What are musical intervals ?

An interval is the ratio in frequency between musical notes. These
intervals are sometimes called a second, third, fourth, fifth etc.
which refers to the position on the scale that the note is to be found.
In the scale of C major: C D E F G A B C, the note ‘E’ is the third
note of the scale and the interval from C to E is therefore called a
third. For the scale D major: D E F# G A B C# D, the third will be F#.
The term ‘interval’ can also be used to indicate that the notes are
sounded together, in which case there are consonant intervals and
dissonant intervals.

The ratio of frequency intervals for Just Intonation is demonstrated
below in the scale of C major, though the same ratios apply to all the
major keys:

C
(9:8)
D
(10:9)
E
(16:15)
F
(9:8)
G
(10:9)
A
(9:8)
B
(16:15)
C <- Octave

The interval between E & F and between B & C is a semitone, whilst the
other intervals are tones. The interval between any two notes above can
be found by multiplying the intervening ratios; thus if all the above
ratios are multiplied together the resultant is 2 because an octave is
twice the original frequency.

The notes of minor scales differ from their major counterparts; one
important difference being the flattened third. E flat is a minor third
above the note C.

The use of Just Temperament causes serious problems of intonation when
music modulates between keys. Equal Temperament is nearly always used
as a compromise to the problem of tuning