Part 17 (1/2)

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.

[Ill.u.s.tration: 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.

CHAPTER XVIII

CHORDS, CADENCES, ETC.

196. A _chord_ is a combination of several tones sounding together and bearing an harmonic relation to each other. The simplest chord is the _triad_, which consists of a fundamental tone called the _root_, with the third and fifth above it. C--E--G is a triad, as are also D--F--A, F--A--C, and G--B--D.

197. Triads are cla.s.sified as _major_, _minor_, _diminished_, or _augmented_.

A _major triad_ has a major third and a perfect fifth, _i.e._, it is a major third with a minor third on top of it. Ex.

C--E--G.

A _minor triad_ has a minor third and a perfect fifth, _i.e._, it is a minor third with a major third on top of it. Ex.

C--E[flat]--G.

A _diminished triad_ has a minor third and a diminished fifth, _i.e._, it is a minor third with another minor third on top of it. Ex. C--E[flat]--G[flat].

An _augmented triad_ has a major third and an augmented fifth, _i.e._, it is a major third with another major third on top of it. Ex. C--E--G[sharp].

198. A triad may be built on any scale-tone, but those on I, IV, and V, are used so much oftener than the others that they are often called the _common chords_. In referring to triads the Roman numerals are used to show on what scale-tone the triad is based, the size of the numeral (with other signs) indicating the kind of triad found on each tone of the scale. Thus _e.g._, the large I shows that the triad on the first tone (in major) is a _major triad_, the small II shows that the triad on the second tone is minor, etc. The following figure will make this clear.

[Ill.u.s.tration: Fig. 65.]