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Ref: Intervals

1,913 bytes added, 03:56, 23 February 2016

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| 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 || 745:5 32 || 745

|-

| C || G || 7 || {{P5|P5}} || (Perfect) 5th || 3:2 || 3

| C || A || 9 || {{M6|M6}} || Major 6th || 5:3 || 5

|-

| C || B{{f}} || 10 || {{Mn7|m7}} || Minor 7th || 169:9 5 || 169

|-

| C || B || 11 || {{M7|M7}} || Major 7th || 15:8 || 15

{| 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 || E{{f}} || 3 || {{Mn3|m3}} || Minor 3rd || 6:5 || 6

|-

| C || G{{f}} || 6 || {{tt|A4, d5, tt}} || Augmented 4th/<br />Diminished 5th/<br />Tritone || 7:5 || 7

|-

| 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 || BG{{f}} || 10 6 || {{Mn7tt|m7A4, d5, tt}} || Minor 7th Augmented 4th/<br />Diminished 5th/<br />Tritone || 1645:9 32 || 1645

|}

{|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 || -0.22618 22560 || 203.91 || 200 || -3.91

|-

| {{Mn3|m3}} || 6:5 = 1.2 || 1.18920 18921 || -0.90028 89941 || 315.64 || 300 || -15.64

|-

| {{M3|M3}} || 5:4 = 1.25 || 1.25991 25992 || 0.79250 79368 || 386.31 || 400 || +13.69

|-

| {{P4|P4}} || 4:3 = 1.333... || 1.33482 33484 || 0.11153 11299 || 498.04 05 || 500 || +1.96

|-

| {{tt|tt}} || 745:5 32 = 1.4 40625 || 1.41419 41421 || 10.01349 56630 || 582590.51 22 || 600 || +179.4978

|-

| {{P5|P5}} || 3:2 = 1.5 || 1.49828 49831 || -0.11491 11286 || 701.96 || 700 || -1.96

|-

| {{Mn6|m6}} || 8:5 = 1.6 || 1.58736 58740 || -0.78975 78743 || 813.69 || 800 || -13.69

|-

| {{M6|M6}} || 5:3 = 1.666... || 1.68175 68179 || 0.90492 90757 || 884.36 || 900 || +15.64

|-

| {{Mn7|m7}} || 169:9 5 = 1.777... 8 || 1.78175 78180 || 0-1.22318 01125 || 9961017.09 60 || 1,000 || +3-17.9160

|-

| {{M7|M7}} || 15:8 = 1.875 || 1.88769 88775 || 0.67669 67993 || 1088.27 || 1,100 || +11.73

|}

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|} 

{|

|-

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

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

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

| Ref: Intervals#Major 7th|{{M7|M7}}

}}

* {|class="wikitable"! Semitones !! Inversion of !! 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|}

{|

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