Musical Scales, Intervals and Chords



Harmonic Tones

The following relations in frequency or in the length of a vibrating string are the harmonic tones, the consonant intervals in music:

1 : 1 = Unison
2 : 1 = Octave
3 : 2 = Fifth
4 : 3 = Fourth
5 : 4 = Major Third
3 : 5 = Major Six

To bring all these intervals together on one basis the number '12' is the most fitting one. This explains why todays music is built by 12 'semi-tones'. All the rations above can be expressed in a ratio on the basis of twelve:

12 : 12= Unison
12 : 6= Octave
12 : 8= Fifth
12 : 9= Fourth
12 : 9.6= Major Third
12 : 20= Major Six

This relationship was fist introduces by Pythagoras two and a half thousand years ago.

The most consonant interval is the octave with a frequency ratio of 2:1. The next most consonant intervals are the fifth and the fourth with a frequency ratio of 3:2 and 4:3.

A vibrating string or any other vibrating body has also overtones as integer multiples of its fundamental frequency.



Major and Minor Scales or Keys

Major Scale / Major Key:   full step / full step / half step / full step / full step / full step / half step

Minor Scale / Minor Key:   full step / half step / full step / full step / half step / full step / full step


The major and minor scales are built of the same notes. They are called parallel scales. The parallel minor scale starts always a minor 3rd below the first note of the major scale.

C major scaleparallel A minor scale
G major scaleparallel E minor scale
B major scaleparallel G# minor scale



Interval Table

C Major Interval half steps scale degrees
       
C unison 0 tonic
D major 2nd 2 supertonic
E major 3rd 4 mediant
F perfect 4th 5 subdominant
G perfect 5th 7 dominant
A major 6th 9 submediant
B major 7th 11 leading tone
C octave 12 octave

An interval is the distance between two notes. Interval values can be referred to as M (Major), m (minor), A (Augmented), or d (diminished).

The perfect intervals are: unison, perfect 4th, perfect 5th und octave,
the major intervals are: major 2nd, major 3rd, major 6th, major 7th,
the minor intervals are: minor 2nd, minor 3rd, minor 6th, minor 7th.

Half-Steps Notes Interval (English) Interval (German)
         
0 C  unison Prime
1 C#Db minor 2nd Kleine Sekunde
2 D  major 2nd (Grosse) Sekunde
3 D#Eb minor 3rd Kleine/Moll-Terz
4 E  major 3rd Grosse/Dur-Terz
5 F  perfect 4th (Reine) Quarte
6 F#Gb diminished 5th Verminderte Quinte
7 G  perfect 5th Quinte
8 G#Ab augmented 5th or minor 6th Übermässige Quinte, kleine Sexte
9 A  major 6th Sexte
10 A#Bb (Hb) minor 7th Kleine Septime
11 B (H)  major 7th Septime
12 c  octave Oktave
13 c#db flat 9th Kleine None
14 d  9th None
15 d#eb sharp 9th == minor 3rd (one octave) Kleine Dezime
16 e  major 10th == major 3rd (one octave) Dezime
17 f  11th Undezime
18 f#gb augmented 11th Überm. Undezime
19 g  perfect 12th == perfect 5th (one octave) Duodezime
20 g#ab flat 13th Verminderte Tredezime
21 a  13th Tredezime

The so called perfect intervals are: unison, perfect 4th, perfect 5th und octave,
the major intervals are: major 2nd, major 3rd, major 6th, major 7th,
the minor intervals are: minor 2nd, minor 3rd, minor 6th, minor 7th.

In the 19th century the British Alexander John Ellis introduced the Cent as a measurement for a tonal difference between two tones.
Every of the 12 half-step tones of one octave is separated by 100 logarithmic steps, the Cent. One full-step tone equals 200 Cent and one octave equals 1200 Cent.
The term TONE refers to an interval, the term NOTE refers to a certain pitch.



Chords

Chords are three or more pitches played simultaneously. The basic musical chords are the major chord and the minor chord.
Major chord: prime, major 3rd, minor 3rd, minor accord: prime minor 3rd, major 3rd.

two major chordstwo minor chords