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The ==== 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 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). 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. ==== Qualities in Relation to Common Scales ====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 {{tt|a4/d5}} rather than the tritone.
→Intervals
|1st and 2nd Strings - Intervals#Hot Cross Buns, Championship Editition|2nd Song}}
Two notes form an '''interval'''. This can describe either the ''distance'' between them, in terms of pitch/semitones (or even further in terms of [[Equal Temperament and Alternate Tunings#Cents|cents]] - a topic discussed later in advanced harmony and tunings), or the sound produced by playing them together (simultaneously or in sequence). '''Understanding intervals ''IS'' understanding harmony.''' Scales and chords are composed of a fixed set of intervals that give them their unique sound. Thus, the key of C Major sounds quite like G Major but quite different from C Minor.
You can determine the interval between any two notes by counting the number of notes between them in the common 7-note major or minor scales (or other modes of these scales). For example, C-D is a 2nd interval, while C-E is a 3rd, and C-F is the a 4th of C:
C D E F
1 2 3 4
The '''quality''' of the interval will be different depending on which scale you are using and which notes of the scale are being measured. 2nds, 3rds, 6ths, and 7ths will have '''minor''' or '''major''' qualities - minor is closer/smaller and major is further/larger. 4ths and 5ths on the other hand are usually the same distance in these most scales, called '''perfect'''; but occasionally, a 5th will be flatted by one semitone, making it a '''diminished''' 5th. Likewise, sometimes the 4th is sharped a semitone, called an '''augmented''' 4th.
Let's look at all the possible intervals inside the 12-tone chromatic scale (which correspond to each set of 12 frets for each string on the guitar).
'''Note: the colors used for the intervals are simply used to more easily visualize the size of the interval and its proximity to the root or its octave. They should not be misinterpreted to indicate harmony - color theory and music theory are very different, particularly as used here!'''
==== Numbering ====The intervals are numbered 2-7 corresponding to number of intervals formed within the common usage of 7-note (heptatonic) scales. A scale will typically These scales 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.
==== Qualities/Types ====
There are 5 different types of intervals:
* '''Perfect''' - The harmonious 4th and 5th intervals near halfway between root and octave
* '''Minor''' - The smaller of the pair of 2nd 3rd, 6th, or 7th intervals
* '''Diminished''' - One half-step smaller than the corresponding major minor or perfect interval
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.
==== Alternative Interval Names ====
Sometimes you may see interval names not listed above, like {{Mn7|A6}} (augmented 6th) or {{M6|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 {{Mn7|A6}} is really the same interval as a {{Mn7|m7}}, and a {{M6|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.
==== Playing Them All ====
Let's play all of the different intervals: