Simple Common.- or having 4 ds or 4 Js to a bar.

The dotted minim (J.), the dotted crotchet (J.), and the dotted quaver () are the notes in use as beat measurers in Compound Time.

Compound Common Time :

means 4.s to a bar = 12 crotchets.*

94 98

2. s

Compound Triple Time:

means 3.s to a bar

=

6 quavers.

Though

and are numerically equivalent, they are totally

distinct as time signatures. The three crotchets in time each take a beat; while the six quavers in g time are formed into two groups, each group taking a beat :

៖

One Two Three One Two Three

One Two One Two

When time is delivered in very slow speed, as in Lento or Grave movement, each quaver may be counted one, two, three; four, five, six; in which case one and four must be emphasized, to mark the correct accent grouping.

* A crotchet is of a semibreve. A quaver is of a semibreve.

EXERCISES.

I.

1. What do you understand by keeping time?

2. What would be the result of removing all bar marks in our music?

3. When is time common, and when triple?

4. Write a few bars of each, using as much variety of note, ́minim, crotchet, etc., as you can.

II.

1. What is to prevent a boy or girl singing bass?

2. Draw the great stave, and bracket the portions which register or mark the compass of bass, tenor, contralto, and soprano voice respectively.

3. Why should a person with naturally a good voice need professional training to excel as a singer?

III.

1. Show by examples how intervals are enlarged or diminished; e.g., how a minor second may be made major, and conversely how a major may be made minor.

2. What intervals have one, two, three, etc., semitones?

3. If a pluperfect fourth and imperfect fifth have each six semitones, what difference can there be between them?

IV.

1. How many minor thirds are there in the natural scale (not counting replicates)? When this number is ascertained, how may you readily know the number of major thirds.

2. How far does the principle extend? Work out the intervals of the fourth and fifth as examples.

3. What help will the complete knowledge of the intervals in one scale be in the study of other scales?

V.

1. What is a tetrachord? Show the construction of an octave by tetrachords.

2. What results follow from transposing these tetrachords? 3. Work out in detail and explain carefully the development of two sharp and two flat scales from this process.

VI.

I. Why does not the list of scales or keys extend further? 2. Verify the statement, "Our list of keys is a redundant list."

3. How does the number seven assert itself in the number of sharps and flats required in the key in F or G, or any other pitch.

VII.

1. How are essential sharps and flats distinguished from accidentals?

2. Write a few bars using the same sharp or flat, first as an essential, second as an accidental.

3. In a piece written in Eb the following are found :-Ab, Ai, Db, Bb, B, and G2; which are essential, and which accidental ?

VIII.

1. Why should the fourth sharpened or the seventh flattened be so frequent as accidentals?

2. What is modulation; and how do you understand modulating two removes?

3. A phrase starts in the open key, but ends in the key of F; what modulation has taken place, and how?

IX.

1. Distinguish between simple and compound time.

2. Copy a few bars of every variety of time you come across, and keep them properly classified.

3. Commit the whole time signatures to memory, and be prepared to quote any on demand.

GEOMETRY.

EUCLID. BOOK I.

DEFINITIONS.

1. A point is that which has no parts, or which has no magnitude.

2. A line is length without breadth.

3. The extremities of a line are points.

4. A straight line is that which lies evenly between its extreme points.

5. A superficies is that which has only length and breadth. 6. The extremities of superficies are lines.

7. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.

8. A plane angle is the inclination of two lines to each other in a plane, which meet together, but are not in the same straight line.

9. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

N.B.-When several angles are at one point, B, either of them is expressed by three letters, of which the letter that is at the