Chapter XVII: Rhythm, Melody, Harmony and Intervals

178. The _four elements_ commonly attributed to music (in the order of their development) are: Rhythm, Melody, Harmony, and Timbre (or tone-color).

179. _Rhythm_ is the regular recurrence of accent. In music it is more specifically the regular recurrence of groups of accented and non-accented beats (or pulses)--according to some specified measure-system. Since rhythm implies continuity, there must usually be at least two such measure groups in order to make musical rhythm possible. (See p. 44, Sec. 97.)

180. A _melody_ is a succession of single tones of various pitches so arranged that the effect of the whole will be unified, coherent, and pleasing to the ear.

The soprano part of hymn-tunes and other simple harmonized
compositions is often referred to as "the melody."

181. _Harmony_ is the science of chord construction and combination.

The term _harmony_ refers to tones sounding simultaneously,
_i.e._, to _chords_, as differentiated from tones sounding
consecutively, as in melody. The word _harmony_ may therefore
be applied to any group of tones of different pitches sounded
as a chord, although specifically we usually refer to a
_succession_ of such chords when we speak of "harmony." It is
possible to use the same combination of tones in either melody
or harmony; in fact these two elements as applied to modern
music have developed together and the style of present-day
melody is directly based upon the development that has
recently taken place in harmonic construction.

_Harmony_ (as contrasted with _counterpoint_) first began to
be an important factor in music about 1600 A.D., _i.e._, at
the time when opera and oratorio came into existence, when
form was established, and when our modern major and minor
scales were adopted. Before this practically all music was
composed on a contrapuntal basis.

182. _Timbre_ is that peculiar quality of sound which enables one to distinguish a tone produced by one instrument (or voice) from a tone produced by an equal number of vibrations on another instrument.

The word _timbre_ is synonymous with the terms _quality of
tone_, and _tone quality_ (Ger.--Klang-farbe), the excuse for
using it being that it expresses adequately in one word an
idea that in our language takes at least two: this excuse
would disappear (and incidentally a much-mispronounced word
would be eliminated) if the single word _quality_ were to be
adopted as the equivalent of _timbre_. Thus, _e.g._, the
soprano voice singing c' has a _quality_ different from the
contralto voice singing the same tone.

(The remainder of this chapter and all of Chapter XVIII deal
with terms commonly encountered in the study of _harmony_.
Courses in this subject usually begin with a study of scales,
but since this subject has already been somewhat extensively
treated, this chapter will omit it, and will begin with the
next topic in harmony study, viz.--the interval.)

183. An _interval_ is the relation of two tones with regard to pitch. If the two tones are sounded simultaneously the result is an _harmonic interval_, but if sounded consecutively the result is a _melodic interval_. Fig. 62 represents the pitches f' and a' as a harmonic interval, while Fig. 63 represents the same pitches arranged as a melodic interval.

184. In classifying intervals two facts should be constantly kept in mind:

(1) The _number name_ of the interval (third, fifth, sixth,
etc.), is derived from the order of letters as found in the
diatonic scale. Thus the interval C--E is a _third_ because E
is the third tone from C (counting C as one) in the diatonic
scale. C--G is a _fifth_ because G is the fifth tone above C
in the diatonic scale.

It should be noted however that the same _number-names_ apply
even though one or both letters of the interval are qualified
by sharps, flats, etc. Thus _e.g._, C--G[sharp] is still a
_fifth_, as are also C[sharp]--G[flat] and C[flat]--G[sharp].

(2) In determining the _specific_ name of any interval
(_perfect_ fifth, _major_ third, etc.), the half-step and
whole-step (often referred to respectively as _minor second_,
and _major second_) are used as units of measurement.

The _half-step_ is usually defined as "the smallest usable
interval between two tones." Thus, C--C[sharp] is a
_half-step_, as are also B--C, F--G[flat], etc.

A _whole-step_ consists of two half-steps. C--D is a
_whole-step_, as are also B[flat]--C, E--F[sharp],
F[sharp]--G[sharp], G[flat]--A[flat], etc.

The expressions _half-step_ and _whole-step_ are much to be
preferred to _half-tone_ and _whole-tone_, as being more clear
and definite. Thus _e.g._, the sentence "The two tones are a
_half-step_ apart" is much better than "The two tones are a
_half-tone_ apart."

185. A _prime_ is the relation between two tones whose pitches are properly represented by the same degree of the staff.

A _perfect prime_ is one whose tones have the same pitch.
Middle C sounded by piano and violin at the same time would
offer an example.

An _augmented prime_ is one whose second tone is one half-step
higher than the first. Ex. C--C[sharp].

186. A _second_ is the relation between two tones whose pitches are properly represented by adjacent degrees of the staff. (The first line and first space are adjacent degrees, as are also the third line and fourth space.)

A _minor second_ is one comprising one half-step. Ex. B--C.

A _major second_ is one comprising two half-steps. Ex.
B--C[sharp].

An _augmented second_ is one comprising three half-steps. Ex.
F--G[sharp].

187. A _third_ is an interval comprising two seconds.

A _diminished third_ has two minor seconds (_i.e._, two
half-steps). C--E[double-flat].

A _minor third_ has one minor and one major second (_i.e._,
three half-steps). C--E[flat].

A _major third_ has two major seconds (_i.e._, four
half-steps). C--E.

188. _A fourth_ is an interval comprising three seconds.

A _diminished fourth_ has two minor and one major second.
C[sharp]--F.

A _perfect fourth_ has one minor and two major seconds. C--F.

An _augmented fourth_ (tritone) has three major seconds.
C--F[sharp].

189. A _fifth_ is an interval comprising four seconds.

A _diminished fifth_ has two minor and two major seconds.
C--G[flat].

A _perfect fifth_ has one minor and three major seconds. C--G.

An _augmented fifth_ has four major seconds. C--G[sharp].

190. A _sixth_ is an interval comprising five seconds.

A _minor sixth_ has two minor and three major seconds.
C--A[flat].

A _major sixth_ has one minor and four major seconds. C--A.

An _augmented sixth_ has five major seconds. C--A[sharp].

191. A _seventh_ is an interval comprising six seconds.

A _diminished seventh_ has three minor and three major
seconds. C--B[double-flat].

A _minor seventh_ has two minor and four major seconds.
C--B[flat].

A _major seventh_ has one minor and five major seconds. C--B.

192. An _octave_ is an interval comprising seven seconds.

A _diminished octave_ has three minor and four major seconds.
C--C[flat].

_A perfect octave_ has two minor and five major seconds. C--C.

An _augmented octave_ has one minor and six major seconds.
C--C[sharp].

193. A _ninth_ is usually treated as a second, a _tenth_ as a third, etc. The interval of two octaves is often referred to as a _fifteenth_.

194. If the major diatonic scale be written and the interval between each tone and the key-tone noted, it will be observed that the intervals are all either major or perfect. See Fig. 64.

In this connection also it will be noted that the interval next smaller than _major_ is always _minor_, while that next smaller than _perfect_ or _minor_ is always _diminished_: but that the interval next larger than both _major_ and _perfect_ is _augmented_.

195. An interval is said to be _inverted_ when the tone originally the upper becomes the lower. Thus C--E, a major third, inverted becomes E--C, a minor sixth.