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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.

Richard
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Randy Zeitman
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  • With "base scale meaning not modes," don't you force "must they be non-diatonic" to be answered in the affirmative? –  Feb 26 '19 at 03:55
  • @DavidBowling I know what diatonic is but I don't know scales outside of major and minor. – Randy Zeitman Feb 26 '19 at 16:21
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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? –  Feb 27 '19 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. –  Feb 27 '19 at 16:16
  • @ggcg I've no idea why you're making such an accusation. My question doesn't require Western or Modern (whatever they are). – Randy Zeitman Feb 27 '19 at 22:34
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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. –  Feb 28 '19 at 12:26
  • @ggcg ?... Sir. What can one say. I made no limit. I see nothing remotely hostile. All I said was I don't understand what you mean. – Randy Zeitman Feb 28 '19 at 19:58
  • "Not modes" is a limit. –  Feb 28 '19 at 21:59
  • @ggcg Sir I was referring to your point about culture. – Randy Zeitman Mar 01 '19 at 01:56
  • My point on culture is on point. You are pigeon holing the question and response by saying "no modes" when "mode" is a western device. Then the answer is that Phrygian has a major chord on the second note. Where Phrygian = the equivalent Carnatic raga. –  Mar 01 '19 at 17:58
  • @ggcg Sir... I have no knowledge about the history or culture of modes except that it's where you start on a different note. Yet again I've no argument with your point ... I am NOT knowledgable about the points you claim I am ignoring or pigeon holing. – Randy Zeitman Mar 01 '19 at 23:00
  • Well then I've caught in a mosh –  Mar 06 '19 at 19:01
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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 04 '19 at 13:58

3 Answers3

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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.
Richard
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  • 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 '19 at 03:09
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    I suppose we could include the *chromatic* scale, which has everything the OP asks for... – Tim Feb 26 '19 at 05:55
  • Dang, @Tim, you beat me to it! – user45266 Feb 27 '19 at 01:00
  • HA! Chromatic ... there's #1! – Randy Zeitman Feb 27 '19 at 22:36
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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 '19 at 02:20
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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 '19 at 06:39
  • @Tim As a really simple explanation, let's say we have the function 2x=y. A "trivial" answer would simply be where both x and y are 0. To me, that's akin to the chromatic scale for this question: it includes all 12 pitch classes, so of course it will have what OP is searching! – Richard Feb 28 '19 at 06:45
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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 '19 at 06:48
  • @Tim I might be a little late here, but I think "trivial" is "obvious to the point of near invalidity". As an example, when professors ask "how can I raise the average score on my tests" on Academia.SE, a trivial solution is to expel every student that doesn't do well enough. Sure, it works, but it's pretty useless to OP. Another example: "If I have 117 apples, and want to split them evenly between some friends without cutting the apples, what number of friends can I have?". "0 friends" is a solution, but it's trivial. If you have 0 friends, you can divide any number of apples among yourself. – user45266 May 06 '19 at 01:44
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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.

Tom Serb
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  • 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 '19 at 03:09
  • A scale is simply a set of notes played in ascending (and descending) order. – Tim Feb 26 '19 at 05:50
  • 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 '19 at 06:42
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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