Which scales have a major chord built on second note? Which scales have a minor chord built on the seventh note?

Question

Which base scales (base scale meaning not modes) have a major chord built on the second note?

(In which scales is the II chord a major? Is this the proper nomenclature?)

Which scales have a minor chord built on the seventh note?

(In which scales is the VII chord a minor?)

Must they be non-diatonic?

I am including these questions together should the answers be the same or clearly related.

Answer 1

Depending on who you ask, some believe there are hundreds of different scale types. I personally prefer a smaller collection of scale types, viewing these other hundreds as alterations of more basic collections. For my answer, I will consider the diatonic modes and the whole-tone and octatonic collections.

Major Chord on Scale-Degree 2

1. Phrygian: On account of its use of ♭2 and ♭6, this has a major chord on scale-degree 2, but note that it's on the lowered second scale degree, so this major chord is only a half step above tonic, not a whole step.
2. Lydian: On account of its use of ♯4, this has a major II chord.
3. Locrian: Like Phrygian, the use of ♭2 and ♭6 creates a major chord on the lowered second scale degree.
4. Whole-half octatonic: The octatonic scale that begins with a whole step creates a major triad on scale-degree 2. In C, this scale (C D E♭ F F♯ G♯ A B C) includes D F♯ A.
5. Whole-tone scale: One could consider the chord built on the second scale degree of the whole-tone scale to be an incomplete major triad. In C, these pitches would be D and F♯. The chordal-fifth A♯ would create an augmented triad, so we could omit this to create a major triad (although our ears might imply the A♯, causing this chord to lose its major quality).

Minor Chord on Scale-Degree 7

1. Phrygian: On account of ♭7 and ♭2, the chord built on ♭7 (a whole step below tonic) is minor.
2. Lydian: On account of ♯4, the chord built on the leading tone is minor.
3. Locrian: Like Phrygian, the chord built on ♭7 is minor.
4. Whole-half octatonic: In the same scale collection from Point 4 above, we have B D F♯, a minor triad built on the leading tone. (But note that this B is now scale-degree 8 of the octatonic scale!)
5. Half-whole octatonic: Similar to Point 5 above, one could create an incomplete minor triad based on the lowered leading tone: B♭ D♭ within the C D♭ E♭ E♮ F♯ G A B♭ C collection.

Answer 2

A major chord is composed of a major 3rd and a minor 3rd. So you'd need a scale where 2 and 4 are a major third apart, and 4 and 6 are a minor third apart.

So you can have: b2-4-b6 or 2-#4-6. So the II will be major using a Locrian, Phrygian, or Lydian scale.

A minor chord is a minor 3rd and a major 3rd. So if the scale has b7-b2-4 or 7-2-#4. Again, it's the Locrian, Phrygian, and Lydian.

None of those scales is non-diatonic, so the answer to the last part is a definite no.

EDIT for the comment: All modes are scales, but almost all scales (with the exception of the whole tone and chromatic scale) are also modes, because you will have a different arrangement of intervals between the tones.

Any scale that has b2-4-b6 or 2-#4-6 will have a major chord on the II. So you could include things like the double harmonic scale, or the major phrygian. You could include non-heptatonic scales like the In scale from Japan. The only real criteria is that it contain the given pitches.

And any scale that has b2-4-b7 or 2-#4-7 will have a minor chord on the 7, like the Japanese Insen scale.

Of course, "7" is now a relative thing, because it could actually be the 5th or 9th or 11th note of the scale. And the harmony would no longer be Tertian. But if you're ok with those tweaks, there will be a lot of scales that will meet your criteria.

Answer 3

Depending on who you ask, some believe there are hundreds of different scale types. I personally prefer a smaller collection of scale types, - Richard

Let me include those other scale types :)

Which base scales (base scale meaning not modes) have a major chord built on the second note?

A base scale is the mode that is prime in The Rahn Prime Form* Rahn Atonal Prime Form Confusion

-> this makes Locrian the base scale of Major

• Debussy's Heptatonic: C D Eb Fb Gbb Abbb Bbb
• Espla's scale: C Db Eb Fb Gbb Abbb Bbbb
• Locrian: C Db Eb F Gb Ab Bb
• Locrian Double-flat 3 Double-flat 7: C Db Ebb F Gb Ab Bbb
• Locrian Double-flat 7: C Db Eb F Gb Ab Bbb
• Locrian/Aeolian mixed: C Db Ebb Fbb Gbb Abbb Bbbbb
• Mela Kantamani: C D E F# G Ab Bbb
• Mela Senavati: C Db Eb F G Ab Bbb
• Messiaen mode 3: C Db Ebb Fb Gbb Abbb Bbbb
• Moravian Pistalkova: C D Eb F Gb Ab Bbb
• Phrygian/Aeolian mixed: C Db Ebb Fbb Gbb Abb

Which scales have a minor chord built on the seventh note?

I am also assuming base scales here*

• Chromatic Hypodorian: C D Eb Fb G Ab Bbb
• Debussy's Heptatonic: C D Eb Fb Gbb Abbb Bbb
• Locrian: C Db Eb F Gb Ab Bb
• Mela Kantamani: C D E F# G Ab Bbb
• Mela Mararanjani: C D E F G Ab Bbb
• Octatonic: C Db Eb Fb Gb Abb Bbb
• Ultralocrian: C Db Eb Fb Gb Ab Bbb

Must they be non-diatonic?

Locrian fits the diatonic requirement