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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.

  • With "base scale meaning not modes," don't you force "must they be non-diatonic" to be answered in the affirmative? – David Bowling Feb 26 at 3:55
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    People keep offering answer and you keep rejecting them because you do not want modes. But the designation of "mode" is western. The "modes" you do not like occur in Carnatic music as unique Ragas. So you should accept them. Otherwise what are you trying to gain from this inquiry? – ggcg Feb 27 at 16:13
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    @RandyZeitman, you may want to expand your horizons and look at other cultures. There are 72, 7 note, Carnatic Ragas based on the 12 step scale (chromatic). By definition diatonic means involving notes in the Key. So, from a western perspective David Bowling is correct, you've force the answer. If you accept each Raga as a "key" then the answer changes. – ggcg Feb 27 at 16:16
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    Then your constraint of "no mode" is unnecessary. And I'm NOT making any accusations of any kind. That is you taking things that way and being hostile. – ggcg Feb 28 at 12:26
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    @RandyZeitman - Composers used D Dorian, E Phrygian and the like for at least 1000 years before someone (Heinrich Glarens) said "hey, these are all the C scale starting from different notes". There's no point to excluding modes, because modes ARE scales, and they always have been. – Tom Serb May 4 at 13:58
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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.
  • Yes... I forgot that all modes are scales but not all scales are modes. I've clarified the question ... no modes. – Randy Zeitman Feb 26 at 3:09
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    I suppose we could include the chromatic scale, which has everything the OP asks for... – Tim Feb 26 at 5:55
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    @Tim Fair enough! I tend to view the chromatic scale as something like a trivial answer in math. It's definitely an answer, I just often skip over it. – Richard Feb 28 at 2:20
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    I don't understand the use of 'trivial' with reference to maths! Is it like the new 'bad' really means good? I really am getting too old for this..! – Tim Feb 28 at 6:39
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    Got it ! Trivial = trivial = as simple as possible! Just like it always meant ! Your chromatic scald sounds painful. Still time to edit... – Tim Feb 28 at 6:48
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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.

  • Yes... I forgot that all modes are scales but not all scales are modes. I've clarified the question ... no modes. – Randy Zeitman Feb 26 at 3:09
  • A scale is simply a set of notes played in ascending (and descending) order. – Tim Feb 26 at 5:50
  • Long ago, I wrote your first sentence. (And a minor triad was m3 + M3). And was scolded for it. Was told a major triad was a maj3 and a P5. – Tim Feb 28 at 6:42
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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

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