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I am learning Music Theory from several different sources and I am currently concentrating on intervals and moving into building chords using intervals.

I am trying to find patterns in order to reduce the amount of raw data that I need to learn.

I have noticed that...

...a Major 7th chord, uses a Major Triad (1-3-5) and adds a Major 7th interval (1-3-5-7)

...a Minor 7th chord, uses a Minor Triad (1-b3-5) and adds a Minor 7th interval (1-b3-5-b7)

This appears to suggest a patten of (Base Chord) + 7th interval also based on the name of the chord.

ie Major Triad + Major 7th = Major 7th or Minor Triad + Minor 7th = Minor 7th

UPDATE: The following text was found to be based on incorrect data found on the internet (Who'd have thought :P)

This does not appear to ring true with 6th chords.

...a Major 6th chord, uses a Major Triad (1-3-5) and adds a Minor 6th interval (1-3-5-b6)

...a Minor 6th chord, uses a Minor Triad (1-b3-5) and adds a Major 6th interval (1-b3-5-6)

ie Major Triad + Minor 6th = Major 6th or Minor Triad + Major 6th = Minor 6th

The interval added to form a 6th chord appears to be the inverse of the name of the chord. So a minor interval is added when the chord is major, and a major interval is added to a minor chord.

Is there a reason for this apparent inconsistency?

Is there some sort of rule which I can use to predict higher order chords? (9ths 11ths etc)

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    That definition of a major 6th chord doesn't look right to me--both en.wikipedia.org/wiki/Sixth_chord and music.tutsplus.com/articles/… say it's a major triad with a major 6th interval. – Dekkadeci Dec 22 '17 at 20:32
  • Thank you very much. I was looking at the first hit on google which led me to -> smithfowler.org/music/Chord_Formulas.htm?i=1. Obviously (well now at least) this is simply wrong. Thanks once again for pointing me in the right direction. – Rory Becker Dec 22 '17 at 20:42
  • Note that there is also the dominant 7th chord which is 1-3-5-b7. Also the fully diminished 7th chord is 1-b3-b5-bb7 and a half diminished 7th chord which is 1-b3-b5-b7. So it's not quite so simple even for just 7th chords. – Todd Wilcox Dec 22 '17 at 21:35
  • Thanks @ToddWilcox I've essentially been trying to establish if I was able to say, for example, that a Major Xth chord was a Major triad with a Major X interval added, and a Minor xth chord was a Minor triad with a minor Xth interval added. Rules like this are very helpful. – Rory Becker Dec 22 '17 at 22:41
  • @ToddWilcox Your points about Dominant and Half diminished chords are well taken. Do these (dominant, fully diminished and half-dimminished) exist as 6th chords also with similar spellings? – Rory Becker Dec 22 '17 at 22:43
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The Wikipedia article on sixth chords contradicts the statements about sixth chord nomenclature in the question.

The article names the following kinds of sixth chords (with respect to popular music only, not the classical music nomenclature, also discussed in the article):

  • Major triad with a major 6th added: sixth chord, added sixth chord, major sixth chord, C6, CM6
  • Minor triad with a major 6th added: minor sixth chord, minor major sixth chord, Cm6

Triads with minor sixths added are not discussed, most likely because they are rarely, if ever, used. Note that a non-diminished triad with a minor 6th added would have a highly dissonant minor second interval present between the perfect fifth and the minor sixth.

See also: Why does a minor sixth chord contain a major 6th interval?

Going to the larger question, when you see an interval beyond the 7th added to a chord, the best assumption to make is that it is the major or perfect form of the interval unless there is an accidental added. For instance, a Gadd13 chord is a G major triad with an added major 13th (or an octave plus a major sixth). If a minor 13th were intended, the chord would be called "Gadd♭13". An augmented interval would be indicated with a sharp sign.

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A few rules for chord naming:

  • Triad names imply the root, third, and fifth (eg. B♭m is B♭-D♭-F).
  • Sevenths are implied by the number 7 at the end. Where X is the root, XMaj7 denotes a major seventh, Xm7 denotes a minor seventh (and also denotes that the triad is minor), X7 denotes a dominant seventh (♭7), etc.
  • Any extensions (notes beyond 7) are named as such, implying the previous notes as well. Note that if the highest extension is altered, the second-highest is listed as well. Examples: D13 has D-F♯-A-C-E-G-B (the major triad is assumed, and with no mention of major or minor the seventh is dominant). G7♭9 has G-B-D-F-A♭ (dominant chord, and we use the seventh to name itbecause the ninth is altered). A♭maj13♯11 has A♭-C-E♭-G-B♭-D-F (Major triad and seventh because of the "maj", all extensions including the 13th because of the "13", and the ♯11 at the end means to sharpen the eleventh.
  • If the chord is suspended, this will be noted after the highest extension. C7sus2 is C-D-G-B♭. A9sus is A-D-E-G-B. -If there's a skip in the extensions, the word "add" can be used so as to exclude the correct tensions. Emadd9 is just E-G-B-F♯, not including the D.

One more thing: The reason the chords don't name themselves by an altered extension (why we have D7♭9 rather tha just D♭9) is because of the confusion that could arise. For example, C♭13. Does that mean a dominant 13 chord on C♭ (enharmonic to B), or is it a C13 chord with a flat 13th? Or is it a C chord with an added 13th? By naming it a C11♭13, there's no confusion, as there's only one possibility.

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