going to have you fully and explicitly informed on every point, if you
will be content to absorb as little at a time as you are prepared to
receive. While it may seem to us that the tempered scale is a very
complex institution when viewed as a specific arrangement of tones
from which we are to derive all the various kinds of harmony, yet,
when we consider that the chromatic scale is simply a series of twelve
half-steps--twelve perfectly similar intervals--it seems very simple.

Bear in mind that the two cardinal points of the system of tuning are:

1. All octaves shall be tuned perfect.

2. All fifths shall be tuned a little flatter than perfect.

You have seen from Lesson VIII that by this system we begin upon a
certain tone and by a circle of twelve fifths cover every chromatic
tone of the scale, and that we are finally brought around to a fifth,
landing upon the tone upon which we started.

So you see there is very little to remember. Later on we will speak of
the various other intervals used in harmony: not that they form any
prominent part in scale forming, for they do not; but for the purpose
of giving the learner a thorough understanding of all that pertains to
the establishing of a correct equal temperament.

If the instruction thus far is understood and carried out, and the
student can properly tune fifths and octaves, the other intervals will
take care of themselves, and will take their places gracefully in any
harmony in which they are called upon to take part; but if there is a
single instance in which an octave or a fifth is allowed to remain
untrue or untempered, one or more chords will show it up. It may
manifest itself in one chord only. A tone may be untrue to our
tempered scale, and yet sound beautifully in certain chords, but there
will always be at least one in which it will "howl." For instance, if
in the seventh step of our system, we tune E a little too flat, it
sounds all the better when used as third in the chord of C, as we have
shown in the experiment mentioned on page 94 of this lesson. But, if
the remainder of the temperament is accurate, this E, in the chord in
which E acts as tonic or fundamental, will be found to be too flat,
and its third, G sharp, will demonstrate the fact by sounding too
sharp.

The following suggestions will serve you greatly in testing: When a
third sounds disagreeably sharp, one or more fifths have not been
sufficiently flattened.[E] While it is tru