Scales (_continued_)

84. The minor diatonic scale is used in several slightly different

forms, but the characteristic interval between the first and third tones

(which differentiates it from the major scale) remains the same in every

case. This interval between the first and third tones consists of four

half-steps in the major scale and of three half-steps in the minor scale

and this difference in size has given rise to the designation major

> for the scale having the larger third, and minor for the scale having

the smaller one.

85. The original (or primitive) form of the minor scale has its tones

arranged as follows.

1 whole 2 half 3 whole 4 half 5 half 6 whole 7 whole 8

step step step step step step step

As its name implies, this is the oldest of the three forms (being

derived from the old Greek Aeolian scale), but because of the absence of

a leading tone it is suitable for the simplest one-part music only,

and is therefore little used at present.

86. The harmonic minor scale is like the primitive form except that it

substitutes a tone one half-step higher for the seventh tone of the

older (i.e., the primitive) form. This change was made because the

development of writing music in several parts (particularly harmonic

part-writing) made necessary a leading tone, i.e., a tone with a

strong tendency to move on up to the key-tone as a closing point. In

order to secure a tone with such a strongly upward tendency the

interval between seven and eight had to be reduced in size to a

half-step. It should be noted that this change in the seventh tone of

the scale caused an interval of a step-and-a-half between the sixth and

seventh tones of the scale.

1 whole 2 half 3 whole 4 whole 5 half 6 step and 7 half 8

step step step step step a half step

87. The melodic minor scale substitutes a tone one half-step higher

than six as well as one a half-step higher than seven, but this change

is made in the ascending scale only, the descending scale being like the

primitive form. The higher sixth (commonly referred to as the raised

sixth) was used to get rid of the unmelodic interval of a

step-and-a-half[15] (augmented second), while the return to the

primitive form in descending is made because the ascending form is too

much like the tonic major scale.

[Footnote 15: The step-and-a-half (augmented second) is unmelodic

because it is the same size as a minor third and the mind finds it

difficult to take in as a second (notes representing it being on

adjacent staff-degrees) an interval of the same size as a third.]

1 whole 2 half 3 whole 4 whole 5 whole 6 whole 7 half 8

step step step step step step step

7 whole 6 half 5 whole 4 whole 3 half 2 whole 1

step step step step step step

This form is used only to a very limited extent, and then principally in

vocal music, the harmonic form being in almost universal use in spite of

the augmented second.

88. The minor scale in its various positions (up to five sharps and five

flats) and in all three forms follows: a composition based on any one of

these forms (or upon a mixture of them, which often occurs) is said to

be in the minor mode. It will be noted that the first four tones are

alike in all three forms; i.e., the lower tetrachord in the minor

scale is invariable no matter, what may happen to the upper tetrachord.

The sign + marks the step-and-a-half.

Note.--The student is advised to recite the harmonic form

of the minor scale as was suggested in the case of the major

scale, noting that the raised seventh does not affect the

key-signature. E.g.,--E--F[sharp]--G--A--B--C--D[sharp]--E;

signature, one sharp, F.

89. A minor scale having the same signature as a major scale is said to

be its relative minor. E.g.,--e is the relative minor of G, c of

E[flat], d of F, etc., the small letter being used to refer to the minor

key or scale, while the capital letter indicates the major key or scale

unless accompanied by the word minor. Relative keys are therefore

defined as those having the same signature. G and e are relative keys,

as are also A and f[sharp], etc.

90. A minor scale beginning with the same tone as a major scale is

referred to as its tonic minor. Thus, e.g., c with three flats in

its signature is the tonic minor of C with all degrees in natural

condition; e with one sharp is the tonic minor of E with four sharps,

etc. Tonic keys are therefore those having the same key-tone.

91. The eight tones of the diatonic scale (both major and minor) are

often referred to by specific names, as follows:

1. Tonic--the tone. (This refers to the fact that the tonic

is the principal tone, or generating tone of the key, i.e.,

it is the tone.)

2. Super-tonic--above the tone.

3. Mediant--midway between tonic and dominant.

4. Sub-dominant--the under dominant. (This name does not

refer to the position of the tone under the dominant but to

the fact that the fifth below the tonic is also a dominant

tone--the under dominant--just as the fifth above is the upper


5. Dominant--the governing tone. (From the Latin word

dominus meaning master.)

6. Super-dominant--above the dominant. Or

Sub-mediant--midway between tonic and sub-dominant.

7. Leading tone--the tone which demands resolution to the

tonic (one-half step above it).

8. Octave--the eighth tone.

92. The syllables commonly applied to the various major and minor scales

in teaching sight-singing are as follows:[16]

[Footnote 16: These syllables are said to have been derived originally

from the initial syllables of the Hymn to Saint John, the music of

which was a typical Gregorian chant. The application of these syllables

to the scale tones will be made clear by reference to this hymn as given

below. It will be observed that this hymn provided syllables only for

the six tones of the hexachord then recognized; when the octave scale

was adopted (early in the sixteenth century) the initial letters of the

last line (s and i) were combined into a syllable for the seventh tone.

[Illustration: Ut que-ant lax-is Re-so-na-re fi-bris Mi-ra

ges-to-rum Fa-mu-li tu-o-rum Sol-ve pol-lu-ti La-bi-i re-a-tum

Sanc-te Jo-han-nes.]]

Major--DO, RE, MI, FA, SOL, LA, TI, DO.

Minor[17]--original--LA, TI, DO, RE, MI, FA, SOL, LA.

harmonic--LA, TI, DO, RE, MI, FA, SI, LA.

melodic--LA, TI, DO, RE, MI, FI, SI, LA,


[Footnote 17: A considerable number of teachers (particularly those who

did not learn to sing by syllable in childhood) object to calling the

tonic of the minor scale la, insisting that both major and minor tonic

should be called do. According to this plan the syllables used in

singing the harmonic minor scale would be: DO, RE, ME, FA, SOL, LE, TI,


There is no particular basis for this theory, for although all scales

must of course begin with the key-tone or tonic, this tonic may be

referred to by any syllable which will serve as a basis for an

association process enabling one to feel the force of the tone as a

closing point--a home tone. Thus in the Dorian mode the tonic would be

RE, in the Phrygian, MI, etc.]

It is interesting to study the changes in both spelling and

pronunciation that have occurred (and are still occurring) in

these syllables. The first one (ut) was changed to DO as

early as the sixteenth century because of the difficulty of

producing a good singing tone on ut. For the same reason and

also in order to avoid having two diatonic syllables with the

same initial letter, the tonic-sol-fa system (invented in

England about 1812 and systematized about 1850) changed SI to

TI and this change has been almost universally adopted by

teachers of sight-singing in this country. The more elaborate

tonic-sol-fa spelling of the diatonic syllables (DOH, LAH,

etc.), has not, however, been favorably received in this

country and the tendency seems to be toward still further

simplification rather than toward elaboration. It is probable

that further changes in both spelling and pronunciation will

be made in the near future, one such change that seems

especially desirable being some other syllable than RE for the

second tone of the major scale, so that the present syllable

may be reserved for flat-two, thus providing a uniform

vowel-sound for all intermediate tones of the descending

chromatic scale, as is already the case in the ascending form.

93. The chromatic scale[18] is one which proceeds always by

half-steps. Its intervals are therefore always equal no matter with what

tone it begins. Since, however, we have (from the standpoint of the

piano keyboard) five pairs of tones[19] which are enharmonically the

same, it may readily be seen that the chromatic scale might be notated

in all sorts of fashions, and this is in fact the real status of the

matter, there being no one method uniformly agreed upon by composers.

[Footnote 18: The student should differentiate between the so-called

tonality scales like the major and minor, the tones of which are

actually used as a basis for key-feeling with the familiar experience

of coming home to the tonic after a melodic or harmonic excursion, and

on the other hand the purely artificial and mechanical construction of

the chromatic scale.]

[Footnote 19: Many other enharmonic notations are possible, altho the

five pairs of tones above referred to are the most common. Thus

E[sharp] and F are enharmonically the same, as are also C[flat] and B,

C[sharp] and B[double-sharp], etc.]

Parry (Grove's Dictionary, article chromatic) recommends

writing the scale with such accidentals as can occur in

chromatic chords without changing the key in which the passage

occurs. Thus, taking C as a type, the first accidental will

be D[flat], as the upper note of the minor ninth on the tonic;

the next will be E[flat], the minor third of the key; the next

F[sharp], the major third of the super-tonic--all of which can

occur without causing modulation--and the remaining two will

be A[flat] and B[flat], the minor sixth and seventh of the

key. According to this plan the chromatic scale beginning

with C would be spelled--C, D[flat], D, E[flat], E, F,

F[sharp], G, A[flat], A, B[flat], B, C--the form being the

same both ascending and descending. This is of course written

exclusively from a harmonic standpoint and the advantage of

such a form is its definiteness.

94. For sight-singing purposes the chromatic scale[20] is usually

written by representing the intermediate tones in ascending by sharps,

(in some cases naturals and double-sharps), and the intermediate tones

in descending by flats (sometimes naturals and double-flats). The

chromatic scale in nine different positions, written from this

standpoint, follows, and the syllables most commonly applied in

sight-singing have also been added. In the first two scales the student

of harmony is asked to note that because of the very common practice of

modulating to the dominant and sub-dominant keys, the intermediate tones

[sharp]4 and [flat]7 are quite universally used in both ascending and

descending melody passages. In other words the scales that follow would

more nearly represent actual usage if in each case [sharp]4 (FI) were

substituted for [flat]5 (SE) in the descending scale; and if [flat]7

(TE) were substituted for [sharp]6 (LI) in the ascending form.

[Footnote 20: The word chromatic means literally colored and was

first applied to the intermediate tones because by using them the singer

could get smoother and more diversely-shaded progressions, i.e., could

get more color than by using only the diatonic tones. Composers were

not long discovering the peculiar value of these additional tones and

soon found that these same tones were exceedingly valuable also in

modulating, hence the two uses of intermediate tones at the present

time--first, to embellish a melody; second, to modulate to another key.]

Note.--In writing chromatic scales from this sight-singing

standpoint the student is urged to adopt a three-step process;

first, writing the major diatonic scale both ascending and

descending; second, marking the half-steps; third, inserting

accidental notes calling for the intermediate tones. In the

above chromatic scales these intermediate tones have been

represented by black note-heads so as to differentiate them

from the notes representing diatonic scale tones.

95. The whole-step scale (the third type mentioned in Sec. 79) is, as

its name implies, a scale in which the intervals between the tones

consist in every instance of whole-steps. This reduces the number of

tones in the scale to seven. Beginning with C the scale reads: C, D, E,

F[sharp] or G[flat], A[flat], B[flat], C. This scale has been used

somewhat extensively by the ultramodern French school of composition

represented by Debussy, Ravel, and others, but is not making any

progress toward universal adoption. The remarks of a recent English

writer[21] on this subject may be interesting to the student who is

puzzled by the apparent present-day tendencies of French music. He says:

The student of some interesting modern developments will also

speedily discover that the adoption of the so-called

whole-tone scale as a basis of music is, except upon a keyed

instrument tuned to the compromise of equal temperament,

unnatural and impossible. No player upon a stringed instrument

can play the scale of whole-tones and arrive at an octave

which is in tune with the starting note, unless he

deliberately changes one of the notes on the road and alters

it while playing it. The obvious result of the application of

the whole-tone scale to an orchestra or a string quartet would

be to force them to adopt the equal temperament of the

pianoforte, and play every interval except the octave out of

tune. When this modification had taken hold all music in the

pure scale would be distorted and destroyed, unless string

players were to face the practically impossible drudgery of

studying both the equal temperament and the pure scale from

the start, and were able to tackle either form at a moment's

notice. A thorough knowledge of the natural genesis of the

scale of western nations will be the best antidote to fads

founded upon ignorance of it. It is a curious commentary upon

this question that Wagner, in the opening of the third act of

Tristan (bars 6 to 10), experimented with the whole-tone

scale and drew his pen through it, as was to be expected from

a composer whose every work proves the writer to have had the

pure scale inbred in him.

[Footnote 21: Stanford--Musical Composition (1911) p. 17.]

There may be some difference of opinion among acousticians as to whether

Mr. Stanford is correct in his scientific assumptions regarding the

difference between tempered and pure scales,[22] but even so, there

is a far more potent reason why the whole-step scale will probably never

become popular as the major and minor scales now are, viz., the fact

that it offers no possibility of inculcating tonality feeling, which

has always been the basis of even the simplest primitive music. Tonality

scales give rise to a feeling of alternate periods of contraction and

relaxation--an active tone (or chord) followed by a passive one, but no

such effect is possible in the whole-step scale, and it seems suitable

therefore only for that class of music whose outlines are purposely

intended to be vague and indefinite--the impressionistic style of music


[Footnote 22: Recent tests in Germany seem to prove conclusively that

the tempered scale is the scale ordinarily employed by both vocalists

and players on stringed instruments, and that the ideal of and agitation

for a pure (i.e., untempered) scale in vocal and in string music

is somewhat of a myth.]