Intervals

Recall, that an interval is the distance between two tones (pitches,notes).

Recall that the chromatic scale contains all of the tones that we are using in the western system we are using.

Recall that the chromatic scale contains the tones:
A,A#/Bb,B,C,C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab.

Recall that the chromatic scale is symmetric and therefore we need only learn one key as it were, and all other keys are the same key (in relation to which tones are in the scale, not in relation to function). We discuss starting at some point rather than contemplating different chromatic keys.

Starting at any point, we define the chromatic scale as containing the intervals:
1,#1/b2,2,#2/b3,3,4,#4/b5,5,#5/b6,6,#6/b7,7

If we consider the chromatic scale starting at C:
C,C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab,A,A#/Bb,B
as being the intervals:
1,#1/b2,2,#2/b3,3,4,#4/b5,5,#5/b6,6,#6/b7,7

And we consider the C major scale:
C,D,E,F,G,A,B
as being the intervals:
1,2,3,4,5,6,7

(This is backwards in the way we define intervals. Actually the numbers 1-7 are defined from the major scale in the simplified western system we are using).

Let's look at those numbers 1-7, they are shorthand for the names of the intervals:
1 = Root (tonic)
2 = Major second
3 = Major third
4 = Perfect fourth
5 = Perfect fifth
6 = Major sixth
7 = Major seventh

To get into the why of perfect vs: major, etc. will entail a discussion of tuning theory, which I'm (in this lesson) currently avoiding as I intend to discuss it at a later time (ad nauseum).

For now, let's define the other number as being shorthand for the following intervals:
#1 = augmented tonic
b2 = minor second
#2 = augmented second
b3 = minor third
#4 = augmented fourth
b5 = diminished fifth
#5 = augmented fifth
b6 = minor sixth
#6 = augmented sixth
b7 = minor seventh

We should also consider simple Vs: compound intervals. Simple intervals are within one octave (numbers 1-8), where compound intervalsgo beyond one octave, often considered to be of the nature octaves+interval.

Common compound intervals:
b9 = minor ninth (octave above m2)
9 = major ninth (8ve+M2)
#9 = aug ninth
b10= min tenth
10 = maj 10th
11 = perf 11th
#11= aug 11th
b12= dim 12th
12 = perf 12th
#12= aug 12th
b13= min 13th
13 = maj 13th
#13= aug 13th
b14= min 14th
14 = maj 14th

In general practice, only 9th's,11th's, and 13th's are commonly refered to.

Let's consider these intervals in standard tuning (= EADGBE).

Starting with intervals in the same range of frets on two adjacent strings. (R = root)

The minor second (m2, b2) is the distance between two adjacent frets on the same string.

|-R-|-O-|    (all strings)
|-1-|b2-|

or 
 
|-O-|---|---|---|---| 
|---|---|---|---|-R-| 

 
|b2-|---|---|---|---| 
|---|---|---|---|-1-| 

(for 2 strings seperated by a perfect 4th, which will from here on be abbreviated as "sep p4")

or 

|-O-|---|---|---|
|---|---|---|-R-|


|b2-|---|---|---|
|---|---|---|-1-|

(for 2 strings seperated by a maj 3rd, which will from here on be abbreviated as "sep M3")

The major second (M2,2) is the distance of two frets from each other (on the same string).

|-R-|---|-O-|

|-1-|---|-2-|
(all strings)

or 
 
|-O-|---|---|---| 
|---|---|---|-R-| 

 
|-2-|---|---|---| 
|---|---|---|-1-| 

 (sep p4)

or 

|-O-|---|---|
|---|---|-R-|


|-2-|---|---|
|---|---|-1-|

(sep M3)

The minor third (m3,b3) is the distance of three frets from each other (on the same string).

|-R-|---|---|-O-|

|-1-|---|---|b3-|
(all strings)

or 
 
|-O-|---|---| 
|---|---|-R-| 

 
|b3-|---|---| 
|---|---|-1-| 

 (sep p4)

or 

|-O-|---|
|---|-R-|


|b3-|---|
|---|-1-|

(sep M3)

The major third (M3,3) is the distance of four frets from each other (on the same string).

|-R-|---|---|---|-O-|

|-1-|---|---|---|-3-|
(all strings)

or 
 
|-O-|---| 
|---|-R-| 

 
|-3-|---| 
|---|-1-| 

 (sep p4)

or 

|-O-|
|-R-|


|-3-|
|-1-|
(sep M3)

The Perfect fourth (P4,4) is the distance of five frets from each other (on the same string).

|-R-|---|---|---|---|-O-|

|-1-|---|---|---|---|-4-|
(all strings)

or 

|-O-|
|-R-|


|-4-|
|-1-|

(sep p4)

or 
 
|---|-O-| 
|-R-|---| 

 
|---|-4-| 
|-1-|---| 
(sep M3)

The augmented fourth (aug4,#4), diminished fifth (dim5,b5), tritone is the distance of six frets from each other (on the same string).

|-R-|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|#4-|
(all strings)

or 

|---|-O-|
|-R-|---|


|---|#4-|
|-1-|---|

|---|b5-|
|-1-|---|

(sep p4)

or 
 
|---|---|-O-| 
|-R-|---|---| 

 
|---|---|#4-| 
|-1-|---|---|

|---|---|b5-| 
|-1-|---|---|

(sep M3)

The perfect fifth (P5,5), is the distance of seven frets from each other (on the same string).

|-R-|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|-5-|
(all strings)

or 

|---|---|-O-|
|-R-|---|---|


|---|---|-5-|
|-1-|---|---|

(sep p4)

or 
 
|---|---|---|-O-| 
|-R-|---|---|---| 

|---|---|---|-5-| 
|-1-|---|---|---|

(sep M3)

The augmented fifth (aug5,#5), minor sixth (m6,b6) is the distance of eight frets from each other (on the same string).

|-R-|---|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|---|#5-|
(all strings)

or 

|---|---|---|-O-|
|-R-|---|---|---|


|---|---|---|#5-|
|-1-|---|---|---|


|---|---|---|b6-|
|-1-|---|---|---|



(sep p4)

or 
 
|---|---|---|---|-O-| 
|-R-|---|---|---|---| 

|---|---|---|---|#5-| 
|-1-|---|---|---|---|

|---|---|---|---|b6-| 
|-1-|---|---|---|---|

(sep M3)

or across three adjacent strings

|-O-|---|---|
|---|---|---| 
|---|---|-R-| 

|#5-|---|---|
|---|---|---| 
|---|---|-1-|

|b6-|---|---|
|---|---|---| 
|---|---|-1-|

(P4,P4)
{this notation p4,p4 means that the three strings are seperated in such a way that the lower two strings are seperated by a perfect 4th. that's the first p4. And the the midlle and higher strings are seperated by a perfect 4th. that's the second p4. This notation will be abbreviated from here on. This occurs in standard tuning in two places . across the strings EAD , and across the strings ADG}

or


|-O-|---| 
|---|---| 
|---|-R-| 


|#5-|---| 
|---|---| 
|---|-1-|


|b6-|---| 
|---|---| 
|---|-1-|
(P4,M3) or (M3,P4)

{same idea behind the notation as above. P4,M3 ocuurs once in standard tuning, across the strings DGB. M3,P4 occurs once in standard tuning, across the strings GBE}

The major sixth (M6,6) is the distance of nine frets from each other (on the same string).

|-R-|---|---|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|---|---|-6-|
(all strings)

or 

|---|---|---|---|-O-|
|-R-|---|---|---|---|

|---|---|---|---|-6-|
|-1-|---|---|---|---|

(sep p4)

or 
 
|---|---|---|---|---|-O-| 
|-R-|---|---|---|---|---| 

|---|---|---|---|---|-6-| 
|-1-|---|---|---|---|---|

(sep M3)

or across three adjacent strings

|-O-|---|
|---|---| 
|---|-R-| 

|-6-|---|
|---|---| 
|---|-1-|

(P4,P4) 


or

|-O-|
|---|
|-R-| 

|-6-| 
|---| 
|-1-|

(P4,M3) or (M3,P4)

The minor seventh (m7,b7) is the distance of ten frets from each other (on the same string).

|-R-|---|---|---|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|---|---|---|b7-|
(all strings)

or 

|---|---|---|---|---|-O-|
|-R-|---|---|---|---|---|

|---|---|---|---|---|b7-|
|-1-|---|---|---|---|---|

(sep p4)

or 
 
|---|---|---|---|---|---|-O-| 
|-R-|---|---|---|---|---|---| 

|---|---|---|---|---|---|b7-| 
|-1-|---|---|---|---|---|---|

(sep M3)

or across three adjacent strings

|-O-|
|---| 
|-R-| 

|b7-|
|---| 
|-1-|

(P4,P4) 


or

|---|-O-|
|---|---|
|-R-|---|

|---|b7-| 
|---|---|
|-1-|---|

(P4,M3) or (M3,P4)

The major seventh (M7,7) is the distance of eleven frets from each other (on the same string).

|-R-|---|---|---|---|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|---|---|---|---|-7-|
(all strings)

or 

|---|---|---|---|---|---|-O-|
|-R-|---|---|---|---|---|---|

|---|---|---|---|---|---|-7-|
|-1-|---|---|---|---|---|---|

(sep p4)

or 
 
|---|---|---|---|---|---|---|-O-| 
|-R-|---|---|---|---|---|---|---| 

|---|---|---|---|---|---|---|-7-| 
|-1-|---|---|---|---|---|---|---|

(sep M3)

or across three adjacent strings

|---|-O-|
|---|---| 
|-R-|---|

|---|-7-|
|---|---|
|-1-|---|

(P4,P4) 


or

|---|---|-O-|
|---|---|---|
|-R-|---|---|

|---|---|-7-| 
|---|---|---|
|-1-|---|---|

(P4,M3) or (M3,P4)

The Octave (P8,8) is the distance of twelve frets from each other (on the same string).

|-R-|---|---|---|---|---|---|---|---|---|---|---|-O-|

|-1-|---|---|---|---|---|---|---|---|---|---|---|-8-|
(all strings)

or 

|---|---|---|---|---|---|---|-O-|
|-R-|---|---|---|---|---|---|---|

|---|---|---|---|---|---|---|-8-|
|-1-|---|---|---|---|---|---|---|

(sep p4)

or 
 
|---|---|---|---|---|---|---|---|-O-| 
|-R-|---|---|---|---|---|---|---|---| 

|---|---|---|---|---|---|---|---|-8-| 
|-1-|---|---|---|---|---|---|---|---|

(sep M3)

or across three adjacent strings

|---|---|-O-|
|---|---|---| 
|-R-|---|---|

|---|---|-8-|
|---|---|---|
|-1-|---|---|

(P4,P4) 


or

|---|---|---|-O-|
|---|---|---|---|
|-R-|---|---|---|

|---|---|---|-8-| 
|---|---|---|---|
|-1-|---|---|---|

(P4,M3) or (M3,P4)


or across 4 strings

|-O-|---|---|---|
|---|---|---|---|
|---|---|---|---| 
|---|---|---|-R-| 

|-8-|---|---|---|
|---|---|---|---|
|---|---|---|---| 
|---|---|---|-1-| 
(P4,P4,P4)
{In standard tuning this happens once, across the strings EADG. Abbreviated hereafter.}

or

|-O-|---|---|
|---|---|---|
|---|---|---|
|---|---|-R-|


|-8-|---|---|
|---|---|---|
|---|---|---|
|---|---|-1-|
(P4,P4,M3) or (P4,M3,P4)
{P4,P4,M3 happens once in standard tuning, across strings ADGB. P4,M3,P4 happens once in standard tuning, across the strings DGBE}

COMPOUND INTERVALS

The minor ninth (m9,b9) is the compound interval of an octave plus a minor second.

Across three adjacent strings


|---|---|---|-O-|
|---|---|---|---| 
|-R-|---|---|---|

|---|---|---|b9-|
|---|---|---|---|
|-1-|---|---|---|

(P4,P4) 


or

|---|---|---|---|-O-|
|---|---|---|---|---|
|-R-|---|---|---|---|

|---|---|---|---|b9-| 
|---|---|---|---|---|
|-1-|---|---|---|---|

(P4,M3) or (M3,P4)


or across 4 strings

|-O-|---|---|
|---|---|---|
|---|---|---| 
|---|---|-R-| 

|b9-|---|---|
|---|---|---|
|---|---|---| 
|---|---|-1-| 

(P4,P4,P4)

or

|-O-|---|
|---|---|
|---|---|
|---|-R-|


|b9-|---|
|---|---|
|---|---|
|---|-1-|

(P4,P4,M3) or (P4,M3,P4)

The major ninth (M9,9) is the compound interval of an octave plus a major second. Across three adjacent strings


|---|---|---|---|-O-|
|---|---|---|---|---| 
|-R-|---|---|---|---|

|---|---|---|---|-9-|
|---|---|---|---|---|
|-1-|---|---|---|---|

(P4,P4) 


or

|---|---|---|---|---|-O-|
|---|---|---|---|---|---|
|-R-|---|---|---|---|---|

|---|---|---|---|---|-9-| 
|---|---|---|---|---|---|
|-1-|---|---|---|---|---|

(P4,M3) or (M3,P4)


or across 4 strings

|-O-|---|
|---|---|
|---|---|
|---|-R-| 

|-9-|---|
|---|---|
|---|---| 
|---|-1-| 

(P4,P4,P4)

or

|-O-|
|---|
|---|
|-R-|


|-9-|
|---|
|---|
|-1-|

(P4,P4,M3) or (P4,M3,P4)

The minor tenth (m10,b10), augmented ninth (aug9,#9) is the compound interval of an octave plus a minor third (or aug 2nd). Across 4 strings


|-O-|
|---|
|---|
|-R-| 

|b10|
|---|
|---| 
|-1-| 

|#9-|
|---|
|---| 
|-1-| 

(P4,P4,P4)

or

|---|-O-|
|---|---|
|---|---|
|-R-|---|

|---|b10|
|---|---|
|---|---|
|-1-|---|

|---|#9-|
|---|---|
|---|---|
|-1-|---|

(P4,P4,M3) or (P4,M3,P4)

The major tenth (M10,10), is the compound interval of an octave plus a major third.
Across 4 strings


|-O-|
|---|
|---|
|-R-| 

|-10|
|---|
|---| 
|-1-| 

(P4,P4,P4)

or

|---|-O-|
|---|---|
|---|---|
|-R-|---|

|---|-10|
|---|---|
|---|---|
|-1-|---|

(P4,P4,M3) or (P4,M3,P4)


or across 5 strings

|-O-|---|---|---|
|---|---|---|---|
|---|---|---|---|
|---|---|---|---|
|---|---|---|-R-|

|-10|---|---|---|
|---|---|---|---|
|---|---|---|---|
|---|---|---|---|
|---|---|---|-1-|

(in standard tuning there is only one pattern. I'll leave to the reader to figure out why).

The perfect eleventh (P11,11), is the compound interval of an octave plus a perfect fourth.
Across 4 strings


|---|-O-|
|---|---|
|---|---|
|-R-|---|

|---|-11|
|---|---|
|---|---|
|-1-|---|

(P4,P4,P4)

or

|---|---|-O-|
|---|---|---|
|---|---|---|
|-R-|---|---|

|---|---|-11|
|---|---|---|
|---|---|---|
|-1-|---|---|

(P4,P4,M3) or (P4,M3,P4)


or across 5 strings

|-O-|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|-R-|

|-11|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|-1-|

The augmented eleventh (aug11,#11), is the compound interval of an octave plus a augmented fourth.
Across 4 strings


|---|---|-O-|
|---|---|---|
|---|---|---|
|-R-|---|---|

|---|---|#11|
|---|---|---|
|---|---|---|
|-1-|---|---|

(P4,P4,P4)

or

|---|---|---|-O-|
|---|---|---|---|
|---|---|---|---|
|-R-|---|---|---|

|---|---|---|#11|
|---|---|---|---|
|---|---|---|---|
|-1-|---|---|---|

(P4,P4,M3) or (P4,M3,P4)


or across 5 strings

|-O-|---|
|---|---|
|---|---|
|---|---|
|---|-R-|

|#11|---|
|---|---|
|---|---|
|---|---|
|---|-1-|

The Perfect twelth (P12,12), is the compound interval of an octave plus a perfect fifth.

Across 5 strings


|-O-|
|---|
|---|
|---|
|-R-|

|-12|
|---|
|---|
|---|
|-1-|

The minor thriteenth (m13,b13), is the compound interval of an octave plus a minor sixth.

Across 5 strings


|---|-O-|
|---|---|
|---|---|
|---|---|
|-R-|---|

|---|b13|
|---|---|
|---|---|
|---|---|
|-1-|---|

The major thriteenth (M13,13), is the compound interval of an octave plus a major sixth.

Across 5 strings


|---|---|-O-|
|---|---|---|
|---|---|---|
|---|---|---|
|-R-|---|---|

|---|---|-13|
|---|---|---|
|---|---|---|
|---|---|---|
|-1-|---|---|

The minor fourteenth (m14,b14), is the compound interval of an octave plus a minor seventh.

Across 5 strings


|---|---|---|-O-|
|---|---|---|---|
|---|---|---|---|
|---|---|---|---|
|-R-|---|---|---|

|---|---|---|b14|
|---|---|---|---|
|---|---|---|---|
|---|---|---|---|
|-1-|---|---|---|


or across six strings

|-O-|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|-R-|

|b14|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|---|
|---|---|-1-|

(again only one pattern in standard tuning 6 string guitar)

The major fourteenth (M14,14), is the compound interval of an octave plus a major seventh.

Across 5 strings


|---|---|---|---|-O-|
|---|---|---|---|---|
|---|---|---|---|---|
|---|---|---|---|---|
|-R-|---|---|---|---|

|---|---|---|---|-14|
|---|---|---|---|---|
|---|---|---|---|---|
|---|---|---|---|---|
|-1-|---|---|---|---|


or across six strings

|-O-|---|
|---|---|
|---|---|
|---|---|
|---|---|
|---|-R-|

|-14|---|
|---|---|
|---|---|
|---|---|
|---|---|
|---|-1-|

Two octaves(the perfect fifteenth) (P15,15), is the compound interval of an octave plus an octave.
Across six strings


|-O-|
|---|
|---|
|---|
|---|
|-R-|

|-15|
|---|
|---|
|---|
|---|
|-1-|

More info on intervals can be found at
http://simianmoon.com/snglstringtheory/archive/july19.html

Any questions? Feel free to ask.

Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated december 24, 2002
Copyright 2002. All rights reserved.