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This article from wikipedia, states:

In the first inversion of a C major triad the bass is E—the 3rd of the triad—with the 5th and the root stacked above it (the root now shifted an octave higher), forming the intervals of a 3rd and a 6th above the inverted bass of E, respectively. A first-inversion triad is also known as a 6/3 chord.

I don't understand this part: forming the intervals of a 3rd and a 6th above the inverted bass of E. The root position chord is C E G. The first inversion would be E G C. But to form an interval of 3rd and 6th over E it would need to be E G C# not E G C.

Can someone clarify this for me?

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Wikipedia says "a 6th". It doesn't say what kind of 6th. An interval from any "flavor" (my word) of an E (such as Eb, E, or E#) up to any flavor of C (Cb, C, C#) is a sixth, because E-F-G-A-B-C is six notes. But the kind of 6th---major, minor, augmented, diminished, double augmented, double diminished, etc.---depends on the respective flavors of the E and C involved.

In the case of a C major chord, both the E and the C are natural, because those are the flavors of E and C that occur in C major (in fact, what distinguishes one key from another are precisely the flavors of the seven notes for that key; in the key of C, all notes are naturals.). Therefore the interval from an E to a C is a minor 6th, not a major 6th.

This will be true for inversions of the root triad of any other key as well. For example, in the key of D, the root triad is D-F#-A. So the first inversion is F#-A-D. F#-G-A-B-C-D is six notes, so an F#-to-D interval must be a sixth. But it's only eight half-steps between them, so it's a minor sixth instead of major sixth.

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http://en.wikipedia.org/wiki/Interval_(music)

An interval is simply the count of notes from one to another. So a sixth just means that, including the root, you've counted up six notes in that scale. It's not the count which determines the sharp/natural/flat-ness of the note. The scale determines that. If the scale contains C, then it will always be C, no matter the note from which you start counting.

Once you've determined the notes, then the specific distance between them can be qualified with a quality (minor, major, etc) that says exactly how many half-steps are between the notes. In the case of E to C, it is a sixth just by virtue of the note names, but that particular distance happens to be a minor sixth, a half step shorter than the major sixth of which you're thinking, which is why it doesn't have to be C#.

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This is correct. A minor 6th above E is C and a major 6th above E is C#. So an interval of 3rd and 6th over E is E G C, as you are in a key where a minor 6th above E is needed. I hope I helped.

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To help you understand where we get the numbers from take the tonic of C for instance. If you would write it on paper it would be C then above it E and then G. Inversions always care about what note is on the bottom. Composers can change the notes above the bottom note as need be without changing the inversion.

If count from C to E you get three (C being number 1) C,d,E. If you count from C to G you get five C,d,e,f,G So that is why you sometimes see a chord in root position noted as I 5/3

If you take that same chord and throw it into first inversion you get the notes E/G/C Let us count from the bottom note now. E,f,G - 3 and then E,f,g,a,b,c - 6 Hence first inversions are sometimes noted as 6/3

Lastly second inversion in this case it would be the notes G/C/E Let us count from G to C. G,a,b,C. That is four Now from G to E. G,a,b,c,d,E. That is six Hence why second inversion chords are sometimes noted as 6/4

Hope that helps.

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Reading this thread is a good reminder for me that music can be approached either mathematically or intuitively. When we talk about intervals, we are basically taking a mathematical approach. Another way of looking at chord inversions is to identify the notes in the chord and combine these with the basic chord "shapes" to determine the different inversions. While I know my theory, I approach music in a more intuitive manner, and this is more helpful and quicker for me than counting intervals.

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Yes E to C is a sixth. A minor sixth, but a sixth.

Indeed sixths and thirds have an inverse relation since both sum a complete octave.

  • So if C to E is a major third, E to C is a minor sixth.
  • .....If C to Eb is a minor third, Eb to C is a major sixth.

Both are called indistiguishly thirds and sixths. For instance, they are usually present when you sing a chorus over a main vocal line.

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