View source for Ref: Intervals

{{Top-Level Crumbs|3}}
{{Reference Crumbs|1}}

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 ==

{| class="wikitable"
|-
! Root<br>Note !! Other<br>Note !! Semitones<br>from<br />Root to<br>Other !! Interval<br>Short<br>Name !! Interval<br>Full<br>Name !! Just<br>Intonation<br>Ratio !! Root<br>Cycles<br>before<br>resync
|-
|  C  || C  || 0  || {{U|U}}  || Unison || 1:1 || 1
|-
| C  || D{{f}} || 1  || {{Mn2|m2}} || Minor 2nd || 16:15 || 16
|-
| C  || D  || 2  || {{M2|M2}} || (Major) 2nd || 9:8 || 9
|-
| C  || E{{f}} || 3  || {{Mn3|m3}} || Minor 3rd || 6:5 || 6
|-
| C  || E  || 4  || {{M3|M3}} || Major 3rd || 5:4 || 5
|-
| C  || F  || 5  || {{P4|P4}} || (Perfect) 4th ||4:3 || 4
|-
| C  || G{{f}} || 6  || {{tt|A4, d5, tt}}  || Augmented 4th/<br />Diminished 5th/<br />Tritone || 45:32 || 45
|-
| C  || G  || 7  || {{P5|P5}} || (Perfect) 5th || 3:2 || 3
|-
| C  || A{{f}} || 8  || {{Mn6|m6}} || Minor 6th || 8:5 || 8
|-
| C  || A  || 9  || {{M6|M6}} || Major 6th || 5:3 || 5
|-
| C  || B{{f}} || 10 || {{Mn7|m7}}  || Minor 7th || 9:5 || 9
|-
| C  || B  || 11 || {{M7|M7}} || Major 7th || 15:8 || 15
|-
| C  || C  || 12 || {{U|U}}  || Unison or Octave || 2:1 || 2
|}

{| class="wikitable"
|+ Ordered by Most to Least Consonant (Harmonic) 
|-
! Root<br>Note !! Other<br>Note !! Semitones<br>from<br />Root to<br>Other !! Interval<br>Short<br>Name !! Interval<br>Full<br>Name !! Just<br>Intonation<br>Ratio !! Root<br>Cycles<br>before<br>resync
|-
|  C  || C  || 0  || {{U|U}}  || Unison || 1:1 || 1
|-
| C  || C  || 12 || {{U|U}}  || Unison or Octave || 2:1 || 2
|-
| C  || G  || 7  || {{P5|P5}} || (Perfect) 5th || 3:2 || 3
|-
| C  || F  || 5  || {{P4|P4}} || (Perfect) 4th ||4:3 || 4
|-
| C  || E  || 4  || {{M3|M3}} || Major 3rd || 5:4 || 5
|-
| C  || A  || 9  || {{M6|M6}} || Major 6th || 5:3 || 5
|-
| C  || E{{f}} || 3  || {{Mn3|m3}} || Minor 3rd || 6:5 || 6
|-
| C  || A{{f}} || 8  || {{Mn6|m6}} || Minor 6th || 8:5 || 8
|-
| C  || D  || 2  || {{M2|M2}} || (Major) 2nd || 9:8 || 9
|-
| C  || B{{f}} || 10 || {{Mn7|m7}}  || Minor 7th || 9:5 || 9
|-
| C  || B  || 11 || {{M7|M7}} || Major 7th || 15:8 || 15
|-
| C  || D{{f}} || 1  || {{Mn2|m2}} || Minor 2nd || 16:15 || 16
|-
| C  || G{{f}} || 6  || {{tt|A4, d5, tt}}  || Augmented 4th/<br />Diminished 5th/<br />Tritone || 45:32 || 45
|}


{|class="wikitable"
|+ Comparing Just Intonation to Equal Temperament
|-
! Interval<br>Name !! Just<br>Intonation<br>Ratio !!  Equal<br>Temperament !! %<br>Difference !! Just<br>Intonation<br>Cents !! 12-TET<br>Cents !! Cent<br>Difference
|-
| {{Mn2|m2}} || 16:15 = 1.0666... || 1.05946 || -0.67563 || 111.73   || 100   || -11.73
|-                                      
| {{M2|M2}} || 9:8 = 1.125       || 1.12246 || -0.22560 || 203.91   || 200   || -3.91
|-                                               
| {{Mn3|m3}} || 6:5 = 1.2         || 1.18921 || -0.89941 || 315.64   || 300   || -15.64
|-                                               
| {{M3|M3}} || 5:4 = 1.25        || 1.25992 ||  0.79368 || 386.31   || 400   || +13.69
|-                                               
| {{P4|P4}} || 4:3 = 1.333...    || 1.33484 ||  0.11299 || 498.05   || 500   || +1.96
|-                                               
| {{tt|tt}} || 45:32 = 1.40625   || 1.41421 ||  0.56630 || 590.22 || 600   || +9.78
|-                                               
| {{P5|P5}} || 3:2 = 1.5         || 1.49831 || -0.11286 || 701.96   || 700   || -1.96
|-                                               
| {{Mn6|m6}} || 8:5 = 1.6         || 1.58740 || -0.78743 || 813.69   || 800   || -13.69
|-                                               
| {{M6|M6}} || 5:3 = 1.666...    || 1.68179 ||  0.90757 || 884.36   || 900   || +15.64
|-                                      
| {{Mn7|m7}} || 9:5 = 1.8   || 1.78180 ||  -1.01125 || 1017.60 || 1,000 || -17.60
|-                                      
| {{M7|M7}} || 15:8 = 1.875      || 1.88775 ||  0.67993 || 1088.27  || 1,100 || +11.73
|}

=== Minor 2nd ===
{{Crumbs|blue|1
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 1 || [[#Major 7th|{{M7|M7}}]] || 16:15 = 1.0666... || 1.05946 || 111.73 || 100
|}

{|
|-
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<pre>
* |i|-|-|-|-|
* |-|-|-|-|p|

* all but G-B
</pre>
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<pre>
B |i|-|-|-|
G |-|-|-|p|

 
</pre>
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D/G |-|-|-|p|
A/D |-|-|-|-|
E/A |i|-|-|-|

</pre>
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<pre>
B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |i|-|-|-|-|

</pre>
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<pre>
G |i|-|-|
D |-|-|-|
A |-|-|-|
E |-|-|r|
</pre>
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<pre>
B/E |i|-|
G/B |-|-|
D/G |-|-|
A/D |-|m|
</pre>
|}

<pre>
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</pre>

=== Major 2nd ===
{{Crumbs|blue|2
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 2 || [[#Minor 7th|{{Mn7|m7}}]] || 9:8 = 1.125 || 1.12246 || 203.91 || 200
|}

{|
|-
|
<pre>
* |i|-|-|-|
* |-|-|-|p|
 
* all but G-B
</pre>
|
<pre>
B |i|-|-|
G |-|-|r|
 
 
</pre>
|
<pre>
D/G |-|-|-|-|p|
A/D |-|-|-|-|-|
E/A |i|-|-|-|-|
 
</pre>
|
<pre>
G/B |i|-|
D/G |-|-|
A/D |-|-|
E/A |-|m|
</pre>
|
<pre>
B/E |i| |m|
G/B |)| |-|
D/G |)| |-|
A/D |i| |i|
</pre>
|}

<pre>
|-|-|-|-|-|-|-|-|-|x|-|o|-|-|-|-|-|-|-|
|-|-|-|-|o|-|-|-|-|-|-|-|-|-|x|-|o|-|-|
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|-|-|-|-|x|-|o|-|-|-|-|-|-|-|-|-|-|-|o|
|-|-|-|-|-|-|-|-|-|x|-|o|-|-|-|-|-|-|-|
</pre>

=== Minor 3rd ===
{{Crumbs|blue|3
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 3 || [[#Major 6th|{{M6|M6}}]] || 6:5 = 1.2         || 1.18920 || 315.64 || 300
|}

{|
|-
|
<pre>
* |i|-|-|
* |-|-|r|
 
* all but G-B
</pre>
|
<pre>
B |i|-|
G |-|m|
 
 
</pre>
|
<pre>
G |i| |m|
D |)| |-|
A |)| |-|
E |i| |i|
</pre>
|
<pre>
B/E |i| |m|
G/B |)| |-|
D/G |)| |-|
A/D |i| |i|
</pre>
|}

<pre>
|o|-|-|-|-|-|-|-|-|x|-|-|o|-|-|-|-|-|-|
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|o|-|-|-|-|-|-|-|-|x|-|-|o|-|-|-|-|-|-|
</pre>

=== Major 3rd ===
{{Crumbs|blue|4
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 4 || [[#Minor 6th|{{Mn6|m6}}]] || 5:4 = 1.25        || 1.25991 || 386.31 || 400
|}

{|
|-
|
<pre>
* |i|-|
* |-|m|
 
* all but G-B
</pre>
|
<pre>
B |i| |r|
G |i| |m|
 
 
</pre>
|
<pre>
G |-|m|
D |-|-|
A |-|-|
E |i|-|
</pre>
|
<pre>
B/E |-|-|r|
G/B |-|-|-|
D/G |-|-|-|
A/D |i|-|-|
</pre>
|}

<pre>
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</pre>

=== Perfect 4th ===
{{Crumbs|blue|5
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 5 || [[#Perfect 5th|{{P5|P5}}]] || 4:3 = 1.333...    || 1.33484 || 498.05 || 500
|}

{|
|-
|
<pre>
* |i|
* |i|

 
* all but G-B
</pre>
|
<pre>
B |-|m|
G |i|-|
 

 
</pre>
|
<pre>
G |-|-|r|
D |-|-|-|
A |-|-|-|
E |i|-|-|

</pre>
|
<pre>
B/E |-|-|-|p|
G/B |-|-|-|-|
D/G |-|-|-|-|
A/D |i|-|-|-|

</pre>
|
<pre>
B/E |i|-|-|
G/B |-|-|-|
D/G |-|-|-|
A/D |-|-|-|
E/A |-|-|r|
</pre>
|}

<pre>
|-|-|o|-|-|-|-|-|-|x|-|-|-|-|o|-|-|-|-|
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</pre>

=== Tritone ===
{{Crumbs|blue|6
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 6 || itself || 45:32 = 1.40625         || 1.41421 || 590.22 || 600
|}

{|
|-
|
<pre>
* |-|i|
* |i|-|

 
* all but G-B
</pre>
|
<pre>
B |-|-|r|
G |i|-|-|

 
 
</pre>
|
<pre>
G |-|-|-|p|
D |-|-|-|-|
A |-|-|-|-|
E |i|-|-|-|

</pre>
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<pre>
B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |-|-|-|-|-|
A/D |i|-|-|-|-|

</pre>
|
<pre>
B/E |i|-|
G/B |-|-|
D/G |-|-|
A/D |-|-|
E/A |-|m|
</pre>
|}

<pre>
|-|-|-|o|-|-|-|-|-|x|-|-|-|-|-|o|-|-|-|
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</pre>

=== Perfect 5th ===
{{Crumbs|blue|7
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 7 || [[#Perfect 4th|{{P4|P4}}]] || 3:2 = 1.5         || 1.49831 || 701.96 || 700
|}

{|
|-
|
<pre>
* |-|-|r|
* |i|-|-|
 

* all but G-B
</pre>
|
<pre>
B |-|-|-|p|
G |i|-|-|-|

 
 
</pre>
|
<pre>
D/G |i|-|-|-|
A/D |-|-|-|-|
E/A |-|-|-|p|


</pre>
|
<pre>
B/E |i|-|-|
G/B |-|-|-|
D/G |-|-|r|


</pre>
|
<pre>
B |i|-|-|-|-|
G |)|-|-|-|p|
D |)|-|-|-|-|
A |)|-|-|-|-|
E |i|-|-|-|-|
</pre>
|
<pre>
E |i| |r|
B |)| |-|
G |)| |-|
D |)| |-|
A |i| |i|
</pre>
|}

<pre>
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</pre>

=== Minor 6th ===
{{Crumbs|blue|8
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 8 || [[#Major 3rd|{{M3|M3}}]] || 8:5 = 1.6         || 1.58740 || 813.69 || 800
|}

{|
|-
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<pre>
* |-|-|-|p|
* |i|-|-|-|
 

* all but G-B
</pre>
|
<pre>
B |-|-|-|-|p|
G |i|-|-|-|-|

 
 
</pre>
|
<pre>
D/G |i|-|-|
A/D |-|-|-|
E/A |-|-|r|


</pre>
|
<pre>
B/E |i|-|
G/B |-|-|
D/G |-|m|


</pre>
|
<pre>
B/E |-|m|
G/B |-|-|
D/G |-|-|
A/D |-|-|
E/A |i|-|
</pre>
|}

<pre>
|-|-|-|-|-|o|-|-|-|x|-|-|-|-|-|-|-|o|-|
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|o|-|-|-|x|-|-|-|-|-|-|-|o|-|-|-|-|-|-|
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</pre>

=== Major 6th ===
{{Crumbs|blue|9
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 9 || [[#Minor 3rd|{{Mn3|m3}}]] || 5:3 = 1.666...    || 1.68179 || 884.36 || 900
|}

{|
|-
|
<pre>
* |-|-|-|-|p|
* |i|-|-|-|-|
 


* all but G-B
</pre>
|
<pre>
D/G |i|-|
A/D |-|-|
E/A |-|m|



</pre>
|
<pre>
B/E |i| |m|
G/B |)| |-|
D/G |i| |i|



</pre>
|
<pre>
B/E |-|-|r|
G/B |-|-|-|
D/G |-|-|-|
A/D |-|-|-|
E/A |i|-|-|

</pre>
|
<pre>
E |i|-|-|-|
B |-|-|-|-|
G |-|-|-|-|
D |-|-|-|-|
A |-|-|-|-|
E |-|-|-|p|
</pre>
|}

<pre>
|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|
|-|-|-|-|-|-|-|-|-|-|-|o|-|-|x|-|-|-|-|
|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|-|-|-|
|-|-|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|
|-|o|-|-|x|-|-|-|-|-|-|-|-|o|-|-|-|-|-|
|-|-|-|-|-|-|o|-|-|x|-|-|-|-|-|-|-|-|o|
</pre>

=== Minor 7th ===
{{Crumbs|blue|10
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 10 || [[#Major 2nd|{{M2|M2}}]] || 9:5 = 1.80   || 1.78180 || 1017.60
 || 1,000
|}

{|
|-
|
<pre>
D/G |i|
A/D |)|
E/A |i|



</pre>
|
<pre>
B/E |-|m|
G/B |-|-|
D/G |i|-|



</pre>
|
<pre>
B/E |-|-|-|p|
G/B |-|-|-|-|
D/G |-|-|-|-|
A/D |-|-|-|-|
E/A |i|-|-|-|

</pre>
|
<pre>
E |i|-|-|
B |-|-|-|
G |-|-|-|
D |-|-|-|
A |-|-|-|
E |-|-|r|
</pre>
|}

<pre>
|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|
|o|-|-|-|-|-|-|-|-|-|-|-|o|-|x|-|-|-|-|
|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|o|-|-|
|-|-|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|
|-|-|o|-|x|-|-|-|-|-|-|-|-|-|o|-|-|-|-|
|-|-|-|-|-|-|-|o|-|x|-|-|-|-|-|-|-|-|-|
</pre>

=== Major 7th ===
{{Crumbs|blue|11
| Ref: Intervals#Minor 2nd|{{Mn2|m2}}
| Ref: Intervals#Major 2nd|{{M2|M2}}
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
| Ref: Intervals#Major 3rd|{{M3|M3}}
| Ref: Intervals#Perfect 4th|{{P4|P4}}
| Ref: Intervals#Tritone|{{tt|tt}}
| Ref: Intervals#Perfect 5th|{{P5|P5}}
| Ref: Intervals#Minor 6th|{{Mn6|m6}}
| Ref: Intervals#Major 6th|{{M6|M6}}
| Ref: Intervals#Minor 7th|{{Mn7|m7}}
| Ref: Intervals#Major 7th|{{M7|M7}}
}}

{|class="wikitable"
! Semitones !! Inversion !! Just Intonation<br>Ratio !! Equal<br>Temperament !! JI Cents !! ET Cents
|-
| 11 || [[#Minor 2nd|{{Mn2|m2}}]] || 15:8 = 1.875      || 1.88775
 || 1088.27 || 1,100
|}

{|
|-
|
<pre>
D/G |-|m|
A/D |-|-|
E/A |i|-|



</pre>
|
<pre>
B/E |-|-|r|
G/B |-|-|-|
D/G |i|-|-|



</pre>
|
<pre>
B/E |-|-|-|-|p|
G/B |-|-|-|-|-|
D/G |-|-|-|-|-|
A/D |-|-|-|-|-|
E/A |i|-|-|-|-|

</pre>
|
<pre>
E |i|-|
B |-|-|
G |-|-|
D |-|-|
A |-|-|
E |-|m|
</pre>
|}

<pre>
|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|
|-|o|-|-|-|-|-|-|-|-|-|-|-|o|x|-|-|-|-|
|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|-|o|-|
|-|-|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|
|-|-|-|o|x|-|-|-|-|-|-|-|-|-|-|o|-|-|-|
|-|-|-|-|-|-|-|-|o|x|-|-|-|-|-|-|-|-|-|
</pre>

=== 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|

 |{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|
 |{{Mn7|m7}}|{{M7|M7}}|{{U|U}}-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|
 |{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|{{U|U}}-|
 |{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|
 |{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|{{U|U}}-|{{Mn2|m2}}|{{M2|M2}}|
 |{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|{{Mn7|m7}}|{{M7|M7}}|'''''{{U|U}}'''''-|{{Mn2|m2}}|{{M2|M2}}|{{Mn3|m3}}|{{M3|M3}}|{{P4|P4}}|{{tt|tt}}|{{P5|P5}}|{{Mn6|m6}}|{{M6|M6}}|

{{top}}
{{Reference Crumbs|1}}

[[Category:Reference]]
[[Category:Intervals]]
[[Category:Harmony]]