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m
u {{U|U}} {{M2 |M2}} {{M3 |M3}} {{P4|P4 }} {{P5|P5 }} {{M6 |M6}} {{M7|M7 o}} {{U|Oct}}
u {{U|U}} {{M2 |M2}} {{Mn3|m3 }} {{P4 |P4}} {{P5|P5 }} {{Mn6|m6 }} {{Mn7|m7 o}} {{U|Oct}}
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! 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
|-
| C || C || 0 || {{U |U}} || Unison || 1:1
|-
| C || D{{f}} || 1 || {{Mn2| m2 }} || Minor 2nd || 16:15
|-
| C || D || 2 || {{M2 |M2}} || (Major) 2nd || 9:8
|-
| C || E{{f}} || 3 || {{Mn3| m3 }} || Minor 3rd || 6:5
|-
| C || E || 4 || {{M3 |M3}} || Major 3rd || 5:4
|-
| C || F || 5 || {{P4 |P4}} || (Perfect) 4th ||4:3
|-
| C || G{{f}} || 6 || {{tt| A4, d5, tt }} || Augmented 4th/<br />Diminished 5th/<br />Tritone || 7:5
|-
| C || G || 7 || {{P5 |P5}} || (Perfect) 5th ||3:2
|-
| C || A{{f}} || 8 || {{Mn6| m6 }} || Minor 6th || 8:5
|-
| C || A || 9 || {{M6 |M6}} || Major 6th || 5:3
|-
| C || B{{f}} || 10 || {{Mn7| m7 }} || Minor 7th || 16:9
|-
| C || B || 11 || {{M7 |M7}} || Major 7th || 15:8
|-
| C || C || 12 || {{U |U, Oct}} || Unison or Octave || 2:1
|}
The intervals are numbered 2-7 corresponding to the common usage of Heptatonic (7-note) scales. A scale will typically use one of each of the numbers. For example, the common major scale uses {{M2|M2}}, {{M3|M3}}, {{P4|P4}}, {{P5|P5}}, {{M6|M6}}, and {{M7|M7}}.
Where the names have ()'s around a word in the description, that word is optional, and often omitted. Major 2nd, perfect 4th, and perfect 5th are all implied by 2nd, 4th, and 5th, as they are present in the common major as well as minor scales.
The lower-pitched of the two notes is referred to as the '''root note'''. You'll notice the 4th and 5th intervals have the most harmonious ratios and reside near halfway between the root note and its octave. The tritone in the direct center is actually less harmonious than the neighboring 4th/5th. In the common major/minor scales, it appears in place of a 4th or 5th, so it is often regarded as a4/d5 rather than the tritone. The other numbered intervals come in pairs of major and minor, with the minor nearer the root and major further. Think minor = smaller and major = larger in terms of the distance between the component pitches.
Sometimes you may see interval names not listed above, like A6 (augmented 6th) or d7 (diminished 7th). Augmented simply means raised a half-step above a major or perfect interval and diminished means lowered a half-step below a minor or perfect interval. So an A6 is really the same interval as a {{Mn7|m7}}, and a d7 is the same as a {{M6|M6}}. The reason the alternate names are occasionally used is that the interval names are sometimes required to fulfill the practice of naming the intervals in a scale while using 2-7 once each, for more exotic scales. Also, interval names imply harmonic function - the alternate names suggest a different function from how such intervals usually act.
Let's play all of the different intervals:
E-0--0--0--0--0--0--0--0--0--0--0--0--0--
B-5--6--7--8--9--10-11-12-13-14-15-16-17-
u {{Mn2|m2 }} {{M2 |M2}} {{Mn3|m3 }} {{M3|M3 }} {{P4|P4 }} {{tt |tt}} {{P5 |P5}} {{Mn6|m6 }} {{M6 |M6}} {{Mn7|m7 }} {{M7|M7 }} o
We start on E on both the 1st and 2nd strings. The 2nd string moves up one fret each time: F, F{{s}}, G, G{{s}}, A, etc. This allows us to hear all the intervals named in the tables above; however, we are hearing them all against the root note of E, not C.
That we are using E instead of C is immaterial. ''Remember: Intervals have their own unique sound. A major 3rd between E and G{{s}} will sound the same compared to a major 3rd between C and E. The pitches themselves are different, but the ratio between them is the same; the relative distance and harmonic interaction between each pair of notes is the same.''
For now you should be mainly concerned with the sound and names of the intervals, not the pairs of notes involved in the example. The line below the tab indicates the interval. Notice how nasty the {{Mn2|m2 }} and tt intervals are. the {{M7 |M7}} can also be a bit nasty, but because there's more space between the notes, it sounds less harsh.
Eventually, you'll want to be able to know all the intervals in terms of every note. Like this:
! Root Names/<br>Intervals !! A{{b}} !! A !! B{{b}} !! B !! C !! D{{b}} !!D !! E{{b}} !! E !! F !! G{{b}} !! G
|-
! {{Mn2|m2}}
| A || B{{b}} || B || C || D{{b}} || D || E{{b}} || E || F || G{{b}} || G || A{{b}}
|-
! {{M2|M2}}
| B{{b}} || B || C || D{{b}} || D || E{{b}} || E || F || G{{b}} || G || A{{b}} || A
|-
! {{Mn3|m3}}
| B || C || D{{b}} || D || E{{b}} || E || F || G{{b}} ||G || A{{b}} || A || B{{b}}
|-
! {{M3|M3}}
| C || D{{b}} || D || E{{b}} || E || F || G{{b}} || G || A{{b}} || A || B{{b}} || B
|-
! {{P4|P4}}
| D{{b}} || D || E{{b}} || E || F || G{{b}} || G || A{{b}} || A || B{{b}} || B || C
|-
! {{tt|tt}}
| D || E{{b}} || E || F || G{{b}} || G || A{{b}} || A || B{{b}} || B || C || D{{b}}
|-
! {{P5|P5}}
| E{{b}} || E || F || G{{b}} || G || A{{b}} || A || B{{b}} || B || C || D{{b}} || D
|-
! {{Mn6|m6}}
| E || F || G{{b}} || G || A{{b}} || A || B{{b}} || B || C || D{{b}} || D || E{{b}}
|-
! {{M6|M6}}
| F || G{{b}} || G || A{{b}} || A || B{{b}} || B || C || D{{b}} || D || E{{b}} || E
|-
! {{Mn7|m7}}
| G{{b}} || G || A{{b}} || A || B{{b}} || B || C || D{{b}} || D || E{{b}} || E || F
|-
! {{M7|M7}}
| G || A{{b}} || A || B{{b}} || B || C || D{{b}} || D || E{{b}} || E || F || G{{b}}
|}
As mentioned above, common scales only contain 1 interval for each of the numbers 2-7. This applies not only to the root note of the scale, but to each additional '''diatonic''' (member) note in the scale. Each scale has its own set of diatonic intervals, just as it has diatonic notes.
As mentioned earlier, intervals can describe the combined sound of two notes as well as the distance between two notes. In a scale, the root note forms a basis point from which we can describe other notes by their distance from it. For instance, I could say to play the note a {{M3 |M3}} above root then the note a {{P5|P5 }} above the root. Ironically, we can use intervals to determine other intervals. For instance, the interval between the {{M3|M3 }} and {{P5|P5 }} above the root note is a {{Mn3|m3}}.
--0----4----7--
|-{{M3|M3}}-| root +4 semitones is a {{M3|M3}} |----{{P5|P5}}---| root +7 semitones is a {{P5|P5}} |-{{Mn3|m3}}-| the {{M3|M3 }} to the {{P5 |P5}} is 3 semitones - a {{Mn3|m3}}
Let's look at the intervals from two different perspectives inside the key of C Major:
! Root<br>Note !! Other<br>Note !! Semitones<br>from<br>Root to<br>Other !! Interval<br>Short<br>Name !! Interval<br>Full<br>Name
|-
| C || D || 2 || {{M2 |M2}} || Major 2nd
|-
| C || E || 4 || {{M3 |M3}} || Major 3rd
|-
| C || F || 5 || {{P4 |P4}} || (Perfect) 4th
|-
| C || G || 7 || {{P5 |P5}} || (Perfect) 5th
|-
| C || A || 9 || {{M6 |M6}} || Major 6th
|-
| C || B || 11 || {{M7 |M7}} || Major 7th
|}
{| 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
|-
| A || B || 2 || {{M2|M2}}|| Major 2nd
|-
| A || C || 3 || {{Mn3| m3 }} || Minor 3rd
|-
| A || D || 5 || {{P4 |P4}} || (Perfect) 4th
|-
| A || E || 7 || {{P5 |P5}} || (Perfect) 5th
|-
| A || F || 8 || {{Mn6| m6 }} || Minor 6th
|-
| A || G || 10 || {{Mn7| m7 }} || Minor 7th
|}
E-0--0--0--0--0--0--0--0--
B-5--7--9--10-12-14-16-17-
E-0--0--0--0--0--0--0--0--
B-5--7--8--10-12-13-15-17-
Notice the difference in the 3rds, 6ths, and 7ths.
P P P A4 P P P P
Notice the major scale only contains one tritone or augmented 4th. We refer to it as {{tt|A4 }} instead of {{tt|tt }} here, because we are using 4ths - in that context it is the {{tt|A4}}. I find it's easiest to flatten the index finger and shift positions for each interval, but add the middle or ring finger for the {{tt|A4}}.
Let's try the same thing but using 5ths:
B-1----8----13
| +7 | +5 |
|-{{P5|P5}}-|-{{P4|P4}}-|
G C G
G-0----5----12
| +5 | +7 |
|-{{P4|P4}}-|-{{P5|P5}}-|
{|class = "wikitable"
!Interval
| {{Mn2| m2 }} ||{{M2| M2 }} ||{{Mn3| m3 }} ||{{M3| M3 }} ||{{P4| P4 }} || tt || {{P5| P5 }} ||{{Mn6| m6 }} ||{{M6| M6 }} ||{{Mn7| m7 }} ||{{M7| M7}}
|-
! Semitones
|-
! Inversion
| {{M7 |M7}} || {{Mn7| m7 }} || {{M6 |M6}} || {{Mn6| m6 }} ||{{P5| P5 }} ||{{tt| tt }} || {{P4 |P4}} | | {{M3 |M3}} || {{Mn3| m3 }} ||{{M2| M2 }} ||{{Mn2| m2}}
|-
! Semitones
A-2--2-----3--3--
E-0--------0-----
{{P5 |P5}} {{P4 |P4}} {{Mn6|m6 }} {{M3|M3}}
In the tab above, the low E string and higher D string are always playing an E, and the A string plays B, then C. This demonstrates an E-B {{P5 |P5}} interval and its inversion, a B-E {{P4 |P4}} interval, then an E-C {{Mn6|m6 }} interval and its inversion, a C-E {{M3|M3 }} interval. Inverting the perfect intervals only create a slight difference in perception, while inverting 3rds or 6ths has a larger impact. The composer cannot simply swap them willy-nilly - they clearly have different qualities in terms of overall harmony although they do sound related.
{{top}}
* Know what an interval is - the "distance" between two notes.
* Memorize all 11 intervals, by name and the number of half-steps that define them.
* Know that the intervals against the root in a major scale are {{M2|M2}}, {{M3|M3}}, {{P4|P4}}, {{P5|P5}}, {{M6|M6}}, {{M7|M7 }} - all major and perfect.
* Play all the interval exercises above without a metronome - go slow and try to hear the sound of the intervals.
* Know how to finger the basic 3rd, 4th, and 5th intervals and play them ascending and descending the C Major scale.