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I came across something odd shown in the picture below.

(What this is from is not very relevant, but in case your interested: I'm building a simple phone app that would allow me to practice particular ear training exercises without requiring any user input so that I can practice while cleaning, walking, driving, etc. The app Functional Ear Training is great but lacks a few features I'd like. Anyhow, there's a programming library for the Python language called Mingus. The picture below is from the documentation explaining the use of the library.)

If I understand the passage correctly, it's showing E triad chords but in different keys. It's saying that in the key of E, as expected, E major is E G# B, but in the key of C it's E G B, and in the key of F it changes yet again to E G Bb. I thought an E major triad is always E G# B, but perhaps this picture is discussing something I'm unfamiliar with or maybe I misunderstand how major chords work?

The link to the documentation page is below. This description is only a couple short paragraphs down the page, so you'll find it quite quickly if you want to read it in context:

bspaans.github.io/python-mingus/doc/wiki/tutorialChords

Python Mingus Library

  • I apologize: I was unaware of how diatonic triads differ from "normal" triads---what I believe are technically called absolute triads. For those who share my misunderstanding, I'll leave the question here and here's a link to what diatonic triads are: reddit.com/r/musictheory/comments/3cidkk/comment/csvuubg musictheory.net/lessons/43 In my opinion, the reddit link is significantly better at quickly getting an idea of what a diatonic triad is because it differentiates between a third as in ABC versus a third as in intervals as in root b2 2 b3 3, which is what was confu – JDG Mar 3 '18 at 1:57
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    I have never heard of absolute triads. What is your source on this? Diatonic intervals are intervals found in a specific scale. Diatonic triads are the triads constructed from a specific scale. Usually when someone talks about thirds without further qualification, they mean diatonic thirds in some understood context. By itself, an interval of a third is under-specified. You might be interested in reading this. – David Bowling Mar 3 '18 at 2:22
  • The source is linked at the bottom of the post, though I just noticed I forgot to highlight it. What they're referring to by "absolute triads" is that, for example, a major triad is always R35, a diminished is always Rb3b5, etc (ignoring inversions). – JDG Mar 3 '18 at 5:20
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I thought an E major triad is always E G# B

That is correct. The notes comprising an E Major Triad are always E-G#-B - irrespective of key. However, the notes comprising a diatonic triad whose root is E do vary depending on the key. The cited illustrations are not only of E major triads, but several different types of triads with E as their root. (The root is the base note of the chord - the first note in the series when describing a triad in its 'default' configuration - iterating through its parent scale in order. This configuration is known as the First Inversion).


Your question arises because you are unclear about how intervals are defined and named, and how the resulting different sorts of triads are built from these intervals. This subject is a source of much confusion among many new to music theory.

There are several good answers on the site explaining the basics of interval definition. I wrote about it here: Are intervals like major 3rd, minor 3rd, and major 2nd all based on the scales, or are they based on how many semitones they have? - so I remember this answer, but there are others as well, as good or better than mine.


Cutting to the chase for the purpose of answering this question, here are the rules you need to know:

  1. Every triad is built from two 3rds. Root->3rd is the first 3rd; 3rd->5th is the second 3rd.
  2. 3rds in this case are comprised of the Major 3rd - 4 half steps: for example, C-E, or Minor 3rd - 3 half steps, for example C-Eb (minor means small or less, as in 3 is smaller than 4).
  3. Those two types of 3rds can be combined in 4 different ways to build triads, giving us four different types of triads (there is no such thing as an 'absolute' or 'normal' triad'), based on the types of 3rds being used to build the triad, in the order they appear :

    • Major 3rd/Minor 3rd: This gives us a Major Triad - ( chords.triad(E,E) )
    • Minor 3rd/Major 3rd: This gives us a Minor Triad - ( chords.triad(E,C) )
    • Major 3rd/Major 3rd: This gives us an Augmented Triad. (Not included in the examples cited)
    • Minor 3rd/Minor 3rd: This gives us a Diminished Triad - ( chords.triad(E,F) )

Now for your specific examples:

chords.triad(E,C) does not mean a major triad. It means the diatonic triad in the key of C Major (second argument in the function) with a root of E (first argument in the function). Same with all of those function calls.

Diatonic in this sense means that we use only the notes of the key in question to build the triad. That is the meaning of the text you posted: Natural Diatonic Triads.

So: chords.triad(E,C) == E,G,B - a triad comprised only of notes of from the key of C major. However, this is an E Minor Triad, because E->G is a minor 3rd and G->B is a Major 3rd - as per the second item in our list of triads.

But: chords.triad(E,E) == E,G#,B - a triad comprised only of notes from the key of E Major. In that case this is an E Major Triad, because the first 3rd is major: E->G# is a major 3rd and the second 3rd G#->B is minor- as per the second item in our list of triads.

Lastly: chords.triad(E,F) == E,G,Bb - a triad comprised only of notes from the key of F Major. In that case this is an E Diminished Triad, - as per the fourth item in our list of triads - because E->G is a minor 3rd, and from G-Bb is also a minor 3rd. Bb here is called a diminished 5th - meaning it is one half step lower than the perfect or 'normal' 5th - it is a 5th that is reduced-diminished in size and diminished gives this triad its name, to distinguish from the minor triad.

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When a triad is built upon the 1st, 4th, or 5th degree of a Major scale it will be a major triad. But when a triad is built upon the 2nd, 3rd, or 6th degree of that same scale, it will be a minor triad. When a Chord is built upon the 7th degree of that same scale, it will be a minor7th flat 5 chord, which means you end up with 3 different kinds of chords whose structure is determined by the scale degree of the root note of the chord. Is this the answer you're looking for?

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Not the best explanation I've ever seen! To simplify, tremendously: it tries to show 3 triads (3 note chords). All with E as the start note. All in different keys. The first uses notes (diatonic notes) from key C. Thus E G B. Making E minor, the most found 'E type chord' in key C. The next shows diatonic notes from key E. Thus E G# B- E major, the most found E chord in key E. The last shows a triad using the notes from key F. Thus, E G Bb. Eo, the most found E chord from key F.

What the example you show fails to explain is that there are four different types of thirds, as Rockin puts in his answer. Yours merely says glibly 'adding its third and fifth'. If it had explained better, you wouldn't have posted the question, true?

To answer your header: No. An E major triad will always be the same three notes, E G# B, in any order, with doubles on some instruments, regardless of what key a piece is in. A triad with E as one of its notes may well have the other two different, dependant on key, but by then, it's obviously not going to be called E major.

Thanks for the link. I looked through it - much as a teacher checking homework - it's in the blood ! - and one omission is a sus2, there's a sus4 included. Not come across the term 'absolute' triads, and wonder if it's necessary. I think all triads would fit into the group, diatonic or not. and it's not a particularly descriptive term.

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