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I understand intervals between notes. Each number of steps between two notes has a particular name. Like this:

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But some times I see people refering to intervals between chords, not single notes. Like this: I, ii, iii, IV, V, vi and vii.

What does that mean?

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See also – Ulf Åkerstedt Oct 19 '13 at 17:30
Counting semi tones is the lazy way to do inversions. A half step up could also be a Augmented Unison. C to D# is also not a Minor Third (Although it is three semitones up.) – Neil Meyer Nov 1 '13 at 7:10

Take a major scale. There are seven different notes in it, so starting from the root note of the scale, number each note (In C major, you'd have C=1, D=2, etc). If you build a chord off of any of those notes, you can give it the number of whichever root note you chose (In C major again, Cmaj would be 1, Dm would be 2, etc). When Roman numerals are used, they indicate the type of the chord -- capital letters are major chords, lowercase letters are minor chords. With a major scale, the chords you build off of each note are going to follow the pattern of major, minor, minor, major, major, minor, diminished or I, ii, iii, IV, V, vi and vii (vii should properly be followed by a degree sign to indicate it's diminished, not minor).

When people are discussing a chord progression, you they might write something like I-vi-IV-V. This means for whatever key the song is in (or whatever key you want), play the Major 1 chord, followed by the Minor 6 chord, then the Major 4 and the Major 5 chords. This system is used because it lets you know the structure of a song independent of the key it's in, making it easy to transpose.

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Joel. Thank you very much. Just to clarify a thing: In the case of the G Major Scale, we have these notes: G, A, B, C, D, E, F#. I understand that to build a chord progression I need to find chords of G, A and B and so forth that uses only these notes. So it would be a G, a Am, a Bm and so forth. But how can I build a chord of F of any kind with these chords? I need a F to build any kind of F chord, don't I? But I only have a F# :(. What do I do? – Anonymous May 22 '11 at 17:26
Figured that out myself. Actually I won't ever build an F chord, but a F#. Thank you so much – Anonymous May 22 '11 at 17:34
You can do an F somehow. It wouldn't fit these established rules of harmony, but there are lots of songs that don't do that. – Dave Jacoby May 22 '11 at 23:30
@André, you could change from G to C/Am. (Shouldn't be an issue) And there you go, now you can use the F :) You just need to fiddle around a bit with the cords to make it smooth. @Joel, you are awesome ;) – Anonymous May 23 '11 at 7:30

This is the notation used in music theory to indicate specific chords in a key.

I - Tonic - Major

i - Tonic - minor

II - Super Tonic - Major

ii - Super Tonic - minor

III - Mediant - Major

iii - Mediant - Minor

iv - Sub Dominant - Minor

IV - Sub Dominant - Major

V - Dominant - Major

v - Dominant - minor - Very rare

vi - Sub Dominant - minor

VI - Sub Dominant - Major

vii - Leading Tone - minor

VII - Leading Tone - Major

○ indicates an diminished chord (Minor third / Diminished fifth)

A plus sign indicates an augmented chord (Major third / Augmented fifth)

7 next to a triad indicates root position so for instance If your chord is C/E/G the see would in this case be bottom.

6 means first inversion. So this case it would be E/G/C or E/C/G.

6 4 means second inversion. So in this case it would be G/E/C or G/C/E

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