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?

• Just wanted to say thanks for asking this question — nearly ten years later and it's proven useful to a new student like myself and I'm sure many others who have come across it. Nov 21, 2023 at 16:04

7 Answers

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:

With that, to answer your questions -

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!

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)

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.

• 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! Jul 13, 2013 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. Jul 13, 2013 at 19:29

If you just count semitones you may get the spelling wrong! 4 semitones up from D, for instance, is a note that could be called Gb or F#. But if we think of it as the third note of D major, it HAS to be F#, because scales (major and minor ones at least) always use one of each letter name.

• 2nd para.: you hint that 'other intervals in a major scale are major' -o.k. But then 'in natural minor they're minor'. What about ^6? I upvoted due to the 1st para., before reading the 2nd.
– Tim
Nov 12, 2022 at 13:41
• Yeah, I was talking b***ocks there. Edited. Thanks. Nov 12, 2022 at 17:01
• @Tim the sixth degree of (e.g.) A minor is F. F is a minor sixth above A. Nov 12, 2022 at 18:10

The numbers represent the notes; we have c d e f g a b which translate to 1 2 3 4 5 6 7 in uniform manner, so since major is 1 3 5; mnor would be 1 3b 5 and diminished would be 1 3b 5b. the b means flat. we have more than these 7 notes in music, there are 5 accidentals in music to make them complete 12, so the remaining are represented with b(flats) or #(sharps). learn more about all these musical theories here

The formulas for all chords reference the major scale. The numbers are called degrees.

{1, 2, 3, 4, 5, 6, 7, 8} = {Do, Re, Mi, Fa, Sol, La Ti, Do}

When building the X major chord you take notes 1, 3, and 5 from the X major scale. In another answer it was stated that if you took the notes form the minor scale you'd get C, Eb, G. While this is correct it is not really how the formula works.

The formula for a minor chord is {1, b3, 5}. The third of the minor scale is already flat so if you flatten it again you'd get a double flat, called diminished 3rd (enharmonic to a 9th). What the formula is saying is take the 3rd note of the Major scale and flatten it. The starting note, X, can be anything.

Other formulas are:

Dominant 7th = (1, 3, 5, b7)

9th = (1, 3, 5, b7, 9)

Diminished triad = (1, b3, b5)

Diminished 7th = (1, b3, b5, bb7)

You could say that these are "intervals" as long as you realize that the starting note is X, the 3 is a 3rd up from X and the 5 is a 5th up from X. In fact this is common notation for chords and their inversions. We notate inversions by listing the intervals relative to the Bass note. For example the notes (1, 3, 5) played in that order from lowest to highest is called the Root Position. It could be noted (3, 5) to indicate that the intervals are 3rd and 5th but this not done. We take it as given that without any other notation the chord is a (1, 3, 5) in that order. The first inversion would have the notes ordered (3, 5, 8) and the intervals are a minor third and a minor 6th. Despite being minor and not major we notate the 1st inversion as a (3, 6). The second inversion would be the ordering (5, 8, 3 (octave higher)) and the intervals relative to the bass are a P4 and major 6th. So we notate it (4, 6). The point of this diversion into inversion (inversion diversion) is that "intervals" are used in multiple contexts to indicate how a chord is structured but that the formula for choosing the correct notes is the same in each case. A C major chord has the notes (C, E, G) regardless of the ordering. And this is what the formula you are asking about truly means, it's a list of the correct notes to choose relative to Root.

What do the numbers represent?

Everything needs a `reference point`. So for the piano keyboard, and for the lines on lead sheets, the reference is the `C-Major scale`.

`Notation` has developed such that:

• lines and spaces on the lead sheet represent white keys (of the C-Major scale, the reference point)
• to indicate black keys flats (b) or sharps (#) are used

(So next time you sit down at a piano, starting with your RH thumb on white key E, identify the other 4 staff lines G, B, D and F. Do you see the spaces between your fingers? And how they do relate to the spaces on sheet notes?)

To this point I'm just talking about `mechanics, or coordinates` if you like, free of any consideration from music theory: `where is which note?` The musical impact, e.g. relationship between whole- and semitones, was already indicated in other answers here.

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?

Yes. And you avoid a lot of theoretical trouble if you just know:

• which notes belong to the scale I'm using
• how to enumerate them
• stay inside this scale, e.g. also for chords

it will take you a long way during playing.