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Why, if the 13th (or, the 6th) of a C minor chord is Ab, and not A.

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The 6th note of of Cm scale is Ab rather than G#, but see my answer below.I bet you're a guitarist !! –  Tim Apr 21 at 18:47
    
Apart from anything else, C minor with an Ab doesn't usually sound that great in some voicings, due to the semitone between the G and Ab. –  sweeneyrod Apr 22 at 15:13
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When a 13th is written in a chord name, this always refers to the major 13th, which is the same as a major 6th - in this case an A natural. This is one of the conventions of how chords symbols are written. It may seem a little odd that the 6th or 13th of a minor chord is major, but there are a number of situations like this. For instance, 7ths are always flattened (minor) sevenths, when only a "7" is written, whether this is on a major or minor chord; if you want a major 7th, you have to write "maj7". (You're probably familiar with this, and wouldn't even think twice about it.)

This is simply the way these chords are written.

But, this has advantages; it means that we always know what interval a 13th (or 7th or 9th or anything else) is going to add to a chord, no matter what the other notes of the chord are. In particular, we know what interval to add even if the tonality or modality of surrounding chords, other parts of the chord itself, or written parts (eg. bass line or melody), might suggest a different interval.

I can see two reasons why you might think a Cm13 chord has an Ab; let me deal with both:

  • The key signature of C minor and the C Natural Minor Scale (Aeolian) have a flattened sixth degree (Ab). Yes, but there are minor modes/scales on C (with a minor triad on the root note, i.e. chord I is Cm) which have MAJOR sixths: C Dorian and C Melodic Minor Ascending are two obvious ones. Tim mentioned these already.
  • It might also be possible that you were reading C…m13 rather than Cm…13, in other words, a C chord with a minor 13th. This would be a completely different chord, and, although we do talk about minor 13th intervals, these would be notated in a chord symbol as b13 (i.e. a flattened 13th - Ab).

Lastly, it is worth mentioning where this misunderstanding arises; through trying to work out what intervals are in a chord by using a supposed mode/scale containing these notes, rather than choosing a mode to use which fits the chords (the harmony). The second way is how we actually play. The chord symbols tell us exactly which notes the composer wants in the harmony at any particular point in a piece/song, we then choose a mode for improvisation or creating a melody, bass or harmony line to fit the chord, not the other way around. For instance, Cm13 suggests the notes C Eb G Bb D (F) A (as a 13th chord is built using tertian harmony - sorry if you don't know anything about that yet!), this in turn would suggest that C Dorian would be a good scale to use with it.

To sum up. When reading a chord, don't worry about the key the piece/song is in, and which mode or scale this might suggest, or the character of the surrounding harmony. The chord you are reading might not relate closely to these anyway! Instead, follow some simple conventions for working out what the intervals in that chord are. The following intervals are presumed to be major unless adjusted with a flat or sharp: 2, 6, 9, 13. (Be aware, though, that the flat or sharp adjustment is relative to the major interval - eg. a 6 on E is G#, so a b6 is G natural!) Thirds are notated in the first bit of the chord itself: so C something-or-other is major, with a major third; Cm something-or-other is minor, with a minor third. Fourths, fifths and 11ths are presumed to be perfect unless adjusted. 7ths are the weird ones; they are presumed to be flattened (minor) unless marked as major - this is because the most common use of 7th chords traditionally is on dominant chords, and 7ths on dominant chords are minor - again, this is a whole other area of discussion and probably merits some study too (this post is useful, but there is also loads on the web…)

You should probably read up on how tertian harmony works, to fully understand which notes you usually put in 9th, 11th and 13th chords, and which ones can be safely left out (very important for guitarists!)

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Yow ay arf bin bizzy !Well done. An erudite explanation at last ! –  Tim Apr 21 at 20:16
    
This seems accurate enough. If one cannot understand this, one should perhaps pursue tiddlywinks instead... –  Tim Apr 21 at 20:22
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This is one of the weird bits with chords. With a maj.6 on C, it's C E G A. With a min.6 on C it's C Eb G A. It's the chord that's minor, not the 6th interval.The minor 6th interval is Ab rather than G# anyway. So for 6th or 13th, which is effectively and in reality the same note - possibly different octave - seems to depend on one's persuasion - its going to be A natural.It would never have been G in any case, as G is the 5th or 12th , and that is in the original triad.

On the subject of notes in scales, in the melodic minor,(classical) ascending, the 6th note IS A natural.

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How did you know I play the guitar!? (= Does it mean we dont use the diatonic minor scale when it comes to a Cm13? –  user10354 Apr 21 at 18:57
    
Nope, we all use the same scales (ish), but us guitarists just think a bit differently…! –  Bob Broadley Apr 21 at 19:02
    
Sorry about that ! Guitarists ( I play as well) tend to use # rather than b for naming notes.The guitar is what I call a 'sharp' instrument, as opposed to something like saxes, which I call 'flat'. Trouble is, notes need to be named from their roots - as in, the note we discuss was A, moved to Ab, rather than G, moved to G#. –  Tim Apr 21 at 19:02
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I still dont get it, why we´re using A rather than Ab? The 6th of C minor is Ab, not A. – What does mean "classical" btw? –  user10354 Apr 21 at 19:10
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It's also a practical thing. The notes C Eb G Ab don't sound like any kind of minor chord, because they would most simply be interpreted as a Major 7th chord in first inversion (Ab C Eb G, with the C at the bottom). –  Bob Broadley Apr 21 at 19:19
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This is not an exception or something illogical. There are many scales whose 1, 3, and 5 form a minor triad. Some of these have a major 6, some a minor 6. A C minor chord could, for example, appear in the key of B flat, where an A natural occurs in the key signature. People reading chord symbols want to be able to connect the symbol with a specific chord, so we use specific rules about what the symbols mean. The rule is that in a 13th chord, the 13 (6) is major.

There's the closely related notation Cm6. Note that if you interpreted Cm6 as having an Ab in it, you'd get C Eb G Ab, which would sound to most people like an Ab maj7 chord, not a C minor triad.

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