The chord formula is 1-3-5 (for a triad). When played with different notes in different scales, there will be a difference in the no. of semitones b/w the notes of the chord. Which will decide on the quality of the chord, wether it is major, minor, augmented, dimunished etc. Is this correct?

Edit: Each comment added something different & gave a more whole perspective. Cheers yall.

The chord formula is 1-3-5 (for a triad).

Yes. And you can keep stacking up the thirds 1 3 5 7 9 11 13 to get 7th chord, 9th chords, etc. Basing chords on thirds in this way is called tertian harmony.

Which will decide on the quality of the chord, whether it is major, minor, augmented, dimunished etc?

The 1 part of the chord is called the root, and of course the 3 and 5 are the third and fifth of the root. All triads will have a root, third, and fifth.

You can determine the quality with different methods but in the end you must consider both the third and the fifth above the root. Some people like to think of the triad as two stacked thirds. I prefer to think about it as a third and a fifth above a root.

• When the fifth is a perfect fifth (seven semitones) the triad will be either major or minor
• if the third is major, the triad is major (C E G)
• if the third is minor, the triad is minor (C Eb G)
• When the fifth is diminished (six semitones)...
• ...and the third is minor, the chord is diminished (C Eb Gb)
• ...and the third is major, the chord is not a diatonic triad and does not have a specific name (C E Gb)
• When the fifth is augmented (8 semitones)...
• ...and the third is major, the triad is augmented (C E G#)
• ...and the third is minor, the chord is not a diatonic triad and does not have a specific name (C Eb G#), enharmonically this is an Ab major triad in first inversion, but with this specific spelling it technically isn't a major triad

I highlighted in both the combinations that make the four basic triad types. The other two bullet points - the ones that make odd triads without names - I included only so you can see those combinations aren't normally used.

You may wonder why I suggested first looking at the fifth, then the third.

Each key has 7 diatonic triads of which 6 have perfect fifths above the root. The 1 chord that is different is the diminished triad using the diminished fifth. The augmented triad isn't even included in the diatonic triads!

The perfect fifth is so important in tertian harmony that I prefer identifying the root and fifth first, then identifying the third.

If I understand your question right, you're forming chords on scale degrees. In the key of C major you'll get a major triad on some notes (C, F, G) a minor triad on some notes (D, E, A) and a diminished triad on one (B).

The way we identify the quality is to compare the tones to the major scale of the chord root. Staying in C, we can compare the triads to the scales, and see which notes are altered:

C-E-G : compared to the C scale (C-D-E-F-G-A-B) it's 1-3-5, a major triad

D-F-A : compared to the D scale (D-E-F#-G-A-B-C#) it's 1-b3-5, a minor triad. The third of the chord (F) is a half step lower than the third of the root tone's major scale (F#), and this is what makes it a minor chord

B-D-F : compared to the B scale (B-C#-D#-E-F#-G#-A#) it's 1-b3-b5, a diminished triad. Both the third and fifth are lower than the corresponding tones in the root's major scale.

You'll get augmented triads if you harmonize some scales. If you were in C harmonic minor (C-D-Eb-F-G-Ab-B) the chord built on Eb will be Eb-G-B. Compared to the Eb scale (Eb-F-G-Ab-Bb-C-D) the fifth has been raised, making the chord formula 1-3-#5.

Correct.

Note that a diatonic triad will never be augmented in any traditional key. Most will be major or minor, a few will be diminished.

• Isn't there only one diminished triad obtainable from a diatonic set of notes - that based on the leading note? Which others make 'a few'? – Tim Apr 18 '19 at 7:49
• @Tim The supertonic in minor. Even though it's the same as the leading-tone triad in major, it functions differently, so my brain categorizes them as different. – Richard Apr 18 '19 at 10:01

Supposing you know how the triads are built - if not look up the theory! - following procedure will help you to derive all chords in all keys on your own:

Draw a scheme of keyboard where all keys (b&w) have the same distance like this picture:

This imgur picture doesn’t fit to my plan. I have to upload my own again:

(You can design the note names if you need)

Then write on a strip with a C-major scale or a movable doremi all triads of all degrees horizontally so you can read all triads in all keys and derive and transpose them yourself.

Strictly speaking, a chord can't be "augmented" or "diminished".

A chord can only be "major" or "minor". The interval between 1 and 3 give the nature:

("T" = "Tone", "ST" = "Semi-tone")

• 1T1/2 between 1 and 3 implies "minor"
• 2T between 1 and 3 implies "major"

All of the other terms — augmented, diminished, etc. — require to define which interval is augmented, diminished, etc. Exception made for some of them (see below).

'augmented' means one semi-tone (ST) over the perfect state.

'diminished' means one semi-tone (ST) under the perfect state or the minor state.

On 6 degrees, the 5th (quint) is perfect. That means 3T1/2 from 1 to 5. So the perfect state, 5th can be 'augmented' (3T1/2 + 1ST) or 'diminished' (3T1/2 - 1ST). The same for the 4th (quart), its mirror interval : 2T1/2 is a perfect 4th. 2T1/2 + 1ST is an augmented 4th, 2T1/2 - 1ST is a diminished 4th.

We call such a chord a chord with augmented 5th (C aug.5th) or a chord with dinunished 4th (F dim.4th).

Sometime, we talk about de "augmented chord" for "chord with an augmented quint", but it's an « artistic licence», an abuse of language ;-). We do so because the 5th is the very most augmented interval, in a chord.

Like 3th which can't be perfect, the 7th can be minor (C-Bb) or major (C-B). Unlike the 3th, the 7th can also be diminished (F#-Eb).

So, you see, we (always) have to know which degree is altered in the chord to qualify it.

• "dim7", where we only talk about 7th. You have to know that in this chord the 3th is always minor and the 5th is always diminished. No exception. It's a so frequent chord that we have to give it a shortname, a pseudo.

• "semi-dim7" (used in english? in french: 7e demi-diminuée). You have to know that 3th is always minor and 7 is always diminished.

• sus (Gsus7, ), where the 3th is replaced with the 4th (G C D F -> 1 4 5 7)

(If someone wants to correct my very bad english, I give him white card ;-)