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Difference between revisions of "Ref: Intervals"

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{| class="wikitable"
 
{| 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>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
+
|  C  || C  || 0  || {{U|U}}  || Unison || 1:1 || 1
 
|-
 
|-
−
| C  || D{{f}} || 1  || {{Mn2|m2}} || Minor 2nd || 16:15
+
| C  || D{{f}} || 1  || {{Mn2|m2}} || Minor 2nd || 16:15 || 16
 
|-
 
|-
−
| C  || D  || 2  || {{M2|M2}} || (Major) 2nd || 9:8
+
| C  || D  || 2  || {{M2|M2}} || (Major) 2nd || 9:8 || 9
 
|-
 
|-
−
| C  || E{{f}} || 3  || {{Mn3|m3}} || Minor 3rd || 6:5
+
| C  || E{{f}} || 3  || {{Mn3|m3}} || Minor 3rd || 6:5 || 6
 
|-
 
|-
−
| C  || E  || 4  || {{M3|M3}} || Major 3rd || 5:4
+
| C  || E  || 4  || {{M3|M3}} || Major 3rd || 5:4 || 5
 
|-
 
|-
−
| C  || F  || 5  || {{P4|P4}} || (Perfect) 4th ||4:3
+
| 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 || 7:5
+
| 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
+
| C  || G  || 7  || {{P5|P5}} || (Perfect) 5th || 3:2 || 3
 
|-
 
|-
−
| C  || A{{f}} || 8  || {{Mn6|m6}} || Minor 6th || 8:5
+
| C  || A{{f}} || 8  || {{Mn6|m6}} || Minor 6th || 8:5 || 8
 
|-
 
|-
−
| C  || A  || 9  || {{M6|M6}} || Major 6th || 5:3
+
| C  || A  || 9  || {{M6|M6}} || Major 6th || 5:3 || 5
 
|-
 
|-
−
| C  || B{{f}} || 10 || {{Mn7|m7}}  || Minor 7th || 16:9
+
| C  || B{{f}} || 10 || {{Mn7|m7}}  || Minor 7th || 9:5 || 9
 
|-
 
|-
−
| C  || B  || 11 || {{M7|M7}} || Major 7th || 15:8
+
| C  || B  || 11 || {{M7|M7}} || Major 7th || 15:8 || 15
 
|-
 
|-
−
| C  || C  || 12 || {{U|U}}  || Unison or Octave || 2:1
+
| 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"
 
{|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
 
! 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
 
| {{Mn2|m2}} || 16:15 = 1.0666... || 1.05946 || -0.67563 || 111.73  || 100  || -11.73
 
|-                                       
 
|-                                       
−
| {{M2|M2}} || 9:8 = 1.125      || 1.12246 || -0.22618 || 203.91  || 200  || -3.91
+
| {{M2|M2}} || 9:8 = 1.125      || 1.12246 || -0.22560 || 203.91  || 200  || -3.91
 
|-                                               
 
|-                                               
−
| {{Mn3|m3}} || 6:5 = 1.2        || 1.18920 || -0.90028 || 315.64  || 300  || -15.64
+
| {{Mn3|m3}} || 6:5 = 1.2        || 1.18921 || -0.89941 || 315.64  || 300  || -15.64
 
|-                                               
 
|-                                               
−
| {{M3|M3}} || 5:4 = 1.25        || 1.25991 ||  0.79250 || 386.31  || 400  || +13.69
+
| {{M3|M3}} || 5:4 = 1.25        || 1.25992 ||  0.79368 || 386.31  || 400  || +13.69
 
|-                                               
 
|-                                               
−
| {{P4|P4}} || 4:3 = 1.333...    || 1.33482 ||  0.11153 || 498.04   || 500  || +1.96
+
| {{P4|P4}} || 4:3 = 1.333...    || 1.33484 ||  0.11299 || 498.05   || 500  || +1.96
 
|-                                               
 
|-                                               
−
| {{tt|tt}} || 7:5 = 1.4        || 1.41419 ||  1.01349 || 582.51  || 600  || +17.49
+
| {{tt|tt}} || 45:32 = 1.40625  || 1.41421 ||  0.56630 || 590.22 || 600  || +9.78
 
|-                                               
 
|-                                               
−
| {{P5|P5}} || 3:2 = 1.5        || 1.49828 || -0.11491 || 701.96  || 700  || -1.96
+
| {{P5|P5}} || 3:2 = 1.5        || 1.49831 || -0.11286 || 701.96  || 700  || -1.96
 
|-                                               
 
|-                                               
−
| {{Mn6|m6}} || 8:5 = 1.6        || 1.58736 || -0.78975 || 813.69  || 800  || -13.69
+
| {{Mn6|m6}} || 8:5 = 1.6        || 1.58740 || -0.78743 || 813.69  || 800  || -13.69
 
|-                                               
 
|-                                               
−
| {{M6|M6}} || 5:3 = 1.666...    || 1.68175 ||  0.90492 || 884.36  || 900  || +15.64
+
| {{M6|M6}} || 5:3 = 1.666...    || 1.68179 ||  0.90757 || 884.36  || 900  || +15.64
 
|-                                       
 
|-                                       
−
| {{Mn7|m7}} || 16:9 = 1.777...   || 1.78175 ||  0.22318 || 996.09  || 1,000 || +3.91
+
| {{Mn7|m7}} || 9:5 = 1.8   || 1.78180 ||  -1.01125 || 1017.60 || 1,000 || -17.60
 
|-                                       
 
|-                                       
−
| {{M7|M7}} || 15:8 = 1.875      || 1.88769 ||  0.67669 || 1088.27  || 1,100 || +11.73
+
| {{M7|M7}} || 15:8 = 1.875      || 1.88775 ||  0.67993 || 1088.27  || 1,100 || +11.73
 
|}
 
|}
  
Line 77: Line 112:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#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
 +
|}
 +
 
 
{|
 
{|
 
|-
 
|-
Line 140: Line 181:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 148: Line 189:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Minor 7th|{{Mn7|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
 +
|}
  
 
{|
 
{|
Line 204: Line 250:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 212: Line 258:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Major 6th|{{M6|M6}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 261: Line 312:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 269: Line 320:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Minor 6th|{{Mn6|m6}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 318: Line 374:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 326: Line 382:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Perfect 5th|{{P5|P5}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 387: Line 448:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 395: Line 456:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of itself
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 456: Line 522:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 464: Line 530:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Perfect 4th|{{{{P5|P5}}|P4}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 533: Line 604:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 541: Line 612:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Major 3rd|{{M3|M3}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 602: Line 678:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 610: Line 686:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Minor 3rd|{{Mn3|m3}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 676: Line 757:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 684: Line 765:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Major 2nd|{{M2|M2}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 741: Line 828:
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Minor 3rd|{{Mn3|m3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
 
| Ref: Intervals#Major 3rd|{{M3|M3}}
−
| Ref: Intervals#Perfect 4th|{{{{P5|P5}}|P4}}
+
| Ref: Intervals#Perfect 4th|{{P4|P4}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Tritone|{{tt|tt}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
 
| Ref: Intervals#Perfect 5th|{{P5|P5}}
Line 749: Line 836:
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
| Ref: Intervals#Major 7th|{{M7|M7}}
 
}}
 
}}
−
* Inversion of [[#Minor 2nd|{{Mn2|m2}}]]
+
 
 +
{|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
 +
|}
  
 
{|
 
{|
Line 808: Line 901:
 
  |m6|M6|m7|M7|'''''U'''''-|m2|M2|m3|M3|P4|tt|P5|m6|M6|m7|M7|U-|m2|M2|
 
  |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|
 +
 +
|{{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}}|
  
 
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Latest revision as of 23:56, 22 February 2016

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 		45:32 45
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 9:5 9
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 A♭ 8 m6 Minor 6th 8:5 8
C D 2 M2 (Major) 2nd 9:8 9
C B♭ 10 m7 Minor 7th 9:5 9
C B 11 M7 Major 7th 15:8 15
C D♭ 1 m2 Minor 2nd 16:15 16
C G♭ 6 A4, d5, tt Augmented 4th/
Diminished 5th/
Tritone 		45:32 45


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 -0.22560 203.91 200 -3.91
m3 6:5 = 1.2 1.18921 -0.89941 315.64 300 -15.64
M3 5:4 = 1.25 1.25992 0.79368 386.31 400 +13.69
P4 4:3 = 1.333... 1.33484 0.11299 498.05 500 +1.96
tt 45:32 = 1.40625 1.41421 0.56630 590.22 600 +9.78
P5 3:2 = 1.5 1.49831 -0.11286 701.96 700 -1.96
m6 8:5 = 1.6 1.58740 -0.78743 813.69 800 -13.69
M6 5:3 = 1.666... 1.68179 0.90757 884.36 900 +15.64
m7 9:5 = 1.8 1.78180 -1.01125 1017.60 1,000 -17.60
M7 15:8 = 1.875 1.88775 0.67993 1088.27 1,100 +11.73

Minor 2nd

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
1 M7 16:15 = 1.0666... 1.05946 111.73 100 
* |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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
2 m7 9:8 = 1.125 1.12246 203.91 200 
* |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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
3 M6 6:5 = 1.2 1.18920 315.64 300 
* |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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
4 m6 5:4 = 1.25 1.25991 386.31 400 
* |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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
5 P5 4:3 = 1.333... 1.33484 498.05 500 
* |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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
6 itself 45:32 = 1.40625 1.41421 590.22 600 
* |-|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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
7 P4 3:2 = 1.5 1.49831 701.96 700 
* |-|-|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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
8 M3 8:5 = 1.6 1.58740 813.69 800 
* |-|-|-|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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
9 m3 5:3 = 1.666... 1.68179 884.36 900 
* |-|-|-|-|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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
10 M2 9:5 = 1.80 1.78180 1017.60 1,000 
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

Semitones Inversion Just Intonation
Ratio 		Equal
Temperament 		JI Cents ET Cents
11 m2 15:8 = 1.875 1.88775 1088.27 1,100 
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|
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