# The chord formula for the Major Chord is 1- 3 - 5. What do the numbers represent?

According to Wikipedia (paraphrased), a Major Chord has a Root, a Major Third, and a Perfect Fifth. One way, therefore, to arrive at the notes in the C Major Chord is to begin with the note name, C; stack onto C a Major Third (which is four half steps) to arrive at E; then stack onto C a Perfect Fifth (seven half steps) to arrive at G. Thus, the C Major Chord has the notes: C - E - G.

So, my question is: Isn’t it just as correct (and, if not, why not), to simply know the notes in the C Major Scale and take the 1st, 3rd, and 5th notes to arrive at the same chord?

And doesn’t the latter method work for all scale types: major, the minors, the pentatonics, blues, and diminished?

Finally, and in the same vein, the chord formula for the Major Chord is 1- 3 - 5. Do the numbers represent intervals, e.g., 5 equals a Perfect Fifth; or can they just as well represent the note names at those positions in the scale?

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The relationship of chords to scales is an important one to understand, as it serves as a foundation for songwriting, composition, and improvisation. In our chromatic system of harmony, there exists a scale (or many scales) for every chord, and there exists a chord (or several chords) for every scale. As an example, here are several chords that can be derived from the C Major Scale:

And, similarly, several scales which include a C Major triad:

Isn’t it just as correct (and, if not, why not), to simply know the notes in the C Major Scale and take the 1st, 3rd, and 5th notes to arrive at the same chord?

It works for major scales, yes, because the major scale is such a scale that the interval relationships line up with the scale degrees. The 3rd degree of this scale happens to be a major 3rd, and the 5th degree happens to be a perfect 5th. I'll expound upon this in a moment.

Also, you should understand that this is not the exclusive relationship that the root, major 3rd, and perfect 5th combination have to a scale. If you wind up trying to improvise an idea or compose a melody over a C Major triad, for example, you can use any of the scales pictured to create ideas which include those tones (and introduce new ones).

And doesn’t the latter method work for all scale types: major, the minors, the pentatonics, blues, and diminished?

Consider this:

If I were to pull the 1st, 3rd, and 5th scale degrees from this scale, I would have myself a minor triad. But, as you can see, that doesn't really encapsulate the entire story that this scale tells - especially considering the tonality of this scale becomes a bit obscured by the presence of both a minor and major 3rd and the absence of a 7th.

To answer your question, there is a better rule to follow: Know the chord tones that comprise those scales. That way you won't be pulling scale degrees and making assumptions about chord quality - you'll have a deeper understanding of the entire tonal function of that particular scale.

Finally, and in the same vein, the chord formula for the Major Chord is 1- 3 - 5. Do the numbers represent intervals, e.g., 5 equals a Perfect Fifth; or can they just as well represent the note names at those positions in the scale?

This sort of relates to what I mentioned previously - in the case of C Major, we are referring to both the scale degree and the intervalic relationships because they happen to be one of the same. However, this is not always the case (as in the above example), so make sure you are aware of whether they are mentioning the scale degree (the order in which the tone appears in the scale) or the interval (the distance that tone is from the root of the scale.)

I hope this helps, and good luck!

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Isn’t it just as correct (and, if not, why not), to simply know the notes in the C Major Scale and take the 1st, 3rd, and 5th notes to arrive at the same chord?

Not only is this correct, but in my opinion, it is a much better way to think of how to build chords than the count-the-half-steps approach you outlined above. Thinking about chords as coming from scales reinforces the relationships between the two and helps you to understand music better.

doesn’t the latter method work for all scale types: major, the minors, the pentatonics, blues, and diminished?

I don't quite understand what you mean here. Do you mean that taking the first, third, and fifth notes from, say, the pentatonic scale yields a pentatonic chord? If so, then this is not exactly correct.

the chord formula for the Major Chord is 1- 3 - 5. Do the numbers represent intervals, e.g., 5 equals a Perfect Fifth; or can they just as well represent the note names at those positions in the scale?

But those two ideas are not unrelated: after all, why do you suppose a fifth is named a fifth? It's because it's the interval from the first note of a major scale to the fifth note of that scale.

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Regarding other scale types (e.g., minor, pentatonic, etc.) my thinking was off. That’s because-- isn’t it correct to say?—all modern, common chord formulas are initially based on the Major Scale (not minor, pentatonic, etc.). In other words, chord formulas begin with the Major Chord (from the Major Scale) and then we modify the Major Chord formula to arrive at other chord types. For example, the Minor Chord formula can begin by using the Major Chord formula and then modifying the Major Third to a Minor Third. Is it inaccurate to think of the process that way? Thanks, Alex! – Otis Gilchrist Jul 13 '13 at 19:22
@OtisGilchrist You're correct, chord and scale formulas are written as they relate to their respective major scales. As you described, a minor triad would be spelled 1 b3 5, the b3 being the 3 present in the major scale lowered by a semitone. This is why the minor scale is written as 1 2 b3 4 5 b6 b7. – Evan Carlstrom Jul 13 '13 at 19:29

I think we're making this a bit complicated.

1-3-5 means the first, third and fifth notes in the associated scale.

Play a C major scale - C,D,E,F,G,A,B. Pick out the 1st, 3rd, 5th - C,E,G. That's the C major triad chord.

But that's not unique to major chords. If you play the 1-3-5 from C minor, you get the C minor triad chord. C,D,Eb,F,G,Ab,Bb -> C,Eb,G

So:

• A major triad uses the 1st, 3rd, 5th notes of the corresponding major scale (which means you need to know what notes are in that scale to use this definition)
• Equivalently, a major triad uses the root note, the root note + 4 semitones, the root note plus 7 semitones (you don't need extra information about the scale if you use this method)
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