# Study Guide. Solutions to Selected Exercises. Foundations of Music and Musicianship with CD-ROM. 2nd Edition. David Damschroder

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1 Study Guide Solutions to Selected Exercises Foundations of Music and Musicianship with CD-ROM 2nd Edition by David Damschroder

3 Solutions to Selected Exercises 2 Chapter 2 P2-1 Do exercise a and b Both exercises a and b have two answers, and each answer requires three consecutive scale degrees. Since it takes two scale degrees to make one whole or half step, it takes three consecutive scale degrees to make two such intervals. For example, Whole- Whole occurs when we ascend ˆ 1 - ˆ 2 - ˆ 3 : ˆ 1 to ˆ 2 is a whole step, and ˆ 2 to ˆ step. 4 ˆ -5 ˆ -6 ˆ and 5 ˆ -6 ˆ -7 ˆ would also be correct answers in that case. 3 is a whole P2-2 Do exercise a and b. First, either ascend the scale to 8 ˆ or descend the scale to ˆ 1 to find the tonic pitch. Both strategies should lead to tonic. (Remember that 8 ˆ is always the highest pitch of a scale: it is the last note of an ascending scale and the first note of a descending scale.) Once you know what pitch is tonic, then you might need to add a key signature. (No signature is required if C is tonic.) When writing in the scale degree numbers, remember that a descending scale is numbered 8 ˆ -7 ˆ -6 ˆ -5 ˆ -4 ˆ -3 ˆ -2 ˆ -ˆ 1. Note: Though the C Major scale is displayed in examples 2-2, 2-3, 2-5, and 2-7 starting on Middle C, any C may serve as the starting point for a major scale. P2-3 Do exercise a and b. To find 6 ˆ, you may ascend the scale ˆ 1-2 ˆ -3 ˆ -4 ˆ -5 ˆ -6 ˆ. However, it would be simpler in that case to descend 8 ˆ -7 ˆ -6 ˆ. Try both! You should get the same answer using either method. Remember that sometimes a sharp (F# ) or a flat (Bb) may be required in an answer. P2-4 Do exercises 1 and 2. The pitches of this exercise may be higher or lower than those displayed in the scales presented in this chapter. For example, the D of exercise 1 does not occur in the G Major scale shown in examples 2-4 and 2-7, and yet it is a diatonic in G Major. Imagine starting with the G above Middle C as 8 ˆ and descending to this D. What scale degree number is appropriate? Rhythm Practice Exercises R2-2 Do exercise a. Remember that the direction of a stem depends on where a note resides on the staff. A stem that points upward in measure 1 may need to point downward in measure 3. Also remember that an augmentation dot goes beside a notehead that is in a space, but in the space above a notehead that is on a line. R2-3 Do exercise a. The reminders for R2-2 apply to this exercise as well.

4 Solutions to Selected Exercises 3 R2-4 Do exercise a. Melodies generally are made of small intervals. Thus you are limited here to intervals no larger than a fourth, calculating from one note to the next. The last three pitch names are D B C. From D, descend a third to B rather than ascending a sixth. This will require the use of a ledger line. L2-1 Play an F or G Major scale (your choice), ascending and descending. While performing, say the words Whole and Half at appropriate spots, as indicated in the instructions. Remember that one black key will be needed to perform your scale. L2-2 Play exercise c or d (your choice). Even though no one is watching you, do use the fingerings indicated. L2-3 Sing one of the exercises (your choice). Sing the exercise using the syllable la. Listen carefully to the starting pitch before you begin. Men, remember to take the melody down an octave or two (that is, to the left on the keyboard) so that it sounds in your vocal range. L2-4 Perform one of the exercises (your choice). Remember to count out loud.

5 Solutions to Selected Exercises 4 Chapter 3 P3-1 Do exercises a and b. Go back to chapter 1 and look at all the treble-clef noteheads displayed in example 1-5. There are three different noteheads named C in that example. Each C could form an interval with another notehead that is either higher or lower than that C. If the C is the lower of the two noteheads, then it is ˆ 1 in relation to some higher number ( 2 ˆ through 8 ˆ ). If the C is the higher of the two noteheads, then it is 8 ˆ in relation to some lower number (ˆ 1 through 7 ˆ ). Thus, in Exercise 3-1b, the C notehead functions as 8 ˆ, because it is higher than the other notehead of the interval. But in Exercise 3-1c, this same C functions as ˆ 1, because the other notehead is even higher. If C functions as ˆ 1, then the interval formed will be of either major or perfect quality. If C functions as 8 ˆ, then the interval formed will be of either minor or perfect quality. (Review example 3-5.) P3-2 Do exercises a and b. Consonance and dissonance are characteristics that one learns about intervals. Which five interval sizes are characterized as consonant? Which three are characterized as dissonant? P3-3 Do exercises a and b. This exercise resembles P3-1, but now there are three choices for tonic: C, F, or G. The key signature will tell you which pitch serves as tonic. So C may be ˆ 1 (in C Major), 4 ˆ (in G Major), or 5 ˆ (in F Major). P3-4 Do exercises a and b. This exercises is like P3-2. P3-5 Do exercises a and b. Example 3-5 shows all the intervals introduced in this chapter, in the context of the key of C Major. The same results will occur in any other major key, such as F Major or G Major. ˆ 1-2 ˆ is a major second, whether formed by C-D (in C Major), F-G (in F Major), or G-A (in G Major). The key signature is important: it ensures that all the interval qualities turn out right. So, starting on C, F, or G as appropriate, and adding a key signature where appropriate, ascend or descend a major scale to find the interval requested. P3-6 Do exercises a and b. Before you complete this exercise, fill in the blanks in the sentences that follow: The inversion of an interval of perfect quality is always of quality. The inversion of an interval of major quality is always of quality.

6 Solutions to Selected Exercises 5 The inversion of an interval of minor quality is always of quality. The sum of the interval sizes of two inversionally related intervals is always. Rhythm Practice Exercises R3-2 Do exercises a c. Rest notation has its quirks. For example, sometimes a half rest is appropriate, but at other times two quarter rests must be used instead. And a whole rest might sometimes mean two beats, three beats, or four beats. The order of the rests can also be important: sometimes a half rest is followed by a quarter rest; sometimes a quarter rest is followed by a half rest. Study examples 3-11, 3-12, and 3-13 and their commentary carefully before completing these exercises. R3-3 Do exercise a. Whether notes or rests are employed, the number of beats per measure must correspond to that indicated by the time signature. Remember the rules about stem placement. Don t forget the double bar at the end. L3-1 Perform one interval from each column (your choice), and identify its quality and size. L3-2 Play one of the exercises (your choice). Be careful not to play the exercise an octave too high or too low. L3-3 Sing exercise c or d (your choice). Sing the exercise using the syllable la. Men should remember to take the melody down an octave or two (that is, to the left on the keyboard) so that it sounds in your vocal range. L3-4 Perform one of the exercises (your choice). Count the appropriate number ( , etc.) out loud even during a rest.

7 Solutions to Selected Exercises 6 Chapter 4 P4-4 Do exercises a and b. Take care in positioning the sharp or flat of the key signature if one is required. The sharp of G Major must go on the fifth line in treble clef, and the flat of F Major must go on the third line. The Roman numeral gives you the information you need to determine where to position the root. (There will be several choices: for example, if the root is C, you may use Middle C or any higher C.) Then add the third and fifth. Though the Roman numeral indicates the triad s quality (major, minor, or diminished), you do not need to do anything special for it to come out right. That s the key signature s job. P4-5 Do exercises a and b. Assess the scale degree of the triad s lowest note (that is, its root) to determine the Roman numeral. If, for example, the root is D in F Major, then, because its scale degree is 6 ˆ (ascend ˆ 1-6 ˆ or descend 8 ˆ -6 ˆ in the F Major scale to confirm this), the Roman numeral is vi. The Roman numeral is small because, in a major key, the triad rooted on 6 ˆ is always of minor quality. (Review example 4-6, which shows the qualities of all the major-key triads.) P4-6 Do exercises a and b. Though this exercise is similar to P4-4, the positions of the key signature s sharp or flat and of the noteheads will differ from corresponding positions in the treble clef. P4-7 Do exercises a and b. This exercise is like P4-5. But now you must read in the bass clef. Rhythm Practice Exercises R4-3 Do exercise a. Consider especially the placement of the augmentation dot. R4-4 Do exercise a. Remember the rules about stem placement. Don t forget the double bar at the end. If two eighth notes fall within the same beat, use beam notation. Only if an eighth note joins with a dotted quarter note or an eighth rest should flag notation be employed.

9 Solutions to Selected Exercises 8 Chapter 5 P5-1 Do exercises a and b. You have already completed a similar exercise for the major scale. Now you have a chance to attain a better familiarity with the location of whole and half steps in the natural minor scale. Remember that it takes three pitches to form two intervals, four pitches to form three intervals, and so on. P5-2 Do exercises a c. In most cases your answer will be a single letter: C, D, etc. But remember that F# and Bb are among the possible answers. P5-3 Do exercises 1 and 2. Though the scales presented in this chapter make use of a variety of noteheads, the given pitches of this exercise may be higher or lower. For example, the D of exercise 2 does not occur in the E Natural Minor scale shown in examples 5-4, and yet it is a diatonic in that key. Scales can be made higher or lower on the staff, and in either treble or bass clef. In fact, this D does appear in example 5-5. P5-4 Do exercises a and b. This exercise is the minor-mode equivalent of exercise P3-1. You will need to make use of information found in example 5-7. P5-5 Do exercises a and b. This exercise resembles exercise P5-4. But now there is an additional step: determining the minor key in which to interpret the interval. P5-6 Do exercises a and b. This exercise is the minor-mode equivalent of exercise P3-5. It will help you confirm the following information: The unison, fourth, fifth, and octave are perfect in both modes. The third, sixth, and seventh above tonic (ˆ 1 ) are major in the major mode and minor in the natural minor mode. The second above tonic (ˆ 1 ) is major in both modes. The second, third, and sixth below tonic ( 8 ˆ ) are minor in the major mode and major in the minor mode. The seventh below tonic ( 8 ˆ ) is minor in both modes. P5-7 Do exercises a and b. This exercise is the minor-mode equivalent of exercise P4-6. If you form the key signature correctly and place the notes on appropriate lines and spaces, the triad quality (major, minor, or diminished) will automatically turn out to be correct.

11 Solutions to Selected Exercises 10 Chapter 6 P6-1 Do exercise a. Remember that relative keys share the same key signatures, but that a different pitch serves as tonic in each. (Eb Major and C Minor both have three flats in their key signatures, for example.) In contrast, parallel keys share the same tonic pitch, but their key signatures are not the same. (C Major and C Minor both have C as tonic, but do not share the same key signature.) P6-2 Do exercises a c. This exercise helps you to understand where the various intervals reside, merging ideas that we have learned separately in the contexts of the major and minor modes. For all perfect intervals (the unison, fourth, fifth, and octave), the two modes are identical. The major/minor intervals are not so uniform. As recommended in chapter 3, it is a good idea to learn intervals in their inversional pairs: since ˆ 1-2 ˆ is a major second (in both modes, in fact), 2 ˆ -8 ˆ will be a minor seventh. Any second, fourth, or seventh will be dissonant. All the other intervals we have explored thus far are consonant. Remember that third, sixth, and seventh above tonic (ˆ 1 ) are major in the major mode and minor in the natural minor mode. The second above tonic (ˆ 1 ) is major in both modes. The second, third, and sixth below tonic ( 8 ˆ ) are minor in the major mode and major in the minor mode. The seventh below tonic ( 8 ˆ ) is minor in both modes. If this paragraph seems dense and complicated, keep reviewing interval qualities until this becomes crystal clear. P6-3 Do exercises 1 and 2. Remember that D# (exercise 1) is not the same as Eb (exercise 5). D# will occur only when the key signature contains four or more sharps. (Keys with five through seven sharps are introduced in the text s enhancement III but will not be explored in our Music 1001 course.) Eb will occur only when the key signature contains two or more flats. P6-4 Do exercises a and b. Though you have completed similar exercises in earlier chapters, now you must assess whether the interval requested occurs in major keys, minor keys, or both. Be very careful to distinguish one from the other. There are two keys with tonic C: C Major and C Natural Minor. Both appear on the diagrams of example 6-5. It is a common mistake for students to apply the key signature of the parallel key, which may result in an incorrect answer. Sometimes it does not matter: the perfect fourth above C is F whether one ascends C-D-E-F in C Major or C-D-Eb-F in C Natural Minor. But a minor sixth above C can be determined only by ascending C-D-Eb-F-G-Ab in C Natural Minor.

13 Solutions to Selected Exercises 12 L6-1 Perform one Major and one Natural Minor scale (your choice), ascending and descending. While performing, say the words whole and half at appropriate spots, as indicated in the instructions. L6-2 Perform one triad (your choice), and name its quality. Make sure to take the key signature into account. In many of these triads, one or more of the three pitches corresponds to a black key on the keyboard. Also make sure that you are playing exactly the notes written, not the triad an octave higher or lower. L6-3 Play one of the exercises (your choice). L6-4 Sing one of the exercises (your choice). L6-5 Perform one of the exercises (your choice). Counting syllables for compound meters is a controversial matter. While many teachers prefer 1 + uh 2 + uh, others prefer Please practice using the syllables in the manner of 1 + uh 2 + uh. This way you will better understand how to deal with triplets in chapter 9.

14 Solutions to Selected Exercises 13 Enhancement I P.I-1 Do exercises a and b. The following chart of accidentals should prove useful: bb - b - n - # - If the melodic motion is ascending, you need the symbol one to the right of that of the preceding note. (For example, starting on Bb you would need a natural to create Bn.) If the melodic motion is descending, you need the symbol one to the left of that of the preceding note. (For example, starting on D you would need a flat to create Db.) Remember to consult the key signature to determine if the first note is a sharp or flat note. P.I-2 Do exercises a and b. Step One: Draw a notehead on the line or space that is just below that on which the two given notes reside. Step Two: Add whatever accidental is necessary to make the note you added be a half step from the given notes. (You may wish to consult a keyboard diagram.) P.I-3 Do exercises a, d, g, and j. This has been one of the most error-prone exercises of this course. Be very careful in how you approach it. The text divides the process of creating a chromatic scale into three steps. (Go back and reread the section titled Chromatic Scales again if you are at all uncertain how to proceed.) Here are some potential errors that you should avoid: Using the wrong key signature. Using the wrong succession of whole and half steps for the diatonic scale. (Remember that the descent is not the same as the ascent, and that natural minor scales are different from major scales.) Forgetting to use the preceding notehead for the chromatic pitch. Forgetting to read the key signature before determining what accidental the chromatic pitch requires. For example, if the diatonic scale starts Ab-Bb and you forget to read the key signature, you may think the scale goes A-B and add A# as the chromatic pitch. Instead, an A n must come between Ab and Bb. Forgetting whether you are ascending or descending. If the descending line begins A- G, you might incorrectly write A# rather than Ab for the chromatic pitch. Trying to add a chromatic pitch between two notes that are just a half step apart. There are only five chromatic pitches per octave, not seven.

17 Solutions to Selected Exercises 16 Chapter 7 L7-1 Perform two chords (your choice). Try to avoid the following two common problems: 1) playing pitches an octave too high or too low, and 2) forgetting about the key signature. Take your time positioning your fingers above the keys, and then play all four pitches at the same time. L7-2 Play one of the exercises (your choice). Choose a tempo slow enough that you can perform all the sixteenth notes without slowing down. L7-3 Sing one of the exercises (your choice). L7-4 Perform one of the exercises (your choice). Count 1 ee + ee... for the entire exercise whenever sixteenth notes occur anywhere within an exercise. For example, it would be incorrect to count the first measure of exercise a as follows: ee + ee 4 ee + ee

20 Solutions to Selected Exercises 19 Chapter 10 P10-1 Do exercise a. The 5 position can be inverted into 3 6 and 3 6 positions. A chord in position has 3 inversions, too. But they are not introduced in this chapter. (If you are curious, consult pages of the textbook.) Thus your strategy for solving these exercises resembles what you did in chapter 7, not chapter 8. As with chords in 7 5 position, the fifth may be 3 omitted in a 7 5 chord. If that is the case, then the root must be doubled, because neither the 3 third nor the seventh may be doubled. P10-2 Do exercise a. Remember that there are often four different pitches in a 7 5 chord. A common mistake is 3 to find three different pitches in the treble clef and then assume that that s all there are, without looking in the bass clef, where a fourth different pitch may reside. For example, in exercise a, if you look only at the treble-clef pitches, you might think that the chord s root is D. But that is not the case. Figured bass always takes the chord as is. Do that step first, taking all four pitches into account. Then, you may need to move some notes around so that you can discover which pitch is the root, as you did in chapter 8. Remember that the Roman numeral is determined from the root, not from the bass. P10-3 Do exercise a. In the major mode, scale degrees 4 ˆ and 7 ˆ, when sounding together, create a special forward push that composers like to employ. In this exercise, you locate which two pitches correspond to these scale degrees, and indicate the pitches to which their forward push is directed. P10-4 Do exercise a. In an introductory course, we cannot explore all the intricacies of harmonic motion. (Music majors spend about two years doing this!) For our purposes of getting a preliminary glimpse of how chords interact, we focus especially on the ends of phrases, where cadences occur. Though you are being asked to practice analyzing chords by examining all the chords of the progression, the cadence depends on only the last two chords of the phrase. (The earlier chords generally confirm that the phrase is in a particular key.) In this chapter, all of the phrases are in the major key indicated by the key signature. In chapter 11, we will explore phrases in minor keys. Note that these exercises are performed on the CD-ROM. So you may listen to them as you analyze them.

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