The Scale Families

Seven families of seven-note scales, each rotated into its modes, and every place where a single altered degree carries a mode of one family onto a mode of another.

What a family is here

A family, on this site, is one set of seven notes and every way of starting it. Take the set and begin on its first note, and you have its first mode; begin on its second note, measure every note from there, and you have the second mode; and so on up the seven. Each family below is declared once, from a published source that defines it, and its modes are worked out by that rotation rather than typed in. The name beside each mode is the one its source prints, exactly as printed.

How the families meet

Two modes are neighbours when they share a root and differ in one degree, raised or lowered by a semitone: Ionian with its fourth raised is Lydian, and the harmonic minor with its third raised is the harmonic major. Most such steps lead out of the atlas into sets nobody here has declared; the tables count only the ones that land on a declared mode. Counted that way, some families touch often and some rarely, and the diatonic family is the only one whose modes are neighbours of each other.

Interval content and mirrors

The interval vector counts how many of a family’s twenty-one pairs of notes lie one, two, three, four, five and six semitones apart, the shorter way round. Every mode of a family shares it, because a rotation changes the starting note and leaves every distance alone. A mirror is the family read upside down: reflect a mode around its root and see where it lands. Four families land back on themselves, the harmonic minor and harmonic major land on each other, and the Neapolitan minor lands on a set this atlas does not declare.

The claims

Where a source says how two of these sets connect, the claim is written out in the table below and tested against the arithmetic. Where a claim describes two alterations at once, the table names each declared mode the route can stop at on the way; a claim nothing in the atlas bears out would stop this site from building.

The seven families side by side

Each family by its first mode: the degrees, the interval vector, where its reflections land, how many pairs one altered degree apart involve it, and which families those pairs reach.
Family Mode 1 Interval vector Mirror Pairs Touches
Diatonic 1 2 3 4 5 6 7 <2 5 4 3 6 1> itself 36 Diatonic, Melodic minor, Harmonic minor, Harmonic major and Neapolitan minor
Melodic minor 1 2 b3 4 5 6 7 <2 5 4 4 4 2> itself 36 Diatonic, Harmonic minor, Harmonic major and Neapolitan major
Harmonic minor 1 2 b3 4 5 b6 7 <3 3 5 4 4 2> Harmonic major 30 Diatonic, Melodic minor, Harmonic major, Double harmonic and Neapolitan minor
Harmonic major 1 2 3 4 5 b6 7 <3 3 5 4 4 2> Harmonic minor 24 Diatonic, Melodic minor, Harmonic minor and Double harmonic
Double harmonic 1 b2 3 4 5 b6 7 <4 2 4 5 4 2> itself 18 Harmonic minor, Harmonic major and Neapolitan minor
Neapolitan major 1 b2 b3 4 5 6 7 <2 6 2 6 2 3> itself 18 Melodic minor and Neapolitan minor
Neapolitan minor 1 b2 b3 4 5 b6 7 <3 4 3 5 4 2> outside the atlas 24 Diatonic, Harmonic minor, Double harmonic and Neapolitan major

Which families touch

How many pairs of modes one altered degree apart join each two families; none means the two never touch.
Diatonic Melodic minor Harmonic minor Harmonic major Double harmonic Neapolitan major Neapolitan minor
Diatonic 6 12 6 6 none none 6
Melodic minor 12 none 6 6 none 12 none
Harmonic minor 6 6 none 6 6 none 6
Harmonic major 6 6 6 none 6 none none
Double harmonic none none 6 6 none none 6
Neapolitan major none 12 none none none none 6
Neapolitan minor 6 none 6 none 6 6 none

What the sources say, checked

Every relation the sources state between these sets, each tested against the atlas: twenty-one claims, read 2026-09-24.
The claim In the atlas The source’s words
Ionian (diatonic, mode 1): raise the 4th, and it is Lydian (diatonic, mode 4). Borne out: the two are one altered degree apart. The single tone that differentiates this scale from the major scale (Ionian mode) is its fourth degree, which is an augmented fourth (A4) above the tonic (F), rather than a perfect fourth (P4). — Mode (music), “Analysis” (Wikipedia, read 2026-09-24)
Ionian (diatonic, mode 1): lower the 7th, and it is Mixolydian (diatonic, mode 5). Borne out: the two are one altered degree apart. The single tone that differentiates this scale from the major scale (Ionian mode) is its seventh degree, which is a minor seventh (m7) above the tonic (G), rather than a major seventh (M7). — Mode (music), “Analysis” (Wikipedia, read 2026-09-24)
Aeolian (diatonic, mode 6): raise the 6th, and it is Dorian (diatonic, mode 2). Borne out: the two are one altered degree apart. The only difference with respect to the natural minor scale is in the sixth scale degree, which is a major sixth (M6) above the tonic, rather than a minor sixth (m6). — Mode (music), “Analysis” (Wikipedia, read 2026-09-24)
Aeolian (diatonic, mode 6): lower the 2nd, and it is Phrygian (diatonic, mode 3). Borne out: the two are one altered degree apart. The only difference with respect to the natural minor scale is in the second scale degree, which is a minor second (m2) above the tonic, rather than a major second (M2). — Mode (music), “Analysis” (Wikipedia, read 2026-09-24)
Ionian (diatonic, mode 1): lower the 3rd, and it is Ascending melodic minor (melodic minor, mode 1). Borne out: the two are one altered degree apart. It may be derived from the major scale with a minor third — Jazz minor scale, “introduction” (Wikipedia, read 2026-09-24)
Dorian (diatonic, mode 2): raise the 7th, and it is Ascending melodic minor (melodic minor, mode 1). Borne out: the two are one altered degree apart. It can also be derived from the diatonic Dorian mode with a major instead of a minor seventh in it. — Jazz minor scale, “introduction” (Wikipedia, read 2026-09-24)
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)
Ionian (diatonic, mode 1): lower the 6th, and it is Harmonic major (harmonic major, mode 1). Borne out: the two are one altered degree apart. The scale is simply a major scale with a lowered sixth. — Harmonic major scale, “Construction” (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)
Ionian (diatonic, mode 1): lower the 2nd and lower the 6th, and it is Double harmonic (double harmonic, mode 1). Borne out in two altered degrees, stopping at Harmonic major (harmonic major, mode 1) on the way. lowering both the second and sixth of the Ionian mode by a semitone. — Double harmonic scale, “Details” (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)
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 major (harmonic major, mode 1): lower the 2nd, and it is Double harmonic (double harmonic, mode 1). Borne out: the two are one altered degree apart. lowering the second note of the harmonic 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)
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)
Double harmonic (double harmonic, mode 1) reflected around its root is itself. Borne out: the reflection lands there. The double harmonic major is its own reflection around the root, itself being the palindromic mode. — Double harmonic scale, “Symmetry and balance” (Wikipedia, read 2026-09-24)
Dorian (diatonic, mode 2) reflected around its root is itself. Borne out: the reflection lands there. In comparison, among the modes of the major scale, the Dorian mode is a palindrome. — Double harmonic scale, “Symmetry and balance” (Wikipedia, read 2026-09-24)
Ionian (diatonic, mode 1) reflected around its root is Phrygian (diatonic, mode 3). Borne out: the reflection lands there. However, the major scale itself (Ionian mode), in contrast to the double harmonic major, is not a palindrome; its reflection around its root gives rise to a Phrygian mode. — Double harmonic scale, “Symmetry and balance” (Wikipedia, read 2026-09-24)

The family pages

  • The Diatonic Family

    The seven church modes: one set of notes, and a chain of single altered degrees from Lydian to Locrian.

    seven modes · touches five families · 36 pairs

  • The Melodic Minor Family

    The ascending melodic minor rotated: the major scale with a lowered third, next door to the church modes.

    seven modes · touches four families · 36 pairs

  • The Harmonic Minor Family

    The natural minor with a raised seventh, rotated — and the harmonic major family seen in a mirror.

    seven modes · touches five families · thirty pairs

  • The Harmonic Major Family

    The major scale with a lowered sixth, rotated: the harmonic minor family reflected around its root.

    seven modes · touches four families · twenty-four pairs

  • The Double Harmonic Family

    Two lowered degrees from the major scale, one from the harmonic major, and symmetric around its root.

    seven modes · touches three families · eighteen pairs

  • The Neapolitan Major Family

    The melodic minor with a lowered second, rotated — a family that touches only two others.

    seven modes · touches two families · eighteen pairs

  • The Neapolitan Minor Family

    The harmonic minor with a lowered second, rotated; its reflection lands on no family declared here.

    seven modes · touches four families · twenty-four pairs