Before we talk modes lets look at intervals. For our example lets use a C chromatic scale as a point of reference. Later you can transpose this knowledge to any key.
Chromatic scale in C: C C# D D# E F G G# A A# B
Now for a brief definition of the term interval. An interval is simply a measurement in distance between two notes. In order to measure we need to specify units of measurement. These units of measurement are usually stated in terms of half-steps (minor second) and whole-steps (major seconds).
Examples:
C to C# = minor second (half step), C to D = major second (whole step)
F# to G minor second (half step), A to B = major second (whole step)
So now that we understand our unit of measure, let's look at our chromatic scale and name all of the intervalic relationships that exist relative to the root note C.
C to C# = min 2nd / half step
C to D = maj 2nd / whole step
C to D# = minor 3rd / step and 1/2
C to E = maj 3rd / 2 whole steps
C to F = perfect 4th / 2 whole steps + 1/2 step
C to F# = augmented 4th / 3 whole steps (same as dininished 5th)
C to G = perfect 5th / 3 whole steps + 1/2 step
C to G# = augmented 5th / 4 whole steps
C to A = major 6th / 4 whole steps + 1/2 step
C to A# = (A# = Bb) minor 7th
C to B = major seventh
Given this information let us build some chords. First lets look at triads. By definition a triad is a chord (major, minor, augmented or diminished) that is comprised of three notes. However, once we've determined the relationship between the root and the third then we have enough information to name a triad. In other words inspite of the what the name implies, we can create triads with as few as two notes:
Examples using intervals:
1. C - E = C major triad because the third note G (the 5th) is omitted but is implied. The distance btw C and E is a major third thus making our triad C major.
2. C - E - G = a major triad also. this time the 5th (G) is included. The intervals envolved in constructing our chord include: C to E (major third) and C to G (a perfect fifth).
3. C - Eb = C minor triad because of the interval that exists btw the root C and the third (Eb) which is a minor third
4. C - Eb - G therefore is a complete minor triad consisting of a minor third(C,Eb) and a perfect 5th (C,G).
5. C - Eb - Gb = C dim because of the intervals btw (C and Eb) minor 3rd and (C and Gb (F#)) an augmented 4th which is the same as a diminished 5th.
Carry this line of reasoning out to include the 7th and you start to understand why we name chords the way we do. The symbols like Dmaj7, F#dim7, and C7+, D7b5 start to make sense. Once you have that down then proceed to study chords that include the harmonic extensions beyond the first octave (9th, 11ths, and 13ths). By then your chord construction should be down pat.
Remember to study intervals within melodies as well. Do this both horizontally and vertically. For example, take the melody of Mary had a little lamb and name the intervals between each two successive notes in the melody. This helps you see the relationship that exists horizontally between the notes of a melody.
Now look at the vertical relationship. Take each note in the melody and compare it against the chord thats being played at that very same moment. What is the relationship btw the note and the chord.
Example:
The chord is F major, the current melodic note is D. This note (D) is a major 6th in relation to the chord. This melodic note in combination w/ the Fmaj chord creates a new chord sound F6. Which is spelled F A C D.
The next melodic note is Eb. Eb is a minor 7th in relation to our F maj chord. This melodic note in combination w/ the F maj chord creates the chord sound F7 (dominant 7th chord form). It is spelled F A C Eb.
I hope I have shed some light.
