"Earth is round, Time is short"
.
... about the musical intervals
 
 

A musical interval is the distance between two notes. The distance is measured in semitones. A semitone is the smallest interval measured in western musical theory. 

The International Note Names are A A# B C C# D D# E F F# G G#
The same Latin Note names are LA LA# SI DO DO# RE RE# MI FA FA# SOL SOL#

Example : the interval between C and C# is a semitone, the interval between E and F is a semitone. 

A tone is an interval that is equal to two semitones. For example, the interval between C and D is a tone, and the interval between E and F# is a tone and so on. 

When about constructions of chords / melodies, tones and semitines have other names : the interval between any two consecutive letter names is called a 'second'. Then, from A to B is a second. The interval between two notes with an extra one in-between is called a 'third'. So from A to C is a third. This continues as follows: 

A to A (same note/frequency) : unison

A to B  :  the second

From A to B is a second.
There is one note in-between A and B, called either A# (also called Bb).

Therefore there are 2 semitones(= a tone) between the notes A and B.

Therefore it is said to be a 'major' second. 

Then, a major second is equal to a tone.

From A to Bb is a second. (because it is two consecutive letter names, even if one's a flat)
There are no notes between A and Bb.

Therefore there is 1 semitone between the notes A and Bb.

Therefore it is said to be a 'minor' second.

Then, a minor second is equal to a semitone.
 

A to C  : the third

From A to C# is a third.
There are 3 notes in-between A and C#. They are: A#, B and C.

Therefore there are 4 semitones between A and C#.

Therefore it is said to be an interval of a major third. 

From A to C is a third.
There are 2 notes in-between A and C#. They are A# and B.

Therefore there are 3 semitones between A and C.

Therefore it is said to be an interval of a minor third. 
 

A to D  : the fourth 
A to E   : the fifth

Moving on to the interval of a fourth and fifth, things change. There are no major or minor fourths. The qualities that can be applied to a fourth are 'perfect', 'diminished', and 'augmented'. A perfect fourth contains 5 semitones, as in C to F. An augmented fourth contains 6 semitones, as in C to F#. A diminished fourth contains 4 semitones, as in C# to F. From this, we can see that diminished intervals are smaller than perfect intervals, and perfect intervals are smaller than augmented intervals. 

The qualities of 'perfect', 'diminished' and 'augmented' are only applied to fourths, fifths. Octaves and unisons have only one quality, and that is perfect. 

A to F   : the sixth (like the second and third, it is either minor or major)
A to G   : the seventh (like the second and third, it is either minor or major)

A to A (from lower to higher A) : the octave (only perfect)

 

No need to memorize the number of semitones in each interval (...) the following chart summerizes it : 
 

(p = perfect, m = minor, M = major, dim = diminished, aug = augmented) :
Interval :
Number of semitones
Example, taking C as first note :
perfect unison / p1
0 semitones
C to C
minor second / m2
1 semitones
C to C#
major second / M2
2 semitones
C to D
minor third / m3
3 semitones
C to Eb
Major third / M3
4 semitones
C to E
diminished fourth / dim4 
4 semitones
C# to F
perfect fourth  / p4 
5 semitones
C to F
augmented fourth / aug4
6 semitones
C to F#
diminished fifth / dim5
6 semitones
C to Gb
perfect fifth / p5
7 semitones
C to G
augmented fifth / aug5
8 semitones
C to G#
minor sixth /  m6
8 semitones
C to Ab
major sixth / M6
9 semitones
C to A
minor seventh / m7
10 semitones
C to Bb
major seventh / M7
11 semitones
C to B
perfect octave / p8
12 semitones
C to C (the next higher one)

Please notice that some have the same number of semitones, but are named different intervals : Some intervals have two names.  

 

 

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