Music Theory

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Music can be defined as organized sound. It is a living language that has been developed over centuries and continues to be refined and reinvented by composers and musicians today. In various parts of the world, different musical languages and "dialects" are used. However, the music written in Europe during the "common practice" period from about 1 !" # 1$"" comprises a very large portion of our musical heritage, and includes such famous composers as %ivaldi, &.'. (ach, Haydn, Mozart, (eethoven, (rahms, %erdi and )agner. Most of the popular music of today still uses the synta* and musical "grammar" of that period. +his type of music is based on both acoustic principles and tradition, constituting what we often refer to as "tonal" music. &ust as words function a certain way within a sentence, chords and rhythms function a special way within tonal music. Even in other types of music # contemporary art, popular, ,azz, eastern, -atin .merican, .frican, /ative .merican # the principles used in western art music can help one to better understand and appreciate the beauty and structure found within each of these musics. 'o whether you are a performer, composer, or simply a person who li0es listening to music, an understanding of how music wor0s is a valuable and essential asset.

+his is intended to be a course of study that will provide a solid and complete bac0ground of the basics of tonal music. 1pon successful completion, it is hoped that you will have an understanding of the fundamentals of the language of tonal music. .lthough it is intended to be a preparation for students hoping to begin music studies at colleges and universities in the 1nited 'tates, it can be of use to anyone who wants to better understand the language of music.


2irst, we need to understand a few terms that are used to tal0 about music. pitch # 3itch refers to what we perceive the fre4uency of a sound to be. 2or instance, the following e*ample consists of three pitches. +he first pitch, .5, has a fre4uency of 66" H7 8cycles per second. +he second pitch, E6, has a higher fre4uency 8 " H79, and so we say it sounds "higher." +he third pitch, .:, sounds "lower" because the fre4uency 8::" H79 is much lower than the first pitch. note # . note is a sound perceived to have a single, constant pitch. rhythm # this is a general term used to refer to when and how long notes occur in time. In the following e*ample, there is a long note, followed by four, even notes, followed by a rhythmic pattern of varying lengths. )hen we try to write down or notate these sounds, we need a system that will allow us to show both the pitch 8how high or low the note sounds9 and rhythm 8how it is played in time9. &ust as an ;#< graph is used to show these relationships in math, music uses a notation system that notates pitch vertically 8higher and lower9 and rhythm horizontally 8forward in time9. 3lay the following e*ample and listen to how the sounds are reflected in the notation. +he following sections in Part One: Fundamentals show how music is notated and read.

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.ctivities for =eview of this section /e*t section> =hythm +able of ?ontents


=hythm is a term we use to describe how music and sounds are placed in time. .s we saw last section, rhythm can be e*pressed by notes with a pitch, li0e a piano, or notes without pitches, li0e a snare drum. Most common practice music has rhythms that conform to a constant, even pulse. +his pulse might be fast 8over 6 pulses per second9 or slow 8less than one pulse per second9. )e often call this pulse the beat 8note> if musicians play a passage very fast or very slow, it may sound li0e there are several pulses per beat or several beats per pulse. it is important to realize that the pulse is what you hear, the beat is what is notated9. +empo is a term we use to describe the rate at which the beats are occuring. =hythmic notation is how we specify where each note begins and ends in relation to the beat. @ur modern system for notating rhythm has a very logical method of describing how long a note should sound. It uses a set of noteheads plus stems and flags to indicate duration. . whole note 8see below9 originally was the standard unit of measure. If it is e4ually divided into two parts, each of these is called a half note. . half note divided into two e4ual parts yields two quarter notes, which are each one 4uarter of a whole note, hence their name. +his process theoretically continues on as far as needed, however in most music, one rarely encounters a note beyond a 5:nd note. +he following chart shows how these notes relate to one another>

+he following e*ample shows the relationship between these notes. Each measure has 6 beats worth of notes. .s you play the e*ample, tap along and listen to how each


measureAs notes are half as long 8so there are twice as many9 as the previous measureAs notes. /otice also that the noteAs value 8Bth, 1 th, etc.9 is also how much of a 6 beat measure that note lasts.

Music also re4uires a method of notating silence. 'ilence is notated by a rest. =ests follow the same hierarchy as notes, as the following chart indicates>

)ith the e*ception of the whole and half, rests are usually centered in the staff. )ith whole and half rests, there is an easy way to remember which is which> )hole rests 8being larger and therefore "heavier"9 always hang down from the fourth line, and half rests 8being smaller9 always float above the third line. )hen a group of notes with flags occur within one beat 8or in vocal music within one word or syllable9 they are beamed together, to ma0e this grouping more apparent to the performer. +he number of beams is e4ual to the number of flags normally found on the note, so a group of eighth notes has a single beam, a grouping of si*teenth notes has two beams, etc. (eaming does not affect how the music sounds, it is only a notational means of ma0ing music easier to read and perform.


+here are two methods used to notate more comple* values. +he first is to use a tie to ,oin two note values together into one, sustained value. . tie is a curved line connecting the insides of the two noteheads. .ny two or more note values may be tied together into longer durations, provided a separate tie is used between each notehead.

. second method uses a dot following the notehead to indicate that the duration is e4ual to one and one-half times the note's normal alue. 'o for e*ample, a dotted 4uarter note e4uals a duration of one 4uarter plus one eighth note, or three eighth notes total duration. . second dot adds half of the dot's value.

. beat may be subdivided into any number of e4ual divisions. )hen the number of subdivisions does not e4ual one of the standard subdivisions listed above, a tuplet must be used. . tuplet adds additional subdivisions to the normal amount that would be e*pected for the rhythmic value employed. If we wish to have three subdivisions of a 4uarter note, 8instead of the normal two eighth notes9 we can use a triplet 8a three#note tuplet9 to accomplish this. +uplets are notated using the ne*t longest rhythmic value and have a number 8with an optional brac0et if there is no beam9 over the grouping.

Listenin" e#ample
-isten to the following e*ample that ma0es use of the above rhythmic considerations. -isten to it and tap or sing along several times,, trying to tap or count the subdivsions during longer note values.


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.ctivities for =eview of this section /e*t section> Meter +able of ?ontents

Most music has a consistent grouping of beats, and within these groupings of beats we find that some receive more emphasis than others. -isten to the following e*ample.

<ou probably found yourself counting or tapping along in a pattern li0e this> %...:...5...%...:...5...%...:...5... <ou also probably heard this e*ample in terms of three#beat groupings. Each of these groupings is called a measure. (eat "1" received more emphasis in our minds, even though it was no louder than the other notes. +his organization of notes into structured groupings is called meter. +here are three types of meter> simple, compound, and asymmetrical.

&imple $eter


In simple meter, each beat is normally subdivided into two parts, and the note receiving the beat is always a standard single note value 8i.e. a 4uarter, half, eight, etc.9 In musical notation, this is indicated by a time signature, which provides information on how many beats are in each grouping, and which note value receives the beat. . time signature is notated by two numbers, one above the other, at the beginning of each piece and whenever there is a change of meter in the wor0. In simple meter> +he top number indicates the number of beats per measure. +he 'ottom number indicates the rhythmic note value that receives the beat. 2or e*ample, a meter with 5 beats per measure with the 4uarter note receiving the beat is called "5C6" time, and is notated with a "5" in the top number and a "6" in the lower number.

+he time signature of "6C6" is so commonly used that publishers and composers often abbreviate it with a "?" for common time. . "?" with a slash through it indicates "cut time" which is e4ual to ":C:"

-isten to each of the following e*amples of music in these commonly found meters. (n )#ample of *+, time si"nature music:


(n )#ample of -+, time si"nature music:

.ompound $eter
?ompound meter is used to notate music that has three instead of two subdivisions per beat. .n e*ample is the familiar tune> "=ow, =ow, =ow <our (oat".

<ou probably found yourself tapping or counting in a pattern li0e this> %...:...%...:...%...:... Most people hear this e*ample in terms of two#beat groupings. However, when they get to "mer#ri#ly, mer#ri#ly, mer#ri#ly, mer#ri#ly, ..." they usually divide each beat into three notes instead of the normal two. In fact, the entire piece has three subdivisions per beat. 8-isten again, counting a fast % # : # 5... * # : # 5... % # : # 5... * # : # 5... 9 In compound meter, each beat is normally subdivided into three parts, and the note receiving the beat is always a dotted note value 8i.e. a dotted 4uarter, a dotted half, a dotted eight, etc.9 +his is because a dotted note value may always be easily divided into three e4ual notes 8i.e. a dotted 4uarter D 5 eighth notes9. (ecause time signatures consist of whole numbers only, the numbers in a compound meter time signature indicate the number of su'di ided values. In compound meter> +he top number indicates the number of su'di ided beats per measure. +he 'ottom number indicates the rhythmic note value that receives the su'di ided beat. (ecause the subdivision is always by three, the top number in a compound time signature will always be a multiple of three> , $, or 1: being the most common. .s an e*ample, a meter with 5 beats per measure 8each su'di ided into 5 parts> 5 * 5 D $9 with the dotted 4uarter note 8or su'di ided into three eighth notes9 receiving the beat is called "$CB" time, and is notated with a "$" in the top number and a "B" in the lower number.


In compound meter, the number of 'eats per measure is always the top number divided by three. 'o a " " in the top number means that there are "si* divided by three" beats, or two beats per measure. (n )#ample of /+0 time si"nature music: (n )#ample of 1+0 time si"nature music: +o 0eep the difference between simple and compound meter straight, remember>

&I$PL) $)(2& 3))P I! &I$PL)4
In simple meter, the top number is the number of beats and the bottom number is the note value receiving the beat.

.O$PO526 $)(2& &5B6I7I6)6 B8 !9R))
In compound meter, the top number is the number of su'di ided 'y - beats and the bottom number is the note value receiving the su'di ided 'y - beat.

(symmetrical $eters
Modern composers have fre4uently made use of meters that have an odd number of subdivisions, which means that the measure cannot be divided into e4ual beats. +hese meters are called asymmetrical meters. .lthough there have been a number of different methods of notation used throughout the twentieth century, the traditional method of notating these time signatures is fre4uently used.


+his type of meter is easy to recognize, since the top number is an odd number. .symmetrical meters may behave li0e simple or compound meters, however, if the lower number is : or 6, it usually will behave li0e simple, if B or greater, it usually will behave li0e compound. In order to determine the beat groupings, however, one must pay careful attention to the beams indicated in the music.

/otice also that the meter may change in the middle of a wor0 in any measure. +he new time signature remains in effect until the end of the piece or another time signature occurs. It is also important to note that there may only be as many beats in a measure as the time signature allows. In :C6 there should be e*actly : 4uarter notes total in each measure. +he only e*ceptions are when a composer notates a cadenza, which is a free, non#metered solo, or in the very first and last measures of a piece. 'ometimes, rather than beginning the first measure with rests, composers will use an anacrusis or "pic0 up. )hen this occurs, the last measure of the piece must be reduced by the total rhythmic value of the anacrusis, so that the entire piece has a full number of beats that matches the meter8s9 employed.

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.ctivities for =eview of this section /e*t section> 3itch


.ll sounds that are perceived as being the same pitch have the same audio fre4uency whether played on a guitar, piano or sung. 3itches are the basic building bloc0s of music. +o tal0 about pitch in general, we use a series of seven letters, ., (, ?, E, E, 2, and F. +hese letters match the white 0ey pattern found on standard musical 0eyboards and pianos>

/otice how the first and last notes sounded similar. (oth are ?s, but one is higher than the other. +his is because of the relationship between the fre4uencies> the lower one, middle c, has a fre4uency of : 1. H7, and the higher one is twice the fre4uency of that 8!:5.: H79 +his type of relationship is called an octave 8coming from the prefi* "octa" meaning eight. /otice that there are eight steps between the two ?s.9 )hen two pitches have the same letter, we say that they belong to the same pitch class.

If we loo0 at a full piano 0eyboard, we will see that it has a pattern of the above 1: notes, repeated seven times 8plus a few 0eys9 for a total of BB notes possible. Each ? is a pitch two times the fre4uency of the ? below it. 'ince all octaves e*ist in this relationship, we


often spea0 of pitch in general terms, such as " ... a chord with ?, E, and F ..." However, when we wish to specify a specific pitch, we also need to specify in which octave it occurs. +here are several ways musicians have specified these different pitch classes. +he figure below shows the two most popular>

)e use the same number for each of the pitches in the octave above each ?. 'o the note right above ?6 is called E6, the white 0ey note above that is E6, etc. +he note right below ?6 is called (5 8it belongs to the octave below9. ?6 8or cA in the old system9 is often refered to as "middle ?." not only because it occurs almost in the middle of the piano, but also because it occupies a central location in our musical notation system, as we will now see.

$usical 2otation
)hile letters are fine when spea0ing about music, they arenAt very practical when actually reading or playing music. In standard musical notation, the pitch is notated with a slanted ovals called noteheads on a system of lines and spaces called a staff. +here are five lines on each staff, each line and space representing a different note. .t the beginning of the staff there is a symbol called a clef which tells us what pitches are assigned to each of the lines and spaces. +o write a pitch that is above or below the five lines of the staff, we can either add a temporary e*tension called a ledger line or change to a new clef that includes the pitch.

+he above clef is called a treble clef. ?6 8middle ?9 is located on the first ledger line below the staff. .s we move up each line or space, we move to the ne*t pitch class. +here are three other clefs commonly used today> .lto ?lef>


+enor ?lef

(ass ?lef

3iano music use two staves, one treble clef and one bass clef, which together are called a grand staff. /otice that this allows for a little "overlapping" using ledger lines. .lso notice that the note right in the middle is "middle c"G

/otice that there are also narrower blac0 0eys between certain white 0eys on the piano. Each step up one 0ey, whether white or blac0, is called a half step. /otice that between the white 0eys of E#2 and (#? there is no blac0 0ey. +his is also a half step. +he distance between every other 0ey, whether white or blac0, is called a whole step. )e refer to the blac0 0eys by adding a symbol to one of the pitch class letters ne*t to it.

. sharp means the pitch is raised one half step.

. double sharpmeans the pitch is raised one whole step. . flat means the pitch is lowered one half step.

. double flat means the pitch is lowered one whole step.

. natural cancels whatever accidental previously applied to the note.


/otice that 2 sharp and F flat occupy the same 0ey on the piano. +he relationship between pitches that "overlap" and occur on the same piano 0ey is called an enharmonic relationship. 2 sharp is an enharmonic of F flat. .lthough they may sound the same they are actually two distinct pitches, and function differently in tonal music. +his dual function is li0e a person who may be called "Er. 'mith" by his or her students at school but is called "Mommy" or "Eaddy" by his or her child at home> he or she is the same person, but functions in different roles at school and at home. &ust as you wouldnAt call your teacher "Mommy", donAt call a F flat an 2 sharpG

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.ctivities for =eview of this section /e*t section> 'cales +able of ?ontents


. scale is an ordered pattern of pitch classes that fill in the space of an octave. +his pattern may be composed of any number of pitch classes in any pattern. @ne of the most basic scales is the chromatic scale, which consists of all 1: pitch classes>

+he chromatic scale consists of a pattern of all 1: pitch classes, each 1C: step apart. If we form a scale using only include the white 0eys, and start on ?, we get the following scale>


/ow we have a scale consisting of seven pitch classes in the following pattern 8where wD whole step or two 1C: steps and hD 1C: step9> If we start the scale on another pitch class, ( for instance, but still include only the white 0eys, we get a different pattern of whole and half steps, which results in a different scale>

+he music of the "common practice" period is based on scales primarily derived from the various white#0ey scales, which also form scales on the staff without using accidentals. Each has a different pattern of whole and half steps, resulting in a different sound or feel. +hese scales are refered to as modes. +he ancient Free0s used various modes to stimulate different emotions and early theorists adopted these Free0 names to their modes as well 8even though we canAt be sure what the e*act patterns of the ancient gree0 modes were9. Historically, some of these modes were prefered over others, with two modes, the Ionian and .eolean being used most commonly. +he Ionian mode is better 0nown today as the ma,or scale and the .eolian as the minor scale. $a:or &cale ;Ionian<






$inor &cale ;(eolian<


)hen using the common practice modes and scales, we can refer to the various pitch classes of the scale by their scale degree. +he first note of the scale is scale degree 1, and is also called the tonic. +he second is scale degree :, the third is scale degree 5, etc. # until we arrive at the tonic again. +here are seven 8H9 scale degrees in each of the common modes. +he scale pattern may begin on any pitch class. .s long as the pattern of whole and half steps remains the same, it is still heard and identified as the same type of scale. However, accidentals need to be added in order to form these patterns. 2or e*ample, to form a Ma,or 'cale begining on E, we need to raise scale degrees 5 and H by a half step 8we do this by adding a sharp to these pitches9 to form the correct pattern of whole and half steps. +he E Ma,or scale has the same pattern of wholeChalf steps # identical to the ? Ma,or scale. )hen we move a scale or a pattern of notes to a new pitch level, we say that we have transposed it. ?ompare the sound of the E Ma,or scale to the ? Ma,or scale as notated above 8Ma,orCIonian9. 6 $a:or &cale:

E Ma,or 'cale> ? Ma,or 'cale>


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.ctivities for =eview of this section /e*t section> Iey 'ignatures +able of ?ontents

3ey &i"natures
In the last chapter, we found that by adding sharps or flats to various scale degrees, we could form a ma,or or minor scale beginning on any pitch class. 'ince these accidentals are used consistantly within each scale, we can use a key si"nature to indicate them. . 0ey signature is a standardized collection of all the sharps or flats used in a scale, occuring at the beginning of each staff. 2or e*ample, instead of adding a flat to each of the notes of a melody built on a E#flat ma,or scale, we can use a 0ey signature to indicate them. +he accidentals used in the 0ey signature apply to all of that pitch class throughout the music ## for e*ample, a (#flat in the 0ey signature means that all (As , in all octaves, are now lowered to (#flat without having to add an accidental. 8'ee the figure below9

In 0ey signatures, the sharps and flats are arranged in a specific order and position. .s the following chart shows, the first sharp is always 2#sharp, and is always located in the same position. +his is the same for all of the 0eys> each 0ey adds another sharp or flat. It is important to memorize the order and arrangement of sharps and flats for all 0eys. +his is part of our basic musical language. &ust as the order of letters within a word is important, 8"teh" and "the" are not the same9 the order of the sharps and flats is also important. )e usually group both the ma,or and minor 0eys together, so that one sharp is the 0ey signature for both F Ma,or and e minor. +his related minor 0ey 8related via the same 0ey signature9 is called the relative minor.


/otice that as you add sharps, each new 0eyAs tonic is the same as the fifth scale degree of the previous 0ey. .s you remo e flats, the new 0eyAs tonic is the same as the fifth scale degree of the previous 0ey. .nother interesting point to note is that at the point of si* flats and si* sharps, the 0eys are F#flat and 2#sharp Ma,or 8and e#flat and d#sharp minor9 # which are enharmonically e4uivalent. +his has the result of forming a 0ind of loop, or cirle around which the 0eys progress in fifths. +his can be summarized by the following chart, showing a simple presentation of the relationships between all ma,or and minor 0eys called the circle of fifths>


J 3K If we move cloc0wise, each new 0ey is build on the fifth scale degree of the previous 0ey. ) ery musician should ha e all of the key si"natures for all keys ;ma:or and minor< memori=ed4 (eing able to "figure it out with enough time" is li0e having to spell each word outloud before you can read it> itAs a starting point, but itAs not "reading music".

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.ctivities for =eview of this section /e*t section> Intervals +able of ?ontents


Inter als
.n interval is distance between two pitches. Intervals can be harmonic, with both pitches sounding at once, or melodic, when one pitch follows another.

Feneral Intervals are based on scale degrees. +he following chart diagrams all of the intervals within one octave>

However, within ma,or and minor scales, some scale degrees are only one half#step apart 8between scale degrees 5#6 and H#19 while the others are a whole step apart. 'pecific intervals refer to the precise distance between pitches. Eerived from the ma,or scale, the following chart lists the 3erfect and Ma,or intervals 8notated by an uppercase "3" or "M" plus the general interval9 and the number of half steps they represent. )hen read out loud, they are read as "Ma,or 'econd", "3erfect 2ifth", etc.

Minor intervals are one#half step smaller than their ma,or counterparts and are indicated by a lowercase "m". Most are found in the minor scale. /otice that the intervals of an octave, fifth and fourth are identical in both ma,or and minor scales. +hese are also the intervals that are mathematically the most pure. +his is why they are referred to as perfect intervals. +hey are neither ma,or nor minor> they are perfectG


?ombining the above specific intervals yields the following chart. +here are two intervals that are missing> the single half#step 8a minor second9 and the interval of half steps between the 36 and 3! which is called the tritone 8because it consists of 5 8tri9 whole steps 8tones99.

Chart of Specific Intervals
Specific Interval unison m2 M2 m M "! $ritone "# m% M% m& M& "' )oct*+e, ! # % & ' ( 10 11 12 Size (# of half-steps) 0 1 2

)hen accidentals are added to pitches, they may e*pand or contract beyond the perfect, ma,or or minor size. )hen a half#step is added to perfect or ma,or intervals, they become au"mented. )hen a half#step is su'tracted from perfect or minor intervals, they become diminished. )e add a plus sign "L" to the general interval for augmented intervals, and a small circle "o" to the general interval for diminished intervals.


+he following chart shows how "augmenting" 8enlarging9 and diminishing 8reducing9 intervals by a half#step alters their specific interval size ## 2O! the general interval. +he general interval always remains the same regardless of how it it altered by accidentals. 'o a m: reduced by a half#step becomes a o:. . 3! increased by a half#step becomes an L! 8/@+ a m 9.

decreased 'y a half-step 'ecomes: diminished o minor m diminished o doubly diminished 8rare9 3erfect or Ma,or 8depending on interval9

Ori"inal Inter al 3erfect 3 Ma,or M minor m

enlar"ed 'y half-step 'ecomes: augmented L augmented L Ma,or M 3erfect or minor 8depending on interval9 doubly augmented 8rare9

diminished o

.ugmented L

/otice that the augmented fourth and the diminished fifth both contain half steps. .lso, an augmented second and a minor third both contain 5 half#steps. &ust as the pitches are enharmonically related, intervals that contain the same number of half#steps are referred to as enharmonically e4uivalent intervals. It is important, however, ,ust li0e with enharmonic pitches, not to change the general interval> a fourth always remains a fourth, whether perfect, augmented or diminished. Even though enharmonically e4uivalent intervals contain the same number of half#steps they may function differently in tonal music, and should never be referred to as their enharmonic e4uivalent.


Inversion of Intervals

/otice that if the lower note of an interval is raised one octave, the interval sounds similar to the original. +his is called in ertin" the interval.

+he following table lists all of the standard intervals and their inversions. /otice the pattern> *nds in ert into >ths -rds in ert into /ths ,ths in ert into ?ths $a:or inter als in ert into minor inter als Perfect inter als in ert into Perfect inter als 6iminished inter als in ert into au"mented inter als@ .lso notice that the chart only has to list up to the interval of a tritone> all intervals larger than that have already been listed.

Importance of Reading Intervals

Intervals are the building bloc0s of tonal harmony. It is vital to the understanding of music theory to be able to 4uic0ly and accurately recognize interval sizes. .t first you may need to count the scale degrees to determine the general interval size and count the number of half#steps to determine the specific interval, but eventually, you should be able to recognize most intervals at sight. &ust as one wouldnAt be able to read very 4uic0ly if you needed to spell out each word 8 c#a#t is "cat"9 one cannot read music effectively without being able to recognize intervals 4uic0ly. Here are some hints to ma0e reading intervals easier at first>


Inter al Identification 9ints:
1. -ener*. inter+*.s become e*sier when one .e*rns to reco/ni0e the 1*tterns o2 the inter+*.s on the st*22. Secon3s *re e*sy4 they *re ri/ht ne5t to e*ch other. $hir3s both on *36*cent .ines or both on *36*cent s1*ces. 7otes * 2i2ths *1*rt *re two .ines or s1*ces *1*rt. Se+enths *re three. A 2ourth is between * thir3 *n3 2i2th8 *n3 * si5th is between * 2i2th *n3 se+enth. 2. 9or 1er2ect inter+*.s4 with the e5ce1tion o2 the inter+*.s between *ny B *n3 98 )sh*r18 n*tur*. or 2.*t, i2 the *cci3ent*.s m*tch )i.e. both *re 2.*ts, it is * 1er2ect inter+*.. $his is * he.12u. hint8 since the i3enti2ic*tion o2 1er2ect 2i2ths is b*sic to ton*. music. Between B *n3 98 one must memori0e th*t B:2.*t to 9 is * 1er2ect 2i2th *n3 B to 9:sh*r1 is * 1er2ect 2i2th. . ;n3oubte3.y8 you wi.. be/in to .e*rn to reco/ni0e cert*in inter+*.s be2ore others. 9or inst*nce8 you m*y *.re*3y reco/ni0e the inter+*. < u1 to = *s * M 8 since the < sc*.e is one o2 our most b*sic *n3 common sc*.es. ;se these e*si.y reco/ni0e3 inter+*.s *s 1oints o2 re2erence to reco/ni0e c.ose inter+*.s. 9or inst*nce8 i2 < u1 to = is * M 8 then we c*n >uic?.y reco/ni0e th*t < u1 to =:2.*t is * h*.2 ste1 .ower8 bec*use o2 the 2.*t8 *n3 so it must be * m . Simi.*r.y8 * m% is one h*.2 ste1 .*r/er th*n * 1er2ect 2i2th. A M& is * h*.2 ste1 sm* th*n * 1er2ect oct*+e8 etc. !. "r*ctice re*3in/ *n3 .istenin/ to them unti. you c*n e*si.y reco/ni0e *.. inter+*.s :: not 6ust the e*sy ones. $here *re m*ny so2tw*re 1ro/r*ms on the Internet *n3 on the commerci*. m*r?et to he.1 with this8 but 1r*ctice is sti.. the best w*y to .e*rn@

o o o Acti+ities 2or Re+iew o2 this section 7e5t section4 $en3ency $ones *n3 Minor Sc*.es $*b.e o2 <ontents

!endency !ones and $inor &cales


.s we saw in the prevous section on scales, the ma,or scale has the following pattern of whole and half#steps >

/otice how strongly the second to the last note, the (, needs to resolve to the tonic ?. )hen a certain tone has a strong pull toward another, we call it a tendency tone. /otes that are only a half#step apart commonly function as tendency tones. /otice that the 6th scale degree, 2, also is only a half#step from E. However, since scale degree H pulls toward the most stable pitch, the tonic, it is the most important tendancy tone.

In a natural minor scale, however, the seventh scale degree is not a half#step from tonic, but rather a whole step 8see the following figure9. +his reduces the "pull" toward the tonic.

(ecause the resolution of the half#step between scale degree H and tonic is so important to tonal music, composers have fre4uently used a raised scale degree H in the minor scale. +his also supports the harmonic function in minor 0eys 8this will be discussed in the later section on harmonic function9. 2or this reason, it is called the harmonic minor scale. . harmonic minor scale is a natural minor scale with a raised scale degree H.

/otice in the above e*ample that by raising the scale degree H, the unusual interval of an augmented second is formed between scale degrees and H. +he half#step between scale degrees and ! cause scale degree to behave as a tendency tone, resolving to scale


degree !. .s a result, melodies in minor 0eys fre4uently avoid the harmonic minor scale, because of this difficult interval. Instead, composers will usually alter the scale degree on ascending passages, and use the natural minor scale on descending passages. +his form of the minor scale is called the melodic minor scale.

. melodic minor scale raises scale degrees and H on the way up, and lowers them bac0 to their natural minor form on the way down. +his results in a scale that 0eeps the half# step between scale degree H and tonic, yet avoids augmented intervals. +he following is a melody that uses the melodic minor scale. /otice that every time that scale degrees or H continue upward, they are raised. )henever they resolve downward, they are lowered.

Relationships Between Major and Minor Keys

.s we noted in the section on 0ey signatures, minor scales built on the si*th scale degree of a ma,or scale have the same 0ey signature. +his is called the relative minor to the ma,or 0ey 8or relative ma,or to the minor 0ey, depending upon from which you are starting.9 2or e*ample> in 2 Ma,or, the si*th scale degree is the pitch class "E">
F Major (1 flat ! d minor relative minor

. second type of relationship e*ists when the tonic is the same> i.e. ? Ma,or and c minor. +his is called the parallel minor 8or ma,or9. .n easy way to find the 0ey signature for the parallel minor of any ma,or 0ey is to add 5 flats 8or remove 5 sharps9 from the 0ey signature. 2or e*ample>

HARQIB HARIS/AHMAD ARSHAD_ISL C Major (" flats # $ flats ! c minor ($ flats F% Major (& sharps ' $ sharps ! f% minor ($ sharps ((( Remem)er ((( Relative *eys have the same *ey signat+re ,arallel *eys have the same tonic

o o o

Acti+ities 2or Re+iew o2 this section 7e5t section4 "AR$ $AB4 $he B+ertone Series $*b.e o2 <ontents


!he O ertone &eries
.s we noted in the section on pitch, an octave consists of two pitches whose fre4uencies are in the ratio of 1>: 8i.e. ."D !!hz and .1D11" hz9. +he upper pitch, being a perfect multiple of the lower, acoustically reinforces it, resulting in what we call a consonance. If we continue to add new pitches that are multiples of the fundimental, we call these multiples overtones or harmonics. +he original pitch on the bottom is called the fundamental. Each multiple is called an overtone 8or harmonic9. +he following chart shows the first fourteen overtones above the pitch ?1>

/ote that some of the overtones are slightly out of tune with our )estern tuning scales. +hese notes are shown in parentheses. +he overtone series forms the basis for tonal music of the common practice period. It is important for musicians to be familiar with the overtone series in order to understand why music functions as it does.

Ahat can we learn from the o ertone seriesB
If we loo0 at the interval of each note above the fundamental 8reducing those greater than an octave9 we discover that the perfect intervals of P0 and P? are closest to the fundamental. +hese most strongly "fit" or reinforce the fundamental, forming what we call a consonance. .s we move from left to right 8farther away from the fundamental9 the fre4uencies are not as closely related, and so we consider those intervals more dissonant. /otice that the interval 36 does not appear until far into the overtone series. +his is why for many years 81"""#1H!" c.a.9 musicians considered the seemingly "perfect" interval of


36 to be a dissonance. In fact, it wasnAt until appro*imately the year 15"" until a third was considered "consonant"G

.lso important is the set of intervals between each of the notes. Including the intervalic inversions, we may derive a more comprehensive chart of relative consonance and dissonance that has influenced musicians of all periods. 'ince the tritone does not appear in the series, it is the most removed or dissonant interval. @ne may also thin0 of consonance and dissonance in terms of harmonic stability and instability, since this is how composers have used these intervals in their music.

+his forms the basis for the theory of tonal harmonic function, which will be e*plored in the following sections.

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/e*t section> ?hords 8+riads and 'eventh ?hords9 +able of ?ontents


. chord is a collection of three or more pitch classes that sound together. 8)hen only two pitch classes sound together, it is simply an interval.9 ?hords in the tonal system are based on the three most stable pitch classes of the overtone series 8fundamental plus the first ! overtones9 /otice that the resulting chord is composed of pitch classes that are each a third apart. +onal harmony is based upon this principle of chords containing stac0ed thirds. +his is also referred to as tertian harmony.

'ince there are three pitch classes present, this is referred to more specifically as a triad. +he lowest pitch class of a triad is called the root. +he names of other notes of the triad are derived from their interval above the root> the third and the fifth. . diatonic triad may be built on any scale degree by adding a third and a fifth above it>

/otice that although the triads all consist of stac0ed ma,or and minor thirds, they may be in different combinations. 2or instance, the triads built on scale degrees 1, 6, and ! consist of a $- on the bottom and a m- on the top. )e call this a ma:or triad. +he triads built on scale degrees , :, M 5 consist of a m- on the bottom and a $- on the top. )e call this a minor triad. (oth are stable chords because of the 3! interval formed by the combination of the two thirds.


+he triad build on scale degree H is different. It consists of two minor thirds that result in a diminished !th when combined. )e call this type of triad a diminished triad. . fourth and more rare type of triad results when two Ma,or thirds are combined, resulting in an augmented !th. )e call this type of triad a augmented triad. (ecause these triads contain the unstable intervals of a o! and L!, these are unstable chords.

&e enth .hords
(y adding another third on top of a triad, we create a more dissonant chord that includes the interval of a Hth9. +his type of chord is called a seventh chord. -i0e triads, the names of other notes of the seventh are derived from their interval above the root> the third and the fifth and the se enth.

'ince four pitch classes are present there are more combinations of ma,or and minor thirds possible. In tonal music, however, only certain combinations are used. +he following chart lists the seventh chords that function in tonal music>


('re iation

)#ample ;click to play<

Ma,or +riad Ma,or Hth


Ma,or +riad minor Hth 8Eominant Hth9



minor triad minor Hth


diminished triad minor Hth 8half#diminished Hth9


diminished triad diminished Hth 8fully diminished Hth9


'eventh chords built upon augmented triads are e*tremely rare, as are minor triads with a ma,or seventh and ma,or or minor triads with diminished sevenths.

9armonic 7oca'ulary
,op-.a// Chord Sym)ols

+here are several common ways to refer to various chords. +he most general method is used in popular and ,azz music and involves refering to the pitch class that serves as the root of the chord. .lterations to the basic chord, or added tones such as sevenths are notated with additional symbols. +his system of notating chords does not specify how the chord functions or relates to other chords, but is a very simple and easy way of specifying the 4uality of the chord. +he following table lists this method>

.hord !ype Ma,or +riad

.hord &ym'ol ?apital letter of root i.e.> .


Minor +riad

?apital letter of root plus "m" i.e.> 6m ?apital letter of root plus "L" i.e.> BD ?apital letter of root plus "dim" i.e.> .Ndim

.ugmented +riad

Eiminished +riad

2dditions-2lterations to 0riads

Ma,or 'eventh

+riad as above plus "ma,H" i.e.> . ma:> +riad as above plus "H" i.e.> E > +riad as above plus "H" i.e.> 6Ndim > add a sharp or flat followed by the chord tone 85, !, H, etc.9 that is to be altered i.e.> 6m > N? same as a minor chord, minor seventh, with a lowered !th i.e.> .m > '?

Minor 'eventh 2ully Eiminished 'eventh ?hord

.ltered chord tones

Half Eiminished 'eventh ?hord

Roman 3+merals

.nother way of specifying chords that reflects their relationships to a particular 0ey uses roman numerals to indicate the scale degree upon which the chord is built instead of pitch names. In this method, the roman numeral is upper case for ma,or 8and augmented chords9, lower case for minor, and lower case plus the small superscript "o" for diminished triads. However, in this method, the 0ey of the music must always be specified in order to determine the e*act pitch classes present in the chord. +his method also uses a "H" to indicate seventh chords but does not need to specify the type of seventh, since it is assumed that the seventh will be whatever pitch class would normally occur within that 0ey. 8/ote> the vii chord is a special e*ception to this and uses the "o" for fully diminished seventh chords and "O" for half diminished seventh chordss.9


/otice that this method defines chords according to their relationship within a 0ey, thus providing a means of discussing functional relationships of chord progressions. 2or this reason, this the prefered method of defining chords for the discussion of harmonic function in music theory.

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7e5t section4 In+ersion o2 <hor3s $*b.e o2 <ontents

.hords in $usical Practice
.lthough chords may appear in their pure, simple form, in musical practice the notes of the chord are fre4uently arranged in a wide variety of manners, depending on the style and effect the composer intends.

.horale &tyle
+he simplest style is often found in church music and was originally written for voices to sing. +his "voicing" 8arrangement style of the notes of the chords9 is called ?horale style. In a pure chorale style, all of the notes move along at appro*imately the same rate, which is often referred to as a homophonic 8all voices sounding at once9. In this style, it is easy to recognize the chords. In chorale style, there are two common arrangements of the chord tones> open 8or '.+( choral voicing9, where the notes are arranged evenly between the top and bottom notes, ma0ing it easy for each voice to sing their part. +he second common arrangement is close 8or 0eyboard voicing9 where the top three notes are all within one octave, ma0ing it easy to play on 0eyboard instruments with the upper


three notes played in the right hand and the bass line with the left. +hese are both shown in the following e*ample> Open + .horale 7oicin":

.lose + 3ey'oard 7oicin":

?omposers of chorales fre4uently embellish the voices to ma0e the music more interesting. In many cases, each voice is embellished so much that we can no longer call it homophonic, but must label it polyphonic 8several separate, individual voices sounding at once9. If all voices have a strong, even harmonic pulse as well, this may still be considered a chorale style, as the following e*ample shows. Polyphonic .horale

)e will e*amine the embellishing tones more closely in 'ection 1 .

(rppe"iated &tyle
In 0eyboard music written for non#sustaining instruments li0e the piano and harpsichord, or pluc0ed instruments li0e guitar, the chorale style does not wor0 as well, since the sound dies away 4uic0ly. Music written for these instruments 8and also for larger ensembles9 often uses a techni4ue called arpeggiation, where one voice or instrument plays the individual notes of the chord in succession, rather than all at once. )hen played rapidly enough, they are still perceived as all part of the same chord. -isten to the


following two e*amples of the same chords, one in chorale style, the other in an arpeggiated style> Block .hord and (rpe""iated &tyles

+his style was very common in the piano music of )... Mozart and composers of the common practice period. @ne popular manner of arpeggiating the chord alternates between chord tones in the pattern of "bottom # top # middle # top" and is commonly refered to as an .lberti (ass. (l'erti Bass

/otice how you still are able to hear the same chords in the arpeggiated style, even though the whole chord is never actually played at once. )hen analyzing music of this style, one must group together all notes that form chords, and treat them as if they were sustaining. +hese notes are then rewritten in a bloc0 chord 8chorale # 0eyboard9 style for easier analysis, 0eeping them in their same pitch locations 8i.e. the lowest note is still the "(ass" note9. +here may be an occasional embellishing tone in the arpeggiation, but you can usually recognize these by the fact that they are fewer and "donAt fit" in with all the other notes. Embellishing tones are not included in this simplification. +his process is called harmonic reduction>


9armonic Reduction of $o=art: Sonata K545

.fter doing a harmonic reduction, it is much easier to see and label the chords. @nce the chords have been identified and labeled, the harmonic function can be identified, which is the topic of the ne*t section.

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/e*t section> (asic Harmonic 2unction +able of ?ontents

Basic 9armonic Function Back"round
In previous sections, we have e*amined how the overtone series has aided in the development of chords, scales and the tonal system. -i0e these other aspects of music, harmony also functions according to some of the primary characteristics of the overtone series. However, since music is both an art and a science, historical tradition and various styles of composers have influenced what we hear as "sounding right". )hen discussing harmonic function in music, it may be helpful to thin0 of it similarly to the function of grammar in a written and spo0en language. +here are general principles that, when followed, allow for a clear and a logical presentation of ideas. 'imilarly, when tonal harmonies follow certain principles, the music seems to move forward more strongly. )hen chords follow these principles, we say they are following a progression. )hen they move the opposite of a progression, it is called a regression. In some cases, chords may not clearly progress or regress ## this is labeled a chord succession. /otice that we are loo0ing only at the roots of these chords at this time 8i.e. only the roman numerals9 and not necessarily the (ass note of the chords.


Root $o ement 5p 'y Fourth+6own 'y Fifth
2rom the overtone series, we learned that the tonic is the most stable pitch class within a 0ey, being lowest on the series. +he dominant 8scale degree !9 is ne*t in the series, which acoustically has a tendancy to want to resolve to tonic. +he 7 chord also contains scale degree H, which also has a tendancy to resolve to tonic. .s a result, the dominant triad has a tendency to most strongly want to resolve to the tonic triad. +his forms a 7 - I progression, and is the strongest type of progression in tonal music. It is even stronger when a seventh is added to the dominant triad, since scale degree 6 8seventh of the 7 chord9 has a tendancy to resolve to scale degree 5 8third of the I chord9. -isten to the following, and notice how at the end, when the final I chord is delayed, there is a very strong desire to have the 7 chord "resolve" 8progress9 to the I chord.

/otice that the roots of the 7 - I progression move down by the interval a fifth or when inverted, up by a fourth. .lthough this type of progression is most strongly felt in the 7 I progression, other chords that progress in a down#by#fifthCup#by#fourth progression also strongly move forward.

?omposers have recognized this principle, and have often used down#by#fifthCup#by# fourth progressions in their music. )hen a composer uses a long string of this type of progression, we call it a circle of fifths pro"ression, since it moves through all of the chords in the 0ey and returns bac0 to the starting chord.


2rom this we can see how most chords have a tendency to wish to resolve using this type of progression. .ll of the following are down#by#fifthCup#by#fourth progressions>
Major1 I ' I45 ii ' 45 iii ' vi5 I4 ' vii65 4 ' I5 vi ' ii5 (vii6 ' iii ( minor (commonly +sed chords 1 i ' iv5 ii ' 45 III ' 4I5 iv ' vii65 4 ' i5 4I ' ii5 (vii6 ' III (

P # because the diminished vii chord is so unstable, and has a strong desire to resolve to the tonic 8see below9, it is rarely used in an down#by#fifthCup#by#fourth progression e*cept as a part of a circle of fifths progression.

5p 'y &econd Pro"ressions
.s noted in the section on 'cales and tendancy tones, the seventh scale degree has a strong tendency to resolve to the tonic. =oot movements that are up by the interval of a second are also very strong harmonically. 1p#by#second root movement progressions are fre4uently used in tonal music, often in combination with down#by#fifthCup#by#fourth progressions>

6own 'y !hird Pro"ressions
-isten to the following e*ample, popularly used in much of the roc0 and roll of the !"As>

HARQIB HARIS/AHMAD ARSHAD_ISL 78ample1 Common 9":s Roc* and Roll ,rogression ( I ' vi ' I4 ' 4

/otice that the root movement of the chords is down by the interval of a third. In progressions of this type, there are always two common tones between ad,acent triads. +he remaining tone resolves up by second, providing the forward movement. .lthough, because of the common tones, this progression is wea0er than the above two types, because of the smooth connections between chords, it is still commonly used. However, it is rarely used at the end of a musical passage, since a stronger resolution is desired at those points.

2rom this we can see how most chords have a tendency to wish to resolve using this type of progression. .ll of the following are down#by#third progressions>
Major1 I ' vi5 ii ' vii65 iii ' I5 I4 ' ii5 (4 ' iii (5 vi ' I45 (vii6 ' 4 (( minor (commonly +sed chords 1 i ' 4I5 ii ' vii65 III ' i5 iv ' ii5 (4 ' III (5 4I ' iv5 (vii6 ' 4 ((

P # because the % chord has such a strong desire to resolve to the tonic, it is rarely used in an down#by#third progression. PP # because the diminished vii chord is so unstable, and has a strong decide to resolve to the tonic, it is rarely used in an down#by#third progression.

&ummary of 9armonic Pro"ressions
.s noted, only the 7 and iiF triad and seventh chords have e*ceptions to the basic harmonic progressions. 2rom this, a simple saying to remember harmonic progressions can be used>

G5p 'y *ndH 6own 'y -rdH 5p 'y ,thH 6own 'y ?th e#cept 7 and iiFH which do not resol e to iii+IIIG
.s a confirmation of the e*ceptions, listen to them and notice how they donAt seem to sound 4uite "right". +his is because both 7 and iiF have a very strong tendency to


resolve to a I+i chord. . iii+III chord is very close to a I+i chord, with only one note difference. 'ince our ears are more used to hearing a resolution to a tonic chord, this "different" note is more often heard as a mista0e rather than an actual, intended progression.

Pro"ressions in $usical Practice
Eoes this mean that all music that follows progressions is good and that which doesnAt is badQ /o, composers have always used harmonic regressions and successions in their music, ,ust as much of the great literature of the world has instances of non#standard grammar. However, if we are to better understand music, it is important to recognize when composers chose to use progressions and when not to use them. '0illful use of progressions in passages where the composer wishes the music to move ahead more strongly, and successionsCless strong progressions when they want the music to rela* a bit is what creates an interesting flow to the music. .n occasional regression may be used to provide a surprising moment in a composition. However, most of the music of the common practice period follows harmonic progressions, so it is very important to memorize and be able to recognize these functions within their musical conte*t. +his will not only allow you to better en,oy listening to music, but will also aid in deciding how to interpret the performance of common#practice music. )hen writing your own harmonies, it is important to 0eep in mind the following guidelines>
o o o o

;se most.y 1ro/ressions. 9or common 1r*ctice e5*m1.es8 use *.. 1ro/ressions. ;se the stron/er 1ro/ressions *t the en3s o2 sections Since the tonic is the most st*b.e8 it m*y be 2o..owe3 by *ny other chor38 whether it is * 1ro/ression or not. Howe+er8 progressions wi.. soun3 stron/er. Be sure to +*ry the ty1es o2 root mo+ement. ;sin/ *.. o2 on.y one ty1e m*y soun3 3u... ;se stron/er 1ro/ressions in 1*ss*/es where you wish the music to 1ress *he*38 *n3 we*?er 1ro/ressions8 successions8 *n3 r*re.y re/ressions in 1*ss*/es when you wish the music to re.*5 * bit.


7e5t section4 <*3ences


$*b.e o2 <ontents

In the previous section on harmonic function, the strong progression of 7 - I was discussed. -isten again to the e*ample, and notice how the phrase does not sound over until the final I chord is sounded.

+he final 7 - I chord progression is what we call a cadence. . cadence is combination of a certain strong harmonic progressions with a resolution to a strong beat that ends a phrase. ?adences might be thought of as the punctuation mar0s in music # some cadences sound 4uite final 8G9 while others only pause a moment 8,9 and still others leave the listener waiting for more 8Q9. ?adences are easy to hear, but are sometimes harder to recognize in printed music. It is important to listen to the musical e*amples, and recognizing these musical punctuations.

(uthentic .adence
+he strongest type of cadence is an authentic cadence. +here are two types of authentic cadences> a perfect authentic cadence ;P(.< and imperfect authentic cadence ;I(.< . In order for an authentic cadence to be perfect all of the following must be true>
o o o

Harmonic progression of 7 - I 8or an added seventh on the 7 chord9 (oth chords must be in root position +he Melody must end on the tonic pitch.

.ll of these strict re4uirements ma0e this the strongest and most final sounding of all cadences. <ou may thin0 of it as a final period at the end of a paragraph or an


e*clamation point 8G9. . 3.? is usually found at the end of wor0s and often at the end of significant sections.

In an imperfect authentic cadence, the only re4uirement is that the harmonic progression must be 7 - I or ii - I, or with added sevenths on the 7 or ii chords. +he chords may be inverted, and the melody may end on a pitch other than tonic. (ecause of the more general nature of the I.?, it sounds less final, but still strong enough to be used at minor stopping points in a wor0 when the composer wishes the music to cadence, but then go on. Musically, this cadence functions li0e a period at the end of a sentence.

6ecepti e .adence
)hen a 7 chord does not resolve up by fourth to a I chord, but instead resolves up by second to a i, we call it a decepti e cadence 8E?9. (ecause a i chord and a I chord have two notes in common. +his cadence is not nearly as conclusive, or final, as an authentic cadence, and is never used to end a tonal wor0. However, it does provide a delightful "surprise" by resolving to a minor chord in ma,or 0eys, and a ma,or chord in minor 0eys. In a deceptive cadence, the i chord is not used in first inversion. +his is because of the similarity to the I chord # it will sound li0e a "wrong note I chord" rather than a i chord.


9alf .adence
+he half cadence 8ending on 79is perhaps most li0e a comma 8,9 because it cannot end a phrase. +he unstableness of the dominant chord sets up the following phrase. In a half cadence 8H?9 the 7 chord may be preceded by any other chord. +he chord that follows a half cadence may be any chord, however, I or i are most common.

.nother specific, but rarer, type of half cadence is a phry"ian half cadence 8i - 79 was popular during the (aro4ue period. 3hrygian Half ?adences only occur in minor 0eys, and must consist of a first inversion i chord that resolves to a root position 7 or 7> chord. It refers to a common type of cadence that was used in music written in the phrygian mode, but was later fre4uently used to end the slow middle movement of a concerto, when the composer wished for the final movement to begin without an e*tended brea0. +he second movement of (achAs Brandenburg Concerto No. 2 is perhaps one of the shortest complete movements in the literature, and consists only of a phrygian cadence.

Pla"al .adence


+he 3lagal cadence, I7 - I is actually a regression, but through continual and prominent use by composers over the centuries, it has become a common, conclusive cadence. +his is the ".men" cadence used at the end of most church hymns.

.adences in $usical Practice
.s mentioned, cadences are usually 4uite easy to recognize when heard. In common practice music, cadences occur at regular intervals, usually every 6 or B measures, but in slower wor0s may occur more fre4uently. /otice also that not every 7 - I, for e*ample, is a cadence. . cadence is both harmonic and melodic ## occurring at important points in the music. -isten to the following e*ample to hear how a variety of cadences are used to bring the music to a regular ebb and flow, and how the type of cadence can lead the listener to e*pect what is to follow.


/e*t section> Melody


+able of ?ontents

)estern .rt Music places e4ual emphasis on both the melodic flow of each voice or part, also called a line, and on the harmonic flow and function of all of the voices put together. +his forms a 0ind of grid, where each note functions in both ways simultaneously. +his ma0es this type of music interesting to listen to, but also ma0es it difficult to compose. )hether composing contemporary music, listening to a (eethoven symphony or playing (ass Fuitar in a '0a band, by understanding how music functions both horizontally 8line9 and vertically 8harmony9, one can better appreciate and create music of nearly all styles. If each line of music is interesting and has a smooth flow, chances are that the whole wor0 will be also. 'o what are some of the traits of a "good melody"Q .lthough this varies from style to style, by studying the refined principles of common practice melodies, an understanding of the principles that govern them can be applied to other styles as well.

Basic $elodic Principles
. good melody, li0e a good house, has a solid basic framewor0. +his is then embellished and refined to create more interest. )hen creating a melody, composers often start with a rhythmically simple line according to the following guidelines, then add the embellishments later. . full understanding of common practice melodic guidelines is essential for writing and understanding these melodies. 19 =hythm # 0eep it simple to start with. . good guideline is one note per beat or pulse. :9 ?ontour # this is the shape of the line. 1sually, there is only one highest or lowest note, called the pea0. If the pea0 note is repeated, it looses itAs effect, so it is important to have only one pea0 to your contour. )here should the pea0 occurQ .lthough there is an infinite number of variations, there are several basic contours that melodic lines generally follow> a9 .rch # the most popular contour. (egins lower, wor0s its way up to a high point between around or ,ust after the midpoint of the melody, then


falls bac0 to a lower ending note. .ll of the following are arch contour melodies>

.n Inverted .rch contour simply flips this shape upside#down, with the lowest pea0 occurring only once.

b9 =amp # Melodies often save the high or low pea0 for the last note, for a more climactic ending. .n ascending ramp contour begins at or near the lowest not, and gradually and continually wor0s itAs way up to the highest pea0. a descending ramp contour reverses this, beginning with the higher point, and ending with the lowest. ascendin" ramp contour

descendin" ramp contour

=emember, these are simplifications. Melodic lines may briefly zig#zag around these shapes, and sometimes may combine both. +his familiar melody has both arch contours and descending ramps>


It is important to note, however, that lines without a contour often sound dull and seem to ,ust "noodle around" on a few notes. ?ompare the above melodies to the following, and see which is the more interesting>

59 . 'mooth ?onnected -ine # @ur ear more easily hears a series of notes as belonging together when they proceed smoothly and without leaps of larger intervals. +he following are the main guidelines used in common practice melodic lines> use about B"R step wise motion 8i.e. only the interval of a second9 and :"R intervals large than a second. 11 avoid using augmented or diminished intervals, as they are harder to sing, play, and hear as belonging together. 11 whenever leaping an interval larger than a fifth, resolve inward by step. 8for e*ample, if you leap down a si*th, the ne*t note should resolve up by second.9

69 resolve tendency tones # 'cale degree seven has a tendancy to resolve to tonic, unless part of a downward scale passage from tonic to dominant. 11 'cale degree four has a tendancy in Ma,or to resolve down to scale degree three. 11 ?hromatically altered pitches should resolve by step 8the interval of a second9 in the same direction as the alteration. 2or e*ample, added sharps should resolve upward by step, and added flats should resolve down by step.

/ote the e*amples of the above guidelines in the following two melodies ## the first follows them, and the second does not. $elody which follows "uidelines:


Melody that does not follow guidelines>

.omposin" a $elody to a Ei en 9armonic Pro"ression
)hen composing a melody to fit a harmonic progression, you may wish to follow these simple steps>
o o o o

)rite the chords below the staff. -ightly place dots on the notes that are a part of the chord in the staff above each chord. +his will 4uic0ly show you what notes are available. 'tarting on tonic or dominant, lightly draw the contour you wish for the melody. Ieep it general yet interestingG /ow that you have completed a s0etch, "connect the dots" to form the framewor0 for your melody, 0eeping close to the contour line, and using only the notes that are parts of the chords. If you hit an area where there does not seem to be any good choices, bac0 up a few notes and choose a different path.

In 'ection 1 > /on#?hord +ones, methods of embellishing this melody will be e*amined. 'ection 1H> (asic 2orm and .nalysis, use of patterns called motives will be discussed. (ut for now, try to create more simple, yet attractive sounding melodies. =emember> an ugly melody with lots of embellishments is usually still an ugly melodyG

9armoni=in" a $elody
+he process of adding chords to a pre#e*isting melody is similar to the above process for composing a melody to fit a harmonic progression. +he following is a simple process to compose a harmonic progression to fit a given melody.



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+ry to determine what the harmonic pulse is. +he harmonic pulse is how often the chords change. In melodies that have faster tempos and melodies that move predominantly by thirds or arpeggiation, the harmonic pulse is fre4uently a half note or longer. ?ommon harmonic pulses for various meters are shown below. If the melody appears to outline triads over a two beat pattern, then use a two#beat 8half note9 harmonic pulse. If the tempo is slow and no chords appear to be outlined, than a harmonic pulse of one chord per note may be appropriate. E*ample # Harmonic pulse 2or each beat of the harmonic pulse, list all possible chords that could contain most if not all of the notes within that beat. 2or single notes, this will be three possible triads 8the note will either be the root, third or fifth of a chord9. 2or beats with more than one note, there may be less, or even only one possible chord for that beat. -ist all of the possible chords, since you can not 0now for certain which you may need to use yet. )hen completed, begin at the end, try to compose a harmonic cadence that fits the melody. ?omplete the last two or three beats. /ow, beginning on I if the melody begins on a down beat or strong beat, or on 7 if the melody begins on a wea0 beat, circle the chords that best form a harmonic progression and connect them with a line. <ou may have two or more possibilities, but find out three chords later that only one of them will wor0 all the way through. )hen you hit a "dead end" simply bac0 up two or three chords and choose another possible chord.

melody only> first harmonization> second harmonization>


third harmonization> +he ne*t step to completing this process involves composing a bass line to go with this melody and harmony. +his re4uires a full understanding of how chords function when a note other than the root is in the bass, and is the topic of the ne*t section.

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/e*t 'ection> ?hords in Inversion +able of ?ontents

.hords in In ersion
&ust as writing a smooth, interesting melody is important, a smooth, interesting bass line is also important. @ur ears are more able to hear the outer voices 8i.e. the highest and lowest9 than inner voices. 2or this reason, special care must be ta0en when writing bass lines. However, when the bass note of a chord is changed, the inversion of that chord also changes. 'ection 11> Inversion of ?hords showed how to label and identify chords in inversion. +his section will discuss how these inversions are used in common practice music.

Music of the common practice is concerned with both the melodic 8horizontal9 and harmonic 8vertical9 aspects of music. 2or this reason, both of these parameters must be considered when writing a bass line. =oot position chords are most stable, because the upper notes more easily fit into the overtone series of the bass note. )hen a chord tone other than the root is in the bass, the chord becomes less stable. However, when only root position chords are used, the bass line becomes rather ,umpy and not very melodic. +here are also times when chords in root position may cause the melody and the bass line to move in parallel motion 8this will be discussed in the following section in greater depth9. =oot position chords are generally used at the beginnings and ends of phrases, where greater stability is desired. -ess stable inversions are found more fre4uently in the middle sections.

First In ersion .hords


1se of first inversion chords is most common. 2irst inversion chords are only slightly less stable than root position chords. ?omposers fre4uently use them when a root position chord would cause an undesired ,ump in the bass. ?ompare the following two e*amples, the first in all root position, the second using first inversion chords.
all root position:

use of first inversion chords to smooth out bassline:

/otice that in first inversion chords, the root or the third of the chord is most commonly doubled 8doubling is a term used to refer to when two voices are on the same pitch class9. 2irst inversion chords also allow the bass line to move in the opposite direction of the root movement. +his is a useful and important feature that will be discussed in the following section.

&econd In ersion .hords
+hese are the least stable of the inverted chords. (ecause of historical and traditional reasons, the interval of a fourth above the bass has been treated as a mild dissonance in much of music of the common practice period. 'econd inversion chords contain this interval and because of this, re4uire special treatment. 'econd inversion chords are not freely substituted or used, but instead, are used in only four specific forms>
0he Cadential &-; chord1

+his is a specific and most common use of second inversion triads, found fre4uently at the end of phrases. It consists of a second inversion tonic triad,


followed by a root position dominant chord, which then usually resolves according to form a cadence. /otice how the bass note is doubled and remains on the same pitch class in a cadential C6, and the other voices resolve smoothly downward. 2or this reason, these two chords 8I C6 and %9 are almost always grouped together as a pair, and as such, form a cadential C6 cadence.

0he ,assing &-;1

3assing C6 chords occur between a root position and a first inversion chord, and result in smooth, step#wise motion in the bass. 3assing C6 chords may be used with ascending or descending bass lines.

0he ,edal &-; chord1

In a pedal C6 chord use, the bass note remains the same, and the C6 chord is preceded and followed by the same, root position chord. +he bass note of the pedal C6 chord is doubled. +his is fre4uently used in the plagal cadence 8amen9 in many hymns.

HARQIB HARIS/AHMAD ARSHAD_ISL Melodic and 2rpeggiated +se1

'ometimes the composer will give the melody to the bass line rather than the highest voice. However, in these cases 0eeping the melody intact and recognizable is more important than the uncommon inversions that may result.
Melodic use:

?omposers also may arpeggiate the bass line in musical practice 8see section 119, and as a result, brief C6 chords may occur in the middle of these passages. However, since they do not actually resolve, these C6 chords are usually not analyzed as such, since they are not functional.
Arppeggiated use:

!hird In ersion .hords ;&e enth chords<
'ince a third inversion chord is both an unstable seventh chord and has the dissonant seventh in the bass, it is less commonly used than other inversions. +he bass always resolves down by step 8as will be discussed in the following section9.


7e5t Section4 " o2 "*rt Aritin/


$*b.e o2 <ontents

Principles of Part Aritin"
+he music of the common practice period did not appear overnight. +he principles that govern it were the result of almost 1""" years of scientific research and artistic e*perimentation. @ne of the principles is that of e4ual emphasis on both harmony 8vertical9 and line 8horizontal9. +he process of writing music that addresses both of these aspects is referred to as oice leadin" or part writin" 8these two terms are used interchangeably9. 2our#part choral music is most often used to demonstrate and teach voice leading, since it addresses most of the problems, methods, and principles for writing for more or fewer voices. 2our voice choral part writing is often referred to as &(!B 8'oprano, .lto, +enor, (ass9 part writing. .lthough all parts follow the smooth, melodic principles discussed in the previous section on melody, the issue of contour is usually reserved for the soprano alone.

+he following are the ranges allowed by most theorists for each voice. .lthough it is certainly possible for good singers to sing beautifully beyond these ranges, it is helpful to have a rather fi*ed limit for each voices range to effectively study this craft.

)hen writing parts, it is important to always 0eep each voice within its range, and also not to allow voices crossing 8when a higher voice becomes lower than a lower voice9. 7oice crossin" blurs the distinction between the parts, especially when played on a 0eyboard instrument. +he following is an e*ample of voice crossing. /otice how when the voices cross in this e*ample, the first two beats will sound as though the alto and tenor repeat the same pitches.


7oice o erlap is when a line crosses above or below a pitch recently sounded by another voice. .lthough this is not voice crossing, when the notes are only one to three beats apart, the ear may still hear the voices as overlapping, and the independence of line is diminished. .lthough (ach and many other great composers occasionally wrote overlapping parts, there was always a good, melodic reason. 'o, unless there is a compelling compositional reason, this error should also be avoided.

!ypes of $otion
(y definition, two or more voices can move in only four basic types of motion> 19 Parallel $otion # both voices move in the same direction by e*actly the same interval. In this e*ample, both voices move down by a M:.


:9 &imilar $otion # when both voices move in the same direction, but by different intervals. In the following e*ample, the top voice moves up by a M:, while the lower voice moves up by a 3!.

59 .ontrary $otion # the voices move by any interval in the opposite direction.

69 O'lique motion # one voice moves in any direction by any interval while the other remains on the same pitch, not moving at all.

Part Aritin" Procedures
In order to achieve a level of independence of line for all four parts, parallel motion of Perfect Octa esH Perfect FifthsH and 5nisons should 'e a oided. 'ince these are the lowest intervals on the overtone series, when two or more voices move in parallel motion in these intervals, they can blur together and sound li0e only one voice 8in the case of unisons, they actually become one voice9. 3arallel motion by thirds, fourths and si*ths is acceptable and often desirable, however, two voices should not move in parallel motion


for several beats in succession. +his would reduce their independence. +o most easily avoid part writing errors, the following procedure is very helpful> &tay within the ran"es of the oices@ If you notice that a voice is getting toward the limit of its range, try to move in the opposite direction if possible. 2. 5se only notes that are a part of the harmony@ /on#?hord +ones will be discussed later. 3. 3eep common tones when possi'le@ @ften there may be a pitch that is a part of ad,acent chords. 'ince parallel motion is to be avoided, avoiding motion of a voice all together eliminates that possibility altogether. 4. $o e the other oices in contrary motion to the 'ass whene er possi'le@ +his one simple step eliminates most part writing errors and creates greater contrast between the melody and bass. 5. !he >+> rule: scale degree seven 8the leading tone9 should resolve to tonic 8always when in an outer voice9, unless a part of a line proceeding down from tonic to dominant, 8i.e.> 1#H# #!9 and the seventh of a chord should always resolve down by second. 6. Resol e chromatic alterations ;notes with added accidentals< 'y step 8the interval of a second9 in the same direction. 2or e*ample, an added flat lowers the pitch, so it should resolve down by step. .dded sharps raise the pitch, and should resolve up by step. 7. 2inally, check each oice for undesira'le parallel motion between voices. =echec0 the ranges for voice crossing and overlap. &ust as good drivers loo0 twice before crossing an intersection, good part writing students double chec0 their wor0.

)hen writing triads, there are only three pitch classes but four voices. +his means that two or more voices will have the same pitch class. +his is called dou'lin". )hen you have a choice, try to double the pitch in the bass or the soprano, e*cept when it is scale degree seven or a chromatically altered pitch. 'ince these must resolve a certain way, if they are doubled, both voices will move in parallel unison or octaves. If you follow these basic steps, most part writing errors may be avoided. .s rigid as they may seem, you often will have several choices yet available. +he following e*ample demonstrates these principles>


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/e*t 'ection> /on#?hord +ones +able of ?ontents

2on-.hord !ones
. non-chord tone 8sometimes referred to as a non-harmonic tone 9is a note which is not part of the accompanying harmony. It may be diatonic or chromatic and usually serves either to embellish or to "smooth out" melodic motion between or around chord tones. Melodic lines rarely remain e*clusively within the confines of the given harmony. )ithout these additional non#chord tones, musical lines would be able to only outline the triad 8li0e a bugle call9 or proceed in a homophonic te*ture. ?onsider the following two e*amples, the first without non#chord tones and the second with /?+s>

E ample !: Nun danket alle Gott

)#ample %': Nun danket alle Gott with NCTs

/on#chord tones 8abbreviated /?+9 may occur on strong beats, wea0 beats, or on subdivisions of the beat. +hey may be used in combination with other types of /?+s or


by themselves. )hen deciding when to use /?+s, a simple analogy may help> adding /?+s to music is li0e adding peppers to a recipe> a few may help ma0e it more interesting, but too many can ruin itG Eepending on how they and when they are approached and resolved, /?+As function in a variety of ways. 'ome function primarily melodically, helping to embellish or smooth out a line. @thers function primarily harmonically creating greater harmonic tension and release. +he table and e*amples below define the various types of /?+As. <ou may clic0 on any of the names for more information on that /?+, or you may simply scroll down the page.

.lassification of 2on-.hord !ones
"on-#hord $one "ame "*ssin/ $one 7ei/hborin/ $one Approache (s%mbol d &esolves b% ) b% 1 n Ste1 Ste1 Ste1 Le*1 Ste1 Ste1 in s*me 3irection Ste1 in o11osite 3irection $%pe Me.o3ic Me.o3ic

7ei/hbor /rou1 n./r or <h*n/in/ or c.t. $ones A11o//i*tur* =sc*1e $one Sus1ension Ret*r3*tion Antici1*tion "e3*. "oint * e s r *nt 1e3

)two notes4 one *bo+e *n3 one be.ow Me.o3ic chor3 tone, Ste1 Le*1 in o11osite 3irection Me.o3ic Me.o3ic H*rmonic H*rmonic H*rmonic H*rmonic

S*me tone Ste1 3own S*me tone Ste1 u1 Ste1 or Le*1 )none, S*me tone *s 2o..owin/ note )sus1ension o2 the s*me tone throu/hout,

HARQIB HARIS/AHMAD ARSHAD_ISL 78amples of 3on'Chord 0ones

<escriptions of Individ+al 3on'Chord 0ones ,assing 0ones

Passin" tones allow smooth, scale#wise motion in tonal music by "filling#in" the space between two primary notes. +hese primary notes are usually a third apart, with the passing tone being the diatonic scale degree in between. However, other intervals may also have passing tones between them. +wo or more passing tones might be used to smooth over a leap of a fourth, or a single, chromatic passing tone may be used to strengthen the movement of a ma,or second. 3assing tones are among the most common and fre4uently used /?+s. /?+ ?hart


2ei"h'or tones are notes one scale degree above or below the primary tone and are used to provide rhythmic interest between common tones. ?hromatic neighboring tones are fre4uently used because of the strong half#step resolution they possess. /?+ ?hart

. suspension holds a consonant chord tone beyond the chord to which it belongs and into the ne*t chord before "dropping" down a step to resolve. . 'uspension has three parts> a preparation 8the initial, consonant attac09, a suspension 8when the chord changes, but the suspended note doesnAt9, and a resolution when the suspension proceeds down to the consonant chord tone a second below.9 )hen several suspensions occur in a row, they are referred to as a chain of suspensions . E*ample 1b has an e*ample of this in the 5rd complete measure. /?+ ?hart

. Retardation is similar to a suspension e*cept that the resolution is up a step, not down. It also has a preparation 8the initial, consonant attac09, a suspension 8when the


chord changes, but the suspended note doesnAt9, and a resolution when the suspension proceeds up a second to the consonant chord tone.9 1nli0e suspensions, retardations seldom occur one after another in a chain. /?+ ?hart

.n (ppo""iatura has an effect similar to a suspension without a preparation. It is a /?+ occurring on the beat 8accented9 and resolves down a step. It is not, however, held over from the previous note, but usually is approached by an upward leap. +his e*pressive type of /?+ is fre4uently found in music of the =omantic period, due to its powerful "yearning" to resolve. /?+ ?hart
7scape 0ones

)scape tones "escape" from the harmony by step, then leap in the opposite direction to freedom in the ne*t chord. In this manner, they are a type of reverse appoggiatura. ?hromatic escape tones are rarely found due to the non#stepwise resolution. /?+ ?hart
3eigh)or =ro+p 0ones


2ei"h'or Eroup !ones 8sometimes referred to as changing tones9 consist of two notes> one a scale degree above and one a scale degree below the primary tone. -i0e neighboring tones, they are used to provide rhythmic interest between common tones. In this type of /?+, either of the two neighboring tones may come first and is followed by the other before resolving bac0 to the initial tone from which they left. /?+ ?hart

.s the name would suggest, an (nticipation is a note that ,ust couldnAt wait for the ne*t chord and sounds early. It is approached by either a step or a leap from a consonant note to the dissonance, then usually resolves by step. )hen resolved by a leap, it is often referred to as a free anticipation . /?+ ?hart
,edal ,oint

. Pedal Point is uni4ue among /?+s in that begins on a consonance, sustains 8or repeats9 through another chord as a dissonance until the harmony, not the /?+, resolves bac0 to a consonance. @ften used in the bass as a device to strengthen a final cadence, a pedal point has a strong tonal effect, "pulling" the harmony bac0 to its root. )hen a pedal point occurs in a voice other than the bass, it is usually referred to as an inverted pedal point . /?+ ?hart


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7e5t Section4 Mo3e Mi5ture $*b.e o2 <ontents

$ode $i#ture
?omposers have found that using only the diatonic scale degrees is very limiting and often results in the music sounding static and dull. (y adding chords that do not naturally occur within a particular ma,or or minor 0ey, music may become more e*pressive and have more variety. @ne of the most common functional non# diatonic harmonic practices involves intermi*ing chords from the parallel ma,or or minor mode. (elow is a chart of the most common diatonic chords in ma,or and minor 0eys. .s you see, many of the scale degrees have chords that have the same root, but a different chord 4uality. .ll of the circled pairs of chords may be interchanged.

)hen chords from the parallel ma,or or minor are used, they are referred to as 'orrowed chords. In chords where the root of the chord is altered by an accidental, that same accidental is added before the roman numeral to indicate this alteration 8i.e.> the borrowed 7I chord above would be referred to as a "'7I" # read "flat si* chord"9. +he most common use is when the music is in a ma,or 0ey, and chords from the minor mode are borrowed. +his often creates a dar0er, "sadder" feel to the music, and is fre4uently used in vocal wor0s to reflect a change in mood in the te*t. 8a process called te#t paintin".9 the following are commonly found borrowed>
Chords Commonly Borrowed from Minor in Major Modes1

i - ii;dim< - 'III - i - '7I


In the following e*ample, the borrowed i and '7I chords create a definite change in the mood of the phrase.

(ecause the use of a melodic minor scale results in I7, 7, and diminished ii chords, these are not considered borrowed. +he only fre4uently found borrowed chord in minor is the borrowed tonic triad, and this is commonly only found as the final chord of a wor0. In this particular usage, it is referred to as a Picardy !hird chord. ?omposers of the common#practice period often ended wor0s on a 3icardy +hird to create the effect of a "happy ending".

$ode $i#ture s@ .han"e of $ode
)hen a musical passage changes to itAs parallel ma,or or minor mode and remains in that new mode for an e*tended period of time, our ears may hear it not as a few borrowed chords, but a chan"e of mode. )hen music changes mode in a more permanent manner, there is often a 0ey change to indicate this. ?hanges of mode may be as short as :#5 measures in a slow tempo, or much longer. In the first e*ample, the music only changes from ma,or to minor for a few borrowed chords. In the second e*ample, it remains in the Ma,or mode and is an actual change of mode. 8+he use of the ?N and FN will be covered in the following 'ection9


Borrowed .hords:

.han"e of $ode:

'ome of the signs that a passage has changed mode, as opposed to ,ust borrowing from the other parallel mode, are>

o o o

* new ?ey si/n*ture * c*3ence in the new mo3e consistent use o2 the new mo3e 2or .on/er th*n #:10 secon3s

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7e5t section4 $onici0*tion $*b.e o2 <ontents

&ust as changes of harmony and changes of mode create a sense of motion and interest in music, changes in tonal centers create a sense of movement and interest in a larger sense. It is e*tremely difficult to find a wor0 in the standard repertoire that functions in the same 0ey throughout. Music that changes 0eys and establishes a new pitch 8other than scale degree 19 as tonic, is said to have modulated. )hen a composition briefly 8i.e. only one or two chords9 emphasizes a new 0ey by use of chords from that 0ey, it is said to tonici=e that 0ey. .s we discussed in 'E?+I@/ 15> (asic Harmonic 2unction, +he 7-I progression is one of the strongest functions in tonal music. . simple I-7-I progression can 4uic0ly establish a tonal center 8tonic9. (y adding a seventh to the dominant chord, this function is further strengthened. -isten to the following three e*amples, and after each tonic#dominant#tonic progression, hum tonic> (ural )#amples ;try to hum tonic after each chord pro"ression<: I-7-I i-7-i I - 7> - I ?omposers have found that by preceding any chord other than tonic with itAs dominant 8i.e. the 7 chord from the 0ey of that chord9, there is a brief emphasis


on that chord and a sense of harmonic movement. In the following e*ample in ? Ma,or, the ii chord 8d minor9 is preceded with a chord from the 0ey of d minor 8ii9. )e call this a tonici=ation of the ii chord. )hen referring to this non#diatonic chord, we call it a 7+ii 8read "five of two"9 chord and may also refer to it as a secondary dominant chord 8since the diatonic dominant chord is the primary 7 chord9. /otice how this results in a pleasant emphasis of d minor, but because the ?N doesnAt remain, the music still sounds li0e it is in ? ma,or.

+he leading tone is the strongest tendency tone in a 0ey. +his tendency tone is present in the dominant 7 chord, and is largely responsible for itAs strong harmonic function. +he seventh of a %H chord, scale degree 6, is also a strong tendency tone. )hen we use a secondary dominant chord, the added accidentals create new tendency chords that need to resolve in the same manner as diatonic ones. 'o the voice leading for a secondary dominant chord is the same as for a diatonic dominant chord> the "new" leading tone, i.e. the third of the chord, should resolve up by step 8especially when in an outer voice9, and the seventh of the chord, if present, should resolve down by step. @bserve the voice leading in the following e*ample. /otice also that because each of the tonicizations is brief, one never looses sense of "F" as tonic.

+he ii#diminished chord also can substitute for the dominant chord in a tonicization, ,ust as it does in diatonic music. +his is also a method of tonicizing a chord, since it is still accomplishing the same result> an emphasis of a new tonic.


/otice that when minor triads are tonicized, they are normally preceded with the form of ii chord that is from minor 0eys 8a ii fully diminished se enth chord9, whereas ma,or triads are commonly preceded with the form of ii chord from ma,or 0eys 8a ii half-diminished se enth chord9.

8/ote> when the 7 chord is tonicized, it is fre4uently preceded by a I /+, chord which then resolves to the dominant. .s noted in 'E?+I@/ 1 > )riting ?hords in Inversion, this cadential C6 chord is often viewed as an e*tension of a 7 chord. +hus, this e*ample does indeed "resolve properly", even though there appears to be a tonic chord between the secondary seventh chord and the dominant chord.9 ?omposers may emphasize a new tonal area by means of chords other than 7 and ii. In the following e*ample, ?hopin uses an e*tended tonicization in the second and fourth measures. )hen several chords all tonicize the same chord, they are usually all notated above a single line, as shown below. /otice how the .b chord on the downbeat of measure : is normally labeled as simply a 7I chord in c minor, but in the larger sense is the I chord of the whole .b Ma,or tonicization in that measure. .s you listen to this e*ample, you may hear these measures as a modulations 8which is the topic of 'E?+I@/ ::> Modulation9. +his is often the case in e*tended tonicizations, and is not incorrect either. It is mostly a matter of personal perception, and is one of the wonderful aspects that ma0es this such an enduring wor0 in the literature.


 

/e*t section> @ther ?hromatic Harmonies +able of ?ontents

Other .hromatic .hords
@ne of the factors that gives chromatic chords such a strong functional use is the presence of tendency tones. +hese tendency tones resolve by half#step, and create strong, functional harmonic flow. 'ince the dominant 879 chord is has the strongest "pull" toward tonic, most chromatic harmonies serve as predominant harmonies and resolve to the dominant. ?ommon diatonic predominant chords are the ii 8or ii>< and I7 chords.

+hroughout the common practice period, composers found that by combining the lowered scale degree from borrowed chords and the raised scale degree 6 from the 7+7 chord, a strong, functional predominant harmony could be created. +ypically, the lowered scale


degree is voiced on the bottom, and the raised scale degree 6 is on top, resulting in the unusual interval of an augmented si*th 8.b up to 2N in the e*ample below9. Hence, this category of chords is 0nown as au"mented si#th chords. .lthough these chords have names which refer to various nations, they were freely used in music of all nationalities.

.ll .ugmented si*th chords contain a lowered 8if in Ma,or 0eys9 scale degree , tonic, and a raised scale degree 6, as shown above. In each case, the chromatically altered tones resolve by half#step to the dominant 8scale degree !9.+here are three basic types of augmented si*th chords>

Italian (u"mented &i#th +he Italian .ugmented 'i*th chord 8notated as ItD/9has the three above listed notes and doubles the tonic in four#part voicing. %oice leading is the same for both ma,or and minor modes. It may resolve to either a 7 or a tonic /+, chord 8which then normally resolves to a 7 chord9.

French (u"mented &i#th . 2rench .ugmented 'i*th chord 8notated as FrD/9 adds scale degree : to the above three pitches. %oice leading is the same for both ma,or and minor modes. /otice how the voice leading smoothly resolves to either a 7 or tonic /+, chord>


Eerman (u"mented &i#th +he third type of augmented si*th chord has two different spellings> one for ma,or 0eys and one for minor 0eys. In minor 0eys, the normal Ferman .ugmented 'i*th 8notated as EerD/9 is used. In this chord, a minor third above tonic 8scale degree 59 is added to the three basic tones. .s this chord resolves, notice how there are two common tones. In ma,or 0eys, the chord is often respelled enharmonically to allow for smoother voice leading. +he lowered scale degree 5 is respelled as a raised scale degree :, forming the strange interval of a doubly#augmented fourth above the lowered scale degree . 2or this reason it is often referred to as a DD, or "6ou'ly(u"mented Fourth" chord. 8It may also be referred to as an "enharmonicly spelled Ferman .ugmented 'i*th" chord9. +a0e careful note of the voice#leading> the raised scale degree : always resolves up by half#step to scale degree 5 as the other tendency tones resolve out to the dominant, forming a I /+, chord. /either form of the Ferman .ugmented 'i*th chord resolves to 7, since this would result in parallel fifths or unresolved tendency tones.

!he 2eapolitan .hord +he /eapolitan ?hord is based on a ii diminished chord from minor, but may be commonly found in both Ma,or and minor 0eys. It uses the lowered scale degree 8from the minor mode9 and a lowered scale degree :, and is almost always found in first inversion. It is analyzed using either the symbol 'II/ or more commonly> 2/. +he /eapolitan chord resolves to either a 7 or a tonic C6 chord. 8/ote> )hen resolving to the


tonic C6 chord, the /eapolitan chord is voiced so that the fifth of the chord is above the root in order to avoid parallel fifths in the resolution. +he parallel fourths in this voicing are acceptable.9 .lso note the voice leading when resolving to the 7 chord> the augmented second is acceptable.

.hromatic $ediant and .oloristic .hord 5sa"e .ll of the chords in this section were not randomly "invented" by theorists, but rather, came about by e*perimentation by composers who used these harmonies fre4uently and consistently enough for their inclusion in our discussion of tonal theory. . .hromatic $ediant relationship e*ists between any two ma,or chords whose roots are a third apart. +his not only includes the familiar 'III and '7I borrowed chords, but also a ma,or III and 7I chord.

+hese chords usually occur in root position and after a tonic triad 8in ma,or 0eys9 and normally resolve bac0 to tonic, to the dominant, or continue in root movement by successive thirds.


/otice that these chords do not appear to have a strong functional resolution, but rather, provide a colorful "other#worldlyness" to the music. In analyzing the music of the 1$th and :"th centuries, you will often encounter chords that do not seem to function according to the normal "rules" of tonal theory, but rather are used for the "color" they add to a progression. )hen these chords are encountered, it is important to remember that music is an art, and it is often the moments when composers write passages "outside the norm" that music becomes itSs most e*pressive. =ichard )agner 81B15#1BB59 used a new set of pitches in his opera Tristan und Isolde that was very shoc0ing at first, but was later favored and used by other composers. It is now referred to as the !ristan .hord>

+his section does not present every possible chromatic harmony, but does list those most commonly encountered. ?omposers today are still "inventing" new chords, some of which may find their way into a theory te*t in the future. In any case, 0eep an open mind and creative approach to this ever#changing and e*panding artform of music.

o o

/e*t 'ection> Modulation +able of ?ontents


)hen music remains in a new tonal area so long that the ear no longer hears the original tonic as "tonic" any more, the music has modulated. +his amount of time varies from person to person, and by the conte*t of each musical passage. 2or e*ample, some people might hear the following passage as modulating to g minor, while for others it might be heard as only tonicizing g minor 8iv9.

However, there are a few guidelines that are helpful in determining whether one should analyze a passage as a modulation or a tonicization. Fenerally, we can say a passage has modulated when one or more of the following is true>

the new accidentals 8or absence of harmonic minor scale accidentals in minor 0eys9 remain consistent for more than !#1" seconds. 8in a slower tempo, this may be only a few chords, but in a faster tempo, it may ta0e many chords to create a new sense of tonic9. +he music comes to a definite cadence in the new 0ey, especially if this is an authentic cadence.

In the above e*ample, the music cadences in g minor, but there is only one chord containing an altered pitch. +his passage could be analyzed either as a tonicization or a modulation. +he following passage, however, is clearly a modulation, since the altered pitch remains until the final cadence. )e call the first chord that contains a pitch from the new 0ey that is not present in the old 0ey as the point of modulation. 2rom this chord on, the passage cannot be analyzed in the old 0ey, so a new series of chord symbols in the new 0ey is used to represent the harmonies.


Basic !ypes of $odulations
6irect $odulation )hen a passage changes 0ey abruptly with no commonly functioning chords or pitches, it is referred to as a direct modulation. +his type of modulation is often used to create a sudden change of mood via itAs sudden change of tonality.

.ommon .hord+Pi ot .hord $odulation (y preceding a modulation with a harmony that functions both in the old and new 0eys, the change of tonic becomes smoother and less abrupt. . chord that functions in both 0eys and is the chord immediately before the point of modulation is called a pi ot chord. 8'ome theorists refer to this as a common chord. Either term is acceptable.9 3ivot chords are identified by using roman numerals in both 0eys 8one above the other9, and a separating line or bo* to highlight their dual function, as in the following e*ample. @ne of the previous e*amples used a pivot chord to smoothly modulate from (b to gm. /otice how the i chord in (b is also the i chord in gm. (y using a common pivot chord, our ears may hear the passage as functioning in g minor before the actual point of modulation.


3ivot chords may be found by listing all of the chords in both the old and new 0eys, rotating the second 0eyAs chords so that the same letter namesCroots are ne*t to each other. +hen identify chords that have both the same root and the same chord 4uality. (oth of these must be the same for a chord to serve as a pivot chord. 2or e*ample, let us say we wish to smoothly modulate from E Ma,or to E Ma,or. 2irst, list all of the chords and identify the common chords>

.s we see above, we could use an fN minor chord 8iii in E Ma,or9 or an . Ma,or chord 87 in E Ma,or9 as a pivot chord. +he following two progressions demonstrate how each of these chords could function in this manner> fIm pi ot ;iii<


( $a:or ;7< pi ot

Pi ot !one $odulations In wor0s that are not in a chorale style, composers often modulate through the use of a common tone in the melody. (y eliminating the harmony, and only sustaining or repeating a pitch that e*ists in both the old and new 0eys, the music may smoothly modulate. +his techni4ue is fre4uently found in solo piano and chamber wor0s of the common practice period.

.losely Related and 6istant keys
Ieys that differ by only a single accidental 8i.e. E Ma,or with : sharps, and fN minor with 5 sharps9 are referred to as closely related keys. (ecause of their similar 0ey signatures, closely related 0eys contain multiple pivot chords, including the tonic in each 0ey. +his ma0es a smooth change of 0ey easier for both composers and listeners. ?losely related 0eys are easy to identify using the circle of fifths chart>


.ll of the 0eys 8both ma,or and minor9 that are ad,acent a selected 0ey are considered closely related. /otice also that the closely related 0eys also form all of the non# diminished, diatonic chords in the original 0ey 8be sure to use the natural minor scale form for minor 0eys9. Hence, these new tonicAs are familiar to the ear, ma0ing modulations smoother and more natural sounding.

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<ouAre EoneG .fterward +able of ?ontents

I ho1e th*t you h*+e en6oye3 your stu3y o2 music 2un3*ment*.s *n3 2oun3 this hy1erte5t use2u.. $his is by no me*ns the *bso.ute *uthority on music nor shou.3 it be the en3 o2 your stu3ies. As *n *rt2orm *n3 .*n/u*/e o2 itCs own8 music is const*nt.y /rowin/8 ch*n/in/8 *n3 3e+e.o1in/. 9or more te5ts co+erin/ Music $heory8 .oo? throu/h the M$ '( section o2 your .oc*. .ibr*ry or +isit your boo?store 2or * number o2 other te5ts th*t co+er more *3+*nce3 to1ics )such *s *3+*nce3 theory8 contem1or*ry theory8 6*00 *n3 1o1u.*r music theory8 2orm8 *n3 music .iter*ture, *n3 t*?e 3i22erent *11ro*ches to 1resentin/ this s*me m*teri*.. 9in*..y8 1.e*se 2ee. 2ree to em*i. me with *ny comments or su//estions.

HARQIB HARIS/AHMAD ARSHAD_ISL All the best, and keep making music!

Ro'ert J@ FrankH 6@$@(@ (ssociate Professor of $usic !heory and .omposition &outhern $ethodist 5ni ersity


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