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Old 03-11-2013, 03:13 PM
XYRN XYRN is offline
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Default Theory Question Regarding Major Chord Construction

I'm trying to learn music theory and fretboard layout as part of learning to play.
Today I think I'm starting to wrap my head around intervals, triad construction and keys. At times I think I've got it, but then something throws a wrench in my understanding. (Partly due to me consulting several sources between books and the internet.) It's fun learning, but slow going.

Anyway, getting to the question

It is said that a major triad is made of the "1st, 3rd and 5th steps" source of a major scale.
But steps seems like a vague term that is messing me up. Another source calls it the "root, 3rd and 5th", which makes a little more sense to me but then when I try to think about semitones and intervals, especially intervals I can't reconcile "root" with "1st step".

Take the C major scale: C D E F G A B (C). And the C major chord, C-E-G.
The C is the root, and it's the first NOTE in the scale, but it's not the first step up, it's the zero'th step up, right?

And then there is the concept of 'whole step, whole step, half step, whole step, whole step, whole step, half step', where a "step" equals two semitones and a half step is one semitone.

Are the various sources using the term "step" differently based on whether they're talking semitones vs position within a scale vs intervals?

Oh, and then chords within a key, they still go by the I ii iii IV V vi vii even if it's the C major scale, right? The chords in that key are C Dminor Eminor F G Aminor Bminor, right? That's independent of whether there are sharps and flats in the key, am I correct?

Am I on the right track or am I just confused?
It feels like it's starting to crystallize but there are some gaps in my comprehension.

Thank you.
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  #2  
Old 03-11-2013, 03:23 PM
walternewton walternewton is offline
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Sounds like you are basically on the right track...

C is the root, calling it the "first step" of the scale maybe isn't the best wording - they basically mean "first note" of the scale (and no, this use of first/third/fifth "step" is not exactly the same as "whole step" meaning 2 semitones.)

The triads in C are

C Dm Em F G Am Bdim

This pattern holds true for all keys, like G (1 sharp) or F (1 flat)

G Am Bm C D Em F#dim

or

F Gm Am Bb C Dm Edim
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Old 03-11-2013, 03:26 PM
oldhippiegal oldhippiegal is offline
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1) you are on the right track
2) it is confusing, the "root vs 1" issue. 1 is the assigning of the number of the scale to the note, normal counting starting with 1, then 2 3 etc. So

C D E F G A B
| | | | | | |
1 2 3 4 5 6 7


Thus, the I chord includes notes number 1, 3, and 5. (OR "Root, 3 and 5) The vi chord includes 6, 8 and 10. (And 8 and 10 are the same as 1 and 3, but an octave higher). Edit, and yes, there tends to be sloppiness about definition of some terms depending on context. "Step" usually means a step in a scale, from 2-3, or from 6-7, no matter if that's a whole tone or semitone or even three semitones.

The vii chord, based on the (with the root of that chord being the) 7th note of a major scale is not minor but diminished. If you haven't gotten to diminished yet as a concept, don't sweat that yet. That chord is seldom used*.

Sounds like you're doing very well to me!

* in most pop musical forms. Some jazz guy will come by and yell at me for saying that, so consider the exception said already.

Last edited by oldhippiegal; 03-11-2013 at 03:37 PM. Reason: clarity, one hopes
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Old 03-11-2013, 03:37 PM
XYRN XYRN is offline
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Thank you both for the replies. I like learning, and there is always that part in wrapping your head around new concepts where you feel like you're just about to break through the clouds or get that leg up over the fence but just can't quite get it, and you slip a few times. (Really, one of the most exciting stages/phases of learning, I feel.)

It's cool to know it's starting to happen with my understanding of theory. But also frustrating at times.

Quote:
Originally Posted by oldhippiegal View Post
1) you are on the right track
2) it is confusing, the "root vs 1" issue. 1 is the assigning of the number of the scale to the note, normal counting starting with 1, then 2 3 etc. So

C D E F G A B
| | | | | | |
1 2 3 4 5 6 7


Thus, the I chord includes notes number 1, 3, and 5. (OR "Root, 3 and 5) The vi chord includes 6, 8 and 10. (And 8 and 10 are the same as 1 and 3, but an octave higher). Edit, and yes, there tends to be sloppiness about definition of some terms depending on context. "Step" usually means a step in a scale, from 2-3, or from 6-7, no matter if that's a whole tone or semitone or even three semitones.

The chord based on the (with the root as the) 7th note of a major scale is not minor but diminished. If you haven't gotten to diminished yet as a concept, don't sweat that yet. That chord is seldom used.

Sounds like you're doing very well to me!
Aha moment!
That "8 and 10" has been stumping me for a while, that's when I start thinking in terms of semitones and get off track.
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Old 03-11-2013, 03:45 PM
stanron stanron is offline
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Quote:
Originally Posted by XYRN View Post

It is said that a major triad is made of the "1st, 3rd and 5th steps" source of a major scale.
But steps seems like a vague term that is messing me up. Another source calls it the "root, 3rd and 5th", which makes a little more sense to me but then when I try to think about semitones and intervals, especially intervals I can't reconcile "root" with "1st step".

Take the C major scale: C D E F G A B (C). And the C major chord, C-E-G.
The C is the root, and it's the first NOTE in the scale, but it's not the first step up, it's the zero'th step up, right?

And then there is the concept of 'whole step, whole step, half step, whole step, whole step, whole step, half step', where a "step" equals two semitones and a half step is one semitone.

Are the various sources using the term "step" differently based on whether they're talking semitones vs position within a scale vs intervals?

Oh, and then chords within a key, they still go by the I ii iii IV V vi vii even if it's the C major scale, right? The chords in that key are C Dminor Eminor F G Aminor Bminor, right? That's independent of whether there are sharps and flats in the key, am I correct?

Am I on the right track or am I just confused?
It feels like it's starting to crystallize but there are some gaps in my comprehension.

Thank you.
Calling the notes of the scale 'steps' is at least careless if not confusing for the reasons you point out. A term I prefer is 'degrees' of the scale.
Whole step and half step are good usage of the word step.
Chord vii is B diminished rather than minor.

In a major chord the interval between the first and third degree is a major third (two whole steps) and the interval between the third and fifth degrees is a minor third (a half step and a whole step).

In a minor chord the interval between the first and third degree is a minor third (a half step and a whole step) and the interval between the third and fifth degrees is a major third (two whole steps).

In B diminished or B dim the interval between the first and third degree is a minor third (a half step and a whole step) and the interval between the third and fifth degrees is also minor third.

Seems to me you are well on the right track. Cheers.
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Old 03-11-2013, 04:27 PM
XYRN XYRN is offline
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Quote:
Originally Posted by stanron View Post
Calling the notes of the scale 'steps' is at least careless if not confusing for the reasons you point out. A term I prefer is 'degrees' of the scale.
Whole step and half step are good usage of the word step.
Chord vii is B diminished rather than minor.

In a major chord the interval between the first and third degree is a major third (two whole steps) and the interval between the third and fifth degrees is a minor third (a half step and a whole step).
I'm not sure that "degrees" isn't confusing me more.

So, E major scale is E, F#, G#, A, B, C#, D#
If I get what you're saying than the 1st degree is E, the third degree (note?) is G# and the 5th degree is the B. E major chord = E-G#-B, right?

I may be confusing myself that the third and fifth notes in the major scale are also the Major Third and the Perfect Fifth. I'm not sure if that is a coincidence or if that's a rule I can follow.

Quote:
In a minor chord the interval between the first and third degree is a minor third (a half step and a whole step) and the interval between the third and fifth degrees is a major third (two whole steps).
So, E-G-B?

Quote:
In B diminished or B dim the interval between the first and third degree is a minor third (a half step and a whole step) and the interval between the third and fifth degrees is also minor third.
So, Edim would be E-G-Bb?

Another confusing thing is that the notes as they are played on the guitar fretboard (in standard tuning) are not necessarily in the order of the intervals, with the exception of the root.

Considering an E major chord (triad), it’s E-G#-B; however, the open E chord plays, from bottom, E, B, E, G#, B, E. (root, fifth, octave, third, octave fifth, double octave?)

An E minor chord is E-G-B, and is played E, B, E, G, B, E. Meaning that the “3rd” of the scale is flatted, NOT the third played note in the open chord.

In this sense, 3rd , means the third degree which is the Major Third, which is then flatted to a Minor Third to make a minor chord, but just because it's flat doesn't equal that it's the 2nd degree, right?
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  #7  
Old 03-11-2013, 04:36 PM
walternewton walternewton is offline
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Your definitions of E, Em, Edim are correct.

The third note of a major scale will always be an interval of a major third away from the root, and the fifth note will always be an interval of a perfect fifth away from the root.

More broadly, for any major scale you have root - major 2nd - major 3rd - perfect 4th - perfect 5th - major 6th - major 7th.

You are correct that in practice on the guitar, the set of notes that define a chord may be played in any order, doubled or tripled up in different octaves, etc.

No, flattening the major third to the minor third (G#-G) does not get you to the second scale degree, which is a semitone lower (F#).
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Old 03-11-2013, 05:11 PM
XYRN XYRN is offline
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Ooo, I think it's starting to fall into place.
If I try to combine what you're saying with what "oldhippiegal" is talking about regarding note number within a scale, I come up with this table in relation to the C major scale, is it correct? Especially the Note column?

Degree_____Interval_________Semitones______Note Name___Note Number
1________Root/unison_________0_____________C____________1
_________Minor 2nd___________1
2________Major 2nd___________2_____________D____________2
_________Minor Third__________3
3________Major Third__________4_____________E____________3
4________Perfect Fourth_______5______________F __________4
_________Tritone_____________6
5________Perfect Fifth_________7______________G__________5
_________Minor 6th____________8
6________Major 6th____________9_____________A___________6
_________Minor 7th___________10
7________Major 7th___________11_____________B___________7
8________Octave_____________12_____________C______ _____8

_________Oct. Maj 2nd_________14_____________D__________10

Is the degree the same as the note number of the scale, or just in the C major scale?
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Old 03-11-2013, 05:18 PM
stanron stanron is offline
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Quote:
Originally Posted by XYRN View Post
I'm not sure that "degrees" isn't confusing me more.
'Notes' will do instead of 'degrees' if you prefer

Quote:
So, E major scale is E, F#, G#, A, B, C#, D#
If I get what you're saying than the 1st degree is E, the third degree (note?) is G# and the 5th degree is the B. E major chord = E-G#-B, right?
Right

Quote:

I may be confusing myself that the third and fifth notes in the major scale are also the Major Third and the Perfect Fifth. I'm not sure if that is a coincidence or if that's a rule I can follow.
With 'Major Third' and 'Perfect Fifth' you are talking about Intervals between notes not the notes individually.

The interval between adjacent notes is called a second. eg C to D or E to F.

Then interval between alternate notes is called a third. eg C to E of D to F.

The number of the interval is counted from the lowest note to the highest ignoring sharps or flats so C to F is a fourth and C to A is a sixth.

Second, third and sixth intervals can be major or minor depending on the scale and position in the scale. The interval between the root note and the fourth and fifth note is the same in major and minor scales. They are called 'Perfect' intervals. If they are sharpened they are 'augmented' and if they are flattened they are 'diminished'.

Quote:
So, Edim would be E-G-Bb?
Yes

Quote:

Another confusing thing is that the notes as they are played on the guitar fretboard (in standard tuning) are not necessarily in the order of the intervals, with the exception of the root.

Considering an E major chord (triad), it’s E-G#-B; however, the open E chord plays, from bottom, E, B, E, G#, B, E. (root, fifth, octave, third, octave fifth, double octave?)

An E minor chord is E-G-B, and is played E, B, E, G, B, E. Meaning that the “3rd” of the scale is flatted, NOT the third played note in the open chord.
Guitar chords don't have to have their notes in the 'correct order' and they don't have to have the root as the lowest note. And yes the 'flattened third' refers to the position in the scale not the position in the chord.

Quote:
In this sense, 3rd , means the third degree which is the Major Third, which is then flatted to a Minor Third to make a minor chord, but just because it's flat doesn't equal that it's the 2nd degree, right?
A repeat here that the 'third degree' is a note and the 'Major or Minor Third' is an interval.

Cheers.
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Old 03-11-2013, 05:21 PM
walternewton walternewton is offline
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Quote:
Originally Posted by XYRN View Post
I come up with this table in relation to the C major scale, is it correct?
Your chart looks good, except the 'note number' (as you're using the term) for the D in the second octave should be 9, not 10 (note that you could call the interval a "major ninth").
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Old 03-11-2013, 05:30 PM
stanron stanron is offline
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XYRN
Our posts crossed but your chart looks OK except for the 9th as walternewton pointed out.
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Old 03-11-2013, 10:14 PM
walternewton walternewton is offline
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And just to add, there is nothing inherently special about the key of C - with no sharps or flats to worry about beginners find it a little easier to work with, but all the interval relationships discussed above are exactly the same for all major keys, it's just the note names that are different (it's a good exercise to write out the scales/chords you're learning in all keys, in circle of fifths order - if you do so you'll quickly start seeing the patterns.)

Last edited by walternewton; 03-11-2013 at 10:20 PM.
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Old 03-12-2013, 05:21 AM
JonPR JonPR is offline
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Quote:
Originally Posted by XYRN View Post
Ooo, I think it's starting to fall into place.
If I try to combine what you're saying with what "oldhippiegal" is talking about regarding note number within a scale, I come up with this table in relation to the C major scale, is it correct? Especially the Note column?

Degree_____Interval_________Semitones______Note Name___Note Number
1________Root/unison_________0_____________C____________1
_________Minor 2nd___________1
2________Major 2nd___________2_____________D____________2
_________Minor Third__________3
3________Major Third__________4_____________E____________3
4________Perfect Fourth_______5______________F __________4
_________Tritone_____________6
5________Perfect Fifth_________7______________G__________5
_________Minor 6th____________8
6________Major 6th____________9_____________A___________6
_________Minor 7th___________10
7________Major 7th___________11_____________B___________7
8________Octave_____________12_____________C______ _____8

_________Oct. Maj 2nd_________14_____________D__________10

Is the degree the same as the note number of the scale, or just in the C major scale?
This is exactly right, except - as pointed out - the last D is 9th (major 9th), not 10th.

As you can see, there are two "perfect" intervals (4th, 5th), and the others all come in two sizes, minor (smaller) or major (larger).
(In fact, technically, unison and octave are also "perfect" intervals.)
It so happens that a "major scale" has major and perfect intervals exclusively.

It's true that (as your source says) a major triad can be made from the 1st, 3rd and 5th steps of a major scale" - but that's not the best way to look at it, IMO. The triad is not "major" because the scale is "major". Both are major because of their 3rd intervals.
IOW, what makes a scale OR a chord "major" is the size of its 3rd interval: 4 semitones rather than the 3 semitones of a minor 3rd.
(Yes, the 2nd 6th and 7th intervals in a major scale are also all major, but in a minor scale they're not all minor. It's the size of the 3rd that makes the scale minor.)

IOW (again), we start from INTERVALS and their names. Chords and scales are both built from intervals, and take their names from their most significant intervals.
"Major" and "minor" only mean "larger" and "smaller" (as your chart shows).

You said:
Quote:
The C is the root, and it's the first NOTE in the scale, but it's not the first step up, it's the zero'th step up, right?
This highlights the two different counting methods we use.
Interval numbers are "ordinal" - that means the first is (er...) the "1st" . So C is "1", not zero. We count letters first.
But when we assess interval quality or size (difference between different kinds of "2nd" or whatever), then we add up the semitones, which means beginning from zero ("cardinal" numbers, assessing quantity rather than order).
Eg:
Code:
    Notes: C  .  D  .  E
           1st   2nd   3rd (order)
Semitones: |  |  |  |  | 
           0  1  2  3  4 (quantity)
The smaller ("minor") type of 2nd would b C-Db, which is 1 semitone.
The smaller ("minor") type of 3rd would b C-Eb, which is 3 semitones.

On the rare occasions when "perfect" intervals change their size, then they are "diminished" when 1 semitone smaller, and "augmented" when 1 semitone larger.
Slightly more rarely, minor intervals can be diminished, and major intervals augmented.

Eg, in the C major scale, F-B is an "augmented 4th": 4 notes (FGAB) but 6 semitones, 1 more than perfect. B-F, meanwhile is a "diminished 5th" - 5 notes (BCDEF) but 6 semitones, 1 less than perfect. IE, although both are 6 semitones in size, they have different names because the note count is different.

In the harmonic minor scale, we also get an augmented 2nd (m6-M7, F-G#), augmented 5th (m3-M7, C-G#), diminished 4th (M7-m3, G#-C) and diminished 7th (M7-m6, G#-F).

As with major and minor intervals, augmented and diminished ones can give their names to chords.
Augmented triad = M3, aug5 (eg, C E G#)
Diminished triad = m3, dim5 (eg B D F)
Diminished 7th chord = m3, dim5, dim7 (eg G# B D F)
In each case, the most distinctive interval is the one the chord is named after.
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Old 03-12-2013, 11:17 AM
XYRN XYRN is offline
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Thank you ALL for the responses, I think it's starting to come together.

JonPR, thanks for clarifying the ordinal vs cardinal counting, that helps!
I haven't even started looking into the harmonic and melodic minor keys, one step at a time.

I'm sure it will be a long time before I just know this stuff off the top of my head, but in the meantime I made a spreadsheet in Excel that helps me organize the concepts.

Just like back in school when the teacher allowed you to write a crib sheet for a test, the process of writing it down helps one remember the info.

In case you're interested I uploaded the file to my webspace and have provided the link for your review.
In fact, I'd appreciate it if someone could take a look in case I have any glaring errors.

Excel Spreadsheet

I plan to keep a copy of this in my guitar cases and in my practice area and will refer to it often, hopefully I absorb it to the point that it's automatic knowledge.

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Old 03-12-2013, 11:34 AM
stanron stanron is offline
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Just one or two points, where you list the notes in the scales for instance of G, the seventh note is F# and not Gb. You get this right in your table of notes in chords except for chord IV in Ab and that may well be a typo. Cheers
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