Solutions to Selected Exercises 1 - Cengage

Study Guide

Solutions to Selected Exercises

Foundations of Music and Musicianship with CD-ROM

2nd Edition

by

David Damschroder

Solutions to Selected Exercises 1

CHAPTER 1

Pitch Practice ExercisesP1-4 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 mustcount lines and spaces to determine the interval’s size. Remember that the line or spaceof 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 sizerequested. 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 selectas your starting pitch, but it will be easier if you choose a notehead that will allow you toavoid ledger lines. This exercise demonstrates that interval sizes are not additive. Answereach question with interval size and direction, such as “ascending fourth.”

Laboratory ExercisesL1-1 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 toMiddle C. For example, exercises a and c both begin with a pitch named C, but the C ofexercise a is to the left of the C of exercise c. If you were to begin exercise c on MiddleC, your performance would be incorrect.

L1-2 Sing an ascending octave, playing only the lower pitchat the keyboard.

If you know the song, “Somewhere Over the Rainbow” from The Wizard of Oz, then thisexercise is like singing the two notes corresponding to the word “some-where.” Makesure that your first pitch matches the pitch that you are playing on the piano. Alsoremember 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:

1 2 3 4 1 2 3 4 . . .Count out one measure before you begin, and do not speed up or slow down during yourperformance.


Chapter 2

Pitch Practice ExercisesP2-1 Do exercise a and bBoth exercises a and b have two answers, and each answer requires three consecutivescale degrees. Since it takes two scale degrees to make one whole or half step, it takesthree 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 3 is a wholestep. ˆ 4 - ˆ 5 - ˆ 6 and ˆ 5 - ˆ 6 - ˆ 7 would also be correct answers in that case.

P2-2 Do exercise a and b.First, either ascend the scale to ˆ 8 or descend the scale to ˆ 1 to find the tonic pitch. Bothstrategies should lead to tonic. (Remember that ˆ 8 is always the highest pitch of a scale: itis the last note of an ascending scale and the first note of a descending scale.) Once youknow what pitch is tonic, then you might need to add a key signature. (No signature isrequired if C is tonic.) When writing in the scale degree numbers, remember that adescending scale is numbered ˆ 8 - ˆ 7 - ˆ 6 - ˆ 5 - ˆ 4 - ˆ 3 - ˆ 2 - ˆ 1 .

Note: Though the C Major scale is displayed in examples 2-2, 2-3, 2-5, and 2-7 startingon Middle C, any C may serve as the starting point for a major scale.

P2-3 Do exercise a and b.To find ˆ 6 , you may ascend the scale ˆ 1 - ˆ 2 - ˆ 3 - ˆ 4 - ˆ 5 - ˆ 6 . However, it would be simpler in thatcase to descend ˆ 8 - ˆ 7 - ˆ 6 . 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 scalespresented in this chapter. For example, the D of exercise 1 does not occur in the G Majorscale shown in examples 2-4 and 2-7, and yet it is a diatonic in G Major. Imaginestarting with the G above Middle C as ˆ 8 and descending to this D. What scale degreenumber is appropriate?

Rhythm Practice ExercisesR2-2 Do exercise a.Remember that the direction of a stem depends on where a note resides on the staff. Astem that points upward in measure 1 may need to point downward in measure 3. Alsoremember that an augmentation dot goes beside a notehead that is in a space, but in thespace above a notehead that is on a line.

R2-3 Do exercise a.The reminders for R2-2 apply to this exercise as well.


R2-4 Do exercise a.Melodies generally are made of small intervals. Thus you are limited here to intervals nolarger than a fourth, calculating from one note to the next. The last three pitch names areD B C. From D, descend a third to B rather than ascending a sixth. This will require theuse of a ledger line.

Laboratory ExercisesL2-1 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 inthe 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 youbegin. Men, remember to take the melody down an octave or two (that is, to the left onthe keyboard) so that it sounds in your vocal range.

L2-4 Perform one of the exercises (your choice).Remember to count out loud.


Chapter 3

Pitch Practice ExercisesP3-1 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 aninterval with another notehead that is either higher or lower than that C. If the C is thelower of the two noteheads, then it is ˆ 1 in relation to some higher number ( ˆ 2 through ˆ 8 ).If the C is the higher of the two noteheads, then it is ˆ 8 in relation to some lower number(ˆ 1 through ˆ 7 ). Thus, in Exercise 3-1b, the C notehead functions as ˆ 8 , because it is higherthan 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. IfC functions as ˆ 8 , 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 characterizedas 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),ˆ 4 (in G Major), or ˆ 5 (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 keyof C Major. The same results will occur in any other major key, such as F Major or GMajor. ˆ 1 - ˆ 2 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 intervalqualities turn out right. So, starting on C, F, or G as appropriate, and adding a keysignature where appropriate, ascend or descend a major scale to find the intervalrequested.

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.


• 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 ExercisesR3-2 Do exercises a–c.Rest notation has its quirks. For example, sometimes a half rest is appropriate, but atother times two quarter rests must be used instead. And a whole rest might sometimesmean 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 followedby a half rest. Study examples 3-11, 3-12, and 3-13 and their commentary carefullybefore completing these exercises.

R3-3 Do exercise a.Whether notes or rests are employed, the number of beats per measure must correspondto that indicated by the time signature. Remember the rules about stem placement. Don’tforget the double bar at the end.

Laboratory ExercisesL3-1 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 downan octave or two (that is, to the left on the keyboard) so that it sounds in your vocalrange.

L3-4 Perform one of the exercises (your choice).Count the appropriate number (1 2 3 4, etc.) out loud even during a rest.


Chapter 4

Pitch Practice ExercisesP4-4 Do exercises a and b.Take care in positioning the sharp or flat of the key signature if one is required. The sharpof G Major must go on the fifth line in treble clef, and the flat of F Major must go on thethird line. The Roman numeral gives you the information you need to determine where toposition the root. (There will be several choices: for example, if the root is C, you mayuse Middle C or any higher C.) Then add the third and fifth. Though the Roman numeralindicates the triad’s quality (major, minor, or diminished), you do not need to doanything 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 theRoman numeral. If, for example, the root is D in F Major, then, because its scale degreeis ˆ 6 (ascend ˆ 1 - ˆ 6 or descend ˆ 8 - ˆ 6 in the F Major scale to confirm this), the Romannumeral is vi. The Roman numeral is small because, in a major key, the triad rooted on ˆ 6

is always of minor quality. (Review example 4-6, which shows the qualities of all themajor-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 flatand 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 ExercisesR4-3 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 twoeighth notes fall within the same beat, use beam notation. Only if an eighth note joinswith a dotted quarter note or an eighth rest should flag notation be employed.


Laboratory ExercisesL4-1 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 threepitches corresponds to a black key on the keyboard. Also make sure that you are playingexactly the notes written, not the triad an octave higher or lower.

L4-2 Perform two triads (your choice), and name theirqualities.

The triad’s quality is something that you can memorize (example 4-6). But by listening tothe 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 “1 + 2 + …” throughout your performance. The symbol “+” should be pronouncedas “and” (not “plus”!).


Chapter 5

Pitch Practice Exercises

P5-1 Do exercises a and b.You have already completed a similar exercise for the major scale. Now you have achance to attain a better familiarity with the location of whole and half steps in thenatural minor scale. Remember that it takes three pitches to form two intervals, fourpitches 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# andBb 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 givenpitches of this exercise may be higher or lower. For example, the D of exercise 2 does notoccur in the E Natural Minor scale shown in examples 5-4, and yet it is a diatonic in thatkey. Scales can be made higher or lower on the staff, and in either treble or bass clef. Infact, 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 useof 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: determiningthe 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 thefollowing 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 inthe natural minor mode. The second above tonic (ˆ 1 ) is major in both modes. The second,third, and sixth below tonic ( ˆ 8 ) are minor in the major mode and major in the minormode. The seventh below tonic ( ˆ 8 ) 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 keysignature correctly and place the notes on appropriate lines and spaces, the triad quality(major, minor, or diminished) will automatically turn out to be correct.


P5-8 Do exercises a and b.This exercise is the minor-mode equivalent of exercise P4-7. Remember that in naturalminor, 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.

Laboratory ExercisesL5-1 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 inthe 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 threepitches corresponds to a black key on the keyboard. Also make sure that you are playingexactly 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 tothe 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-handfingerings 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 theappropriate syllable arrives. For example, in exercise a, count “1 + 2” and then beginwith the following syllable, “+.”


Chapter 6

Pitch Practice ExercisesP6-1 Do exercise a.Remember that relative keys share the same key signatures, but that a different pitchserves as tonic in each. (Eb Major and C Minor both have three flats in their keysignatures, for example.) In contrast, parallel keys share the same tonic pitch, but theirkey signatures are not the same. (C Major and C Minor both have C as tonic, but do notshare the same key signature.)

P6-2 Do exercises a–c.This exercise helps you to understand where the various intervals reside, merging ideasthat we have learned separately in the contexts of the major and minor modes. For allperfect intervals (the unison, fourth, fifth, and octave), the two modes are identical. Themajor/minor intervals are not so uniform. As recommended in chapter 3, it is a good ideato learn intervals in their inversional pairs: since ˆ 1 - ˆ 2 is a major second (in both modes,in fact), ˆ 2 - ˆ 8 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 andminor in the natural minor mode. The second above tonic (ˆ 1 ) is major in both modes.The second, third, and sixth below tonic ( ˆ 8 ) are minor in the major mode and major inthe minor mode. The seventh below tonic ( ˆ 8 ) is minor in both modes. If this paragraphseems dense and complicated, keep reviewing interval qualities until this becomes crystalclear.

P6-3 Do exercises 1 and 2.Remember that D# (exercise 1) is not the same as Eb (exercise 5). D# will occur only whenthe key signature contains four or more sharps. (Keys with five through seven sharps areintroduced in the text’s enhancement III but will not be explored in our Music 1001course.) 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 assesswhether the interval requested occurs in major keys, minor keys, or both. Be very carefulto distinguish one from the other. There are two keys with tonic C: C Major and CNatural Minor. Both appear on the diagrams of example 6-5. It is a common mistake forstudents to apply the key signature of the parallel key, which may result in an incorrectanswer. Sometimes it does not matter: the perfect fourth above C is F whether oneascends C-D-E-F in C Major or C-D-Eb-F in C Natural Minor. But a minor sixth above Ccan be determined only by ascending C-D-Eb-F-G-Ab in C Natural Minor.


P6-5 Do exercises a and b.Often there are several different routes for achieving the correct answer. It does notmatter which route you use: only that you come up with the correct answer. Always, oneof the two pitches of the question will serve as a tonic in one of the 18 keys that aredisplayed in example 6-5. Your strategy should be to find a key (there may be more thanone correct choice) that contains both of the pitches of the interval. When you havereached this point, determine the scale degrees of the two pitches in the key you haveselected, 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 ˆ 4 ), C Natural Minor (ˆ 1

to ˆ 4 ), F Major ( ˆ 5 to ˆ 8 ), or F Natural Minor ( ˆ 5 to ˆ 8 ). The answer would be Perfect Fourthregardless of the route followed. But if the interval is G# up to E, then only one route ispossible, given the keys that you have learned up to this point: E Major ( ˆ 3 to ˆ 8 ). As youlearned in chapter 3, these scale degrees always form the interval of a Minor Sixth in themajor mode.

P6-6 Do exercises a and b.If you draw the key signature and the noteheads correctly, then the triad quality willalways turn out to be correct. You don’t need to worry about making the iii triad in BbMajor be minor, for example. It will be minor automatically if you do the other steps ofthe 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 youshould have memorized by now. (The information you need is in example 5-8.) On thatchart, notice that I in major keys and III in minor keys are major; that ii in major keys andiv in minor keys are minor, and so on. That is because relative keys share the samecollection of triads. It’s just that, since the tonics of the two keys are a third apart, what isI in one key will be III in the other, and so on.

Rhythm Practice ExercisesR6-1 Do exercises a–c.Remember that a measure in 6

8 contains the equivalent of 6 eighth notes; a measure in 98

contains the equivalent of 9 eighth notes; and a measure in 128 contains an equivalent of

12 eighth notes. Two eighth notes merged together make a quarter note. Three eighthnotes merged together make a dotted quarter note. What kind of note is the equivalent ofsix 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 forgetabout the rules of stem direction. Use a beam when eighth notes occur within the samebeat, but a flag when a single eighth note occurs (along with a quarter note) within a beat.


Laboratory ExercisesL6-1 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 inthe 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 ofthe three pitches corresponds to a black key on the keyboard. Also make sure that you areplaying 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 teachersprefer “1 + uh 2 + uh …,” others prefer “1 2 3 4 5 6 …”.

Please practice using the syllables in the manner of “1 + uh 2 + uh …”. This way youwill better understand how to deal with triplets in chapter 9.


Enhancement I

Pitch Practice ExercisesP.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 thepreceding note. (For example, starting on Bb you would need a natural to create Bn.) Ifthe melodic motion is descending, you need the symbol one to the left of that of thepreceding 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 twogiven notes reside.Step Two: Add whatever accidental is necessary to make the note you added be a halfstep 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 howyou approach it. The text divides the process of creating a chromatic scale into threesteps. (Go back and reread the section titled “Chromatic Scales” again if you are at alluncertain 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 minorscales 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 readthe key signature, you may think the scale goes A-B and add A# as the chromaticpitch. 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.


P.I-4 Do exercises a and b.The instructions for this exercise were carefully written in order to be as clear and helpfulas possible. It’s a challenging exercise which requires that you have a solid command ofthe diatonic situation, as presented in chapter 6, before dealing with the additionalcomplication that the chromatic pitch(es) add. Do not proceed with this chromaticassignment 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 aninterval is raised, then the distance between the two pitches becomes smaller! You needto be very clear in your understanding of example I-9 in order to determine whether anaccidental 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 theinterval size: put the appropriate notehead on the staff. Then assess the situation so thatyou know what quality pertains to the interval at this stage.

Second, add whatever accidental is required to alter the quality appropriately, ifnecessary. (Example I-9 provides essential information.) Remember that only the noteyou add may be modified: keep the given note “as is”!

Laboratory ExercisesL.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. Thisconvention will affect how you interpret the music notation in exercise b. Also, adding aflat beside a notehead that is already flat from the key signature does not imply a doubleflat. 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 implya double flat. It is just a reminder. In exercise b, the last note of the third completemeasure is Eb, not E bb.


Chapter 7

Pitch Practice ExercisesP7-1 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) mayprove 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 fifthwill expand into a perfect twelfth (5 + 7) or a perfect nineteenth (5 + 7 + 7), 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, youneed 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 thechord is constructed. If the Roman numeral is ii, build a triad whose root is ˆ 2 ; if theRoman numeral is VI, build a triad whose root is ˆ 6 ; etc. Though the Roman numeralsindicate chordal qualities, you do not need to worry much about that. If you haveemployed the correct key signature and have positioned the correct noteheads on thestaff, the quality will automatically turn out as indicated.

Rhythm Practice ExercisesR7-1 Do exercises a and b.Work on this exercise by dividing the measure into its component beats. The timesignature will tell you how many beats there are in all. In each exercise, the note you aremodifying 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 thatbeat, use flag notation.

R7-2 Do exercise a.Begin a new beam at the beginning of each beat.


Laboratory Exercises

Chapter 7L7-1 Perform two chords (your choice).Try to avoid the following two common problems: 1) playing pitches an octave too highor too low, and 2) forgetting about the key signature. Take your time positioning yourfingers 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 withoutslowing 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 anywherewithin an exercise. For example, it would be incorrect to count the first measure ofexercise a as follows:

1 2 + 3 ee + ee 4 ee + ee


Chapter 8

Pitch Practice ExercisesP8-1 Do exercises a and b.A triad always appears on three adjacent lines or three adjacent spaces. Its inversion willhave a different form. For the first inversion, move the lowest pitch up an octave; for thesecond 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 todouble. (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 stepsrequired to build inverted chords.

Rhythm Practice ExercisesR8-1 Do exercises a and b.Isolate the beat that contains the arrow, and place the appropriate counting syllablesunderneath the other pitches and/or rests of the beat. Whatever is “left over” must beutilized 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.)

Laboratory ExercisesL8-1 Perform two chords (your choice).Try to avoid the following two common problems: 1) playing pitches an octave too highor too low, and 2) forgetting about the key signature. Take your time positioning yourfingers 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 . . .”


Chapter 9

Pitch Practice ExercisesP9-1 Do exercises a and iClearly distinguish between the concepts of bass and root, and keep in mind how each isused in the analysis of chords. From the bass, one calculates the numbers of figured bass

( 53 ,

63 ,

64 ). 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 movethe notes around so as to form the parent triad, which will always be in the form line-line-line 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 needto read treble and bass clefs simultaneously. You need to be very careful to rememberthat the bass is the pitch on the lower staff, not the lowest pitch of the upper staff. Tocalculate the figured bass, do not by mistake look only at the right-hand notes. In exercise

a, the right-hand notes appear as 53 . But the chord is not in

53 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 usesome scratch staff paper to write out some triads in various keys. Remember that thetriad’s lowest pitch is the “root,” its middle pitch is the “third,” and its highest pitch is the“fifth.”

Rhythm Practice ExercisesR9-1 Do exercise a.Remember to write the number “3” outside a triplet’s beam.

Laboratory ExercisesL9-1 Play one of the exercises (your choice).There is a danger that your triplets will be “lumpy”—that is, that the three componentpitches of a triplet will not be even. (Review example 9-4.) It might be helpful to performthis exercise for a musically sophisticated friend or family member, because moststudents 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.


Chapter 10

Pitch Practice ExercisesP10-1 Do exercise a.The 5

3 position can be inverted into 63 and 6

4 positions. A chord in 753 position has

inversions, too. But they are not introduced in this chapter. (If you are curious, consult

pages 279-281 of the textbook.) Thus your strategy for solving these exercises resembles

what you did in chapter 7, not chapter 8. As with chords in 753 position, the fifth may be

omitted in a 753 chord. If that is the case, then the root must be doubled, because neither the

third nor the seventh may be doubled.

P10-2 Do exercise a.Remember that there are often four different pitches in a 7

53 chord. A common mistake is

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’sroot is D. But that is not the case.

Figured bass always takes the chord “as is.” Do that step first, taking all four pitches intoaccount. Then, you may need to move some notes around so that you can discover whichpitch is the root, as you did in chapter 8. Remember that the Roman numeral isdetermined from the root, not from the bass.

P10-3 Do exercise a.In the major mode, scale degrees ˆ 4 and ˆ 7 , when sounding together, create a specialforward push that composers like to employ. In this exercise, you locate which twopitches correspond to these scale degrees, and indicate the pitches to which their forwardpush 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 apreliminary 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 byexamining all the chords of the progression, the cadence depends on only the last twochords of the phrase. (The earlier chords generally confirm that the phrase is in aparticular key.) In this chapter, all of the phrases are in the major key indicated by the keysignature. 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 asyou analyze them.


P10-5 Do exercise a.Later in the textbook, in enhancement VI, you are provided more details about passingnotes 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 “non-harmonic” notes are left outside the circles, so that you can focus your attention on thechord-building notes which form the harmonies you are familiar with by now. Thus youfollow the same procedure to complete these exercises as you used in P10-4. Treat all thenotes within a given circle as if they occurred at the same moment, with the lowestsounding pitch serving as the bass.


Rhythm Practice ExercisesR10-2 Do exercise a.For the A in measure 1, you may use either a quarter note or two eighth notes connectedby a tie. Remember that when using a tie (also over the bar line between measures 1 and2), the same notehead must be written twice, and connected by the tie symbol. If thestems point downward, the tie is placed above the noteheads; if the stems point upward,the tie is placed below the noteheads.

Laboratory ExercisesL10-1 Perform one progression (your choice). Answer the

cadence question.The right pedal of your piano is called the damper pedal. You could experiment with itwhen 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 cycleuntil the phrase is over.

In this way, you should create a smoother, more pleasant performance. Don’t worryif 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).


Chapter 11

Pitch Practice ExercisesP11-1 Do exercises a and b.Since you have already learned the minor-mode key signatures, your principal concern inthis exercises will be to make sure that you raise the appropriate pitch(es). Example 11-5displays four circled pitches. They are your responsibility: the accidental must be addedmanually beside the notehead. Once you establish where an accidental goes, you mustthen consider which accidental to use: a natural or a sharp. For this decision, consult thekey 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 doublesharp in enhancement I, you may wonder why you will never encounter a sharp note thatneeds raising by means of a double sharp. That situation does occur, but not in any of thekeys that you know. Some of the keys introduced in enhancement III would require adouble 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 theeasier situation: just add that same accidental beside the corresponding notehead whenyou create the chord. (As a general rule, don’t double a pitch to which an accidental isapplied.) The harder situation is when no accidental appears in the analysis, but isnevertheless required. In exercise a, for example, the Roman numeral is “V”. Rememberthat, in the natural minor mode, the dominant is of minor quality. Here the dominantrequested is major! You must take the necessary step to raise the appropriate pitch (thetriad’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, ratherthan 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). Whenan accidental is employed, using a pitch from harmonic minor or melodic minor, thesetriads become IV (major), V (major), and vii° (diminished). Though there are otheralterations of this sort used in music, this textbook introduces only these three. So formyour Roman numerals in accordance with the symbols given above. Also remember thatthe figured bass may need to be modified by an accidental, but only if the accidentalapplies to one of the noteheads above the bass. If the bass is the modified pitch (as inexercise b), the figured-bass numbers will not be affected.


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 lowerstaff. Do not restrict your view to only the notes of the upper staff! View all four notes.Exercise b is not in 6

4 # position. Exercise e is not in 53 position.

P11-5 Do exercise a.All of the information about phrases and cadences introduced in chapter 10 applies hereas 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.


P11-6 Do exercise a.As in chapter 10, the chordal formations are indicated by the circles. If you continue yourstudy of music beyond this chapter, you likely will develop the ability to distinguishbetween “harmonic” and “non-harmonic” pitches. But for now, simply pay no attentionto the pitches that are outside the circles.


Rhythm Practice ExercisesR11-1 Do exercises a and b.Each note or rest value is doubled in the conversion from a meter in which a quarter noterepresents the beat to a meter in which a half note represents the beat (as in exercise a). Ifyou are converting in the opposite direction (as in exercise b), each note or rest value ishalved.

R11-2 Do exercise a.The notehead provided at the beginning of each exercise will likely require a stem andmay also need to be attached to a beam.

P11-5 Do exercises b–e.

Laboratory ExercisesL11-1 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).

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Solutions to Selected Exercises 1 - Cengage