1 Study Guide Solutions to Selected Exercises Foundations of Music and Musicianship with CD-ROM 2nd Edition by David Damschroder
2 Solutions to Selected Exercises 1 CHAPTER 1 P1-4 Do exercises a-c. Remember to answer all parts of the question. (Read the instructions carefully.) Comparing exercises d and m will remind you of some conventions of interval notation. (In some cases, the notes of a harmonic interval are not in vertical alignment.) You must count lines and spaces to determine the interval s size. Remember that the line or space of the first notehead counts as 1. Thus your answers will be numbers from 1 to 8, never zero (0). P1-5 Do exercises a, d, g. You must count lines and spaces to find the note that corresponds to the interval size requested. Remember that the line or space of the given note counts as 1. P1-6 Do exercises a and b. Use the work area at the bottom of the page. It does not matter what notehead you select as your starting pitch, but it will be easier if you choose a notehead that will allow you to avoid ledger lines. This exercise demonstrates that interval sizes are not additive. Answer each question with interval size and direction, such as ascending fourth. L1-1 Play one interval from each row (your choice). Be very careful in assessing where the key of the interval s first note is in relation to Middle C. For example, exercises a and c both begin with a pitch named C, but the C of exercise a is to the left of the C of exercise c. If you were to begin exercise c on Middle C, your performance would be incorrect. L1-2 Sing an ascending octave, playing only the lower pitch at the keyboard. If you know the song, Somewhere Over the Rainbow from The Wizard of Oz, then this exercise is like singing the two notes corresponding to the word some-where. Make sure that your first pitch matches the pitch that you are playing on the piano. Also remember not to play the second pitch on the piano, at least until after you have sung it. L1-3 Perform one of the exercises (your choice). In all rhythm exercises, you are expected to count out loud in even syllables, such as: Count out one measure before you begin, and do not speed up or slow down during your performance.
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.
8 Solutions to Selected Exercises 7 L4-1 Perform two triads (your choice), and name their qualities. Make sure to take the key signature into account. In many of these triads, one 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. L4-2 Perform two triads (your choice), and name their qualities. The triad s quality is something that you can memorize (example 4-6). But by listening to the triads you perform, you might be able to distinguish their quality. L4-3 Play exercise a, c, or d (your choice). The left hand s thumb is fingered as 1, and the little finger as 5. L4-4 Sing exercise a or c (your choice). L4-5 Perform one of the exercises (your choice). Count throughout your performance. The symbol + should be pronounced as and (not plus!).
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.
10 Solutions to Selected Exercises 9 P5-8 Do exercises a and b. This exercise is the minor-mode equivalent of exercise P4-7. Remember that in natural minor, the i, iv, and v triads are of minor quality, the ii triad is of diminished quality, and the III, VI, and VII triads are of major quality. Rhythm Practice Exercises R5-2 Do exercise a. Be careful in determining the note value for the final pitch. L5-1 Perform a D or E Natural Minor 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. L5-2 Perform one triad (your choice). Make sure to take the key signature into account. In many of these triads, one 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. L5-3 Perform one triad (your choice). The triad s quality is something that you can memorize (example 5-8). But by listening to the triad you perform, you might be able to distinguish its quality. L5-4 Play one of the exercises (your choice). Left-hand fingerings for bass-clef melodies are written below the staff, while right-hand fingerings for treble-clef melodies are written above the staff. L5-5 Sing one of the exercises (your choice). L5-6 Perform one of the exercises (your choice). When there is an upbeat, start counting with 1 and begin the performance when the appropriate syllable arrives. For example, in exercise a, count and then begin with the following syllable, +.
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.
12 Solutions to Selected Exercises 11 P6-5 Do exercises a and b. Often there are several different routes for achieving the correct answer. It does not matter which route you use: only that you come up with the correct answer. Always, one of the two pitches of the question will serve as a tonic in one of the 18 keys that are displayed in example 6-5. Your strategy should be to find a key (there may be more than one correct choice) that contains both of the pitches of the interval. When you have reached this point, determine the scale degrees of the two pitches in the key you have selected, and from that information determine the size and quality of the interval. If the interval is C up to F, then you could think in C Major (ˆ 1 to 4 ˆ ), C Natural Minor (ˆ 1 to 4 ˆ ), F Major ( 5 ˆ to 8 ˆ ), or F Natural Minor ( 5 ˆ to 8 ˆ ). The answer would be Perfect Fourth regardless of the route followed. But if the interval is G# up to E, then only one route is possible, given the keys that you have learned up to this point: E Major ( 3 ˆ to 8 ˆ ). As you learned in chapter 3, these scale degrees always form the interval of a Minor Sixth in the major mode. P6-6 Do exercises a and b. If you draw the key signature and the noteheads correctly, then the triad quality will always turn out to be correct. You don t need to worry about making the iii triad in Bb Major be minor, for example. It will be minor automatically if you do the other steps of the problem correctly. P6-7 Do exercises a and b. Here you do need to be concerned about the quality of each triad. This is something you should have memorized by now. (The information you need is in example 5-8.) On that chart, notice that I in major keys and III in minor keys are major; that ii in major keys and iv in minor keys are minor, and so on. That is because relative keys share the same collection of triads. It s just that, since the tonics of the two keys are a third apart, what is I in one key will be III in the other, and so on. Rhythm Practice Exercises R6-1 Do exercises a c. Remember that a measure in 6 8 contains the equivalent of 6 eighth notes; a measure in 9 8 contains the equivalent of 9 eighth notes; and a measure in 12 8 contains an equivalent of 12 eighth notes. Two eighth notes merged together make a quarter note. Three eighth notes merged together make a dotted quarter note. What kind of note is the equivalent of six eighth notes? (Review example 6-11.) R6-2 Do exercise a. You should be familiar with exercises of this type from previous chapters. Don t forget about the rules of stem direction. Use a beam when eighth notes occur within the same beat, but a flag when a single eighth note occurs (along with a quarter note) within a beat.
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.
15 Solutions to Selected Exercises 14 P.I-4 Do exercises a and b. The instructions for this exercise were carefully written in order to be as clear and helpful as possible. It s a challenging exercise which requires that you have a solid command of the diatonic situation, as presented in chapter 6, before dealing with the additional complication that the chromatic pitch(es) add. Do not proceed with this chromatic assignment until you understand the diatonic situation (as in Exercise P6-5) fully. Do not assume that a sharp will always make an interval larger. If the lower pitch of an interval is raised, then the distance between the two pitches becomes smaller! You need to be very clear in your understanding of example I-9 in order to determine whether an accidental makes the interval larger or smaller, and by how much. P.I-5 Do exercises a and b. Success will come only if you break the exercise down into two steps. First deal with the interval size: put the appropriate notehead on the staff. Then assess the situation so that you know what quality pertains to the interval at this stage. Second, add whatever accidental is required to alter the quality appropriately, if necessary. (Example I-9 provides essential information.) Remember that only the note you add may be modified: keep the given note as is! L.I-1 Play two of the exercises (choose one in treble clef and one in bass clef). Remember that an accidental, once inserted, is valid until the next bar line. This convention will affect how you interpret the music notation in exercise b. Also, adding a flat beside a notehead that is already flat from the key signature does not imply a double flat. It is just a reminder. In exercise a, the second note of measure 6 is Bb, not B bb. L.I-2 Sing one of the exercises (your choice). Adding a flat beside a notehead that is already flat from the key signature does not imply a double flat. It is just a reminder. In exercise b, the last note of the third complete measure is Eb, not E bb.
16 Solutions to Selected Exercises 15 Chapter 7 P7-1 Do exercise a and e. The naming of the original interval is a skill you should remember from earlier chapters. A quick review of example 3-5 (for major keys) and example 5-7 (for minor keys) may prove useful. By expanding to form a compound interval, the interval size will change (add seven for every octave of expansion) but the quality will not change. A perfect fifth will expand into a perfect twelfth (5 + 7) or a perfect nineteenth ( ), for example. P7-2 Do exercises a and b. There are quite a few things to think about for this exercise. Here is a checklist. Do the three noteheads of the right hand all fall within a single octave? (A wider span could not be played comfortably.) Is the doubled pitch a legal pitch to double not one of the pitches whose doubling is prohibited? Are stems correctly affixed? Be especially careful when adding a stem to the bass pitch. P7-3 Do exercises a and b. For this exercise, keep in mind everything that was required for P7-2. In addition, you need to add the key signature and decide which pitches to employ in forming the chord. Remember that the Roman numeral indicates the root of the parent triad from which the chord is constructed. If the Roman numeral is ii, build a triad whose root is 2 ˆ ; if the Roman numeral is VI, build a triad whose root is 6 ˆ ; etc. Though the Roman numerals indicate chordal qualities, you do not need to worry much about that. If you have employed the correct key signature and have positioned the correct noteheads on the staff, the quality will automatically turn out as indicated. Rhythm Practice Exercises R7-1 Do exercises a and b. Work on this exercise by dividing the measure into its component beats. The time signature will tell you how many beats there are in all. In each exercise, the note you are modifying will be part of a single beat. When two or more notes fall within a single beat, beam notation is appropriate. When the note you are modifying is the only note in that beat, use flag notation. R7-2 Do exercise a. Begin a new beam at the beginning of each beat.
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
18 Solutions to Selected Exercises 17 Chapter 8 P8-1 Do exercises a and b. A triad always appears on three adjacent lines or three adjacent spaces. Its inversion will have a different form. For the first inversion, move the lowest pitch up an octave; for the second inversion, move the lowest two pitches up an octave. P8-2 Do exercises a and b. Most of these exercise have more than one possible solution. You choose which pitch to double. (Remember that certain pitches may not be doubled.) P8-3 Do exercises a and b. Follow the instructions carefully, and go back into the chapter to review the five steps required to build inverted chords. Rhythm Practice Exercises R8-1 Do exercises a and b. Isolate the beat that contains the arrow, and place the appropriate counting syllables underneath the other pitches and/or rests of the beat. Whatever is left over must be utilized for the note that you add. R8-2 Do exercise a. Begin a new beam at each new beat. (The final G does not require a beam.) L8-1 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. L8-2 Play one of the exercises (your choice). As a practice strategy, first clap the rhythm. Once that is secure, add the element of pitch. L8-3 Sing one of the exercises (your choice). L8-4 Perform one of the exercises (your choice). In all compound meters with sixteenth notes, count as follows: 1 ee + ee uh ee 2 ee + ee uh ee...
19 Solutions to Selected Exercises 18 Chapter 9 P9-1 Do exercises a and i Clearly distinguish between the concepts of bass and root, and keep in mind how each is used in the analysis of chords. From the bass, one calculates the numbers of figured bass 5 ( 3, 6 3, 6 4 ). From the root, one determines the Roman numeral. The bass will always be the lowest note of the chord as it is presented. To determine the root, you may need to move the notes around so as to form the parent triad, which will always be in the form line-lineline or space-space-space. P9-2 Do exercises a, b, j, and k. This exercise is very similar to P9-1. However, because there are four notes you will need to read treble and bass clefs simultaneously. You need to be very careful to remember that the bass is the pitch on the lower staff, not the lowest pitch of the upper staff. To calculate the figured bass, do not by mistake look only at the right-hand notes. In exercise a, the right-hand notes appear as 5 3. But the chord is not in 5 3 position, because those numbers must be calculated above the bass C! and not above inner-voice F. P9-3 Do exercises a c. This exercise will help you learn the new terms of this chapter. You might want to use some scratch staff paper to write out some triads in various keys. Remember that the triad s lowest pitch is the root, its middle pitch is the third, and its highest pitch is the fifth. Rhythm Practice Exercises R9-1 Do exercise a. Remember to write the number 3 outside a triplet s beam. L9-1 Play one of the exercises (your choice). There is a danger that your triplets will be lumpy that is, that the three component pitches of a triplet will not be even. (Review example 9-4.) It might be helpful to perform this exercise for a musically sophisticated friend or family member, because most students who perform triplets incorrectly don t realize that they are wrong. L9-2 Sing one of the exercises (your choice). The triplet difficulty mentioned above is also a factor in this exercise. L9-3 Perform one of the exercises (your choice). The triplet difficulty mentioned above is also a factor in this exercise.
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.
21 Solutions to Selected Exercises 20 P10-5 Do exercise a. Later in the textbook, in enhancement VI, you are provided more details about passing notes and neighboring notes. We will not reach that portion of the textbook in this course, though at this point you may want to take a glance at it. Here, all of these nonharmonic notes are left outside the circles, so that you can focus your attention on the chord-building notes which form the harmonies you are familiar with by now. Thus you follow the same procedure to complete these exercises as you used in P10-4. Treat all the notes within a given circle as if they occurred at the same moment, with the lowest sounding pitch serving as the bass. Note that these exercises are performed on the CD-ROM. So you may listen to them as you analyze them. Rhythm Practice Exercises R10-2 Do exercise a. For the A in measure 1, you may use either a quarter note or two eighth notes connected by a tie. Remember that when using a tie (also over the bar line between measures 1 and 2), the same notehead must be written twice, and connected by the tie symbol. If the stems point downward, the tie is placed above the noteheads; if the stems point upward, the tie is placed below the noteheads. L10-1 Perform one progression (your choice). Answer the cadence question. The right pedal of your piano is called the damper pedal. You could experiment with it when performing this exercise, as follows: 1) Perform the first chord. 2) Capture that sound by immediately pressing down the damper pedal. 3) Move your fingers to the keys that will be utilized in the next chord, keeping your right foot down on the pedal. 4) Simultaneously play the next chord and lift the pedal that is holding the sound of the previous chord. Then capture it, as you did in step 2 above, and repeat the cycle until the phrase is over. In this way, you should create a smoother, more pleasant performance. Don t worry if your tempo is slow. There are lots of notes to find! L10-2 Play one of the exercises (your choice). L10-3 Sing one of the exercises (your choice). L10-4 Perform one of the exercises (your choice).
22 Solutions to Selected Exercises 21 Chapter 11 P11-1 Do exercises a and b. Since you have already learned the minor-mode key signatures, your principal concern in this exercises will be to make sure that you raise the appropriate pitch(es). Example 11-5 displays four circled pitches. They are your responsibility: the accidental must be added manually beside the notehead. Once you establish where an accidental goes, you must then consider which accidental to use: a natural or a sharp. For this decision, consult the key signature. If the given note is a flat note (from the key signature), apply a natural. If it is unaffected by the key signature, apply a sharp. (Since you have studied the double sharp in enhancement I, you may wonder why you will never encounter a sharp note that needs raising by means of a double sharp. That situation does occur, but not in any of the keys that you know. Some of the keys introduced in enhancement III would require a double sharp.) P11-2 Do exercises a and b. In many ways, this exercise duplicates what you have already done in previous chapters. The difference comes in the application of accidentals. In some case (such as exercises c, d, etc.), an accidental appears beside one of the numbers in the figured bass. That s the easier situation: just add that same accidental beside the corresponding notehead when you create the chord. (As a general rule, don t double a pitch to which an accidental is applied.) The harder situation is when no accidental appears in the analysis, but is nevertheless required. In exercise a, for example, the Roman numeral is V. Remember that, in the natural minor mode, the dominant is of minor quality. Here the dominant requested is major! You must take the necessary step to raise the appropriate pitch (the triad s third, which in this case, due to the inversion of the chord, resides in the bass). There is no accidental beside the 6 or 3 of the figured bass because the bass itself, rather than one of the pitches above the bass, is the altered pitch. P11-3 Do exercises a and b. The triads of the natural minor keys include iv (minor), v (minor), and VII (major). When an accidental is employed, using a pitch from harmonic minor or melodic minor, these triads become IV (major), V (major), and vii (diminished). Though there are other alterations of this sort used in music, this textbook introduces only these three. So form your Roman numerals in accordance with the symbols given above. Also remember that the figured bass may need to be modified by an accidental, but only if the accidental applies to one of the noteheads above the bass. If the bass is the modified pitch (as in exercise b), the figured-bass numbers will not be affected.
23 Solutions to Selected Exercises 22 P11-4 Do exercises a c. This exercise is similar to P11-3, but now four-note chords are presented. Don t forget: the figured bass is calculated by counting intervals above the bass the note on the lower staff. Do not restrict your view to only the notes of the upper staff! View all four notes. Exercise b is not in 6 # position. Exercise e is not in 4 5 position. 3 P11-5 Do exercise a. All of the information about phrases and cadences introduced in chapter 10 applies here as well. You must keep in mind the additional considerations (drilled in P11-3 and P11-4) when an accidental appears beside one of the noteheads of a chord. Note that these exercises are performed on the CD-ROM. So you may listen to them as you analyze them. P11-6 Do exercise a. As in chapter 10, the chordal formations are indicated by the circles. If you continue your study of music beyond this chapter, you likely will develop the ability to distinguish between harmonic and non-harmonic pitches. But for now, simply pay no attention to the pitches that are outside the circles. Note that these exercises are performed on the CD-ROM. So you may listen to them as you analyze them. Rhythm Practice Exercises R11-1 Do exercises a and b. Each note or rest value is doubled in the conversion from a meter in which a quarter note represents the beat to a meter in which a half note represents the beat (as in exercise a). If you are converting in the opposite direction (as in exercise b), each note or rest value is halved. R11-2 Do exercise a. The notehead provided at the beginning of each exercise will likely require a stem and may also need to be attached to a beam. P11-5 Do exercises b e. L11-1 Perform one progression (your choice). Answer the cadence question. Follow the instructions for the damper pedal provided for L10-1. L11-2 Play one of the exercises (your choice). L11-3 Sing one of the exercises (your choice). L11-4 Perform one of the exercises (your choice).