MAJOR SCALE

Many cultures recognize the octave as the main interval between two sounds. However, this interval is rather wide and leaves space for further subdivisions. Inside an octave we actually have room for other smaller intervals. In the history of music these intervals divide the octave in many different ways, into equal or unequal parts. There are scales that divide the octave into five parts (pentatonic scales), others that divide the octave into twenty-four, and others, more experimental, like Harry Partch’s, that divide the octave into more than forty parts. However, in various cultures there is a certain tendency to prefer scales that divide the octave into seven parts; these scales are called heptatonic and the major scale is one of them.

MAJOR SCALE

The major scale comes from the division of the octave into seven parts. The result is seven distinct sounds plus the arrival octave, eight notes in total. The arrival octave has the same name as the starting note. The starting note is called the fundamental.

The C major scale is composed of the notes: C, D, E, F, G, A, B, C and corresponds to the white keys on the piano keyboard.

TRANSPOSITION

However, it is not necessary to start from C to build a major scale, we can start from any other note. What is important for a scale to be defined as major is that each note within it respects the correct distance from the fundamental, and this distance can be conveniently measured in semitones.

THREE EXAMPLES IN THE SCALES OF C, G, AND D MAJOR

	C	G	D
+2 (SEMITONS)	D	A	E
+4	E	B	F#
+5	F	C	G
+7	G	D	A
+9	A	E	B
+11	B	F#	C#
+12	C	G	D

When we talk about the major scale, it’s important to remember that the seven parts into which the octave is divided are not equal. Between one note and the next we almost always have a distance of two semitones, but between the third and fourth note, and between the seventh and eighth, the step is smaller and measures only one semitone.

DISTANCE BETWEEN THE NOTES

Another practical method to derive the notes of the major scale is to calculate the distance in semitones between one note. Considering that not all the distances are equal, one must learn this pattern, where T stands for tone, that is the unit of measure that includes two semitones.

T=tono S=semitono

T - T - S - T - T - T - S

THE SCIENTIFIC PERSPECTIVE

The intervals of the major scale were born well before semitones, and what truly characterizes a given scale is the relationship between the frequency of the notes that compose it and the frequency of the fundamental note. The frequency of the octave is exactly double the frequency of the fundamental; the frequency of the fifth note of the major scale is 3/2 of the frequency of the fundamental, and so on:

Nome	Rapporto armonico	Frequenza (Do = 261,63 Hz)
C(ROOT)	1/1	261,63 Hz
D	9/8	294,33 Hz
E	5/4	327,04 Hz
F	4/3	348,84 Hz
G	3/2	392,45 Hz
A	5/3	436,05 Hz
B	15/8	490,56 Hz
C	2/1	523,26 Hz

Calculating the hertz of each note of the scale using these ratios is the most sensible method, however it is not at all practical if we are faced with instruments derived from the equal temperament scale, based on semitones. Using semitones to calculate intervals always leads to approximations, because the equal temperament scale does not precisely respect the ratios between frequencies. However, this is not to be understood as a problem, but as the trademark of Western-style music which, by slightly sacrificing these ratios, gains the freedom to transpose notes into various keys. Moreover, small deviations from the scientific ratios yield pleasant dissonances that are the trademark of a system with great global success. However, if one wants to experiment with the purity and rigor of science, certain software and unconventional instruments lend themselves to this purpose.