Intervals

Name	Symbol	Semi-tones	Tones	Equivalent (see Inversions):	Interval Quality
Unison		0			Perfect Consonance
Minor 2nd		1		half-step/semi-tone	Dissonance
Major 2nd		2		whole-step/tone	Dissonance
Minor 3rd	m3	3	1.5		Imperfect Consonance
Major 3rd	M3	4	2		Imperfect Consonance
*Diminished 5th	d5	6	3	Augmented 4th or Tritone	Dissonance “Devil’s interval”
Perfect 5th	P5	7	3.5		Perfect Consonance
*Augmented 5th	A5	8	4	Minor 6th	Imperfect Consonance
Minor 7	m7	10	5	whole-step below octave	Dissonance
Major 7	M7	11	5.5	half-step below octave	Dissonance
Octave	P8	12	6	Perfect 8th	Perfect Consonance

*I have chosen the terminology “Diminished 5th” and “Augmented 5th”, as they are used to construct of Diminished and Augmented chords. They are more commonly referred to as “Tritone” and “Minor 6th”, respectively.

Chords

Just the essentials

Inversions:

Interval Quality	Inversion
Perfect	Perfect
Major	Minor
Augmented	Diminished

Interval Number	Inversion
Unison	Octave
2nd	7th
3rd	6th
4th	5th

Interval + Inversion = 12 half-steps →

Interval (# half-steps)	Inversion(# half-steps)
Minor 2nd (1)	Major 7th (11)
Major 2nd (2)	Minor 7th (10)
Minor 3rd (3)	Major 6th (9)
Major 3rd (4)	Minor 6th (8)
Perfect 4th (5)	Perfect 5th (7)
Augmented 4th (6)	Diminished 5th (6)
Tritone (6)	Tritone (6)
Diminished 5th (6)	Augmented 4th (6)
Perfect 5th (7)	Perfect 4th (5)
Minor 6th (8)	Major 3rd (4)
Major 6th (9)	Minor 3rd (3)
Minor 7th (10)	Major 2nd (2)
Major 7th (11)	Minor 2nd (1)

Triad/Chord Inversion:

Chords of Major Scale:

Untitled

The 1,4,5 are Major , as expressed by upper case roman numerals I, IV, V.
The 2,3,6 are Minor, as expressed by lower case roman numerals ii,iii,vi.
The 7 is Diminished, denoted by lower case roman numeral with dominant superscript, vii°.
To build each chord’s triad, simply use the 1,3,5 from the each respective root.
Using C Major as our example framework:
- Primary chords are C Major, F Major, and G Major.
  - C Major triad is C-E-G. F Major is F-A-C. G Major is G-B-D.
- Secondary chords are D Minor, E Minor, and A Minor.
  - D Minor triad is D-F-A. E Minor is E-G-B. A Minor is A-C-E.
- The leading tone is B Diminished, which can build tension as it wants to resolve to the tonic - C Major.

*C Major is chosen as the example because it has only natural notes (no #/♭). Be sure to change the tonic and use notes of it’s major scale for different keys.

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