A Dictionary of Music and Musicians/Scale

SCALE (from the Latin Scala, a staircase or ladder; Fr. Gamme; Ger. Tonleiter, i.e. sound-ladder; Ital. Scala). A term denoting the series of sounds used in musical compositions.

The number of musical sounds producible, all differing in pitch, is theoretically infinite, and is practically very large; so that in a single octave a sensitive ear may distinguish 50 to 100 different notes. But if we were to take a number of these at random, or if we were to slide by a continuous transition from one sound to another considerably distant from it, we should not make what we call music. In order to do this we must use only a certain small number of sounds, forming a determinate series, and differing from each other by well-defined steps or degrees. Such a series or succession of sounds is called a scale, from its analogy with the steps of a ladder.

It is unnecessary here to enter into the æsthetical reason for this;[1] it must suffice to state that all nations, at all times, who have made music, have agreed in adopting such a selection, although they have not always selected the same series of sounds. As a first step towards the selection all musical peoples appear to have appreciated the intimate natural relation between sounds which lie at that distance apart called an octave; and hence replicates of notes in octaves are found to form parts of all musical scales. The differences lie in the intermediate steps, or the various ways in which the main interval of the octave has been substituted.

For modern European music, in ascending from any note to its octave above, we employ, normally, a series of seven steps of unequal height, called the diatonic scale, with the power of interposing, accidentally, certain intermediate chromatic steps in addition. The diatonic scale is of Greek origin, having been introduced about the middle of the sixth century b.c. The main divisions of the octave were at the intervals called the fifth and the fourth, and the subdivisions were formed by means of two smaller divisions called a tone and a hemitone respectively. The tone was equal to the distance between the fourth and the fifth, and the hemitone was equal to a fourth minus two tones. The octave was made up of five tones and two hemitones, and the entire Greek diatonic scale of two octaves, as settled by Pythagoras, may be accurately represented in modern notation as follows:—

The Greek Diatonic Scale.

\new ChoirStaff <<
  \new Staff \relative c' { \time 16/1 \override Score.TimeSignature #'stencil = ##f s1 s s s s s s s s c d e f g a }
  \new Staff \relative a, { \clef bass a1_\markup \small \rotate #90 "tone" b_\markup \small \rotate #90 "semitone" c_\markup \small \rotate #90 "tone" d_\markup \small \rotate #90 "tone" e_\markup \small \rotate #90 "semitone" f_\markup \small \rotate #90 "tone" g_\markup \small \rotate #90 "tone" a_\markup \small \rotate #90 "tone" b_\markup \small \rotate #90 "semitone" s_\markup \small \rotate #90 "tone" s_\markup \small \rotate #90 "tone" s_\markup \small \rotate #90 "semitone" s_\markup \small \rotate #90 "tone" s_\markup \small \rotate #90 "tone" s } >>

Thus the essence of the diatonic scale was that it consisted of tones, in groups of two and three alternately, each group being separated by a hemitone from the adjoining one; and, combining consecutive intervals, any two tones with a hemitone would form a fourth, any three tones with a hemitone would form a fifth, and any complete cycle of five tones with two hemitones, would form a perfect octave.

Now it is obvious that in this series of notes, proved to be in use above two thousand years ago, we have essentially our diatonic scale; the series corresponding in fact with the natural or white keys of our modern organ or pianoforte. And as this series formed the basis of the melodies of the Greeks, so it forms the basis of the tunes of the present day.

Although, however, the general aspect of the diatonic series of musical sounds remains unaltered, it has been considerably affected in its mode of application by two modern elements—namely, Tonality and Harmony.

First, a glance at the Greek scale will show that there are seven different diatonic ways in which an octave may be divided; thus, from A to the A above will exhibit one way, from B to B another, from C to C a third, and so on—keeping to the white keys alone in each case; and all these various 'forms of the octave' as they were called, were understood and used in the Greek music, and formed different 'modes.' In modern times we adopt only two—one corresponding with C to C, which we call the Major mode, the other corresponding with A to A, which we call the Minor mode. And in each case we attach great importance to the notes forming the extremities of the octave series, either of which we call the Tonic or Keynote. We have, therefore, in modern music, the two following 'forms of the octave' in common use. And we may substitute for the Greek word 'hemitone' the modern term 'semitone,' which means the same thing.

Internals of the Diatonic Scale for the Major Mode.

\new Staff \relative c' { \time 32/1 \override Score.TimeSignature #'stencil = ##f
  c\breve_\markup \small \center-column { Key note. }_\markup \small \rotate #90 "tone"
  d1_\markup \small \rotate #90 "tone"
  e_\markup \small \rotate #90 "semitone"
  f_\markup \small \rotate #90 "tone"
  g_\markup \small \rotate #90 "tone"
  a_\markup \small \rotate #90 "tone"
  b_\markup \small \rotate #90 "semitone"
  c\breve_\markup \small \center-column { Key note. } }

Intervals of the Diatonic Scale for the Minor Mode.

\new Staff \relative a { \time 32/1 \override Score.TimeSignature #'stencil = ##f
  a\breve_\markup \small \center-column { Key note. }_\markup \small \rotate #90 "tone"
  b1_\markup \small \rotate #90 "semitone"
  c_\markup \small \rotate #90 "tone"
  d_\markup \small \rotate #90 "tone"
  e_\markup \small \rotate #90 "semitone"
  f_\markup \small \rotate #90 "tone"
  g_\markup \small \rotate #90 "tone"
  a\breve_\markup \small \center-column { Key note. } }

Although these differ materially from each other, it will be seen that the original Greek diatonic form of the series is in each perfectly preserved. It must be explained that the minor scale is given, under particular circumstances, certain accidental variations [see Ascending Scale], but these are of a chromatic nature; the normal minor diatonic form is as here shown. The choice of particular forms of the octave, and the more prominent character given to their limiting notes, constitute the important feature of modern music called Tonality.

Secondly, a certain influence has been exercised on the diatonic scale by modern Harmony. When it became the practice to sound several notes of the scale simultaneously, it was found that some of the intervals of the Greek series did not adapt themselves well to the combination. This was particularly the case with the interval of the major third, C to E: according to the Greek system this consisted of two tones, but the perfect harmonious relation required to be a little flatter. The correction was effected in a very simple manner by making a slight variation in the value of one of the tones, which necessitated also a slight alteration in the value of the semitone. Other small errors have been corrected in a similar way, so as to make the whole conform to the principle, that every note of the scale must have, as far as possible, concordant harmonious relations to other notes; and in determining these, the relations to the tonic or keynote are the more important.

The diatonic series, as thus corrected, is as follows:—

Major Diatonic Scale as corrected for Modern Harmony.

\new Staff \relative c' { \override Score.TimeSignature #'stencil = ##f \time 32/1
  c\breve_\markup \small \rotate #90 "major tone"
  d1_\markup \small \rotate #90 "minor tone"
  e_\markup \small \rotate #90 "semitone"
  f_\markup \small \rotate #90 "major tone"
  g_\markup \small \rotate #90 "minor tone"
  a_\markup \small \rotate #90 "major tone"
  b_\markup \small \rotate #90 "semitone"
  c\breve }

The several intervals, reckoned upwards from the lower keynote, are—

C to D, Major tone,
{{{1}}} E, Major third,
{{{1}}} F, Perfect Fourth,
{{{1}}} G, Perfect Fifth,
{{{1}}} A, Major sixth,
{{{1}}} B, Major seventh,
{{{1}}} C, Octave.

It has been stated, however, that for modern European music, we have the power of adding, to the seven sounds of the diatonic scale, certain other intermediate chromatic notes. Thus between C and D we may add two notes called C♯ and D♭. Between G and A we may add G♯ and A♭, and so on. In order to determine what the exact pitch of these notes should be, it is necessary to consider that they may be used for two quite distinct purposes, i.e. either to embellish melody without change of key, or^ to introduce new diatonic scales by modulation. In the former case the pitch of the chromatic notes is indeterminate, and depends on the taste of the performer; but for the second use it is obvious that the new note must be given its correct harmonic position according to the scale it belongs to: in fact it loses its chromatic character, and becomes strictly diatonic. For example, if an F♯ be introduced, determining the new diatonic scale of G, it must be a true major third above D, in the same way that in the scale of C, B is a major third above G. In this manner any other chromatic notes may be located, always adhering to the same general principle that they must bear concordant harmonic relations to other notes in the diatonic scale they form part of.

Proceeding in this way we should obtain a number of chromatic notes forming a considerable addition to the diatonic scale. For example, in order to provide for eleven keys, all in common use, we should get ten chromatic notes in addition to the seven diatonic ones, making seventeen in all, within the compass of a single octave. This multiplication of notes would produce such a troublesome complication in practical music, that in order to get rid of it there has been adopted an ingenious process of compromising, which simplifies enormously the construction of the scale, particularly in its chromatic parts. In the first place it is found that the distance between the diatonic notes E and F, and between B and C is nearly half that between C and D, or G and A; and secondly, it is known that the adjacent chromatic notes C♯ and D♭, G♯ and A♭, etc., are not very different from each other. Putting all these things together, it follows that if the octave be divided into twelve equal parts, a set of notes will be produced not much differing in pitch from the true ones, and with the property of being applicable to all keys alike. Hence has arisen the modern chromatic scale, according to what is called equal temperament, and as represented on the keyboard of the ordinary pianoforte. According to this, the musical scale consists of twelve semitones, each equal to a twelfth part of an octave; two of these are taken for the tone of the diatonic scale, being a very little less in value than the original major tone of the Greek divisions.

This duodecimal division of the octave was known to the Greeks, but its modern revival, which dates about the sixteenth century, has been one of the happiest and most ingenious simplifications ever known in the history of music, and has had the effect of advancing the art to an incalculable extent. Its defect is that certain harmonic combinations produced by its notes are slightly imperfect and lose the satisfactory effect produced by harmonies perfectly in tune. The nature and extent of this defect, and the means adopted to remedy it will be more properly explained under the article Temperament, which see.

[ W. P. ]

  1. More complete information on the subject generally may be found in Helmholtz's 'Tonempflndungsn,' or in 'The Philosophy of Music,' by W. Pole (London. 1879).