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Musical Notes & Intervals

In music, continuous sounds (i.e.: those with a particular Pitch or Frequency) are assigned letter names called "Notes". There are only seven Notes, the letters A, B, C, D, E, F, and G.

"Intervals" are the distance or relationship between those sounds (i.e.: the ratio of one Frequency to another). For example:

Interval Number Of Half-Steps
Unison (P1) 0
minor 2nd (m2); also called a Half-Step, Semitone 1
Major 2nd (M2); also called a Whole-Step, Wholetone 2
minor 3rd (m3) 3
Major 3rd (M3) 4
Perfect 4th (P4) 5
diminished 5th (dim5); also called a Tritone 6
Perfect 5th (P5) 7
minor 6th (m6) 8
Major 6th (M6) 9
minor 7th (m7) 10
Major 7th (M7) 11
Octave (P8) 12

• When two instruments are playing the same note at the same time, then they are playing in "Unison".

• An "Octave" spans eight letter names. [The prefix "oct-" means 8.] Since we we only use seven letters (i.e.: A through G), this is the first loop from one letter back to itself (e.g.: from C to C). In general, the names "2nd", "3rd", "4th", and so on, describe how many letter names an Interval spans (e.g.: a 3rd encompasses 3 letters, like from A to C).

• Extra symbols called "Accidentals" are added after the letter name to shift that sound either slightly higher, or slightly lower.

Lower
←
←
↔
→
→
Higher
♭♭
♭
♮
♯
x
Double Flat
Flat
Natural
Sharp
Double Sharp

♭ and ♯ are equivalent to lowering ("flattening") or raising ("sharpening") a Note by a Half-Step.
♭♭ and x are equivalent to either lowering or raising a Note by a Whole-Step.
♮ after the letter cancels out any Sharps or Flats.

Accidentals change the quality of Intervals. The "Major Intervals" (i.e.: M2, M3, M6, and M7) generally sound bright and cheery. They can be made into "minor Intervals" that sound dark and sad by flattening them a Half-Step.

"Perfect Intervals" (i.e.: P1, P4, P5, and P8) sound "pure", without any oscillation (or "beats") being created between the two Notes. If a minor or Perfect Interval is flattened by a Half-Step it is called a "diminished Interval". If a Major or Perfect Interval is sharpened by a Half-Step it is called an "Augmented Interval".

• Intervals can be "inverted", meaning that the order of the Notes that make it up can be reversed. When we do this, the size and quality of the Interval change. For example, a Major 3rd Interval (such as from C to E) becomes a minor 6th Interval (from E to C) when reversed. Therefore, M3 and m6 are "Inversions" of one another.

This is useful for quickly finding larger Intervals using smaller ones (e.g.: going up a 7th is the same as coming down a 2nd one Octave up).

• A "Tritone" is an Interval of three Wholetones or Whole-Steps. It divides the Octave in half and all other Intervals mirror around it. In other words, the Intervals across from each other in the following table are Inversions:

Unison (P1) Octave (P8)
minor 2nd (m2) Major 7th (M7)
Major 2nd (M2) minor 7th (m7)
minor 3rd (m3) Major 6th (M6)
Major 3rd (M3) minor 6th (m6)
Perfect 4th (P4) Perfect 5th (P5)

In summary: If we reverse the order of the Notes making up an Interval within the left column, then we will get the Interval in the right column, and vice versa.