# Why is the tonic chord of a key formed with the 1,3 and 5 notes of the key but the major chords in that key are the I IV and V?

The tonic chord in a given key is formed by using the 1 and 3 and 5 notes of the scale in whatever key you are in. However, in chord theory, the Major chords that work in that key are the one, four and five Major (I IV and V) chords.

If the harmonic relationship between the sonic frequencies of the 1 3 and 5 notes blend together well to form a major chord, why don't the major chords based on those three notes comprise the major chords that work well in that key? In other words - why not the I III and V major chords?

• Note that I edited the question because it originally contained an inaccurate statement. I meant the 1 and 3 and 5 notes of the tonic chord (or I chord) in a key. This makes some of the very good answers opening statement no longer fit the question. Please feel free to revise your answers. Thanks for the great response from all. – Rockin Cowboy Jan 20 '15 at 22:28
• But then your question sort of answers itself - if you're in a given key, then there are only three POSSIBLE major chords. Given the notes CDEFGAB, the only possible majors are C, F, and G. Sit down at a piano and see for yourself. – Darren Ringer Jan 22 '15 at 16:20

Actually, a major chord is formed by using a root, a major third and a perfect fifth. Doesn't necessarily have to be the 1,3 and 5 of the scale.

Let's take the C major scale and see for which root notes we have the major third and the perfect fifth:

• C; the third is E (major third), the fifth is G (perfect) -> Major Chord (I)
• D; the third is F (minor)
• E; the third is G (minor)
• F; the third is A (major), the fifth is C (perfect) -> Major Chord (IV)
• G; the third is B (major), the fifth is D (perfect) -> Major Chord (V)
• A; the third is C (minor)
• B; the third is D (minor).

SO, you see that in a major scale, the I,IV and V and the root notes that have a major third and a perfect fifth -> what it takes to form a major chord.

No. The definition of a major triad in canonical form (in practice it can be spaced out in terms of octaves, inverted and its members doubled, obviously, hence "canonical") is not 1-3-5 in terms of major scale degrees; it is 4 semitones (a major third) and 7 semitones (a perfect fifth) from a given root, any given root.

In a major scale, it happens that diatonic major triads (i.e., those built with members of the scale) are found on I, IV & V. Let's look at it, eh?

``````Triad on C: C-E, major 3rd    C-G, perfect 5th    - major triad
Triad on D: D-F, minor 3rd    D-A, perfect 5th    - minor triad
Triad on E: E-G, minor 3rd    E-B, perfect 5th    - minor triad
Triad on F: F-A, major 3rd    F-C, perfect 5th    - major triad
Triad on G: G-B, major 3rd    G-D, perfect 5th    - major triad
Triad on A: A-C, minor 3rd    A-E, perfect 5th    - minor triad
Triad on B: B-D, minor 3rd    B-F, diminished 5th - diminished triad
``````

The way the major and minor thirds fall is because of the interval order that is used to distinguish a major scale: C-D, 2 semitones; D-E, 2 semitones; E-F, 1 semitone; F-G, 2 semitones; G-A, 2 semitones; A-B, 2 semitones; B-C, 1 semitone.

Just a brief meta-theoretical note:

Rockin' Cowboy's answer above recapitulates a whole line of 19th-ct attempts to derive the basic functions of tonal music from the major triad (which at least one theorist called the "Chord of Nature" because of the way it follows the overtone series). In order to do that, they constructed a dualist system: that is, for a tonic note, C, they imagined a balanced, dual system of fifths, one above (C-G) and one below (C-F), and then filled in the fifths to create the tonic (CEG) and subdominant (FAC) triads.

The problem that immediately arose was how literal to make this "mirroring"? Some theorists argued that the two balanced triads should really be C major (CEG) and F minor (C-Ab-F), because if F is the lower fifth, then its triad should be created downward from C using the same sequence of intervals (M3, m3) that got you from the tonic to the upper fifth. The world of the lower fifth was a perfect inversion of the world of the upper fifth, and by this logic, influential theorists (Hugo Riemann, for example) assumed that acousticians would soon discover a series of undertones (C-F-Bb-Eb etc.) to match the overtone series.

They didn't, because undertones don't exist. And most 20th-ct theorists rejected tonal dualism in favor of a monist theory based on fifth motion in one direction only. (This is what is now taught in conservatories and music theory programs, although interest is growing in exploring the formal possibilities of dualist theories again.)

So where does the IV chord come from in monist theory? One clue lies in its traditional name: the IV chord was called the "sub-dominant," which is NOT the same as the "under-dominant." It referred to the note in the modal scale one step below (ie, "sub") the dominant scale degree, degree V. It is more historically accurate to explain the subdominant as a melodic function of Western chant formulas ("psalm tones"), where it supports the dominant, the main reciting tone of any mode.

Much, much later, chords arrive, and tonal functionality with them.

If you are a dualist, you think of the dominant and subdominant as balanced, antithetical worlds -- which is what they actually are in Romantic and late-Romantic harmonic practice. (Think about the tonal cliche of ending a romantic piece with the progression V-I, iv-I -- ie, first an authentic cadence, then a minor plagal one, bowing to "both sides," first the dominant and then subdominant -- before finishing.)

If you are a monist, you consider the dominant-tonic pair as THE tonal relation, with the subdominant serving as a "pre-dominant" function, which, as in the old chants, prepares and supports the crucial upper fifth. This makes sense if you consider 18th-ct "classical period" tonality as primary: almost every single piece modulates to the dominant, and you almost never tonicize the subdominant for any length of time.

The music historian will simply note the difference between the "sub" dominant (older, melodic) and "lower" dominant (newer, harmonic), and let you choose which one you prefer.

• Not sure how brief your note was - but it's very interesting. I'm just a singer songwriter and I compose music for the lyrics I write - so most of what you said was way over my head. But I did just try using a V-I, iv-I progression (something I would have NEVER thought to do before) and it works! I plan to play around with the ideas you illustrated to create arrangements that are fresh and different compared to what everyone else seems to be composing these days. Very useful information to me in my practice. Wish I could give it more than one up-vote! – Rockin Cowboy Jan 23 '15 at 22:25

The thing is simply, that the structure of major chords and the harmonic pattern I IV V do not depend on the same laws of tonality. A major chord is built with the overtones 4, 5 and 6, and this comes out to be a structure depending on thirds.

Meaning in overtone scale the overtones 4, 5 and 6 build up the major chord of the base tone.

The harmonic pattern I IV V is a pattern based on fifths. IV is one fifth under I, V one fifth over I. Overtones 1 and 2 have one fifth distance, which is a very "powerful" distance. If you hear let's say a c on a guitar string, the g above this c feels very present. if you sing this g to the string's c, you might feel this almost creational power. So the g "wants" to materialize even if the c alone is played, because the 2nd overtone is very present in c's overtones. So comes, that in horizontal (time) progression of tonal music, fifths are a very strong interval and draw harmonical progression in a certain direction, unlike other intervals. And this might be the reason, why I IV V is a common pattern, because the fifths make it very transparent, clear, and easy to follow.

• What do you mean by "A major chord is built with the overtones 4,5 and 6"? – Rockin Cowboy Jan 20 '15 at 22:05
• See the overtonescale of C-1: C-1, C, G, C+1, E+1, G+1, (Bb+1), C+2 ... So the overtones 4, 5 and 6 build a major chord of C. – MW1971 Oct 21 '15 at 13:03
• For example here: jazzguitar.be/forum/theory/… – MW1971 Oct 26 '15 at 9:31

As others have pointed out, the "1, 3, 5" of a chord are relative to the root of the chord, not the key. It's important to realize that any note in the key (or even outside of it, but let's ignore that) can be the root of a chord. What these numbers mean, is that once you've picked some note of the scale as a root for your chord, you create the rest of the chord by adding a 3rd and a 5th above that (in other words, every other note). So while a chord built on the first note of the scale will contain the 1st, 3rd, and 5th notes of the scale, another chord built on the second note of the scale will have the 2nd, 4th, and 6th notes of the scale (which would still be called the root, 3rd, and 5th of the chord). If we start on the third note of the scale, our chord will contain the 3rd, 5th, and 7th notes of the scale, and so on...

To know whether a chord is major or minor, you have to know the scale, and where the whole steps and half steps fall. Specifically, you need to look at the distance between the root and the third of the chord. If there are two whole steps, it is a Major Third; if there is only a step and a half, it is a Minor Third.

Here's a generic major scale. The numbers represent the notes of the scale (so this works in any key) and the W's and H's are the whole and half steps between them (WWHWWWH). Remember that we have to loop around back to 1 after 7.

1 (W) 2 (W) 3 (H) 4 (W) 5 (W) 6 (W) 7 (H) 1

As an example, let's build a chord on the 4th note of the scale. We've just picked our root (4), so now we need a third above that (which gives us 6), and and fifth above it (which gives us 1). The distance between the root and the 3rd of the chord is from 4 to 6, which contains two W's -- a major third. So the chord on the 4th note of the scale is a major chord, containing the notes 4, 6, and 1. Since it is a major chord, we use a capital roman numeral to refer to it: IV.

If, instead, we were to start on the 3rd note of the scale, our chord contains the notes 3, 5, and 7. From 3 to 5 is only H+W, so this is a minor chord, and we use a lowercase roman numeral to refer to it: iii.

• I like that you presented a different way to look at the intervals in determining minor or major third. Instead of speaking in terms of 3 semitones or 4 semitones, you used whole half vs whole whole. Both are correct but I like having alternate ways of looking at it. – Rockin Cowboy Jan 20 '15 at 22:12

There are a few misconceptions you have. Let's take a look at your first statement in your question:

A major triad (chord) is formed by using the 1 and 3 and 5 notes of the scale in whatever key you are in.

This is not true because if you were in a minor key, the 1st, 3rd, and 5th note of the scale would make a minor triad. 1, 3, and 5 are just scale degrees that are relative to whatever scale you are playing in.

As others have pointed out you need a root, third, and a fifth to make a basic triad and a root, major third, and perfect fifth to make a major chord. The possible qualities of each are as followed:

• Root - Perfect (if it is somehow altered the you have a different root.)
• Third - Major (4 semitones), Minor(3 semitones)
• Fifth - Perfect (7 semitones), Diminished (6 semitones), Augmented (8 semitones)

So major is just one of the possibilities you could have as there are other triads you can make from the qualities above.

Others have shown all the chords constructed from the major scale so you know why the chord built on the 3rd scale degree can't be major, but I'll show you why it is not possible for a natural scale to have I,III, and V be major. Let's first define "natural scale" as a scale that has seven notes wit each letter repeating only once. Now let's choose the root of C to start this out on. So the chord we will need are C major, E major, and G major which contain the following notes:

• C - C, E, G
• E - E, G#, B
• G - G, B, D

As you can see above we need a G and a G# to make a scale with this chord pattern which is impossible in the scale we defined above. So there is no scale that fits that pattern. It is however possible to see and E major chord that in a C major progression as a borrowed chord it just does not occur naturally.

Lets say you are talking about C major: You say the E (third chord in the scale) and G (fifth chord in the scale) should be major chords. The problem with that lies in the major chord itself. By definition the major chord is a major third (equivalent to two whole steps distance) followed by a minor chord (a distance of a whole step plus a half step). This means that in C major the distance between C and E (1 and 3) is longer than the distance between e and g (3 and 5). In order for the E minor chord to be a major chord the distance between 1 and 3 would have to be the same as that of 3 and 5, and that would fall out of bounds of the major chord definition. (in other words EGB is a minor chord, by definition. If the C chord was CEG# then the E chord could be major (EG#B), but then the C chord would not be Major (CEG# is augmented).) So the answer to your question is that by the definition of a major chord, it is impossible to have a major III (chord at the third position), in a major key.

I would also point you to @user1579378's answer.

At a certain point, a Major chord is a definition of a note structure with distances between notes. It is not entirely and abstract judgement where "Major" exactly translates to English as "Important" even though it is important.

You said that it's the relationship between the three notes that makes it sound good. So why do you think picking out those notes individually and basing new chords on them is the way to do it? You lose the relationships that the original chord had.

In the key of C Major, the I chord is the C Major chord (C-E-G). The iii chord in C Major is E minor (E-G-B), whereas the E Major chord is E-G#-B. How do you propose to resolve the use of both G and G#? What note are you now going to remove from the key of C Major to make room for G#, if not G, and why would you still call it C Major when you've changed what C Major is defined to be (C-D-E-F-G-A-B, no sharps or flats)?

Individual notes cannot be conflated with chords based on or involving them. A key defines a specific set of notes; a chord also defines a specific set of notes. If a particular chord uses only notes from a specific key, then great, that chord fits into the key. There's nothing really to it beyond that.

• I guess that gives a different perspective on why a 3 chord can't be a major chord and fit into that key. By reading all the answers it is becoming crystal clear. – Rockin Cowboy Jan 20 '15 at 22:16

To answer my own question after edification from the community, the theory behind why the notes of a chord blend well together and the theory behind which chords in a major key are the major chords that work for that key are basically two different theories.

A major chord is comprised of a root, a major 3rd (4 semitones or two whole steps above root) and a perfect fifth (7 semitones or 3 and one half steps above root). These notes blend well together because of the way the sonic frequencies merge together and compliment one another verses clashing with one another. A chord can be formed using any note as a root note.

The chords available for any given key which will sound correct with that key based on music theory, are limited to the chords which can be formed using the notes in that key. Any given diatonic key will have 7 notes that are in that key and these are the 7 notes we can use to form chords that go with that key.

Since our melody notes will be taken from the notes in the key we are composing in, it follows that the chords that will sound good with the notes we choose for the melody, should be comprised of the notes in the melody. Therefore the chords that will support any melody in a given key must be formed using the 7 notes in that particular key. Using the 7 notes in a major key, limits which chords we can form and only gives us three options for major chords that can be formed using those 7 notes. And those 3 options for major chords will always end up being the I chord, IV chord and V chord (all major). Let's look at an example using the key of C major. The chart below was provided by Community member Patrx2 and perfectly illustrates this.

As you can see, the major triads which can be formed in the key of C major are the C Major (I chord) the F Major (IV) chord and the G Major (V chord). This holds true in every key.

While the foregoing explains why you don't have a choice of which chords you can use without venturing outside they key - it falls short of explaining why the I, IV, and V chord sound good in a given key.

To understand this better, we must revisit the idea presented in part one, that suggests that certain notes blend well together because of the way the sonic frequencies merge together and compliment one another. Our brains will instinctively have a desire to gravitate towards complimentary frequencies that will blend together to form pleasing sounds. The relationship between the sonic frequency of two notes is described in music theory as an "interval" which is how far apart the sonic frequencies are - commonly measured in what we call semitones (with one semitone being the smallest step in a Western Music chromatic scale).

The most congruent and consonant sounding intervals are the unison (same exact frequency or 1:1 ratio) and an octave (exactly double the frequency or a 2:1 ratio). It's easy to visualize how the sound waves will line up evenly and blend together if you have exactly 2 crests of one wave for every one crest of the second. Besides the octave and unison, the next most consonant (harmonious) interval is the perfect fifth. This is because the ratio between the sonic frequency of two notes that form a perfect fifth (7 semitones apart) is 3:2. Because these two numbers are small, the crests of the sound waves will peak at the same place more often than they would if the ratio were say 15:8. So any two notes with an interval between them of a perfect fifth, will sound good together.

If we start with the note of a particular key (say C in C Major for example) we can get to a perfect fifth interval from there by going up 7 semitones which lands on G if we start with C. That happens to end up being the 5th note in a diatonic major scale. (1)C (2)D (3)E (4)F (5)G. We know, that the interval between C and G in the key of C major will result in two notes that blend together because they form a perfect fifth, and we know that these notes will sound good together whether they are played at the same time or successively.

So if we build a chord using the G note as the root of the chord (since G is on the other end of a perfect fifth interval from the home note of our key (C), and that chord is formed using only the notes in our key, then it makes sense that the chord (in this case G Major) naturally evolves from the tonic I chord - C Major (which uses our key's home note as it's root). It's like we use the tonic chord and pivot to the G chord because the G note is a perfect fifth interval using C at the other end. So the chord using this note as the root (G major) evolves naturally from the tonic chord C (with C as the root).

If we pivot from C in the opposite direction on our piano keyboard (or our scale carried out over several octaves), and we count in descending order seven steps to the note that forms the other perfect fifth that can occur in the key of C major using a C as a note on one end of the interval, we land on the note F - seven semitones from C. So if we use our home note (C) as the anchor point and count a perfect fifth descending, we get the fifth interval formed with the notes F and C. So if the interval F to C is a perfect fifth we know those notes will blend together in a harmonious manner. We know that using C as an anchor point in the key of C Major, we can reach a perfect fifth using the C in two and only two ways - ascending the scale by 7 semitones to get to G, or descending the scale by 7 semitones which lands us on the other option - F. So if the relationship between the C and F can also form a fifth interval, it makes sense that leaving C Major and going to a chord with a root based on F (F Major - our IV chord) or going from an F back to C, will sound natural in the key of C Major.

To further illustrate why the IV and V chord segue well with the tonic I chord which anchors the key, I might point out that the next most consonant interval between notes is the perfect fourth with a sonic frequency ratio of 4:3. If you start with the triad that forms the tonic chord of a given Major key, and use the root note of that Major triad as the anchor point, there are two notes you can reach that will each form BOTH a perfect fourth interval AND a perfect fifth interval using your home note of the key (which is the root note of the tonic chord) as one end of the interval.

Again using the key of C major for illustration, the interval between C and G is a perfect fifth and the interval between G and C (same two notes now inverted) is a perfect fourth. Thus using C as an anchor point, and G at the other end of the interval, you can form both a perfect fifth (if you ascend from C) and a perfect fourth (if you descend from C). Remember, these are the two most consonant (pleasing sounding) intervals available outside of the octave and unison. You can also achieve this same feat using one other note - F. The interval between F and C is a perfect fifth and the interval between C and F (ascending the scale) is a perfect fourth. Again the C is the home note or anchor point.

This provides further logic to explain why chords with root notes based on the two notes in the diatonic scale for a particular key, that are each capable of combining with the home key note to make both a perfect fourth and perfect fifth, will be the most stable sounding chords in that key and will naturally evolve from or resolve to the tonic (I) chord that anchors the key.

Because in a major key:

• the tonic must not contain the scale's fourth (iv) tone
• the subdominant must contain the scale's fourth tone but not the seventh
• the dominant must contain at least the scale's seventh or both the seventh and fourth
• check out Robert Fink's "brief" meta-theoretical note (His Answer) for an interesting read. Apparently there may be two sets of rules (Monist vs. Dualist) - even though one may have been virtually abandoned. – Rockin Cowboy Jan 23 '15 at 22:32

In general, the octave is a circle that loops upon itself. You are not ever really using a 1 3 or 5 note, you're simply using x..x+2..x+4 which loops upwards and downwards. Majr IV chord overlaps with the circle of major 'notes' as you progress up the scale. Anyway, the interval is circular, and I think if you reflect on that for a while it will make sense.