T | T | S | T |
The Diatonic Polygon
Diatonic Polygon in Major Scale (Ionian Mode) orientation
This orientation also accounts for A Aeolian, B Locrian, D Dorian, E Phrygian, F Lydian, and G Mixolydian, which all contain the same set of notes (C, D, E, F, G, A, B).
Rotating the polygon allows you to change the set of notes, and thereby change the set of key-mode combinations that are accounted for (where a key here is basically like the ‘C’ in “C Major” or “C Ionian”, or the ‘D’ in “D Dorian”).
As an example, rotating so that the point currently marked ‘2’ is situated at D#/Eb gives the key-mode combinations D#/Eb-Dorian, F-Phrygian, F#/Gb-Lydian, G#/Ab-Mixolydian, A#/Bb-Aeolian, and C-Locrian.
The diatonic polygon in the upright orientation is what you would consider its Dorian orientation. Whatever that top point on the shape is pointing to is in the Dorian mode. If the polygon is upright, and that top point is pointing at C, then C is in Dorian mode. If the polygon is rotated, and that point is then pointing at C#/Db, then C#/ Db is now what’s in Dorian mode.
The symmetry of the shape in this “upright” position is reflected in the interval sequence for the Dorian mode, which is also symmetric (T, S, T, T, T, S, T). Its sequence pattern reflects onto itself.
The other modes’ pattern sequences, on the other hand, reflect across the Dorian pattern. The Mixolydian pattern is a reflection of the Aeolian pattern (i.e. the Mixolydian pattern is the Aeolian pattern backward). The Lydian pattern is a reflection of the Locrian pattern, and the Phrygian pattern is a reflection of the Ionian pattern.