which are a musical ear and some degree of mechanical
ability. Having these, all else may be acquired by study. It is not
necessary to possess a musical education or to be a musician; although
a knowledge of music will be found a great aid. Still, an elementary
knowledge of the principles of music is a necessity to the student of
this course, as it has been found impossible to avoid the use of a few
technical terms. In most cases, however, they are set forth in such a
way that they will be readily apprehended by anyone who has even a
slight knowledge of the fundamental principles of music.

In teaching Piano Tuning, it is the custom of the "Central School of
Piano Tuning," for which these lessons were originally prepared, to
have all students prepare two lessons in harmony as a test of their
acquaintance with the intervals and chords used in tuning. The lessons
are not difficult, and they embody only those principles which are
essential to the proper understanding of the key-board: the intervals
of the diatonic scale and the major common chord in the twelve
different keys, C, D, E, F, G, A, B, B-flat, D-flat, E-flat, G-flat,
and A-flat. In connection with the harmony lessons, we use as a
text-book "Clarke's Harmony,"[A] and the student is required to master
the first two chapters and prepare manuscripts upon each of the
lessons. Below is a number of the most important questions selected
from those lessons upon which manuscripts have been written:

1. Every white key on the piano represents an "absolute pitch."
By what names are these pitches known? How are the black keys
named?

2. How many tones constitute the diatonic scale? Give numerical
names.

3. Intervals are measured by steps and half-steps. How many steps
from 1 to 3 in the diatonic scale? 1 to 4? 1 to 5? 3 to 5? 5 to
8? 1 to 8?

4. Why is there no black key between E and F, and between B and
C?

5. From 1 to 3 is called an interval of a third; from 3 to 5,
also a third; from 1 to 5, a fifth: they are so called because
they include, respectively, three and five members of the
diatonic scale. What is the interval 3 to 6? 2 to 5? 5 to 8? 2 to
6? 1 to 8?

6. Thirds are of two kinds: major (larger) thirds embrace two
whole-steps; minor (smaller) thirds embrace a step and a half.
What kind of a third is 1-3 in the diatonic scale? 2-4? 3-5? 6-8?

7. What do we m