Difference between revisions of "Ref: Intervals"

Revision as of 14:20, 30 January 2016

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Intervals Scales Circle of 5ths Fret Maps CAGED Charts Diatonic Chords Diatonic Keys Chord Fingerings Chord Naming Progressions Modes Counting Rhythm Arpeggios Reading Tab Other Notation Injury

An interval is the "distance" in terms of pitch between two notes. This is usually defined in terms of the number of steps between them in the 12-tone chromatic scale. The actual pitch difference depends on the tuning system used. The two relative pitches also form a ratio that determine how harmonic they are.

Pitches and Ratios

Root Note	Other Note	Semitones from Root to Other	Interval Short Name	Interval Full Name	Just Intonation Ratio	Root Cycles before resync
C	C	0	U	Unison	1:1	1
C	D♭	1	m2	Minor 2nd	16:15	16
C	D	2	M2	(Major) 2nd	9:8	9
C	E♭	3	m3	Minor 3rd	6:5	6
C	E	4	M3	Major 3rd	5:4	5
C	F	5	P4	(Perfect) 4th	4:3	4
C	G♭	6	A4, d5, tt	Augmented 4th/ Diminished 5th/ Tritone	7:5	7
C	G	7	P5	(Perfect) 5th	3:2	3
C	A♭	8	m6	Minor 6th	8:5	8
C	A	9	M6	Major 6th	5:3	5
C	B♭	10	m7	Minor 7th	16:9	16
C	B	11	M7	Major 7th	15:8	15
C	C	12	U	Unison or Octave	2:1	2

Ordered by Most to Least Consonant (Harmonic)
Root Note	Other Note	Semitones from Root to Other	Interval Short Name	Interval Full Name	Just Intonation Ratio	Root Cycles before resync
C	C	0	U	Unison	1:1	1
C	C	12	U	Unison or Octave	2:1	2
C	G	7	P5	(Perfect) 5th	3:2	3
C	F	5	P4	(Perfect) 4th	4:3	4
C	E	4	M3	Major 3rd	5:4	5
C	A	9	M6	Major 6th	5:3	5
C	E♭	3	m3	Minor 3rd	6:5	6
C	G♭	6	A4, d5, tt	Augmented 4th/ Diminished 5th/ Tritone	7:5	7
C	A♭	8	m6	Minor 6th	8:5	8
C	D	2	M2	(Major) 2nd	9:8	9
C	B	11	M7	Major 7th	15:8	15
C	D♭	1	m2	Minor 2nd	16:15	16
C	B♭	10	m7	Minor 7th	16:9	16

Comparing Just Intonation to Equal Temperament
Interval Name	Just Intonation Ratio	Equal Temperament	% Difference	Just Intonation Cents	12-TET Cents	Cent Difference
m2	16:15 = 1.0666...	1.05946	-0.67563	111.73	100	-11.73
M2	9:8 = 1.125	1.12246	-0.22618	203.91	200	-3.91
m3	6:5 = 1.2	1.18920	-0.90028	315.64	300	-15.64
M3	5:4 = 1.25	1.25991	0.79250	386.31	400	+13.69
P4	4:3 = 1.333...	1.33482	0.11153	498.04	500	+1.96
tt	7:5 = 1.4	1.41419	1.01349	582.51	600	+17.49
P5	3:2 = 1.5	1.49828	-0.11491	701.96	700	-1.96
m6	8:5 = 1.6	1.58736	-0.78975	813.69	800	-13.69
M6	5:3 = 1.666...	1.68175	0.90492	884.36	900	+15.64
m7	16:9 = 1.777...	1.78175	0.22318	996.09	1,000	+3.91
M7	15:8 = 1.875	1.88769	0.67669	1088.27	1,100	+11.73

Minor 2nd

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
1	M7	16:15 = 1.0666...	1.05946

* |i|-|-|-|-|
* |-|-|-|-|p|

* all but G-B

B |i|-|-|-|
G |-|-|-|p|

D/G |-|-|-|p|
A/D |-|-|-|-|
E/A |i|-|-|-|

B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |i|-|-|-|-|

G |i|-|-|
D |-|-|-|
A |-|-|-|
E |-|-|r|

B/E |i|-|
G/B |-|-|
D/G |-|-|
A/D |-|m|

|-|-|-|-|-|-|-|-|-|x|o|-|-|-|-|-|-|-|-|
|-|-|-|o|-|-|-|-|-|-|-|-|-|-|x|o|-|-|-|
|-|-|-|-|-|-|x|o|-|-|-|-|-|-|-|-|-|-|-|
|o|-|-|-|-|-|-|-|-|-|-|x|o|-|-|-|-|-|-|
|-|-|-|-|x|o|-|-|-|-|-|-|-|-|-|-|-|o|-|
|-|-|-|-|-|-|-|-|-|x|o|-|-|-|-|-|-|-|-|

Major 2nd

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
2	m7	9:8 = 1.125	1.12246

* |i|-|-|-|
* |-|-|-|p|
 
* all but G-B

B |i|-|-|
G |-|-|r|

D/G |-|-|-|-|p|
A/D |-|-|-|-|-|
E/A |i|-|-|-|-|

G/B |i|-|
D/G |-|-|
A/D |-|-|
E/A |-|m|

B/E |i| |m|
G/B |)| |-|
D/G |)| |-|
A/D |i| |i|

|-|-|-|-|-|-|-|-|-|x|-|o|-|-|-|-|-|-|-|
|-|-|-|-|o|-|-|-|-|-|-|-|-|-|x|-|o|-|-|
|-|-|-|-|-|-|x|-|o|-|-|-|-|-|-|-|-|-|-|
|-|o|-|-|-|-|-|-|-|-|-|x|-|o|-|-|-|-|-|
|-|-|-|-|x|-|o|-|-|-|-|-|-|-|-|-|-|-|o|
|-|-|-|-|-|-|-|-|-|x|-|o|-|-|-|-|-|-|-|

Minor 3rd

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
3	M6	6:5 = 1.2	1.18920

* |i|-|-|
* |-|-|r|
 
* all but G-B

B |i|-|
G |-|m|

G |i| |m|
D |)| |-|
A |)| |-|
E |i| |i|

B/E |i| |m|
G/B |)| |-|
D/G |)| |-|
A/D |i| |i|

|o|-|-|-|-|-|-|-|-|x|-|-|o|-|-|-|-|-|-|
|-|-|-|-|-|o|-|-|-|-|-|-|-|-|x|-|-|o|-|
|-|-|-|-|-|-|x|-|-|o|-|-|-|-|-|-|-|-|-|
|-|-|o|-|-|-|-|-|-|-|-|x|-|-|o|-|-|-|-|
|-|-|-|-|x|-|-|o|-|-|-|-|-|-|-|-|-|-|-|
|o|-|-|-|-|-|-|-|-|x|-|-|o|-|-|-|-|-|-|

Major 3rd

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
4	m6	5:4 = 1.25	1.25991

* |i|-|
* |-|m|
 
* all but G-B

B |i| |r|
G |i| |m|

G |-|m|
D |-|-|
A |-|-|
E |i|-|

B/E |-|-|r|
G/B |-|-|-|
D/G |-|-|-|
A/D |i|-|-|

|-|o|-|-|-|-|-|-|-|x|-|-|-|o|-|-|-|-|-|
|-|-|-|-|-|-|o|-|-|-|-|-|-|-|x|-|-|-|o|
|-|-|-|-|-|-|x|-|-|-|o|-|-|-|-|-|-|-|-|
|-|-|-|o|-|-|-|-|-|-|-|x|-|-|-|o|-|-|-|
|-|-|-|-|x|-|-|-|o|-|-|-|-|-|-|-|-|-|-|
|-|o|-|-|-|-|-|-|-|x|-|-|-|o|-|-|-|-|-|

Perfect 4th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
5	P5	4:3 = 1.333...	1.33482

* |i|
* |i|

 
* all but G-B

B |-|m|
G |i|-|

G |-|-|r|
D |-|-|-|
A |-|-|-|
E |i|-|-|

B/E |-|-|-|p|
G/B |-|-|-|-|
D/G |-|-|-|-|
A/D |i|-|-|-|

B/E |i|-|-|
G/B |-|-|-|
D/G |-|-|-|
A/D |-|-|-|
E/A |-|-|r|

|-|-|o|-|-|-|-|-|-|x|-|-|-|-|o|-|-|-|-|
|-|-|-|-|-|-|-|o|-|-|-|-|-|-|x|-|-|-|-|
|-|-|-|-|-|-|x|-|-|-|-|o|-|-|-|-|-|-|-|
|-|-|-|-|o|-|-|-|-|-|-|x|-|-|-|-|o|-|-|
|-|-|-|-|x|-|-|-|-|o|-|-|-|-|-|-|-|-|-|
|-|-|o|-|-|-|-|-|-|x|-|-|-|-|o|-|-|-|-|

Tritone

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Inversion of itself

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
6	itself	7:5 = 1.4	1.41419

* |-|i|
* |i|-|

 
* all but G-B

B |-|-|r|
G |i|-|-|

G |-|-|-|p|
D |-|-|-|-|
A |-|-|-|-|
E |i|-|-|-|

B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |-|-|-|-|-|
A/D |i|-|-|-|-|

B/E |i|-|
G/B |-|-|
D/G |-|-|
A/D |-|-|
E/A |-|m|

|-|-|-|o|-|-|-|-|-|x|-|-|-|-|-|o|-|-|-|
|-|-|-|-|-|-|-|-|o|-|-|-|-|-|x|-|-|-|-|
|o|-|-|-|-|-|x|-|-|-|-|-|o|-|-|-|-|-|-|
|-|-|-|-|-|o|-|-|-|-|-|x|-|-|-|-|-|o|-|
|-|-|-|-|x|-|-|-|-|-|o|-|-|-|-|-|-|-|-|
|-|-|-|o|-|-|-|-|-|x|-|-|-|-|-|o|-|-|-|

Perfect 5th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Inversion of P4

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
7	P4	3:2 = 1.5	1.49828

* |-|-|r|
* |i|-|-|
 

* all but G-B

B |-|-|-|p|
G |i|-|-|-|

D/G |i|-|-|-|
A/D |-|-|-|-|
E/A |-|-|-|p|

B/E |i|-|-|
G/B |-|-|-|
D/G |-|-|r|

B |i|-|-|-|-|
G |)|-|-|-|p|
D |)|-|-|-|-|
A |)|-|-|-|-|
E |i|-|-|-|-|

E |i| |r|
B |)| |-|
G |)| |-|
D |)| |-|
A |i| |i|

|-|-|-|-|o|-|-|-|-|x|-|-|-|-|-|-|o|-|-|
|-|-|-|-|-|-|-|-|-|o|-|-|-|-|x|-|-|-|-|
|-|o|-|-|-|-|x|-|-|-|-|-|-|o|-|-|-|-|-|
|-|-|-|-|-|-|o|-|-|-|-|x|-|-|-|-|-|-|o|
|-|-|-|-|x|-|-|-|-|-|-|o|-|-|-|-|-|-|-|
|-|-|-|-|o|-|-|-|-|x|-|-|-|-|-|-|o|-|-|

Minor 6th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Inversion of

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
8	M3	8:5 = 1.6	1.58736

* |-|-|-|p|
* |i|-|-|-|
 

* all but G-B

B |-|-|-|-|p|
G |i|-|-|-|-|

D/G |i|-|-|
A/D |-|-|-|
E/A |-|-|r|

B/E |i|-|
G/B |-|-|
D/G |-|m|

B/E |-|m|
G/B |-|-|
D/G |-|-|
A/D |-|-|
E/A |i|-|

|-|-|-|-|-|o|-|-|-|x|-|-|-|-|-|-|-|o|-|
|-|-|-|-|-|-|-|-|-|-|o|-|-|-|x|-|-|-|-|
|-|-|o|-|-|-|x|-|-|-|-|-|-|-|o|-|-|-|-|
|-|-|-|-|-|-|-|o|-|-|-|x|-|-|-|-|-|-|-|
|o|-|-|-|x|-|-|-|-|-|-|-|o|-|-|-|-|-|-|
|-|-|-|-|-|o|-|-|-|x|-|-|-|-|-|-|-|o|-|

Major 6th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
9	m3	5:3 = 1.666...	1.68175

* |-|-|-|-|p|
* |i|-|-|-|-|
 


* all but G-B

D/G |i|-|
A/D |-|-|
E/A |-|m|

B/E |i| |m|
G/B |)| |-|
D/G |i| |i|

B/E |-|-|r|
G/B |-|-|-|
D/G |-|-|-|
A/D |-|-|-|
E/A |i|-|-|

E |i|-|-|-|
B |-|-|-|-|
G |-|-|-|-|
D |-|-|-|-|
A |-|-|-|-|
E |-|-|-|p|

|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|
|-|-|-|-|-|-|-|-|-|-|-|o|-|-|x|-|-|-|-|
|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|-|-|-|
|-|-|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|
|-|o|-|-|x|-|-|-|-|-|-|-|-|o|-|-|-|-|-|
|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|

Minor 7th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
10	M2	16:9 = 1.777...	1.78175

D/G |i|
A/D |)|
E/A |i|

B/E |-|m|
G/B |-|-|
D/G |i|-|

B/E |-|-|-|p|
G/B |-|-|-|-|
D/G |-|-|-|-|
A/D |-|-|-|-|
E/A |i|-|-|-|

E |i|-|-|
B |-|-|-|
G |-|-|-|
D |-|-|-|
A |-|-|-|
E |-|-|r|

|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|
|o|-|-|-|-|-|-|-|-|-|-|-|o|-|x|-|-|-|-|
|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|o|-|-|
|-|-|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|
|-|-|o|-|x|-|-|-|-|-|-|-|-|-|o|-|-|-|-|
|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|

Major 7th

m2 M2 m3 M3 P4 tt P5 m6 M6 m7 M7

Semitones	Inversion	Just Intonation Ratio	Equal Temperament
11	m2	15:8 = 1.875	1.88769

D/G |-|m|
A/D |-|-|
E/A |i|-|

B/E |-|-|r|
G/B |-|-|-|
D/G |i|-|-|

B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |-|-|-|-|-|
A/D |-|-|-|-|-|
E/A |i|-|-|-|-|

E |i|-|
B |-|-|
G |-|-|
D |-|-|
A |-|-|
E |-|m|

|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|
|-|o|-|-|-|-|-|-|-|-|-|-|-|o|x|-|-|-|-|
|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|-|o|-|
|-|-|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|
|-|-|-|o|x|-|-|-|-|-|-|-|-|-|-|o|-|-|-|
|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|

All Intervals

|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|
|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|
|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|
|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|
|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|
|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|

|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|
|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|
|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|
|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|
|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|
|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|m3|M3|P4|tt|P5|m6|M6|

Top

Intervals Scales Circle of 5ths Fret Maps CAGED Charts Diatonic Chords Diatonic Keys Chord Fingerings Chord Naming Progressions Modes Counting Rhythm Arpeggios Reading Tab Other Notation Injury

@@ Line 189: / Line 189: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of
 {|class="wikitable"
@@ Line 259: / Line 258: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Major 6th|{{M6|M6}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 3 || [[#Major 6th|{{M6|M6}}]] || 6:5 = 1.2         || 1.18920
+|}
 {|
@@ Line 316: / Line 320: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Minor 6th|{{Mn6|m6}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 4 || [[#Minor 6th|{{Mn6|m6}}]] || 5:4 = 1.25        || 1.25991
+|}
 {|
@@ Line 373: / Line 382: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Perfect 5th|{{P5|P5}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 5 || [[#Perfect 5th|{{P5|P5}}]] || 4:3 = 1.333...    || 1.33482
+|}
 {|
@@ Line 443: / Line 457: @@
 }}
 * Inversion of itself
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 6 || itself || 7:5 = 1.4         || 1.41419
+|}
 {|
@@ Line 512: / Line 531: @@
 }}
 * Inversion of [[#Perfect 4th|{{P4|P4}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 7 || [[#Perfect 4th|{{P4|P4}}]] || 3:2 = 1.5         || 1.49828
+|}
 {|
@@ Line 588: / Line 612: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Major 3rd|{{M3|M3}}]]
+* Inversion of
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 8 || [[#Major 3rd|{{M3|M3}}]] || 8:5 = 1.6         || 1.58736
+|}
 {|
@@ Line 657: / Line 686: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Minor 3rd|{{Mn3|m3}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 9 || [[#Minor 3rd|{{Mn3|m3}}]] || 5:3 = 1.666...    || 1.68175
+|}
 {|
@@ Line 731: / Line 765: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Major 2nd|{{M2|M2}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 10 || [[#Major 2nd|{{M2|M2}}]] || 16:9 = 1.777...   || 1.78175
+|}
 {|
@@ Line 796: / Line 835: @@
 | Ref: Intervals#Major 7th|{{M7|M7}}
 }}
-* Inversion of [[#Minor 2nd|{{Mn2|m2}}]]
+{|class="wikitable"
+! Semitones !! Inversion !! Just Intonation Ratio !! Equal Temperament
+|-
+| 11 || [[#Minor 2nd|{{Mn2|m2}}]] || 15:8 = 1.875      || 1.88769
+|}
 {|

Difference between revisions of "Ref: Intervals"

Revision as of 14:20, 30 January 2016

Contents

Pitches and Ratios

Minor 2nd

Major 2nd

Minor 3rd

Major 3rd

Perfect 4th

Tritone

Perfect 5th

Minor 6th

Major 6th

Minor 7th

Major 7th

All Intervals