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→Intervals Above vs. Intervals Below and Inversions
{{Beginner Lesson Crumbs|8}}
Playing on a single string is a complete pain. You are constantly changing positions, restricted to simple melodies, and cannot create any harmony. Let's add another string: the '''2nd string''' or '''B string'''. Below you can see both the notes of the 1st and 2nd strings together.
E|F|-|G|-|A|-|B|C|-|D|-|E|
B|C|-|D|-|E|F|-|G|-|A|-|B|
0 3 5 7 9 12
E--0--1--3--5--7--8--10-12--
B--0--1--3--5--6--8--10-12--
B C D E F G A B
If you look at the 2nd string frets that fall in are used for the C major scale, you'll notice this is identical to they're the same ones as the 1st string frets, except here we use the 6th fret instead of 7th. On the 1st string, that note is a B - the leading tone, which is a semitone below the tonic note. Here, that note is an F, the 4th, a whole tone below the 5th.
Remember that the 1st string is tuned a fourth 4th above the 2nd string. E is a fourth above B. As we go up the fretboard, we see each note on the 2nd string has its relative 4th directly above it on the 1st string. Starting with open we have:
{| class="wikitable"
|}
Now that we have two strings to play simultaneously, we can start to explore the concept of '''intervals ''' and how they drive all harmony.
== PreReqs ==
==== Numbering ====
The intervals are numbered 2-7 corresponding to the intervals formed within the common 7-note (heptatonic) scales. These scales use one of each of the numbers, counting up from with each next note in the root notescale. For example, the common major scale uses {{M2|M2}}, {{M3|M3}}, {{P4|P4}}, {{P5|P5}}, {{M6|M6}}, and {{M7|M7}}. A note played against itself with the same pitch (for instance on two different instruments) is called a {{U|Unison}} interval. The same notes played as different pitches are referred to as an {{OctU|Octave}}.
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.
==== Counting Up/Down and Octaves ====
Given any two notes forming an interval, the lower-pitched of the two notes in an interval is typically referred to as the '''root note'''. Whether you measure the interval from the higher note to the lower or lower to higher is immaterial - it's the same distance either way. However, this can get confusing if which note is actually lower is ambiguous. For example, if you have a C and a D, if and the C is the root note, you have a 2nd interval (C D). If the D is lower, you have a 7th interval (D E F G A B C). U 2 C D U 2 3 4 5 6 7 D E F G A B C
When an interval spans 8 or more notes, the intervals could be considered to get larger and larger. For example, the interval from C to the D over one octave higher is technically a 9th (C D E F G A B C D). In terms of harmony, however, these intervals are often transposed to be within an octave. Just as octaves are considered harmonically equivalent, intervals are considered harmonically equivalent to intervals one or more octaves larger. This keeps understanding harmony simpler and let's us focus on note names more than pitch - we have 12 notes to worry about instead of the 49 fretted notes of a 24-fret, 6-string guitar and 88 keys of a full size piano.
U 2 3 4 5 6 7 8 9 U 2
C D E F G A B C D ~= C D
==== Qualities in Relation to Common Scales ====
==== Playing Them All ====
Let's play all of the different intervals- fret the 2nd string using your index or middle finger, and make sure it's curled enough so the the 1st string is left open and can resonate at the same time as the 2nd string. Pluck both strings at the same time, sliding up one fret on the 2nd string each time:
E-0--0--0--0--0--0--0--0--0--0--0--0--0--
{{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|Oct}}
We start on E on both the 1st and 2nd strings. The 2nd string moves up one fret semitone 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.''
The line below the tab indicates the interval. Notice how nasty the {{Mn2|m2}} and {{tt|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. On the other hand, the {{P4|P4}} and {{P5|P5}} sound very harmonious. The other notes sound less and less so going from the major 3rd/6th, minor 3rd/6th, and major 2nd/7th.
==== Don't Get Ahead of Yourself ====
Notice in the table of all the intervals I've included columns for Just Intonation Ratio, Just Intonation Cents, and 12-Tone Equal Temperament Cents. If you don't know what the hell I'm talking about, don't feel bad. The J.I. Ratio merely indicates roughly how harmonic each interval sounds, with the smaller ratios more harmonic than the larger - this follow the experience of playing the tab above. [[Equal Temperament and Alternate Tunings#Cents|Cents]] are a strict measure of relative pitch that are covered way later on. Each semitone covers 100 cents - each octave spans 1,200 cents. This measure is often used for tuning strings, but applies well for understanding intervals and harmony. I merely want to pique your interest now - guitar is a fun instrument in allowing us to play with pitch and harmony in ways other instruments cannot. Mastering the instrument goes beyond simply knowing the strict intervals listed above but knowing the math and core concepts of harmony as well as how to achieve this in your playing. For now you should be mainly concerned with the sound and names of the intervals, not the pairs of notes involved in the tab. For example, you should know what a perfect 4th interval sounds like in comparison to a minor 3rd, but not worry about knowing that E-A is a perfect 4th and E-G is a minor 3rd. ''That will come with time. Don't stress!'' Eventually, you'll want to be able to know all the intervals in terms of every note. Like this:
{|class="wikitable"
Let's look at the intervals from two different perspectives inside the key of C Major:
{||
{| class="wikitable"
|+ Intervals with Root Note of C
|-
! 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 || B || 11 || {{M7|M7}} || Major 7th
|}
|
{| class="wikitable"
|+ Intervals with Root Note of A
|-
! 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 || G || 10 || {{Mn7|m7}} || Minor 7th
|}
|}Inside any particular major scale, every note has a different set of intervals for all the other notes in the same key. In C Major, C and A both have major 2nd, perfect 4th, perfect 5th intervals but have different 3rd, 6th, and 7ths. If we added a harmony line a 3rd above the melody, we'd have a major 3rd when the melody played C (C - E), but a minor third when the melody played A (A - C).
When we get to diatonic chords, we will explore the common diatonic intervals for each note of the major and minor scales. For now, let's hear what the different sets of intervals sound like when played in sequence:
B-5--7--9--10-12-14-16-17-
{{U|U}} {{M2|M2}} {{M3|M3}} {{P4|P4}} {{P5|P5}} {{M6|M6}} {{M7|M7}} {{U|Oct}}
E-0--0--0--0--0--0--0--0--
B-5--7--8--10-12-13-15-17-
|1st and 2nd Strings - Intervals#Intervals Above vs. Intervals Below and Inversions|Inversions}}
One last thing about intervals - intervals refer to distance between two pitches. However, we regard the octave of notes as harmonically equivalent. If you increase or reduce both the notes of an interval by one octave, it does not change distance at all. However, if you increase the lower note by one octave such that it now the higher note, or lower the higher note one octave, you still have the same notes but a different amount of distance and thus a different interval. This is called an '''inversion'''.
For example, G is 7 semitones above C, making it a Perfect 5th ''above'' C. However, it is only 5 semitones below C, making it a perfect 4th ''below'' C. Similarly, a G is a perfect 5th above C, but a C is only a perfect 4th above G.