Intervals

Recall, that pitch is the highness or lowness of a sound.
If we have 2 sounds, they can have the same or different pitches.
We relate the pitch of one sound to the pitch of another sound as being the distance between the pitches.
We call the distance bewteen the pitches the "interval" between them.

In the western system we are using, the smallest distance between two different pitches (smallest interval) is the 1/2 step (We also call this interval a minor second, abbreviated m2 or b2).

Two half-steps are equivalent to the distance of a whole-step, also called a major second (abbreviated W, M2, or 2).

12 (adjacent) half-steps are equivalent to the distance of an octave (abbreviated 8ve, or 8).

The other simple intervals (found within one octave) have names, and abbreviations as given in the chart(s) below.

Compound intervals are intervals larger than an octave, and are for most analysis considered in the same way as their simple counterparts. So a major 13th interval is equivalent to a major 6th interval plus an octave.

Why are intervals important?
We use them to understand melodic and harmonic structures (like harmonies, chords, progressions, and scales).

Reconsider that the letters A through G are used (along with the accidentals - sharps and flats) to describe/distinguish pitches.

The following distances are of a whole-step:
A to B, C to D, D to E, F to G, G to A.

The following distances are of a half-step:
B to C, E to F.

This can be abbreviated :

A   B   C   D   E   F   G   A
  W  1/2  W   W  1/2  W   W

Filling in the other names for pitches, we have the chromatic scale:
A,A#/Bb,B,C,C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab,A

Rearranging to start from C:
C,C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab,A,A#/Bb,B,C

|----------------------------------------------------------------|
|                                                                |
|----------------------------------------------------------------|
|                                                             O  |
|------------------------------------------------------/bO--O----|
|                                             /bO O #O/          |
|----------------------------------/bO--O--#O/-------------------|
|                            O  #O/                              |
|--------------------/bO--O--------------------------------------|
            /bO O #O/
   -O- -#O-/


distance	name		___	___	half-steps
C'to C'		perfect Unison 	PU	1	0
C to C#		Aug unison	aU	#1	1
C to Db		minor 2nd	m2	b2	1
C to D		Major 2nd	M2	2	2
C to D#		aug second	a2 	#2	3
C to Eb		minor 3rd	m3	b3	3
C to E		Major 3rd	M3	3	4
C to F		Perfect 4th	P4	4	5
C to F#		Aug fourth	a4	#4	6
C to Gb		dim 5th		d5	b5	6
C to G		Perfect 5th	P5	5	7
C to G#		aug 5th		a5	#5	8
C to Ab		minor 6th	m6	b6	8
C to A		Major 6th	M6	6	9
C to Bbb	diminished 7th	d7	bb7	9
C to A#		augmented 6th	a6	#6	10
C to Bb		minor 7th	m7	b7	10
C to B		Major 7th	M7	7	11
C to C		Perfect Ocatve	P8	8	12

Types of intervals (perfect, maj, min, aug, dim)

Now for historical reasons, all of the intervals in the major scale are either considered "perfect" or "major".
The perfect intervals are Perfect unison, perfect 4th, perfect 5th, and perfect octave. (A unison is when you play two of the same note. Think relative tuning for an everyday example)
The major intervals are major 2nd, major 3rd, major 6th, major 7th.

Note: the perfect intervals (unison, 4th, 5th, 8ve) are never major, and the major intervals (2nd, 3rd, 6th, 7th) are never perfect. ( you would never call an interval a perfect 3rd, or a major octave, etc. It's not done).

These names (P5, etc.) are intervallic names that are given to a note to tell its distance from a relative note (the 1). Since there are 12 notes in our system, and we compare all the notes against the major scale, we have the above names for the twelve notes/intervals in reference to the 1 note (tonic, root note). Multiple names for a note are enharmonic equivalents (different names for the same note). They show that there may be more than one context in which to view an interval.

Careful examination of the names will show that there is a half-step-wise progression through the names. that is to say you can go by half-steps through dim4-P4-aug4 or dim3-m3-M3-aug3, etc. (amjor and minor never show up in a perfect interval, perfects never show up in a major/minor type interval.) we do not use names below diminished or above augmented.

Interval inversions
If I go fropm the note C up to the note A and find the distance, it is the equivalent of 9 half-steps. We call this a M6. However, if I go from C down to the note A and find the distance, it is equivalent to 3 half-steps distance between them. We call this a m3. And here we have two different intervals created by the same two notes.. we call this behavior/phenomena an interval inversion. when you move one of the notes in an interval an octave from its original position (and on the other side of the note that it is in context with), then you are said to have inverted the interval.
Some interesting properties happen in interval inversion.
They are the following:

Perfect intervals invert to become perfect intervals
Major intervals invert to become minor intervals
Minor intervals invert to become major intervals
Diminished intervals invert to become augmented intervals
Augmented intervals invert to become diminished intervals
2nd intervals invert to become 7th intervals
3rd intervals invert to become 6th intervals
4th intervals invert to become 5th intervals
5th intervals invert to become 4th intervals
6th intervals invert to become 3rd intervals
7th intervals invert to become 2nd intervals
Octave intervals invert to become unison intervals
Unison intervals invert to become octave intervals
always.

identifying intervals
When looking at a melody or harmony we can analyze the intervals. Let's try some

examples:

a.)    b.)   c.)
|-----|-----|-----------|
|     |     |           |
|-----|-----|-----------|
|  O  |     |           |
|-----|--O--|-----O-----|
|     |     |        O  |
|--O--|-----|-----------|
|     |     |  O        |
|--O--|--O--|-----------|

  -O-   ---
        ---
        #O 

Fill in the following:
a.) from C to E = _______, 1/2 steps =
from C to G =_______, 1/2 steps =
from C to C = _______, 1/2 steps =

b.) from E to G# = _______, 1/2 steps =
from E to B = _______, 1/2 steps =
from G# to B = _______, 1/2 steps =

c.) from F to B = _______, 1/2 steps =
from B to A = _______, 1/2 steps =

Worksheets will be coming.

Next lesson is on Intro to scales.

Peace,
Christopher Roberts

snglstringtheory@aol.com


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Last updated March 13, 2003
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