cartazes de teoria

8/12/2019 Cartazes de Teoria

1/46

music notationis the art ofrecording music in written form.

modern music notation is a productofcenturies of transformation...

and it is neitherefficient nor intuitive!

Notation: Pitch

##g#F#d#DD#SS#d#Mf#SSg#F

pitch is the highness orlowness of a sound.

the system of musical notationwe use is essentially astylizedgraph ofpitch versus time.

thefive lineson which notesappear is called astaff.

the white noteson the keyboardare labeled with letters fromAtoG

otation is based on thepiano keyboard;nes andspaces on the staff represent

the white noteson the keyboard.

heclefdetermines what notes each staffline corresponds to. thefour modern

clefs are shown here; the note displayedon each staff corresponds tomiddle c.

To notate theblack notes

on the pianoeyboard, we use

accidentals,which alter thenote by one orwohalf steps.

ahalf stepisthe distancebetween twodjacent keys

on the pianokeyboard,

regardlessof whatcolorthe keys are.

these symbols are placed totheleft of the note that theyaffect, and they apply to all the

notes on that line or spacefor the rest of the measure.

twonotes which have the samepitch (for example,f sharpand

g flat) are calledenharmonics

middle cis thecthat is closest tothemiddle of the piano keyboard.

Thedouble sharp raises thenote by two half steps.

Thedouble flat lowersthe note by two half steps.

Thesharp raises thenote by one half step.

Thenatural cancels outany previous accidental.

Theflat lowers thenote by one half step.

treble clef

alto clef tenor clef

bass clef

for example, aflute hasahigh pitch,while a tuba

has alow pitch.

anote is awritten representation

of a particularpitch.

pitch

pitch

F g a b c d e F g a b c d e

time

to display notesoutside thestaff, we useshortenedstaff lines

called

ledger lines.

F g a b c d e F g a b c d e


2/46

whole

note

doubl

e

whole

note

h

alf

note

eighth

note

sixt

eenth

note

thirty

-second

note

sixty-

fourth

note

one-hundred-

twent

y-eighth

note

quarter

note

wholer

est

double

who

le

rest

half

re

st

eighthr

est

sixteenth

rest

thirty-secon

d

rest

sixty-fourt

h

rest

one-hund

red-

twenty-eighth

rest

quarter

rest

Notation: Rhythm

whilepitch is pretty clearly notated on a

vertical axis,note lengthis indicated using

somewhat arcane system involving

noteheads, stems and flags.

in this chart, each successive type of note ishalf as long

as the note to its left. none of these notes has astandard

length;a half note in one piece may be the same length as

an eighth note in a different piece.

note lengths in a piece

are indicated by the temp

markingat the beginning

of a piece or section.

arest is a period of

silence that a length

which corresponds to a

particular note.

usually rests are

placed on the staff at a

particular vertical

position as shown here.

theaugmentation dot

is a dot placed to the

right of a notehead. though small, this dot

wields someserious power:it changes the

length of the note by150%.In other words,

it makes the note half again as long!

multiple dots can also be added,

each one adding half of the

previously added value.

= + = + + = + + + = + + + +ties are curved marks which connect

two notes together to create

asingle, extended sound.

to tiemore than twonotes together,

draw ties betweeneach note;do not

use a single, extended tie.

a tuplet is any non-standard division of a

note. these are usually written as a group

of notes delinated with abracket and

anumber showing the division being made.

most tuplets are simple divisions, like

the triplets to the left. but anything is

possible!chopin,for example, would

oftengo to townwith these things.

= =

3 for example, these arentexactly quarter notes;they are each a third aslong as ahalf note.

wha...gah!chopin,no!

down, boy!


3/46

Notation: Meter

a fundamental feature of

most pieces of music is a

consistent rhythmic pulse.

this pulse is called thebea

and a single pulse

is called abeat unit.

here are two types of beat units:

those containing two divisions,

calledsimplebeat units...

...and those containing

three divisions,

calledcompound beat units.

in music, beats are organized into patterns ofaccented andunaccented beat units.

in fact, if you listen to a sequence of repeated notes, your brain will probably start to

perceive the notes as groups of two, three,orfour,even if no accents are present!

these groups are calledmeasures,

and they are delineated withbarlines.

the organization

of beat units

and measures in

a piece is called

meter.Meter is

described by two

numbers placed

at the beginning

of the piece:

the time signature.

by looking at the top

numberof the time signature,

you can tell two things aboutthe meter: whether itssimple

orcompound,and how many

beats are in ameasure.

be

ats

per

measure

simple compound

2

3

4

the top number

indicates thenumber

of beatsin a measure.

the bottom number

indicates the type of

notewhich serves as

thebeat unit.

simple metersareeasy.

measurebarline

the code for the bottom note

is pretty easy: refers to

a quarter note, to an eighth

note, to a sixteenth note,

and so on.

the top number indicates thenumberof divisions in a measure. to get thenumber of beats, divide it by three. in fact, wouldnt this bean easier way to notatecompound meters?sorry... theman says

you have to do it

the other way.

the bottom number indicates the type of

notewhich serves as thedivision.

to get thebeat unit,use the note that

is equal to three of these notes.

in a compound meter, the beat unit is

always adotted note!

compound metersarestupidly complicated.

notes that haveflags can

be grouped together by using

beams in place of flags.

however, beaming is only used to group notes within beats.

for the most part, you shouldntbeam notesbetween beats,

nor should you tie notes withinbeats.


4/46

notes should be beamed in groups that illustrate th meter.for simple rhythms, this is pretty easy to do;simply group any notes that can be beamed (eighth notes and smaller) intogroups that areequal to the beat unit of the current meter.

rcomplex rhythms,however, things can get complicated... when a rhythm includes thingsesyncopations or other off-beat figures,illustrating the meter may involvedividing

otesacross beat units with ties.fortunately, there is astep-by-step systemfor correctaming these complicated rhythms!

*translation:

step 1:

y,kids!

itsSparkythemusic theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN

Q:

A:WOOF!*

Dear Sparky:

I understand that were supposed to beam rhythms to show the organization o

beats in the measure, but is there an easy way to beam complex rhythms?

--A.Y., Owatonna, MN

or example, letstake this rhythm,which is written

without beaming.

find the smallest note value used, and fill a complete measure with this type ofnote, beamed in groups that are equal to a beat unit in the current meter.

step 2:add ties between individual notes to recreate the original rhythm. make sure thateach tied group corresponds to a note in the rhythm you started with!

step 3:findevery group of two or more notes that areboth tied together and

beamed together,and replace them with asingle noteofequivalent value

acorrectly beamed rhythmmay include ties,but it willvery clearlyshow thebeatsin the measure... which, inturn, makes iteasier for the performer to read!

yes, i know itlooks weird...but were not

done yet!

you have notesthat are tied orbeamed, but not

both,then leavethemalone!

=

ont

uch!

hands

off!

yes...

simplify it!

original rhythm:


5/46

he Major Scale

one of the reasons that a particular piece ofmusicsounds the way it doeshas to do with thgroup of notesthe composer decided to use.

take this melody,for example...lets first remove all theduplicate notes, regardless of which octave theyre in.

next, lets put the notesinalphabetical order,starting on the notethat the melody soundedlike it wascenteringon.

what we end up withis the paletteforthis particular piece...

there are actually manydifferent types of scales,

each with a different pattern

of whole stepsandhalf steps.

ahalf stepis thedistance between

two adjacent keys

on thepiano keyboard,regardless ofcolor.

like theboardon which a painter holdsthebits of paintbeing used in the painting being created.

in music, this palette is calledascale.though we usually write

scales fromlow tohigh,the order is actually unimportant;its thenotescontained in the scale that help make a piece sound the way it does.

a whole step is theequivalent oftwo half steps.thisparticulararrangement, wherehalf steps occur betweensteps three and fourand between stepsseven and eight(or between seven and one, since eight and one are the

same note), is called the major scale.

knowing this formula, you can create a major scale onany note!

(this scale, by the way, is called theg major scale,because it starts ong.)

thef majorscale

theb majorscale

thed flat majorscale

theg flat majorscale

but remember..with

great power

comesgreatresponsibility

wholestep

wholestep

halfstep

halfstep

wholestep

wholestep

wholestep


6/46

f you start writingmajor

calesand pay attention to

eaccidentals that occur,

you are going to start

noticing apattern...

for example look at the flatkeys, starting with the key

that has one flat,all the

way through the key with

seven flats:the flats accrue

in aspecific order.

same with thesharp keys!

so if you look for a key that

has only ad flat,you wont

find it: if a key has ad flat,

it must also have ab flat,an e flatand ana flat!

A

A

b

b

c

c

c

d

d

e

e

f

f

g

g

Key Signatures

B E A D G C F

f c g

f c g d a

f c g d a e b

f c

f c g d

f c g d a e

f

B E A D

B E

B E A D G

B E A

B

B E A D G C

nce writing an entire piece in

sharp majorwould have

een a sure-fire way to get

arpal tunnel syndromewith

l the sharps involved,

omposers pretty quickly came

p with a way to simplify things:

ey signatures.

key signatureis a group of

ccidentals placed at the

eginning of every line of music,

ust to the right of the clef,

at instructs the performer

o apply those accidentals to

very corresponding notein

e piece unless specified

therwise.

h, andanother thing:the

ccidentals have to be placed

thecorrect order,and

ey need to follow a

articular patternof

lacement that variesslightly

epending on theclef being used!

you deviate from this, you, as

composer, will bemocked!

for example, this key

signature indicates that

everyf, c,andgin the

piece should besharped,regardless of octave!

tenor clef sharps!whats

yourproblem?you need to

conform!ha ha...never!


7/46

F

A

E

B

D

G

C

theorists find itconvenient to

organize all the possiblekey signatures

into achart that shows their relationship

to one another.

this chart, called the circle of fifths,

displays each key as aspoke on the circle,

beginning withc majorat the top and

adding accidentals,one at a time, to the

key signatures around the perimeter. wellreturn to this chart

as we continue learning about

how composers usekeys.

as you moveclockwise around the

circle, you addsharps to the key signature.

as you movecounterclockwise around,you addflats to the key signature.

notice how that

beadgcf pattern

ops upall over

the circle of

fifths?

weird!

so could you

continue the

enharmonic

deal and have

the key of

f flat major?

yes, if you want

adouble flat

in your

key signature

nooooo!

to determine thekey

signaturefor a key, look to

see which spokeof the circle

its on to determine how many

flats orsharps it has, and

addaccidentals to the key

signature appropriately.

the keys down here line up

enharmonically...for example,

the key ofd flat majorwill sound

just like the key ofc sharp major.

B

E

A

DG

C C

F

he Circle of Fifths

for example,

e flat major

has three flats,

so it should

look like this:

0

1

2

3

4

56

7

1

2

3

4

56

7

when addingflats to

a key signature, add them

in this order:

when addingsharps,

use thereverse

of the order above.

beadgcf


8/46

an interval isthedistance inpitchbetween two notes.the most basic way which weidentify different intervals isbycounting the stepsbetweenthe two notes.specifically, wecountscale degrees,but theeasiest way to do it isto countlines and spaceson thestaff.when counting,begin with the

bottom noteasone and countuntil you reachthe top note.

this intervalis aseventh!

two notes onhe same line orspace is called

aunison.

when we are talking aboutintervals we sometimes discuss

harmonic intervalsandmelodic intervals.

and when youswap the two notes(move the lower noteup by an octave

so it becomes thehigher note),

that is called inverting the interval.

its helpful to rememberthatseconds always invert

tosevenths, thirdstosixths,and so forth...

the fact that each of

these pairs add up tonineis known to theorists as

the rule of nines.

a harmonic interval is simplytwo notes playedsimultaneously;

a melodic interval isone note

played after the other.

harmonic

interval

melodic

interval

thatslatin forone sound!

and thatslatinfor eight!

the distance froma note to the nextclosest note with

the same letter nameis called an octave.

second

unison

third

fourth

fifth

sixth

seventh

octave

when countinthelines anspaces,wecan safelyignore any

accidentals

this intervalis also a

seventh...

well discushow itsdifferent

verysoon!

1

23

4

5

6

7

smallerintervals

iatonic Intervals

largerintervals

2nd 7th3rd 6th

4th 5th

5th 4th

6th 3rd

7th 2nd

THE RULE

OF NINES


9/46


10/46


11/46

the following chart shows an approach for identifyin

any interval.a similar approach can be used when you

need to write a particular interval above or below agiven note:first, ad

a note above or below the given note at the correctdistance,then follo

steps2through 4of this chart to identify it. Then, if necessary,alter the

note you added with anaccidental to create the interval called for.

determine thedistance of the interval

by countinglines andspaces.

count thebottom

note as one, an

continue until yo

reach the top not

*translation:

STEP 1:

cover up allaccidentals.STEP 2:

determine the inflection of the interval

currently shown as follows:

if it is a

unison or octave:

the interval shown

is a

perfect unisonor

perfect octave.

if the interval uses

the notesfandb,

it is either an

augmented fourthor a

diminished fifth.

if the top noteis

in the major key of

thebottom note,

the interval is

major.

if thebottom noteis

in the major key of

the top note,

the interval is

minor.

otherwise, the

interval is

perfect.

really.

itjust is.

if it is a

fourth orfifth:

if it is a

second, third,

sixth orseventh:

STEP 3:

add the original accidentalsback,

one at a time,and track how the

interval changes inflection.

remember:accidentals cannever affect

thedistance of an interval... distance is

determinedsolely by the number of

ines and spacesbetween the two notes!

This method may seemcomplicated at first

but as you use it, youll internalize it and

becomefaster...so get out there and

identify some intervals!

STEP 4:

y,kids!

itsSparkythemusic theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN

Q:

A:WOOF!*

Dear Sparky:

Since we are supposed to use different approaches for identifying perfect and

imperfect intervals, can you summarize them all into one system?

--I.M., Staten Island, N

poof!poof!


12/46

There are actually two things that define akey:

thekey signatureis the most obvious one, but

another important part of a key is the tonic...

thenote around which the keycenters.

he Minor Scales

s key is defined

a key signature

fno sharps and

ats,but also by

e fact that it

nters aroundc.

the

natura

l

minor

scale

the

harm

onic

minor

scale

the

melodi

c

minor

scale

but what if wechange the tonic?what if we use the same notes for the key signature,

but change thenote that the key is centered around?

the thing is,common practice periodcomposers

werent all that crazy about this scale, because

it lacks something themajor scalehas:

a half-step fromsevento one.

his scale is great for buildingchords,so we refer to it as theharmonic minor scale

however, composers didnt use it for writingmelodies,because it had aproblem:

anaugmented secondbetween thesixth andseventh scale degrees.

so, formelodies,they made another change:

they addedanother accidental to raise

thesixth scale degreeby a half-step.

ow, remember... the reason weraised theleading tonein the first place was to create

ension from theseventh scale degreeto tonic.but in a melody, if the seventh scale

degree is followed by thesixth scale degree,we dont need that tension, so we dont

eed to raise the leading-tone at all.

he way we illustrate this is by differentiating betweenascending melodic minorand

descending melodic minor;for descending melodic minor, we dont raiseanything!

now we only

have whole steps

andhalf-steps!

the whole step

here didnt have

the tension

they liked going

into the tonic!

if we center the key around thesixth scale degreeof the major scale,

we get a new scale: theminor scale.

so heres what they did: theyraised the leading-tone by ahalf-stepwit

anaccidental.This gave them the tension they were looking for

half-

step!


13/46

C+

Cc c

although achord is technicallyany combination of notesplayed simultaneously, inmusic theory we usually definechords as the combination of three or more notes.

riads

secundal

harmonyhords built fromseconds formtone clusters,

which are notarmonic so much

as timbral.

tertial

harmony

quartal

harmonychords built from

perfect fourths

create a differentsound, used in

compositions fromtheearly 1900s

and onward.

quintal

harmonychords built fromperfect fifths

can be respelled asquartal chords,

and as such theydo not create a

separate system ofharmony.

sextalharmony?septalharmony?

as

with

quintalharmony,

these

are

the

same

as

ter

tialand

chords built fromthirds(MORE

SPECifically, frommajor thirdsand

minor thirds)form the basis ofmost harmony in

thecommonpractice period.

is the chord still tertialif it is built fromdiminished

thirdsoraugmented thirds?

well, diminished thirds soundjust likemajor seconds,andaugmented thirds sound justlikeperfect fourths,so...

thelowest note in the chordwhen the chord is insimple

form is calledtheroot.thenames of the

other notesare based ontheir intervalabove the root.

when we stack

the chord inthirds within one octave,

we get what is called thesimple form of the chord.

no. rootthirdfifthlets get startedon tertial harmonywith the smallestchord possible:the triad.there arefour ways to create a triad

usingmajorandminor thirds:

th

e

diminish

ed

tria

d

the

m

inor

tria

d

the

maj

or

tria

d

the

aug

mented

tria

d

triad is defined as a three-note chord,but in practice it is almost always used

to refer to tertial three-note chords.

we label triads using theirroot (ac minor triad). the abbreviations shown above, which useupper case, lower case,andsymbols to show chord type, are calledmacro analysis.

twominor thirdsstacked together

amajor thirdon topaminor thirdon bottom

aminor thirdon topamajor thirdon bottom

twomajor thirdsstacked together

min 3rd

min 3rd

maj 3rd

min 3rd

min 3rd

maj 3rd

maj 3

maj 3


14/46


15/46

6

(5)(3)

6 6 6# 6# 6# ##

Figure 1.e Basso Continuo

musical works written in thebaroque erawould ofteninclude a part called thebasso continuowhich wouldconsist of asingle bass clef melodic linewith various

numbersandaccidentalsprinted beneath the notes.

he numbers and symbolsrinted below the bassoontinuo part are calledhefigured bass.So how

o you turn figured basstochords?

first of all, its important to know that thenotegiven on the bass clef part is alwaysthebass note of the chord.and remember: thebass is not necessarily theroot!

econd, thenumbersepresent intervalsbove thebass, evenhough some numbersre usually left out.

lastly,accidentals arapplied to the interva

they appear with. if yohave an accidentalb

itself,it applies to th

thirdabove the bass

by the time theclassical periodgotgoing, composersstopped including a

basso continuo part,and so figuredbass fell out of use... with only oneexception:music theory classes!

wooo!

realizingfigured bass (writing chordsgiven a figured bass line) makes for an

excellent exercisefor students to learnhow to writein thecommon practiceperiod style!

dont overthinktheseif the composer want

a noteraised by ahalfstepand itsflatted i

the key signature, thfigured bass will hav

anatural,not asharp

ote that the intervalsre alwaysdiatonic.ont worry aboutnflection...just usehe notes from theey signature!

if there are

no numbers,add a third and

afifth above thebass... you get a

root position triad!

here, thesharpapplies to the

sixth above thebass, so we add asharp to theg.

here, there isnonumber next to thesharp,so we applyit to the third above

the bass note.

note that there isanatural,not aflat,

next to the six...if it were a flat, we

would write ac flat.

asixby itself

indicates asixthand a third abovethe bass, whichcreates afirst

inversion triad!

asixand afour

indicate asixthand afourthabove the bass,

giving you asecondinversion triad!

in performances, the bass clef instrument would simply playthegiven notes,but the keyboard player would improvise

part based on thenotes and the symbols below the par

no, no, no...there wasnt an actual instrumentcalledabasso continuo!the part was played by two

instruments:a bass clef instrument likecello orbassoon,and a keyboard instrument like aharpsichord

igured Bass

6 6 9 55

65

65

so this...

could be played as this!

6

(3)6

6 6n##

4


16/46

now that were familiar with how

triads work, its time to put them

into the context of akey.

since writing music in a particularkey means using the notes in that key signature

it stands to reason that most of thechords will be built from those same notes

chords which use notes from a particular key signature are said to bediatonic

to that key. diatonic means from the key.that meansno accidentals!

we can quickly show all thediatonic triadsin a particular key by writing ascale

in that key and buildingtriads

oneach note,

using only the notesin that key.

riads Within Tonality

I ii iii IV V vi vii

tonic

Supertonic

mediant

subdominant

dominant

submediant

le

ading-tone

we refer to

hese chords

withroman

numerals as

shown here.

notice how

chord type

is shown by

capitalsor

ower case?

these chords are also

sometimes referred to by

their official names!

menamesdroman

merals...

ferent

pitalization!

this pattern of

major, minoranddiminished

triads is thesame inevery major key!

thesubdominant triadis alwaysmajor,

and theleading-tone triadis always

diminished,whether youre in

c majororf sharp major!

why is the sixth chord called thesubmedian

well, just as themediant chord is halfw

between the tonic anddominant chord

thesubmediant chord is halfway between th

tonic... and thesubdominanta fifthbelo

the diatonic triads inminor work the same way... since were dealing withchords,we

use theharmonic minor scale.however, its important to note that common practic

period composersraised the leading toneonly overdominant function harmon

thedominantandleading-tone triads!

because thedominant andleading-tonetriads bot

have a strong tendency to resolve to tonic,we say th

have a dominant function.thesubdominant andsupertonic chords both tend t

resolve to thedominant,so we say they both have a subdominant function

i ii III iv V VI vii


17/46


18/46


19/46

art-Writing: The Horizontal Rules

**

thesupreme goalof part-writing isgood voice leading...making each individual voice parteasy to singby avoiding

awkward intervalsorlarge leaps!

before we get to the specificdosanddonts,lets take a lookat some important characteristicsof four-voice part-writing:

note how each voice movesaslittle aspossible,goingto thenearest chord tonein each subsequent chord!

the bass line, since it providesthefoundation of theharmony

in each chord, tends to includelarger leapsthan the other

three voices, but thats okay.

there are also a few otherrules that apply to this style:

when you have theleading tonein an outer voice(soprano or

bass) it must resolve to thetonic in the next chord.

you may not moveany voiceby an interval of anaugmented second

or anaugmented fourth.

its common for the bass tomove in the opposite direction

of theupper three voices.this is calledcontrary motion

and it helps maintainvoice independence.

four-voice harmony is a form ofcounterpoint,which is the combination ofmore than onemelodyplayed simultaneously. in counterpoint,each voice isequally important;no voice isgiven a role of accompaniment to another voice.

thegood news:you can avoid all three of

these by doing the followingwhenever possible:

1. keep the common tone!

2. move to the nearest chord tone

3. use contrary motion!

in counterpoint, it is important for each voice tobe independent; that is, no two voices should be

doing theexact same thing. if two (or more)voices were moving inparallel,therichness

of the texture would bereduced.

as a result, common practice composers werevery consistentin avoiding two or more voicesthat moved inparallel perfect octaves, parallelperfect fifths, orparallel perfect unisons!

paralleloctaves!

parallelfifths!

parallelunisons!

in some cases, the voicecan simply stay on thesame

note.This is calledkeeping the common tone,

and itsalways cool!

voice independence?


20/46

art-Writing: Using Inversionswhen common practice composers used inverted chordsin

four-voice writing, they followed somegeneral patterns

regarding which note of the chord should bedoubled.

root position

bass

first inversion second inversion

inroot

position triads,

omposers usually

doubled the root,

which is in the

of the chord.

bass

insecond

inversion triads,

composers usually

doubled the fifth,

which is in the

of the chord.

soprano

soprano

inmajor first

inversion triads,

composers

doubled the

of the chord.

bass

inminor first

inversion triads,

composers

doubled the

the doubling offirst inversion triadsdepends

on the type of the chord being written.

heresanother way to think of it: the only time you cant double thebass is

infirst inversion major triads,where you should double thesoprano instead.

vii6

ii6

the only rule regarding

root position triads

andfirst inversion triads

is thatdiminished triadsare

always placed infirst inversion.

other than that, you can use

root position and first inversion

essentially whenever you want!

if you write a

second inversion triadand

its not one of these three situations,

then you arenot writing in thecommon

practice period style!the composers of

the style just didnt use these chords

willy-nilly.

itssecond inversion triadsthat

have thebig restrictions.

of the chord.

or

bass

indiminished

first inversion

triads, they

doubled the

of the chord.

thecadential chord

s a tonic triad in

second inversion

followed by a

root-position

dominant chord

at a cadence.

64

thepedal chord

s a second inversion

chord where the

bass is treated like

apedal tone.

64

thepassing chord

is a chord placed in

second inversion

where the bass is

treated like a

passing tone.

64

4I6

V IF: 4V6

I6

IF:

4IV6

I IF:

okay, we knowhow to use inversions in four-part writing... but when can we use them?


21/46

art-Writing: Melodic Minor

so anyway,

after we got

him transposed

back to tonic, he

began to modulate

again, and...

what seems to be

theproblem, sir?well, I thought Id transpose to

minor,you know, to surprise the

family... so I did, and then I raised

all myleading tones, because

Im a common practice period

progression, right?

okay, sure. so whats wrong?

attention! attention!

we need assistance

with anew patient

in emergency treatment

room3b...stat!

ive got

augmented

seconds!

*gasp*

my

augmented

seconds...

theyre

cured!

all in adays work,

my good man.

now lets turn to

the unpleasant matter

of thebill.

in thecommon

practice period,

composers used

harmonic minor

by default. but

whenaugmented

secondsoccurred

they turned to a

hero for help:

melodic minor!

cure your augmented seconds withmelodic minor today!

and for thesedescendingaugmented seconds,were going to useanunraised seventh!v

and that

makes a

minor v

chord!

paging... dr. melodic minor!

doctor, what

can wedo?for this case ofascendingaugmented seconds,

I prescribe araised sixth scale degree!

ooh... amajor iv chord! IV6


22/46

he Harmonic CadencesAcadence is generally considered to be the

last two chordsof aphrase, section or piece.there arefour types of cadences, each withtheir own specificrequirements and variations.

authentic cadenceconsists of adominant function chord (vor vii) moving to tonic.

perf

ect

authen

tic

impe

rfec

t

auth

entic

impe

rfec

t

authen

tic

perf

ect

plag

al

half

phry

gian

decept

ive

phry

gian

impe

rfec

t

plag

al

impe

rfec

t

plag

al

be considered aperfect authentic cadence,

cadence must meetall of the following criteria:

be considered aperfect plagal cadence,cadence must meetall of the following criteria:

if the cadencedoesnt meet

all of thosecriteria, itsconsidered tobe animperfect

authenticcadence!*

***

must use a vchordot a vii)

th chords must beroot position

e soprano mustd on the tonic

e soprano mustveby step

plagal cadenceconsists of asubdominant function chord (ivor ii) moving to tonic.

half cadenceisany cadence that ends on thedominant chord (v).

deceptive cadenceis a cadence where thedominant chord (V)resolves to somethingther than tonic...almost always thesubmediant chord (vi).

a specific type of half cadenceis thephrygian cadence,whichmust meet the following criteria:

if the cadencedoesnt meet

all of thosecriteria, itsconsidered tobe animperfect

authenticcadence!*

***

must use a iv chordot a ii)

th chords must beroot position

e soprano mustd on the tonic

e soprano mustep thecommon tone

*

***it occurs only inminor

it uses a iv chord moving to v

the soprano and bass moveby stepincontrary motion

the soprano and bass bothend on thefifth scale degree

V I vii6

I V64 I

IV I IV6

I ii I6

I V

VG:

G:

G:

G: G: G:

G: G:

e: e:

vi

iv6

V iv V

really, its thepsych-out cadence,in thatyouexpect it to resolve to tonic, but itdoesnt.

and, in fact, its more common to see this inthemiddle of the phrase rather than theend...

where you might call it a cadence-like structure!


23/46ii iii vii6

V IC:

how did composers of thecommonpractice perioddecide which orderto putchords in? did they just throwthem down on paperhaphazardly?

s a matter of fact, there are certain chord progressions that appearmorerequently,and there are others that areavoided pretty consistently. whilehe choices were always based on whatsounded goodto the composer, asheorists there is apattern in their choices that we can use to easily rememberhich chord progressions work and which onesdont.

o understand this pattern, we need to think in terms ofroot movements.a root movementhe basic interval between the root of one chord and the root of the next chord. youont have to worry about the intervals inflection, just itsdistance anddirection.

or example, to determine the root movementere, we look at theroot (notbass) of eachhord and figure the interval between them.

so heres the pattern: common practiceperiod composers generally used root

movements ofup a second, down athird, anddown a fifth!

remember... sincenflection doesnt

matter, we cannoreaccidentalswhen we figure the

root movements.

so, for example, ag chordto ane chord is down a third, but so is

gtoe flat,andg sharptoe flat!

thats not say that theynever used other rootmovements, but it didnthappen very often.

sequences of chords thatdontfollow this patternare calledretrogressions,and they are consideredunstylistic.

here are also four simple exceptions to this pattern:

any chord canmove to tonic,

tonic can moveto any chord,

any chord canmove to dominant,

and the leading-tonetriad must move to tonic

itsdown a seventh, butsince octaves dont matter,we invert it toup a second

armonic Progression

2

3

5

I I V vii I

lets try it...say you havea supertonicchord and

you are tryingto decide what

chord to useto follow it. yo

u

can

move

upasecondto

a

me

diantchord...

yo

u

can

move

dow

nafifthto

a

dom

inantchord...

oryo

u

can

use

the

first

exception

and

go

to

a

tonicchord!

yo

u

can

move

dow

nathirdto

aleading-tone

chord...


24/46

iatonic Common Chord Modulationmodulation is the process ofchanging to a different keywithin a piece of music.

there are several differentways to modulate; perhaps the

simplest is theunpreparedmodulation, where the musicpauses and suddenly changes

key, often up ahalf-step.

common practice period composers,however, preferred a particular typeof modulation that required a littlemore planning: thediatonic common

chord modulation.as the namesuggests, this uses a chord whichisdiatonic in both the outgoing keyand thenew key.

lets say were starting off inc major...here is a list of all the keys whichhave chords in commonwith c major (the specific chords are highlighted):

ys which haveords in commone this arelledrelated keys.

notice how these keyare all close to on

another on thcircle of fifths

hey... what is thisportrait doing here?

manilow

i ii III iv V VI viia:

I ii iii IV V vi viiB :i ii III iv V VI viib:

I ii iii IV V vi viiD:

i ii III iv V VI viid:

i ii III iv V VI viie:I ii iii IV V vi viiF:

I ii iii IV V vi viiG:

I ii V I viC:e: iv V VI iv V i

to use this type ofmodulation, a composerouldpivot the harmonyaround the chord that

fit into both keys.As theorists, we show

thispivot chordbyanalyzing the chord in

both keys.

note that the pivotchord isalwaysthe

last chordthat canbe analyzed in theold key...the firstaccidentals will alwaysoccur in the chord

immediately followinthepivot chord!


25/46

uspensions are typically further identifiedy number.The first number represents theterval between thenote of suspensionandhebass.The second number represents theterval between thenote of resolutionandhebass.

he exception to this rule is the2-3orasssuspension, where the numbersepresent the intervals between thebasswhere the suspension occurs) andhichever voice has the note which is a

econd (not counting octaves) abovehe bass.

anon-harmonic toneis a note thadoesnt fit into a chord. we classifynon-harmonic tones by how they are

approached andresolved!

Non-Harmonic Tones

passing

tone

name

abbr

eviatio

n

appr

oach

reso

lutio

n

notes

exam

ple

step steppt

resolves by continuing inthe same direction as the

approach.

ppoggiatura leap stepapp resolves in oppositedirection from approach.

changingtones

any step cttwo non-harmonic toneson either side of thenote of resolution.

suspension commontone

stepsus a note held over froma previous chord andresolved down.

pedal tone common

tonecommon

toneped

4-3sus

9-8sus

2-3(bass)sus

7-6sus

a chord tone whichtemporarily becomesa non-harmonic tone.

eighboringtone

step step Ntresolves by returning tothe note preceding the

non-harmonic tone.

scape tone step leapet resolves in opposite

direction from approach.

anticipation any common

toneant

a chord tone playedbefore the rest ofthe chord arrives.

retardation common

tone stepret

a note held over froma previous chord and

resolved up.


26/46


27/46

iatonic Seventh ChordsWhat are they?

Remember,diatonic

means from the key.

so a diatonic chord is one

that only uses notes in

the key signature.

No accidentals!

diatonic seventh chordsare the

seventh chords you can create using

only the notes in a particular key.

I7

ii7

iii7

IV7

V7

vi7

vii7

there are eight possible types of

seventh chords in tertial harmony

but the composers of the commo

practice period only usedfive:

C: i7

ii7

III7

iv7

V7

VI7

vii7

a:

re they are

major and

minor.

emember:

we only

raise the

eading-tone

over

dominant-

function

harmony!

thema

jor

seventh

major 7th

above root

major triad

the

majo

r-mino

r

seventh

the

mino

r

seventh

the

half-diminish

ed

seventh

the

fullydi

minis

hed

sevent

h

minor 7th

above root

major triad

minor 7th

above root

minor triad

minor 7th

above root

diminished tria

diminished 7th

above root

diminished tria

we use 07 for

half-diminished sevenths

and 07 for

fully diminished sevenths.

n harmonic progressions,diatonic sevenths can

e used anywhere you can use a diatonic triad with the

ame root. V

7I7

ii7

vi7

iiiviiIVIV 7

in fact, these chords can

be approached and resolved

using any of the same threeroot movements

as triads use.

2

3

5

ith the diatonic seventh chords, we add a

ourth root movement: the common root.

owever, this root movement can only be

sed to increase tension,so going from

seventh chord to a triad is avoided.

1

V7

VV7

V

respect the seventh!respect the seventh!

hen using these chords in four-part writing in

act, when you useany seventh chord in four-part

riting, you must always,alwaysremember to... e seventh of the chordmost often approachedthe common tone.owever, it is okay toproach the seventhom below by a stepr a leap, or from above

a step.

u mustneverapproach

e seventh by aleapfrombove!

The seventh of the chord

isalways resolveddown

by step.always!

no, im serious. dontever

resolve the seventh of a

seventh chord any other

way.

doing so will cause you

certain death!

seventh chords havefour notes,so doubling in four-p

harmony is not an issue... but if you need to use irregu

doubling,double the root and omit the fif

theadd-a-seventh-inator

pat.pending


28/46

he Dominant Seventh

I

I

I

IVV7

V7

V7

I6

V7

V6

V7

V

7

V

7hedominant seventh is thediatonic seventhchordbuilt on thefifth scale degree.wealready discussed diatonic seventh chords...why give this oneall this special attention?for one thing, thedominant seventh is,

by far, themost common

seventh chordused bythe composers of the

common practice period.

rst, a note on terminology:

he terms major-minor seventhnd dominant seventh are notterchangeable! Major-minoreventh is the chords type,anddominant seventh is therole

he chord plays in thecontext

of a particular key.

the reason these are oftenconfused is that inpopular

and jazz theory,the termdominant is used to labelthe chord type as well asthe chordsrole.

but the primary reasonfor spending a little extratime with it is the fact that

there are a few thingsthat apply to it thatdont

applyto the other diatonicseventh chords.

its just a major-minor seventh...

until its placed in a particular key!

he other important thing to know about the dominant seventh chord is that common practiceriod composers would sometimes use somenon-standardways of resolving thesevent

n this resolution, the seventh is stillresolveddown by step,but it takes anornamental detourbefore getting there.

Here, the resolution of the seventh isdelayed by moving to some other chord(usually thesubdominant) and having theseventh of the chordhold outuntil thedominant seventh returns.

in this resolution, the seventh of the choris still resolveddown by step,but the noit resolves to appears in thebass voice.

the voice thathad the seventhresolvesup,usually bystep.

after the V7

returns,thevoice that hasthe seventhshouldstill

resolve itappropriately!

this is the hot potato resolution: instead obeing resolved down by step in the same voicthe seventh ispassed to another voiceinanother dominant seventh chord.

the ornamentcan be anyshape orlength, but it

must resolveto the note

down a step

from theseventh of theseventh chord.

seventh

seventh

ornamentresolution

resolution

transferredto tenor

ornamental resolutionhe

delayed resolution

he

bass resolutionth

e

transferred resolutionthe

the seventh stillneeds to resolvedown by stepbywhatever voice isthe last to have it.

If the bass voice gets it, heresolves itimmediately,ending the fun for everyone.

5

resolutionseventh


29/46


30/46

were going to take a little breakfrom the usual stuff and... hey,

itsludwig van beethoven!

Ill tell you whatsgoing on: ImgrumpyI bet archduke rudolp

20 guldenthat Icould write

500 measures

of music this week andso far Ive onlycome up with

four stinkin notes!whats going on, maestro?

repetition

motive repetition

nversion

nterval contraction

nterval expansion

diminution

augmentation

rhythmic

metamorphosis

mitation

hey, itscool,mr. b...we can use these notesas amotive,and createa ton more music based

on them. watch!

the simplest form of motivicdevelopment: repeating a phrase

immediately gives you twice asmuch music!

Motivic Development

beethoven

woooot!

read it andweep,rudy!

you sly fox...506 measures!wait... we are in

4/4 time,right?

so lets use2/4 timeinstead!

uh, yeah...

so, heh heh....hat gets us to253

measures...

beethoven

aw, dang!lets go

double or

nothing!

motive

motive

augmentation of original motive

metamorphosis of original motive

motive

imitation

int. expansion

sequence

inversion of original motive

sequence sequence

repeating a motive at a higheror lower level pitch. as withall of these, the intervals

dont have to match exactly.

flipping the motive upside-down:if the original motive leapsdownward, an inversion will

leap upward.

making the intervals within themotive smaller (contraction) or

larger (expansion).

changing the speed of the motiveso it is played faster (diminution)

or slower (augmentation).

any change of the motives rhythm(other than just changing the

tempo, as described above)

an echo effect between different voices

(between instruments in an ensemble, forexample, or between registers on the piano)

original motive


31/46

when we talk about theform of a piece,we are referring to the large-scale layoutof the piece... specifically, the arrangementof sections of music, how and when they

are repeated, and what keys are being used.

inary Form

baroque dance suites were written for varying instrumentation; many were writtenforkeyboard(usuallyharpsichord orclavichord), others were written for chamber

groups, and some were even written forfull orchestra.

each movement of these suites would be written in the style of a particular baroque danceallemande, gavotte, bouree, courante, sarabande, louree, gigue,and others,

each of which had a specific character.

because baroque dance form is so common in baroque instrumental music, whentheorists and musicologists are talking about baroque music and say binary form,

they are actually referring tobaroque dance form.

One of the simplest forms isbinary form,which consists oftwo contrasting sections.werefer to these two sections as

aandb.

the sections might be contrastinginmood, tempo, key,or even in a

combination of these characteristics.

A Bb i n a r y f o rm

another somewhat rare variation ofbinary form isrounded binary form,where theAsection returns after theend of thebsection. this reprise of

theasection, however, isshortened,

so we refer to it as a prime.

A ABrou n ded b i n a r y f o rm

binary form is used inbaroque dancesuitesin a very specific way. In thesepieces, both sections are repeated.theAsection begins in the primary keyand modulates to thekey of the

dominant,and the B section begins inthat key and modulates back to theoriginal key. performers of the timewould typically improvise ornamentationwhen repeating each section.

A Bb a roqu e d a n c e f o rm

I V V I

1010111011011110111011100100001001000000101100101101111011101010010000001

00010111001001100101001000000111001001100101011000010110110001101100011110

10010000001101001011011100110001101110010011001010110010001101001011000100

11011000111100100100000011001110110010101100101011010110111100100101110


32/46

ernary Form

in ternary form, theasection appearsboth at the beginning and at the end;

like binary form, thebsection iscontrasting in character.

the reprisedasection may be an exactrepeat of the firstA,or it may be

slightly different, but thelength oftheasections should be similar.

theminuet and triois a variation on

ternary form used for instrumentalmusic. instead of writing out the reprised

asection, the score will place theinstruction da capo al fineafter the

bsection, which means to return to thebeginning, play through theasection,and end the piece.

its worth mentioning thatthere is a common formthat is descended from

minuet and trioform:themilitary march form

favored by john philipsousa and other american

march composers.

in themilitary march form,the a section is split into twosubsections, called thefirst strainandsecond strain.the trioadds a flat(or removes a sharp) from the keysignature, modulating to the key of thesubdominant.most marches begin with a shortfanfare, and repeat thetrio, placing a short, intensely dramatic passage between

repetitions called thedogfight orbreakstrain.

this is different fromrounded binary,where the reprisedasection (which wecalleda prime) issignificantly shorterthan the firstasection.

this same form is commonly used in baroque and classical opera, where it is calledada capo aria.In both minuet & trio and da capo aria, anyrepeats are ignored

when playing through the repriseda section.

ternary formis a three-part form.rather than using three completelydifferent sections,most pieces internary form consist of two sections,

the first of which isreprised.

A ABt e r n a r y f o r m

A Bm i n u e t & t r i o f o r m

minuettrio

Fine Da capoal Fine

m i l i t a r y m a r ch f o r m

A B(dogfight)

fanfare

1st & 2nd

strains

trio

I IV

sousa


33/46

sonata allegro formis a specific form

first used byearly classicalcomposers i

opening movements of multi-movement

works for solo, chamber or large groups

it was eventually adopted by other composers

of the classical and early romantic eras.

he form itself is based from

ternary form, in that the

irst large section is reprised

at the end of the form,

one of the most important features of sonata allegro form is the two primary themes

hat make up the exposition. THese two themes will beconstrasting in characterand, at

east in the exposition, will be indifferent keys.in a major work, the second theme will

e in the key of thedominant;in a minor piece, the second theme will be in therelative

major.in therecapitulation,however,both themes are played in the tonic!

he diagram above shows therequired elementsof sonata form; in the diagram below,

everal other elements, which are optionallyincluded, are also shown.

ear in mind that composers did what they wanted to... some of the greatest pieces written

n sonata allegro form feature places where the composer artfullybroke these rules!

onata Allegro Form

s o n a t a a l l e g r o f o r m

A ABfirst

theme

major

keys:

minor

keys:

second

theme

development

of main themes

first

theme

second

theme

development recapitulationexposition

I V I Ii III i i

s o n a t a a l l e g r o f o r m ( w i t h o p t i o n a l e l e m e n ts )

A ABintroductio

n

transition

codetta

coda

first

theme

second

theme

development

of main themes

addition of

others

first

theme

second

theme

development recapitulationexposition

I V I I

i III i i

major

keys:

minor

keys:


34/46

up to this point, all the chords weve

been talking about have been built using

only the notes in thecurrent key.

essentially, this means

no accidentals,with the

exception of the raisedsixth

andseventh scale degrees

inminor,which we

consider to be

part of the key.

first, every altered chord has to

have at least oneaccidental...

f it doesnt have any accidentals,

then bydefinitionits a

diatonic chord!

with few exceptions,

altered chords can use

the samebasic root

movementsthat weve

been using.

avoidcross relations.

a cross relation occurs when a note

appears with two different accidentals

in two consecutive chords,in two

different voices.

lastly, when you use these chords

inpart-writing, you should,

whenever possible, resolve the

altered notesin thedirection

of their alteration.

so if a note has aflat, try to

resolve itdown by step or by leap.

and we generally avoiddoublingaltered tones,

since doing so would tend to causeparallel octaves

second, altered chords can be easily used in place of their

diatonic counterparts. in other words, you can add somepizazzto a composition by replacing adiatonic chordwith an

altered chord

that has the

same root.

now that weve covered all

the possiblediatonic chordsin

tertial harmony, its time to open

the door to notes outside the key

these altered chordsadd a

certain richness to the harmony

by using one or more notes

that arenot in the key signature

and thus requireaccidentals.

diat

onic

altere

d(c

hrom

atic)

27theory

diatoni

ctriads

diatoni

cseve

nths

extend

edhar

monies

8

15

88

5

Altered Chords

BORROWED

CHORDS 26NEAPOLITAN

SECONDARY

DOMINANTS

dAUGMENTED

SIXTHS

V Secondary

Subdominants

$

well be covering

several categories

of altered chords,

each of which have

their own unique

rules for use.

however, there are

a few things that

they all have in

common!

V/

V ii

altered diatonic

I IV

6IV V

7vi

VI

23

5

1

like the diatonic sevenths,

however, thecommon root

should only increase tension...

dont move from an altered chord

to its diatonic counterpart.

ii65 V


35/46

orrowed Chords

altered chords use notes outsidethe scaleas a means of adding adifferent colorto the chord.

for example, the following chords arediatonic chordsinc minor:

orrowed?

hy call themt when majoreverbringsthem back?

but if we use them in a major key, they requireaccidentals and arethereforealtered chords.we call theseborrowed chordsbecause they

areborrowedfrom theparallel minor.

how does a composer decide whichaltered notes to use? in amajor key,

one possibility is using notes and chordsfrom theparallel minor.

iic: ii7 III iv VI vii7

iiC: ii7 III iv VI vii7

hey, minor!ll have themck by tuesdaythis time, Ipromise!

and, in fact, these six chordsare the six most commonly used

borrowed chordsin the commonpractice period. (One of them, the

major triad on the lowered mediant,or flat three,was not used much

by composers beforetheromantic era.)

some theoristsefer to the usethese chords as

mode mixture. two of these chords,the flat threeand flat six,havealtered tonesasroots.

we place afull-sized flatsymbolbefore the roman numeral itselfto indicate thisaltered root.

all the usual part-writing rules apply to thesechords. for example:

theborrowed supertonicis adiminished triad,and is thereforealways used infirst inversion.

its usually best to resolve alterednotes in the direction of theiralteration, but doing so in the two

altered rootchords wont work.

the borrowedseventh chords

an be used in any inversion, but theseventhmust beapproached

andresolvedproperly.

the leading-tone fully diminished

seventh is theking ofdominantfunction.dont even think of

resolving it to anything but tonic!

ii6

vii7

vii7ii7

IIIVI

VI V

VI V

wait... why? since we

double the root,moving both rootsthe same directioncan often result in

parallel octaves.

its more important toavoid parallelism thanto resolve the notesa certain way, so this

use ofcontrarymotionis better.

5 8

V7 ii6i i VI Vg:

I

theres another chord that is ofte erroneously called a borrowed chor used inminor,taken from the parallel

major.its thepicardy third:a tonicchord with araised thirdused as thefinal chordof the piece.

named for24th-century

explorerjean-luc

picard!*

*Nope.


36/46

*****he Neapolitan Six

in addition to thealtered root borrowed chords,there is anotheraltered root chordthat fits well

with the borrowed chords, even though it is notactually borrowed from theparallel minor.

that chord is amajor triad

built on the

lowered secondscale degree.

there are a couple of interestingthings about this chord. one is

the fact that it isalmostexclusivelyused infirst inversion.

seriously!although thischord isextremely common

in the common practiceperiod, there are very few

examples of it used inroot position.

second inversionisevenrarer.

the second interesting thing aboutthe chord is itsname:you might expectit to be called a flat two,in keepingwith the other altered root chords.

but, in fact, this is the first of a few chordsthat have special names. This particular oneis called theneapolitan chord.

Naples scarlatti

neapolitan means from naples,

referring to the city ofnaples,italy.the chord isnt actually

from naples, though; it wasjust associated with the operaswritten by neapolitan composerslikealessandro scarlatti.

funny thing is, this chord was used pretty

commonlybeforescarlattis time, incompositions far from the courts of italy.

its also worth noting that although nearlevery theorist and theory textbook calls thchord a neapolitansixth chord, it is mor

properly called a neapolitansixchord. thatbecause in the rare situations where it is use

in root position, it is simply called theneapolitanchord,and when it is found in second inversion

its called theneapolitan six-four

since we dont pronounceI6as one sixth,we shouldnt say Neapolitan sixthforN6!

N6

C:

The Neapolitan six chord, since it isbuilt on a form of thesupertonic,has some characteristics of a

subdominant function chordin that it often resolves toward a

dominant function. in fact, it is verycommon to see the neapolitan chordresolve to adominant seventhinthird inversion,or to acadential

six-four chord.

(even though the neapolitan chordhas a lot in common with othersubdominant function chords, it ismost often referred to as part ofa larger group of chords calledpredominants,and the label ofsubdominant function is generallylimited to thesubdominantandsupertonic chords and their

variants.)

since its not a borrowedchord, this chord can be usedin bothmajor andminor.

N6

N6

V42 I

64C:


37/46

econdary Dominants

the answer, of course, is withsecondary dominants.

lets say we wanted toapproach this vichord.

what if we wanted to usethatdominant-tonicmagic

ere is aduality at the heart of commonactice period harmonic progression.e the ancient conflict ofjedi andth, it consists of forces that,one level, workagainst eachher... but at another, higherel, work together, creatingergy that drives all else.

that duality, of course, is the relationsofdominant functionand tondominant harmony typifies tensioin the common practice period, a

the tonic represents releasits simplest form, theauthen

cadence,has been ubiquitoin western music for centurie

V

I

he progression of dominantmoving to tonic is so strong, itwould be nice to be able to use

to provide motion to chordsother than tonic.

but thatscrazy talk,thoughisnt it? I mean, how could we

control that magic and make iobey ourcompositional whim?

vi

?vi

vi

? we could use one of the usualdiatonic chords, the tonic, thesubdominant, the mediant... butwhat if were looking for a bitmore tension and release?

Va: C:i

viVa

aV

if we pretend for a moment that the chord were resolving to is a tonic chord, what woule correspondingdominant chord be?altered,yes, but were not afraid of those anymor

while we might have once called this ashortmodulation,it is really more likeborrowing another keys dominant chord.

if we think of the Vchord in the keyas theprimary dominant, Vchords ofelated keys aresecondary dominants.

inmajor keys,the xabove can be anydiatonic chord other than tonic(obviously)or theleading-tone triad.why? becauseadiminished triadhas a hard time acting

like a temporary tonic chord.

inminor keys,the composers generallyonly used secondary dominants

of ivand of V.

these chords often resolve to thechord under the slash,but they ca

actually be approached and resolvedusing thebasic root movements!

yes.yes theydo

now, were not just limited to the vchord:there arefive chords with a dominant function

V viiV7

vii7

vii7

dominant function chords

the secondary dominants

Vx x x x x

viiV7 vii7 vii7that gives us

a huge list ofpossibilities!

2

3

5

1

the basic

root movementsrock!


38/46

Fr.6

on 2

I

Augmented Sixth Chords

first, well start with

the doubled root of a

V chord...

V

...andapproach that

octave with a half step

below the top note,

...and a half stepabove

the bottom note...

V

...and, finally, add the

tonic as the third note.

V

like that moment of incredible tensionjustbefore thehero finally kisses theleading

lady,thehalf-stepis thego-to interval

for creating tension in music of the common

practice period. itdrives theentire style!

f one half-step can create such strong tension, how

bouttwo

half-steps soundingsimultaneously?

Lets

get creative here for a minute to find a cool new way

o approach a diatonic chord. in this case, well use them to approach thedominant triad.

the result is a new chord, one we call theaugmented sixth chord,

after the interval created by the top and bottom notes.

augmented sixth chords arepredominant chords

meaning they are used to approach dominant chord

they are usually used to approach dominant triads

not dominantsevenths,because of thedoubled

rootspresent in dominant triads.

however, they also often

approach tonic chords

insecond inversion,

which also contain a

doubled fifth scale degree.

rarely, augmented sixth chord

are found transposed down

aperfect fifth,analyzed ason flat two,and used to

approach a tonicchord in

root position.

It.6f we just usethree notesnd double thenic, we get theitaliangmented sixth. Fr.6f we add thesecond scaleegree insteadf doubling thenic, we get thefrenchgmented sixth.

Ger.6

and if we

replace the

second scale

egree with the

owered third

cale degree,

we get the

germangmented sixth.

Ger.6

I

64

Ger.6 V

5

and, finally, when resolving

the german augmented sixth

chord to a dominant triad,

you might find yourself

writingparallel fifths...

but itsperfectly okay!

mozart did itall the time!


39/46


40/46

C:

econdary Subdominantsafter learning aboutsecondary dominants,

you might wonder if its possible to extend the

concept to other chords.

for example, if we can use adominant functionchord

from a related key, what about asubdominant function

chordfrom a related key, likeIV of V?

well, the answer is yes,and the chords that result are calledsecondary subdominants

but before we talk about them, you need tounderstand a few things.

toapproachthese chords,

use any of thebasic rootmovements.

the most common way toresolve

secondary subdominants is to

the correspondingsecondary

dominant.which areawesome.

first of all, the veryexistence of

these chords isdebatable.

what one theorist might call

asecondary subdominant:

another might call a

shortmodulation.

V6 Iii7V

V42

V

C:

C:

G:

V

6

I6

I

ii7

V42

second, the only place

we find chords that

we cancall secondary

subdominants is in the

music of thex

romantic era.x

Lastly, since these chords are alread

pushing the limits of tonality, composer

would only use secondary subdominant

fromclosely related keys.I

other words, secondary subdominant

should only be of IVand of V

iv

IV iv

V

keeping these things in mind, lets look at thepossibilities:

what are all thesubdominant function chordsweve encountered?

first, there are

thediatonic triads:

ii IV

next, thediatonic

seventh chords:

ii7

IV7

and, lastly, a few

borrowed chords:

ii ivii7

so a secondary subdominant can

have anysubdominant function

chordabove the slash, and

aIVor Vbelow the slash.

however, the most commonly

found secondary subdominants

are those that use thehalf-

diminished supertonic seventh.

ii7

IV

ii7

VV

V

ii7

V


41/46

IF: IV V I DM B M

the music of thebaroque, classical

andromanticeras share a consistent use

fharmony andcounterpoint, enough to cause

heorists and historians to group them together

as the Common Practice Period.

however, the music of theromantic

eraemployed some interesting

techniquesthat set it apart from

the baroque and classical eras...

...andforeshadow some o

the big changes coming in

the twentieth century!

2000

1900

1800

1700

1600

1500

romanticearly 20th

centurycontemporaryclassicalbaroquerenaissance

Romantic Era Techniques

weve already mentioned a few chords

that were specific to the romantic era:

dominant eleventhand

thirteenth chords,

the flat threeborrowed chord,

andsecondary subdominants.

V11

V13

III

ii

IV

ii

V

iv

IV

V7

Ger.6

another technique that is unique to the romantic era isthe resolution of anaugmented sixth chordto adominant seventh chordrather than a dominant triad,

causing the interval of the augmented sixth to resolve

obliquelyinstead of moving outward to the octave.

finally, romantic era composers would sometimes use a particular type of chord

progression that had the effect ofsuspending tonalityfor a portion of the

piece. By temporarily removing the feeling of being in a certain key, the composer

could easilymodulate to a distant key!

this technique is called

third relationsbecause it

involves moving by root

movements of amajor or

minor thirdwithout respect

to key signature.

for example...

here, were

in F major...

*whump*

...thirdrelations

areliketurning

offthegravity

intheroom

forabit...

...and then turning

the gravityback

on... but in a

different

direction!

if you think of

tonality like

being in a

room...

F M E M IB: IV V I

...here, were just moving

down by Major thirds...

and then we land

in b major!

...which obscures any

sense of key we had...


42/46

m2 P4

P4

m2 M2P5

P5

!"#$%" '" ()*%)!"#$%&%&' #)*"+%),-'" +"",)$ -+,"%()*+, '.*) /$+()0)-)"( *'""+ #)*"+.

0+ )." (1()"2 $# (3"/0"( /$-+)"%3$0+)4

$.5 *+, ,$+6)/)0)12 &"2),708" ).0(4/$+)%*3-+)*7 2"7$,0"( +"", )$ !"

%&2)/),2%&'- +$)$"/%&'3

%& ')&)/1*-2"7$,0"( (.$-7, !" 3%02*%071,2)04%,)-'0). *,%&'*)-+)5%&%2) 6%'6 0"%&2 $%*"4 0"%&23 "##"/)09" 2"7$,0"( )"+, )$ 3%$:%"(( (7$'71 )$'*%,)." .0:. $% 7$' 3$0+) *+, )."+ 2$9" !*/8 )$'*%, )." ()*%)0+: 30)/.4

*( 1$- /*+ ("" *!$9"5 $//*(0$+*7*)10, *%" $8*1444!-) )."1 /$2" '0). *$7&!6 $#/),2/%!2%"&,3

0%()5 7"*3( (.$-7, !" +$ 7*%:"% ).*+ *0)/5)!2 5%526-'0). )'$ ";/"3)0$+(< 7"*30+: !1 *0)/5)!2 "!218)-*+, 7"*30+:7041/+ !1 *#%&"/ ,%9263 ,$+6) ,$ )."(" 9"%1 $#)"+5 ).$-:.

.0%,5 7"*3( $# * 3"%#"/) #$-%). +"", )$ !"0/)!)+)+ $%5"**"4)+ !1,2)04%,) #"2%"& )." "00",%2) +%/)!2%"&-)$!"7&2)/$1*1&!) )." 7"*34 *+, 0# * 7"*3 0(*1/')/ ).*+ *"%#"/) #$-%).5 0) +"",( )$ !" /$-+)"%!*7*+/", !$).$)5"/) 1&+ 152)/:

>.0(0)/5)!2 5"7/260( /$-+)"%!*7*+/",!1 )." ()"3 ).*) $//-%( !"#$%" )." 7"*34

>.0(0)/5)!2 5%526 0( /$-+)"%!*7*+/",!1 ()"3( $+ !$). (0,"( $# )." 7"*34

>.0(0)/5)!2 5"7/260( (-%%$-+,", !1 ()"3(5!-) )."1 *%"+6) 0+ )." $33$(0)" ,0%"/)0$+4

>.0(0)/5)!2 5%526 .*( ()"3( $+ !$). (0,"(5!-) )." #0%() $+" 0(+6) 0+ )." $33$(0)" ,0%"/)0$+4

*()715 ,$+6) '%0)" 2$%" ).*+ 24" *)10, %& 1 /"4-*+, '."+ 1$- ,$5 )."1 +"", )$ $-)70+" *1;"/ $%#%&"/ 2/%1+3+$ ,020+0(.", )%0*,(444 )."1 .*9" 2/%2"&), 0+ )."2=

)8%*:

("/$+,5 #$%6)18)&+)8%* %& #7,%!:?

*)10%&' !1 * )%0)$+" 0( !*,5 !-) 0)6(1*,"023$%)*+) )$ *9$0, )." )%0)$+" 0+ "26)/

'*1(444 #$% ";*237"5 ).0( 3*))"%+5 '."%"* )%0)$+" 0( "72*%&)+ 0+ )."#)*"+%! *%&)-'$-7, !" /$+(0,"%", 0+*33%$3%0*)"4 2/%2

"&)

*+, %"*7715 )$ !"51%/-)."(" *%":$$, :-0,"70+"(

#$%1&. #)*"+.3330)6( A-() ).*)5790( * 70))7" 2$%"

,2/%!2 *!$-) 0)4

"#$%#& ()*+,#-")%+,. /#0)12

6%'6 0"%&2


43/46

!"#$%& %()*#)%+ *,-.&)$(,#.&"# $%& '(#$$/0&/1#*2330 %#1(3)$)*& (+ ,(-.$&/*(".$01($% 2(", %32& $%&)42*& %21) $/0&/153# 3 /-4$5 "$6#233 26,-& &/) #.&)$723%8

7 $%3$ $38 -# $( $%&"#$%& $-3)9.4) -#&*,.%,.2.& #.&)$723%5

&9$ /-4&0 2(", ,3.6$*$,%% (/ ,7)$32(5

%& .&9$ /-4 %32& $( 7( :"$%()$")*& #.&)$723%;:;< :=555 /&'&'1&/5:? "#@#%%,.2.&8


44/46

!"#$%& !("#)"!

!"#$%&'(")$% +,,- +%"#!. /"'&

#$*(+",)-./

.&'& +'& -0$ %$-"!+0+)$-% &1&'2 $%" )$.%-2! 3)4*2!5

"'%#$+%&425 %.+% ,"&-$6% /+7& )% -0)#" 1! &)33)#2+-/)$ 3+!%5 /"-% "3 %.&(4"6)$2! 42+"!%)44 +((42 8)%."#% +$2 !.+$0&-9

%.&'& +'& "$42 + 3&8",#"(-)$%!/

(4"6)$2!

42+"/

%"0

42+"/

$%+. 2!"

#$%!$%1%-

)%-"461+!5

2%)!$%!

#1% $%+.

7" 2!"&

$% -8"

3)4!- 1%&

+1!- %$-"!5

1((4$1#8

("43"#-

)%-"461+!

2!)%9

#$%-414.

*$-)$%

0)-8 1- +"1!-

$%" 6$)#"

*$6)%9

7. !-"(5

%$ +"1(!

+149"4 -81%

1 ("43"#-3)3-8:

4&+(- +'& -%)443)%";:#% ,"$6% 4&+( %" +%"0 8)98 ($)%-"$ +&$0%7"1-5

%.&1)$ %.& %.)', /&+-#'&

)- +%"0 8)98 ($)%-3"'%.& 4)$&5 -" 4&+()$0 %" )%"$ %.&&$0%7"1- )-71&5

-%)44 %'#&999 3"'&$0%7"1-!53"' %.&2%1##"%-"& :&+%-5 ,)--"$+$% )$%&'1+4-+'&3)%";+- 4"$0 +- %.&2 .+((&$ +-

(1!!)%9 -$%"!/$"%&- %.+% 3)44 )$ +-8)4& !'&+%&, :2 -#''"#$,)$0 $"%&-9

".5 +$, $"%)!& ."8&)!!$%1%- )%-"461+!.+1& %.&)'%2*7"4! !)'!4&,; )-

#$)-"$-#1% :& #-&, "$2%1##"%-"&%$-"!555)% 31#-;)%6- +4-" $"% "7+2 %" .+1& (+'+44&4 (&'3&!% )$%&'1+4- 3'"/%.&2%1##"%-"& 7"1-%" %.&&$0%7"1-;:#% )3 2"# +'& +(('"+!.)$0

8)%.#$%-414. *$-)$%;%.+% 8"#4,$6% .+((&$1%.01.5?

8$0"6"4;2"# /#-% +4-" :& !+'&3#4 $"%%" .+1& %.&!1*"(&'3&!% )$%&'1+4 "$-0$ !2##"!!)6" &$0%7"1-!5@.)- )-!+44&,(141++"+ ("43"#- )%-"461+!+$, )%6- 0")$0 %" :& +%$>%$3"' +

9$$& +$%9 -)*"5

"#$%#& ()*+,#-")%+,. !"#$%#& //

6 7 10 8

8 7

8 10 8 6

3 1

E&F!&(%)$05 "3 !"#'-&51!#"%&)%9 *)%$4 !),-8!+$,("43"#- $#-16"!;:#% 2"# +4'&+,2?%"0 %.+%9


45/46

"#$%#& ()*+,#-")%+,. !"#$%#& ///

8 9 8 9

!"#$% '()*#)'+ 6' $"& .0+(! (687 +&7''79:0;8"*87',-.$ /-!)'6+60;'! ";7)

6;9: -".,6%79 !" !(7 "!(7%',7-07': 0!5(0-( -"%%7',";9' !" !(7 -,,56)0!0; ',7-07' !5"? -6; #7%#''-/0/!+#&! ";*$ 0= 0! 0' 6(0''#/7 !-/)4

5("6))) '" 5(6! 9" 57 !6*@ 6#"&! ;"5A 57 (687 6*."'! (6*= 6 ,6+7)))

57**:-801444

("5 6#"&! !5"'()*#03 ,#7.$)'!(6! 5"%@ 57** 50!( !"#$% '()*#)'9

!(7%-.63) /)#7"6-$ !-/)0;8"*87' 6;.(()$ /)#7"6-$

6;9 63-:)$ /)#7"6-$,*6$79";7 6=!7% 6;"!(7%: !(7;

%7!&%;0;+ !" !(7 ;"!7 !(6!0(($-0*")% #!4

!(7/-!0 *0;6#0!0>"%*"0/7#/7 !-/)? ="**"5'

!(7 ,6!!7%; "= 6'!)( %-:/+6 !"#$% %-:/+!(7;

!:- '!)(' .(4!(7;#%%3) ;"!7"= !(0',#

!"#$%=

,#$'!= 033 0;!7%86*' *6%+7% !(6; 6 !"#$%+0;-*&90;+()$,)*! ,-.$!"'+.&'! #7-"&;!7%#6*6;-79 #$'!)(' ";#"!( '097')

>?@ABC=

3 2 4 38 7 5 5 6

-6; #7%#''-/0/!2

.&'! #7

*-/'-/0/!2

-6; #7%#''-/0/!2


46/46

he Modern Modes

v.williams aristoxenus

platohildegard

es,but we only call them modernbecause we need to differentiate between a bunch of

nrelated thingsacross music history that, ever so inconveniently, use thesame names!

and, to make matters worse,each of these things use the names to representdifferent

concepts! fortunately, right now, were only worried about themodern modes.

these modes are used a lot...

especially infolk music.as for

standard western repertoire,

hey are first prominently featured

in thepost-romantic musicof theearly twentieth century

british isles.

ll, remember when we created thenatural minor scaleby starting with amajor scale,

t using thesixth note of the scale as the tonic? it gave us a new pattern of whole steps

d half steps... anew scale.

by starting on the other notes of the major scale, we get the other five modes.

a moreeffective

method of keeping

the modes straight

involves memorizingminor + raised 6th

in fact, these are two of the seven modern modes:

major is the ionian mode,and natural minor is theaeolian mode.

minor

keeping the same key signature,

we use this note as our new tonic!

one of theprimary characteristicso

theseenglish modalistsis that they

tended to avoid thestrong tensions

of thecommon practice period...

for example, they avoided chords

that used a tritone...and avoided

raising theleading tonein minor key

the modern

modes names

came from the

various keys

used in medieval

church music

which were, in

turn, named in

honor of the

lute rangesused

in laterancient

greekmusic

and those

used the same

names asscale

tunings discussed

byplato in

380 bc!

brita

in!

so what are they?

major

c ionian

a aeolian

DtoD: thedorian mode

EtoE: thephrygian mode

F toF: thelydian mode

GtoG: themixolydian mode

B toBthelocrian modebecause it hasadiminished tonic,

locrian is a theoretical

mode...its not used

inactual practice.

the modes here all sharethe samekey signature...

they arerelated,like

c major and a minor!

modern?

wait, isnt this stuff, like,

100 years old?

cartazes de teoria

Documents