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Reading online says the scale intervals are 1-3-5 for a major chord, so I look at the order of C-D-E-F-G-A-B and start at 1 which is E then add two and get G and then add two again and get B, clearly this is wrong but I don't know why.

So, how come notes in E chord are E-G#-B and not E-G-B?

Dom
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user3486373
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5 Answers5

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Triads are built with the root (1), 3rd, and 5th. If the interval from the root to the 3 is a major third, AND the interval from the 3 to the 5 is a minor third, that triad is called major. So M3 + m3 = major

m3 + M3 = minor

M3 + M3 = augmented

m3 + m3 = diminished.

Any major scale will have several major triads (built off of the 1st, 4th, and 5th scale degrees), several minor triads (built off of the 2nd, 3rd, and 6th scale degrees), and one diminished triad (built off of the 7th scale degree).

The Chaz 2.0
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Put simply, your problem started when you counted. You started at 3. If you'd started at 1, you'd have Cmaj.

You need to start at 1 for the key you're in. So, in E, with notes E F# G# A and B, 1,3,5 gives E G# B. Voila - Emaj.

Tim
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I think @Tim has summarized it very nicely in his answer. This answer is just an elaboration on what he subsequently posted:

You have built a triad with E,G,B, but it's not a major triad. Here's how it works:

  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, based on the types of 3rds being used to build the triad, and the order in which they appear :

    • Major 3rd/Minor 3rd: Major Triad.
    • Minor 3rd/Major 3rd: Minor Triad.
    • Major 3rd/Major 3rd: Augmented Triad. (Augmented meaning enlarged - 2 major 3rds).
    • Minor 3rd/Minor 3rd: Diminished Triad.(Diminished meaning reduced - 2 minor 3rds).

E,G,B - the triad you built, is 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 E,G#,B - is 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 first item in our list of triads. Whatever your tonic (first note of the scale) happens to be, when you count the triad from that note - in this case E - then you get a major triad.

Note that you also get a major triad if you start on 4th or 5th note of the scale. Try it in the key of C.

Stinkfoot
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Your question is linked to diatonic chords:

Diatonic chords are chords that naturally occur within a key. They contain only the notes found in the scale (or key) that you’re working in.

Playing in the key of C (as in your example : C-D-E-F-G-A-B) is like only playing the white keys on a piano.

Which chords can you build if you apply your technique of playing 3 notes, each time leaving a white key inbetween?

  • C E G : C major
  • D F A : D minor
  • E G B : E minor
  • F A C : F major
  • G C D : G major
  • A D E : A minor
  • B E G : B diminished

Except for the last one, you might notice that those are all very common chords. The reason is that they're the easiest chords to play in the easiest key, and they sound good together.

This sequence of chords:

1(Major) - 2(minor) - 3(minor) - 4(Major) - 5(Major) - 6(minor) - 7(diminished)

is the same in any key.

As you noticed, the 3rd diatonic chord is minor, not major. If you want a diatonic E major, you'll either have to play in the key of E, A or B.

Eric Duminil
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I don't like the way these artsy people explain it. :) Here's the simplest way to understand it, in my opinion, that will also help you in general when it comes to music theory and its applications:

  • Take any note, regardless of key or scale. (That you're building a major chord from this note has nothing to do with the key or scale it's being used in.) We'll go with C, which is the root note of our chord.
  • Count up 4 half steps to the next note, E, which is the third note of our chord:
    • C -> C# -> D -> D# -> E
  • From the third note, E, count up 3 more half steps to the next note, G, which is the fifth note of our chord:
    • E -> F -> F# -> G

And there you have it: C E G.

So you can do this from any starting note for any chord type. There are multiple ways of looking at this, pick whichever you like:

  • For any major chord, in terms of half steps up from the root note, it's 0, 4, 7.
  • For any major chord, in terms of half steps up from the prior note, it's 0, 4, 3.

While we're here, minor is a very simple adjustment:

  • For any minor chord, in terms of half steps up from the root note, it's 0, 3, 7.
  • For any minor chord, in terms of half steps up from the prior note, it's 0, 3, 4.

This yields C Eb G.

Thinking this way will help you with a lot of other music theory concepts as well.

For instance, for a diminished chord, you just take a minor chord: 0, 3, 7, and you lower the fifth note: 0, 3, 6. Thus, a C dim chord would be C Eb Gb.

For an augmented chord, you just take a major chord: 0, 4, 7, and you raise the fifth note: 0, 4, 8. Thus, a C aug chord would be C E G#.

Basically all chords are constructed and modified this way, and this will help you with different scales, because the scales will depict which notes to use in your chord to fit with the key you're working in. If you know anything about music modes, you'll notice that all these are are regular keys (Ionian) which have all of their whole/half steps shifted. That's all. It's all relative!

Andrew
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    As someone who teaches music theory for a living, I *strongly* advise against thinking of intervals only in terms of half-step distances. You *will* make mistakes, and it causes absolute havoc when you get to enharmonics. – Richard Mar 14 '18 at 17:48
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    @Richard How so? I've played, sung, and composed a fair amount of music in my life and this is my favorite way of understanding things. It works best for me. You'll have to give a little more justification for how this can be detrimental. – Andrew Mar 14 '18 at 17:49
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    @Andrew apply this method to the following : What's the interval of a C to a D#? – Dom Mar 14 '18 at 17:54
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    As one example, why can't the `0, 3, 6` diminished chord be `C D♯ G♭`? As the topics become more complex, half-step thinking becomes more detrimental. Understanding the enharmonic equivalence of the German augmented sixth and dominant seventh, for instance, is very difficult for half-step thinkers. – Richard Mar 14 '18 at 17:54
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    @Dom `C -> C# -> D -> D# == 3 half steps`? That was easy? – Andrew Mar 14 '18 at 20:18
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    That's not the answer. It's an augmented 2nd which is a different interval than a minor third even though they are both 3 semitones apart. These differences matter especially in a tonal context. – Dom Mar 14 '18 at 20:24
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    @Richard It can be! `D#` == `E b` in my view. They are one and the same. I thoroughly disagree with your perspective. I find it much easier to compute chords and all music theory into terms of half steps (or maybe some whole steps) than whatever other confusing mechanisms you would use. If the notes are the same on the piano then as far as I'm concerned and as far as I care, they **are** the same. – Andrew Mar 14 '18 at 20:24
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    When talking about naming chords via a tonal system it's not . Yes there is a set notation where we can get into a whole discussion on prime form, vectors, algorithmic analysis, but this is outside the typical tonal concepts and it should also be noted that set theory only works in ET systems where enhamonics end up on the same note. If you're calling a chord a major chord ((not the set <001110> which btw is the same for major _and_ minor chords )[http://openmusictheory.com/setClassAndPrimeForm2.html]) then you have to work with traditional intervals or nothing will make sense. – Dom Mar 14 '18 at 20:40
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    @Dom What? That all looks like a bunch of spam spewed out from a Bing commercial. Look: I've worked with sound synthesis, digital music production, etc. before. I've written music programmatically. From a mathematical standpoint, these notes are the same. Anything else in the field of music is just unnecessary B.S. – Andrew Mar 14 '18 at 20:52
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    @Andrew not always which is why it's important and even when when they are the context. And the system your using is a post-tonal mindset which does work well the digital music production, but horribly when trying to use the tonal system set up like you are trying to do. For example back to the E major chord. If you try to tell someone the chord contains the notes E, __Ab__, and B you're wrong because you haven't spelled the chord right. People can figure it out, but you're working around and trying to use the system at the same time. – Dom Mar 14 '18 at 21:05
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    @Dom But even then, I can gauge the situation, what instrument they're using, what key we're in, w/e, and say `E G# B` to that person. Thinking with a different system doesn't really even change that anyways. In the end you still have to make that calculation, one way or another. My way is the least complex. – Andrew Mar 14 '18 at 21:15
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    Again 1. this isn't your system it's [set theory](https://en.wikipedia.org/wiki/Set_theory_(music)) 2. Major/minor chords, keys are tonal ideas and you should use tonal terms when talking about it. – Dom Mar 14 '18 at 21:18
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    @Andrew - I have to downvote this answer. I've worked with people who have similar mindsets, and I found it very confusing, inaccurate and downright hard work. I sometimes have to read music written by people who write Cm as C D# G - because it sounds the same. It might well do so, but when there's a correct, accepted, widely understood way to do something, why try to impose different views when the original works for most. If the other way is better, why hasn't it taken over? Because it's not accurate enough, and contains many discrepancies. – Tim Mar 14 '18 at 22:14
  • @Tim Or worse, as I've seen: C major spelled C Fb G! – Richard Mar 14 '18 at 22:41
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    @Tim Actually no, it's because people are driven to hold to stupid methodologies "because they work" and they're too closed-minded to consider anything else. Also, people like tradition and oppose change because change is "hard". Your example doesn't apply to my methodology. I've actually developed it naturally and intuitively after having been taught the other way but dealing with it from a more scientific and digital side of things. But you continue to do as you're going to do no matter what I say or how effectively I present any alternatives. – Andrew Mar 15 '18 at 00:42
  • @Andrew again, you didn't invent anything. This concept has existed for a long time and it's best used outside the context of tonality. You are free to think of this however you want, but if you want to dive any deeper than basic theory you have to think of it either full post tonal where you don't think in terms of major and minor or tonally which isn't that hard you just have to understand the basics and then it's counting. – Dom Mar 15 '18 at 01:16