_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.

[Illustration: 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 classified 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