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 Major | 1 b2 b3 4 5 6 7 | 3 | itself |
| Mode 2 | Leading Whole Tone (or Lydian Augmented #6) | 1 2 3 #4 #5 #6 7 | 2 | Altered Dominant bb3 |
| Mode 3 | Lydian Augmented Dominant | 1 2 3 #4 #5 6 b7 | 3 | Half-Diminished b4 |
| Mode 4 | Lydian Dominant b6 (or Melodic Major #4) | 1 2 3 #4 5 b6 b7 | 3 | Major Locrian |
| Mode 5 | Major Locrian (Locrian natural 2 natural 3, Aeolian Dominant b5, Arabian) | 1 2 3 4 b5 b6 b7 | 3 | Lydian Dominant b6 |
| Mode 6 | Half-Diminished b4 (or Altered Dominant #2) | 1 2 b3 b4 b5 b6 b7 | 2 | Lydian Augmented Dominant |
| Mode 7 | Altered Dominant bb3 | 1 b2 bb3 b4 b5 b6 b7 | 2 | Leading Whole Tone |
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 <2 6 2 6 2 3>. | Semitones apart | 1 | 2 | 3 | 4 | 5 | 6 |
| Pairs | 2 | 6 | 2 | 6 | 2 | 3 |
Mirror and symmetry
Reflected around its root, every mode of the Neapolitan major family lands on another mode of the same family, and Neapolitan Major lands on itself. 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 |
| Ascending melodic minor (melodic minor, mode 1): lower the 2nd, and it is Neapolitan Major (Neapolitan major, 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
The Neapolitan major family starts from the Neapolitan major, 1 b2 b3 4 5 6 7: the ascending melodic minor with its second lowered, which is how its source tells the two apart. Its rotations run through the leading whole tone, 1 2 3 #4 #5 #6 7, the Lydian augmented dominant and the major Locrian to the altered dominant bb3.
Two families next door, and no more
No family here touches fewer of the others. Every altered degree that stays inside the atlas lands either in the melodic minor family, which it meets as often as any two different families meet here, or in the Neapolitan minor family, which the Neapolitan major itself becomes when its sixth is lowered. Its modes are sparse in neighbours: none has more than three, and three have only two.
Degree by degree
Every mode of the family is one altered degree from a melodic minor mode, and several of the names say which. The leading whole tone is Lydian augmented with its sixth raised; the major Locrian is the Aeolian dominant with its fifth lowered; the half-diminished b4 is the half-diminished with its fourth lowered. Read the other way, the melodic minor family is the Neapolitan major with one degree put back.
Mirror
Reflected around its root, the Neapolitan major is itself, and its other modes pair off: the leading whole tone with the altered dominant bb3, and the Lydian augmented dominant with the half-diminished b4. That makes it one of four families here that are their own mirror image.