matches the upper note. Try singing the two notes in the other order, with the upper note first. Be careful not to transpose either of the notes up or down an octave, as this would invert the interval. Depending on your vocal range and where the interval is played, you might have to transpose them both up or down. If so, be careful to transpose them both by the same number of octaves.
To figure out what interval you're hearing, you may also find it useful to refer mentally to well-known melodies from pop and classical music. Due to copyright restrictions, it's not possible for us to publish even short excerpts from certain of the tunes listed on the next page. If you can't find them in sheet music form, doubtless a musically knowledgeable friend will be able to play any of the melodies that you don't already know, so that you can hear and become familiar with the intervals. Some of the tunes listed are in the public domain, which means we could publish them here, but a sketchy set of examples in which some of the more useful melodies are omitted would look pretty silly.
You may be able to think of other songs besides the ones listed. Note that some of these tunes use the ascending version of the interval (the lower note before the upper one), while others use the descending version (upper note first).
Quiz
1. What is the name of the interval created by removing one half-step from a perfect 4th? Give two answers - one for the interval in which the letter-names of the two notes have not changed, and another for the interval in which one of the two notes has a new letter-name.
2. When two intervals can be stacked to form a perfect octave, what is their relationship called?
3. If a minor 2nd is increased by an octave, what interval results?
4. How many half-steps are there in a diminished 7th? In a diminished 3rd?
5. Give three different names for the interval that contains six half-steps.
6. Explain why there's no such interval as a perfect 3rd, and no such interval as a minor 5th.
7. Which is larger - a major interval or a minor interval? (Assume that each is spelled with the same two letter-names, so that each has the same number of scale steps.)
8. What note is a major 6th above A? A minor 3rd below G? A diminished 5th below B?
9. What interval is the inversion of a major 3rd? Of a minor 2nd? Of an augmented 4th?
10. What is the name of the interval between the D below Middle C and the D# above Middle C?
3
TRIADS
ith some exceptions in the area of contemporary classical music, all harmonic activity in conventional European/American music is based on the triad. As its name implies, a triad is a set of three notes. Not just any three notes will do, however. The notes in a triad have specific relationships to one another. (In Chapter Six we'll look at a few three-note chords that are not triads.)
A triad is built by stacking two 3rds. As Figure 3-1 shows, there are four ways to do this. We can put a major 3rd on the bottom and a minor 3rd on the top, reverse the order and put a minor 3rd on the bottom and a major 3rd on the top, or combine either two major 3rds or two minor 3rds.
These four triads have names. The first two, which are used somewhat more often, are named after the lower of the 3rds: The triad in which the major 3rd is on the bottom and the minor 3rd on top is referred to as a major triad. When the minor 3rd is on the bottom and the major 3rd on top, the triad is a minor triad. The other two types are named after the type of 5th that lies between the bottom and top notes: The triad built out of two major 3rds is called an augmented triad, because its outer two notes form an augmented 5th, and the triad built of two minor 3rds is called a diminished triad, because its outer two notes form a diminished 5th.
Figure 3-1. Triads are created by stacking pairs of 3rds. Since each 3rd can be either major or minor, there are four possible triads.
Figure 3-2. The names of the notes within a triad.
Each of
To figure out what interval you're hearing, you may also find it useful to refer mentally to well-known melodies from pop and classical music. Due to copyright restrictions, it's not possible for us to publish even short excerpts from certain of the tunes listed on the next page. If you can't find them in sheet music form, doubtless a musically knowledgeable friend will be able to play any of the melodies that you don't already know, so that you can hear and become familiar with the intervals. Some of the tunes listed are in the public domain, which means we could publish them here, but a sketchy set of examples in which some of the more useful melodies are omitted would look pretty silly.
You may be able to think of other songs besides the ones listed. Note that some of these tunes use the ascending version of the interval (the lower note before the upper one), while others use the descending version (upper note first).
Quiz
1. What is the name of the interval created by removing one half-step from a perfect 4th? Give two answers - one for the interval in which the letter-names of the two notes have not changed, and another for the interval in which one of the two notes has a new letter-name.
2. When two intervals can be stacked to form a perfect octave, what is their relationship called?
3. If a minor 2nd is increased by an octave, what interval results?
4. How many half-steps are there in a diminished 7th? In a diminished 3rd?
5. Give three different names for the interval that contains six half-steps.
6. Explain why there's no such interval as a perfect 3rd, and no such interval as a minor 5th.
7. Which is larger - a major interval or a minor interval? (Assume that each is spelled with the same two letter-names, so that each has the same number of scale steps.)
8. What note is a major 6th above A? A minor 3rd below G? A diminished 5th below B?
9. What interval is the inversion of a major 3rd? Of a minor 2nd? Of an augmented 4th?
10. What is the name of the interval between the D below Middle C and the D# above Middle C?
3
TRIADS
ith some exceptions in the area of contemporary classical music, all harmonic activity in conventional European/American music is based on the triad. As its name implies, a triad is a set of three notes. Not just any three notes will do, however. The notes in a triad have specific relationships to one another. (In Chapter Six we'll look at a few three-note chords that are not triads.)
A triad is built by stacking two 3rds. As Figure 3-1 shows, there are four ways to do this. We can put a major 3rd on the bottom and a minor 3rd on the top, reverse the order and put a minor 3rd on the bottom and a major 3rd on the top, or combine either two major 3rds or two minor 3rds.
These four triads have names. The first two, which are used somewhat more often, are named after the lower of the 3rds: The triad in which the major 3rd is on the bottom and the minor 3rd on top is referred to as a major triad. When the minor 3rd is on the bottom and the major 3rd on top, the triad is a minor triad. The other two types are named after the type of 5th that lies between the bottom and top notes: The triad built out of two major 3rds is called an augmented triad, because its outer two notes form an augmented 5th, and the triad built of two minor 3rds is called a diminished triad, because its outer two notes form a diminished 5th.
Figure 3-1. Triads are created by stacking pairs of 3rds. Since each 3rd can be either major or minor, there are four possible triads.
Figure 3-2. The names of the notes within a triad.
Each of
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