The seven modes, by rotation
Each mode starts the family on the next degree up. Names are the source’s; degrees, neighbour counts and mirrors are worked out here. | Mode | Name, as printed | Degrees | One degree away | Reflected |
| Mode 1 | Harmonic minor | 1 2 b3 4 5 b6 7 | 5 | Mixolydian b2 |
| Mode 2 | Locrian #6 | 1 b2 b3 4 b5 6 b7 | 4 | Lydian b3 |
| Mode 3 | Ionian #5 | 1 2 3 4 #5 6 7 | 4 | Phrygian b4 |
| Mode 4 | Ukrainian Dorian | 1 2 b3 #4 5 6 b7 | 4 | Dorian b5 |
| Mode 5 | Phrygian Dominant | 1 b2 3 4 5 b6 b7 | 5 | Harmonic major |
| Mode 6 | Lydian #2 | 1 #2 3 #4 5 6 7 | 4 | Locrian bb7 |
| Mode 7 | Altered Diminished | 1 b2 b3 b4 b5 b6 bb7 | 4 | Lydian Augmented #2 |
Names as printed in Mode (music), “Other heptatonic scales” (Wikipedia, read 2026-09-24).
Interval content
How many of the twenty-one pairs of notes in the family lie each distance apart, the shorter way round: the interval vector <3 3 5 4 4 2>. | Semitones apart | 1 | 2 | 3 | 4 | 5 | 6 |
| Pairs | 3 | 3 | 5 | 4 | 4 | 2 |
Mirror and symmetry
Reflected around its root, every mode of the harmonic minor family lands on a mode of the harmonic major family, so the two are mirror images of each other. No shift short of the octave maps the family onto itself: seven notes cannot divide twelve evenly.
One degree away
What the sources say about it
Every relation a source states that involves this family, tested against the atlas. | The claim | In the atlas | The source’s words |
| Aeolian (diatonic, mode 6): raise the 7th, and it is Harmonic minor (harmonic minor, mode 1). | Borne out: the two are one altered degree apart. | a musical scale derived from the natural minor scale, with the minor seventh degree raised by one semitone to a major seventh — Harmonic minor scale, “introduction” (Wikipedia, read 2026-09-24) |
| Ionian (diatonic, mode 1): lower the 3rd and lower the 6th, and it is Harmonic minor (harmonic minor, mode 1). | Borne out in two altered degrees, stopping at Ascending melodic minor (melodic minor, mode 1) and Harmonic major (harmonic major, mode 1) on the way. | A harmonic minor scale can be built by lowering the 3rd and 6th degrees of the parallel major scale by one semitone. — Harmonic minor scale, “introduction” (Wikipedia, read 2026-09-24) |
| Harmonic minor (harmonic minor, mode 1): raise the 3rd, and it is Harmonic major (harmonic major, mode 1). | Borne out: the two are one altered degree apart. | It is also the harmonic minor scale with a raised third. — Harmonic major scale, “Construction” (Wikipedia, read 2026-09-24) |
| Harmonic minor (harmonic minor, mode 1): lower the 2nd and raise the 3rd, and it is Double harmonic (double harmonic, mode 1). | Borne out in two altered degrees, stopping at Neapolitan Minor (Neapolitan minor, mode 1) and Harmonic major (harmonic major, mode 1) on the way. | lowering the second note and raising the third note of the harmonic minor scale by one semitone. — Double harmonic scale, “Details” (Wikipedia, read 2026-09-24) |
| Phrygian Dominant (harmonic minor, mode 5): raise the 7th, and it is Double harmonic (double harmonic, mode 1). | Borne out: the two are one altered degree apart. | raising the seventh of the Phrygian dominant scale (a mode of the harmonic minor scale) by a semitone. — Double harmonic scale, “Details” (Wikipedia, read 2026-09-24) |
| Phrygian (diatonic, mode 3): raise the 3rd, and it is Phrygian Dominant (harmonic minor, mode 5). | Borne out: the two are one altered degree apart. | The Phrygian dominant in turn is produced by raising the third of the diatonic Phrygian mode (a mode of the major scale) by a semitone. — Double harmonic scale, “Details” (Wikipedia, read 2026-09-24) |
| Harmonic minor (harmonic minor, mode 1): lower the 2nd, and it is Neapolitan Minor (Neapolitan minor, mode 1). | Borne out: the two are one altered degree apart. | The scales are distinguished from the harmonic and ascending melodic minor scales by the lowered supertonic or second scale degree. — Neapolitan scale, “introduction” (Wikipedia, read 2026-09-24) |
The family itself is read from Harmonic minor scale, “introduction” (Wikipedia, read 2026-09-24): a musical scale derived from the natural minor scale, with the minor seventh degree raised by one semitone to a major seventh
.
One raised seventh
The harmonic minor family starts from the harmonic minor, 1 2 b3 4 5 b6 7: Aeolian with its seventh raised. Rotated, it gives Locrian #6, Ionian #5, the Ukrainian Dorian, the Phrygian dominant, Lydian #2 and the altered diminished, 1 b2 b3 b4 b5 b6 bb7, each named as the source prints it. The neighbour table lists every altered degree that leaves one of these modes and lands inside the atlas, mode by mode.
Five families next door
No family here touches more of the others. One altered degree takes its modes to the diatonic, melodic minor, harmonic major, double harmonic and Neapolitan minor families, each in the same number of pairs, and never to each other; every mode has four or five neighbours. Raise its third and it is the harmonic major; lower its second and it is the Neapolitan minor; and the Phrygian dominant becomes the double harmonic when its seventh is raised, while being itself Phrygian with a raised third. All four of those steps are claims a source makes, and the table of claims shows each one borne out.
Its mirror is another family
Reflect a harmonic minor mode around its root and it lands in the harmonic major family: the harmonic minor itself turns into Mixolydian b2, and the Phrygian dominant into the harmonic major. A reflection keeps every distance between notes, so both families share one interval vector even though no mode of one is a mode of the other. The harmonic major page shows the same pairs from the other side, degree for degree.