### Intervals

A simple definition for an interval would be the difference between two notes’ pitches. However, there are various important aspects of the interval going further than this definition. The two main aspects that are expressed by interval names are quality and quantity. The quality refers to the sound of the interval and the quantity refers to the size of the interval.

### Generic Intervals

Generic intervals are best described using a music staff, so we will accompany all descriptions in this subsection with diagrams. These intervals involve only the quantity aspect of the space between two notes. All you really need to do to find the generic interval is to count, starting with 1, from the lower note to the higher note.

Two notes that are placed on the same space or same line are a prime or a first apart. This does not necessarily mean that the two notes are the same; for example, F and F# are a first apart and yet they are different notes. This is another demonstration of why spelling is important in music theory.

When two notes are set apart on the staff by only one place, they are a second apart.

If two notes are placed on two consecutive lines or spaces, they are a third apart.

This pattern continues up to an eighth or an octave apart. Note that there are no such intervals of ninths, tenths or anything higher. Any intervals larger than an octave are merely called compound intervals.

### Specific Intervals

These intervals are harder to understand because they cannot be directly named by looking at the involved notes’ places on the music staff. Specific intervals are built on the generic intervals – in addition to the quantity of the interval, we now consider the quality of the interval.
There are several ways to describe the different kinds of specific intervals. We will begin with major intervals, which defined as intervals where the higher note is in the major scale of the lower note. For example, the interval from C to D is a major second because D is in the C major scale and is a second apart from C.

A major interval may also be found by counting. Note that a major interval is notated with a capital M followed by the quantity of the interval. For example, a major second interval is notated as M2.
 Major Second (M2) Two half steps (ex. D to E) Major Third (M3) Four half steps (ex. C to E) Major Sixth (M6) Nine half steps (ex. C to A) Major Seventh (M7) Eleven half steps (ex. F to E)

You may be wondering why there is no major first, fourth, fifth, or eighth. These intervals are not considered major intervals but perfect intervals. The reason for this is that not only is the higher note in the major scale of the lower note, but the lower note is also in the major scale of the higher note. For example, G is in the C major scale and C is in the G major scale. Their interval is a perfect fifth (when C is the lower note) because G is a fifth apart from C. When G is the lower note, their interval is a perfect fourth because C is a fourth apart from G.

Like major intervals, perfect intervals may also be found by counting. Perfect intervals are notated with a capital P followed by the quantity of the interval. For example, a perfect fifth is notated as P5.
 Perfect Unison (P1) Zero half steps (the two notes must be the same; ex. C to C) Perfect Fourth (P4) Five half steps (ex. A to D) Perfect Fifth (P5) Seven half steps (ex. F to C) Perfect Octave (P8) Twelve half steps (the two notes must have the same name but differ in pitch by an octave; ex. C to C an octave higher)

Another common interval is the minor interval, which is one half step smaller than the corresponding major interval. This may be done with a sharp on the lower note or a flat on the higher note. Of course, this is not the only method by which a minor interval may be found. The lower note of the interval is in the major scale of the higher note (not the minor scale). For example, the interval from B to C is a minor second because B is in the C major scale and the two notes are a second apart.

 Minor Second (m2) One half step (ex. E to F) Minor Third (m3) Three half steps (ex. C to Eb) Minor Sixth (m6) Eight half steps (ex. C to Ab) Minor Seventh (m7) Ten half steps (ex. F# to E)

Diminished intervals are one half step smaller than their corresponding perfect or minor intervals. This is usually done with an accidental. An example of a diminished interval would be that from F to Cb, which is a diminished fifth (d5).

 Diminished First (d1) Negative one half step (ex. C to B) Diminished Second (d2) Zero half steps (the same note; ex. D to D) Diminished Third (d3) Two half steps (ex. G# to Bb) Diminished Fourth (d4) Four half steps (ex. C# to F) Diminished Fifth (d5) Six half steps (ex. D to Ab) Diminished Sixth (d6) Seven half steps (ex. C to Abb) Diminished Seventh (d7) Nine half steps (ex. D to Cb) Diminished Eighth (d8) Eleven half steps (ex. C to Cb)

Augmented intervals are one half step larger than a perfect or a major interval (usually with an accidental). An example would be from G to E#, which is an augmented sixth (A6).

 Augmented First (A1) One half steps (ex. C to C#) Augmented Second (A2) Three half steps (ex. F to G#) Augmented Third (A3) Five half steps (ex. E to Gx) Augmented Fourth (A4) Six half steps (ex. D to G#) Augmented Fifth (A5) Eight half steps (ex. C to G#) Augmented Sixth (A6) Ten half steps (ex. G to E#) Augmented Seventh (A7) Twelve half steps (ex. E to Dx) Augmented Eighth (A8) Thirteen half steps (ex. F to F#)

You have perhaps noticed that there are many overlapping or enharmonic notes once you take diminished and augmented intervals into account. This is where spelling is especially important. Of course, the spelling does not matter when you are completing a listening exercise, as enharmonics sound the same, but it is important in written music theory.
http://www.vt2000.com/basswork/chords/interval.htm

### Inverting intervals:

All intervals can be inverted to another interval, for example a minor third can be inverted into a major sixth. To invert an interval, it is as simple as “moving” the top note to the bottom (moving the top one octave down or moving the bottom one octave up), or rather, just starting the interval on the other note.

A key idea to remember is that all intervals and their inversions add up to 9. For example, all 5th invert into 4ths (5+4=9) and all unisons invert into octaves (1+8=9). Furthermore, all minors invert into majors and vice versa and all augmented invert into diminished. If you look at the composition of a major or minor triad it makes sense that inverting it will turn it into the other. Major intervals mean the top note is in the major scale or the bottom, thus if you flip it over the new bottom note (the previous top) will now be in the scale of the top note. For example, A and C make a minor third because A is in the scale of C major. The inversion, C and A, makes a major sixth because the top note (now A) is in the scale of C major (the bottom note).

### Consonance and Dissonance

Consonance refers to the pleasing sound of two tones. They are stable whereas dissonant tones are tense and unpleasing. Dissonance is often used to lead to consonant tones in music, making a satisfying composition. There exist, however, modern musical works that contain only dissonant sounds according to the style of the composer.
 Consonant Intervals Dissonant Intervals Perfect Unison Perfect Fourth Perfect Fifth All Seconds and Sevenths Perfect Octave All Diminished Major and Minor Third All Augmented Major and Minor Sixth