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 | Neapolitan Minor | 1 b2 b3 4 5 b6 7 | 4 | outside the atlas |
| Mode 2 | Lydian #6 | 1 2 3 #4 5 #6 7 | 3 | outside the atlas |
| Mode 3 | Mixolydian Augmented | 1 2 3 4 #5 6 b7 | 3 | outside the atlas |
| Mode 4 | Romani Minor, Aeolian/Natural Minor #4, or Hungarian/Gypsy Minor b7 | 1 2 b3 #4 5 b6 b7 | 4 | outside the atlas |
| Mode 5 | Locrian Dominant (or Locrian natural 3) | 1 b2 3 4 b5 b6 b7 | 4 | outside the atlas |
| Mode 6 | Ionian/Major #2 | 1 #2 3 4 5 6 7 | 3 | outside the atlas |
| Mode 7 | Ultralocrian/Altered Diminished bb3 | 1 b2 bb3 b4 b5 b6 bb7 | 3 | outside the atlas |
Names as printed in Neapolitan scale, “Modes” (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 4 3 5 4 2>. | Semitones apart | 1 | 2 | 3 | 4 | 5 | 6 |
| Pairs | 3 | 4 | 3 | 5 | 4 | 2 |
Mirror and symmetry
Reflected around its root, no mode of the Neapolitan minor family lands inside the atlas: its mirror image is a set none of the seven families declares. 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 |
| Neapolitan Minor (Neapolitan minor, mode 1): raise the 3rd, and it is Double harmonic (double harmonic, mode 1). | Borne out: the two are one altered degree apart. | raising the third of the neapolitan minor 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 Neapolitan scale, “introduction” (Wikipedia, read 2026-09-24): The scales are distinguished from the harmonic and ascending melodic minor scales by the lowered supertonic or second scale degree.
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One lowered second, again
The Neapolitan minor family starts from the Neapolitan minor, 1 b2 b3 4 5 b6 7: the harmonic minor with its second lowered, which is also Phrygian with its seventh raised. Its rotations include the Romani minor, 1 2 b3 #4 5 b6 b7, and the Locrian dominant, each named as the source prints it.
Four families next door
Its modes are one altered degree from the diatonic, harmonic minor, double harmonic and Neapolitan major families. Raise its third and it is the double harmonic, a step the double harmonic’s own source describes; raise its sixth and it is the Neapolitan major.
The Romani minor, 1 2 b3 #4 5 b6 b7, is the family’s best-connected mode: its four neighbours are Aeolian, the Ukrainian Dorian, the Hungarian minor and the Lydian dominant b6, one mode in each of the four other families it touches. Ionian/Major #2 is Ionian with its second raised, just as its name says. Every other mode of the family has three or four neighbours, and all of them but the seventh mode have one in the diatonic family.
A mirror outside the atlas
This is the one family here whose reflection leaves the atlas. Reflected around its root, the Neapolitan minor becomes 1 b2 3 4 5 6 7, a set none of the seven families holds, and every other mode of the family does the same. It is left as an open edge rather than given a family of its own, because no source read for this atlas declares one.