us navy course navedtra 10244 - basic music

8/14/2019 US Navy Course NAVEDTRA 10244 - Basic Music

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DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.

SPECIAL P UBLICATION

September 1980

Basic Music

NAVEDTRA 10244


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DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.

ACKNOWLEDGEMENT

The contents of this SpecialPublication were furnished by the courtesy ofthe United States Army.


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PREFACE

Special Publications (SPs) are manuals or catalogs that provide information of general benefit and careerdevelopment. SPs have no associated assignments or tests.

Basic Music provides a basic reference for music theory. This SP is available ONLY in electronicPortable Document Format from the following web site: http://www.advancement.cnet.navy.mil

Refer questions about this SP to:

COMMANDING OFFICERSCHOOL OF MUSICATTN TRAINING OFFICER1420 GATOR BLVDNORFOLK VA 23521-2617

DSN: 253-7509COMM: (757) 462-7509FAX: DSN 253-4836/COMM (757) 462-4836

Provided byNAVAL EDUCATION AND TRAINING

PROFESSIONAL DEVELOPMENTAND TECHNOLOGY CENTER


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Sailors Creed

I am a United States Sailor.

I will support and defend theConstitution of the United States of

America and I will obey the ordersof those appointed over me.

I represent the fighting spirit of theNavy and those who have gonebefore me to defend freedom anddemocracy around the world.

I proudly serve my countrys Navycombat team with honor, courageand commitment.

I am committed to excellence andthe fair treatment of all.


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BASIC MUSIC

C O N T E N T S PageCH AP TE R 1 - N a t u r e of S ou n d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Chara cter ist ics of a Musica l Sound.

CH AP TE R 2 - Fu n d a m en t al N ot a ti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Nota t ion of Pit ch, Nota t ion of Dura t ion .

CH AP TE R 3 - M et er . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

The Bea t , Meter or Time Signa tu re, Composite Meter , Metr ica lSt ress E xcept ion s.

CH AP TE R 4 - R h y t h m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

Regula r Rhythm, Ir regula r Rhythm , Rhythmic Phra se In it ia t ion

and Com plet ion , Rela t ed Meter s, Equivalent Meter s.

CH AP TE R 5 - S ca l es a n d T et r a ch or d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

Sca les, Tet rachords, Sca le Const ruct ion Using Tet ra chords.

CH AP TE R 6 - M a jor S ca les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

Sha rp Sca les, F la t Sca les, Keys and Major Key Signa tur es, Circle of

Ma jor Keys, Enha rmonic Keys, Na mes of Sca le Degrees, Sca le

Degree Act ivity in Major .

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CH AP TE R 7 - M i n or S ca les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

Na tura l Minor Sca le, Ha rmonic Minor Sca les a nd Keys, Melodic

Minor Sca les and Keys, Circle of Minor Keys, Rela t ive and Pa ra llel

Keys.

CH AP TE R 8 - Mod a l S ca l es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

Lydian, Ionian , Mixolydian , Dor ian, Aeolian , Phrygian , Locr ia n,

Compar ison of Moda l Sca le Degrees to Major Sca le Degrees

CH AP TE R 9 - Ch r om a t ic , W h ol e T on e, a n d P en t a t on i c S ca l es . . . . . . . . 9-1

Chroma t ic Sca le, Whole Tone Sca le, Pen ta ton ic Sca les.

CH AP TE R 10 - I n t e r v a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1

Qua lit ies of Int erva ls, In terva l Quality Rela t ionsh ips, Enha rmonic

Int erva ls, Inversion of Simple In terva ls, Compounding andReducing Int erva ls, Consonan t a nd Dissona nt In t erva ls, Dia ton ic

and Chroma t ic In terva ls.

CH AP TE R 11 - T r i a d i c Ch or d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1

Ma jor Tr iad, Minor Tr ia d, Augmented Tr iad, Dimin ished Tr ia d,

Consonan t a nd Dissonan t Tr iads, Inversion of Tr iads, Dia ton ic

Tr iads in Ma jor and Minor Keys.

CH AP TE R 12 - O v er t on e S er i es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1

Charact er ist ics of a Vibra t ing Str ing, The Over tone Ser ies, The

Over tone Ser ies and Timbre.

CH AP TE R 13 - Tr a n s p o s i t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1

Tra nsposit ion by Sca le Degree, Transposit ion by Int erva l,

Tra nsposit ion by Change of Key Signa ture.

CH AP TE R 14 - I n s t r u m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1

Woodwinds, Transverse Woodwinds, Double Reed Inst r ument s,

Single Reed Inst r um ent s (Cla r inet s, Saxophones), Br a sswinds

(Treble Clef Bra ss, Bass Clef Br ass), P er cussion (Indefin it e Pit ch

P ercussion, Definit e Pitch Percussion), Keyboa rd, Rhythm Sect ionStrings.

CH AP TE R 15 - Ch or d S ym bol s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1

Chord Symbol Int erpreta t ion , Chord Str uctu res.

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CH AP TE R 16 - Ch or d S ca les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1

Major Sixth and Major Seven th Ch ord Sca les, Minor Sixth and

Minor /Major Seven th Chor d Sca les, Dominan t Seven th Ch ord

Scales, Minor Seven th Chord Sca les, Minor Seven th (F lat Five)

Chor d Scales, Augmen ted Seven th Chord Sca les, Dimin ished

Seven th Chor d Scales, The Blues Scale, Pen ta ton ic Sca les.

C H AP TE R 17 - S w in g R h yt h m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1

Ant icipa t ion , Divided Bea t in Swing Time, Shor t Per cussive Note,

Long Per cussive Note.

CH AP TE R 18 - M el od y Con s t r u c t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1

Chord Tones, Approach Tones.

CH AP TE R 19 - E x t en d ed a n d A l t er ed Ch or d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-1The Nin th , The Eleven th , The Th ir t een th , Specified Bass Note.

AP P E NDIX A - Ma n u scr ip t T ech n iq u es . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Clef Signs, Key Signa tu res, Time Signatu r es, Leger Lines,

Noteheads, Stems, Fla t s, Beams, Dots, Spacing, Ties, Slu rs, Rest s,

Numer als, Repea t Signs, Acciden tals, Direct ions for Per for mance,

Rehearsal Signs, Pr oofreading.

AP P E NDIX B - Di r ec t ion s f or P er for m a n ce . . . . . . . . . . . . . . . . . . . . . . B-1

Musical Abbreviat ions, Melodic Or namen ts, Ar t icu lat ions and

Accen t s, J azz Expressive Devices, Tempo Indicat ions, Dynamic

Indicat ion s, It alian Terms (Three List s).

AP P E NDI X C - I t a l i a n T er m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1

Explanat ion of Suffixes, List ing.

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B A S IC MUS IC

P UR P OSE AND SCOP E

This t rain ing cir cu lar is the pr incipal basic music theory

INTR ODUC TION

User s of th is publicat ion are encour aged to recommend

changes and submit commen ts for it s improvemen t . Commen ts

shou ld be keyed to the specific page, paragraph and line of the

text in wh ich the change is recommended. Reason s will be

pr ovided for each commen t to in su re understanding and

complete evalua t ion . Commen ts shou ld be pr epared using DA

Form 2028 (Recommended Changes to Publicat ions) andforwarded direct ly to the Commandan t , US Army Elemen t ,

School of Music, ATTN: ATTNG-SM-DTD, US Naval Amph ibi-

ou s Base (Lit t le Creek). Norfolk , Virgin ia 23521.

reference for all Ar my Bandsmen . It may be used, in

con junct ion with academic mater ia ls, as a text for cou r ses of

in str uct ion at the US Army Elemen t , School of Music. It

encompasses the basic aspect s of sound, pit ch , rhythm and

musical notat ion .

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CH AP TE R 1

NATUR E OF SOUND

Sound is produced by vibra t ion; there is no sound without a sound source in

the physica l st a te of vibra t ion. The vibra t ing sound source t ransfer s vibra t iona l

energy to the medium of t ransmission (gas, liquid, or solid) forcing it t o vibra te.

The medium, in tu rn, t r ansfer s vibra t iona l energy to the ea r , forcing the ea r

drum to vibra t e. The human bodys nervous syst em processes the vibra t ion from

the ea r to the bra in where the vibra t ion is in terpreted a s sound.

Fig u r e 1.1: N a t u r e of S ou n d .

CH AR ACTE R ISTICS OF A MUSICAL SOUND

P i t ch

The number of sound waves per second produced by a sounding body is

called frequency. Frequency is oft en expressed as the number of cycles per

second (CPS) refer red to as her tz (Hz). High frequencies a re expressed in

kilocycles or kiloher tz (1 kHz = 1000 Hz).

When frequency of vibra t ion is regula r , it is ca lled pitch. The pitch is higher

when frequency is grea t er . When frequency of vibra t ion is ir r egula r , it is a sound

sour ce but is not pitched.

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A regu la r vibrat ion a t 440 Hz (440 CPS)

pr oduces the pit ch A.

Doubling the frequency (880 Hz) pr oduces A

an octave h igher .

Halving the fr equency (220 Hz) pr oduces A an

octave lower .

The appr oximate range of human hear ing capacity is fr om 20 Hz to 16 kHz.

I n t e n s i t y

The magn itude of force or energy of r egula r or ir regu lar vibra t ion is known

as in tensity. In tensity, musica lly refer red to as volume, is deter mined by the

amplitude of the vibrat ion of the sound sou rce. The sound is louder when

amplitude is greater .

Fr equency and amplitude (pit ch an d volume) may be graph ically

repr esen ted by a simple wave for m.

Figu r e 1.2: S in g le Cycle Wa ve For m .

Frequency, the number of complete cycles with in a given per iod of t ime, is

r epresen ted hor izon ta lly. Amplitude is the displacemen t fr om cen ter of the wave

form and is r epresen ted ver t ica lly. Greater frequency indica tes h igher pit ch ;

gr ea ter amplitude indica tes gr ea ter volume.

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Figu r e 1.3: Wa ve For m R ep r esen t a t ion of Fr eq u en cy a n d

A m p l i t u d e .

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D u r a t i o n

The length of t ime of vibrat ion is ca lled duration. Durat ion is the length of

sound.

Ti m b r e ('tam-bar or 't im-bm)

The dist inct ive tone or quality of a singing voice or a musical in st rumen t is

known as timbre. Sou nds iden t ical in pit ch , in tensity, and dur at ion produ ced by

differen t types of in st r umen ts a re dissimilar an d reveal a difference in t imbre or

t on e qu ality.

Timbre is affected by:

method of sou nd product ion (bowed, blown , plucked, or st r uck)

physical na tu re of in st rumen t (r elat ive st rength of over tones)

condit ion of in st rumen t

individual per forman ce character ist ics

SUMMARY

Pi tc h h ighness or lowness of the soun d.

I n t e n s i t y volume of the sou nd.

D u r a t i o n length of the sou nd.

Ti m b r e quality of the sound.

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CH AP TE R 2F U NDAME N TAL N OTAT IO NNOTATION OF P ITCH

P i t ch N om en cl a tu re

Ea ch line and space of the grea t st a ff (F igure 2.1) has a let t er -name. In

ascending order , t he lines and spa ces a re na med from A through G. After G, t he

seven-let ter ser ies repea t s. A note placed on the sta ff takes the name of the line or

space on which it is placed.

ten

Th e great staff is a theoret ica l const ruct ion consist ing of eleven lines and

spaces with middle C a s the middle or sixth line.

Fi g u r e 2.1: Gr ea t S t a f f .

The grea t st a ff is not used for the nota t ion of music. Inst ead, a five-line st a ff

is used. A symbol (clef sign) m ust be used to indica te which five lines of the grea t

st a ff a re to be used for the nota t ion of pit ch.

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G, C, a n d F Clefs

The lower loop of the G clef sign encircles G above middle C.

Converging a rm s of the C clef sign designa t e middle C.

The two dot s of the F clef sign designa te the line passing between

them a s F below middle C.

Fi g u r e 2.2: G, C, a n d F Clefs.

F ig u re 2.3: G, C , a n d F Clef s on t h e Gr ea t S t a f f .

Gr a n d S t a f f /T r eb l e a n d B a ss Cl ef s

G clef is m ost commonly used to place G on the second line of a five-line

st a ff. This clef is known as treble clef.

F ig u r e 2.4: T r eb l e Cl ef .

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F clef is most commonly used to place F on the four th line of a five-line sta ff.

This clef is known as bass clef.

F ig u re 2.5: B a ss Clef .

The treble and ba ss clefs, joined together , form the grand

commonly used in keyboa rd music and scor ing.

staff which is

F i g u r e 2.6: T h e R el a t ion sh i p b et w een t h e Gr ea t S t a f f a n d Gr a n d

S t a f f .

L eg er L i n es

It is fr equent ly necessa ry to wr ite pit ches above or below a five-line or grand

sta ff. These temporary extensions above or below the st a ff a re leger lines.

Fi g u r e 2.7: L eg er L in es.

Key b o ard

The keyboa rd may be used as a visua l dem onst ra tor for pit ch rela tionships.

Keyboa rd pitch nomencla ture is similar to st a ff pitch nomencla ture (Figure 2.8).

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Note tha t the black keys ar e found in gr oups of two and th ree. Immediately to the

left of each gr oup of two black keys is found the pit ch C. When ascending on the

keyboard, the pit ch names A through G are u sed, beginn ing again with the let t er

name A a t the complet ion of the ser ies.

Figu re 2.8: Keyboa rd .

Ch r om a t i c S ign s

Pitches occu rr ing between let t er names cannot be r epresen ted by let t ernames alone. Addit iona l symbols a re requ ired for pr oper iden t ificat ion . These

symbols, known as chrom atic signs, ar e five in number .

Sharp

Flat

#Raises the pit ch of the let t er name ah alf s tep

~ Lowers the pit ch of the let ter name ah a lf s te p.

Dou ble s ha rp x Raises the pit ch of the let ter name

t wo h alf st eps.

Dou ble F la t bb Lower s the pit ch of the let t er namet wo h alf st eps.

Natural h Ca ncels a pr eviou sly u sed ch r om at icsign (in clu ding x a nd bb).

Fig u r e 2.9: Ch r om a t i c S ign s .

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Any two adjacen t keys on the keyboard soun d a half step or semitone apart .

When expressin g the pit ches occu rr ing between the let t er names as sh ar ps or

fla ts, the pit ches are expressed as ch rom atic alterations of the let t er names.

Sh ar p Alt er at ion s

F la t Alt er a t ion s

Figu r e 2.10: Ch r om a t i c P i t ch N a m es .

En h a r m on ic P i t ch es

A single pit ch may have more than one name. Pitches that have differ en t

names bu t sou nd the same are enharm on ic pitches.

Figu r e 2.11: E n h a r m on ic P i t ch es .

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Adding double sha r ps a nd double fla ts incr ea ses the num ber of enha rmonic

pitches.

Fi g u r e 2.12: E n h a r m on i c P i t ch es w i t h Dou b l e S h a r p s a n d Dou b l e

F l a t s .

P i t ch N om en cl a t u r e i n t h e Gr ea t S t a f f

Octave designa tor s m ust be used to dist ingu ish between ident ica l pitch

na mes in differen t oct aves. Th is is one way a pit ch maybe represen t ed precisely

withou t st a ff not a t ion or reference to the keyboa rd. Middle C is t he cen ter line

of the grea t st a ff a nd the imagina ry line between t reble a nd ba ss clefs in the

gra nd st a ff. Middle C or c1 is the C closest to the cen ter of the st a nda rd

keyboard.

piano

Fi g u r e 2.13: cl i n Gr ea t a n d Gr a n d S t a v es .

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From Cbb immedia tely below c1 t o above c1, all pit ch es spelled wit h in

th e octave are design a ted first octave an d are iden t ified by lower case let ter s an d

th e n u mber 1.

Fi g u r e 2.14: Fi r s t Oct a ve.

Th e octave immedia tely above th e fir st octave is design a ted second octave

an d is iden t ified by lower case let t ers an d th e n u mber 2.

Fi g u r e 2.15: S econ d Oct a ve.

Th e octaves a r e n u mbered con secu t ively in h igh er oct aves in clu din g a third

octave an d fou rth octave. Th e h igh est pitch on th e pian o keyboard is

Th e octave immediately below th e fir st octave is design a ted sm all octave

an d is iden t ified by lower case let ter s.

Fi gu r e 2.16: S m al l Oct a ve.

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The octave immediately below the small octave is designa ted Great Octave

an d is iden t ified by capital let t ers. Below the Grea t Octave is the Contra Octave

where pit ches are iden t ified by two capital let t ers

S ubcon tra Octave where pit ches are iden t ified by th ree capit al let ter s

The lowest note on the piano keyboard is Subcon t ra A (AAA).

Figu r e 2.17: Gr a n d S t a f f a n d

S in g le-S t a f f Clef s

Keyboa r d P i t ch N o m e n c l a t u r e .

Treble and bass clefs a re used more frequen t ly than any oth er five-line clefs,

bu t other clefs a re u sed. Their r anges have developed fr om the need to br ing a

specific range with in th e compass of the staff.

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Fi gu r e 2.18: S in g l e-S t a f f Clef s.

N OT AT ION OF DUR AT ION

N ot e a n d R est V a l u es

Dura t ion of sound is the bu ilding block for the crea t ion of rhythm. Rhythm

is composed of two element s: sound and silence. Notat iona l symbols for sounds

are called notes. Nota t ional symbols for silences a re called rests. Each note

va lue and symbol has a cor responding rest value and symbol. These va lues are

expressed ar ithmet ica lly a s fract ions. The symbols have cha ract er ist ics in

common and a re genera lly a single nota t iona l a ltera t ion from an adjacent

value.

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Fig u r e 2.19: N ot e a n d R est V a l u es a n d S ym b ol s .

Notes and r est s indica t e the crea t ion of sound a nd silence to form rhythm.

When specific pitches a r e desir ed, they a re placed in a given clef to indica te the

pitch.

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Note and rest symbols do not indica te actual dura t ion of t ime unt il t em po

and metr ic grouping a re indica ted. They do indica te rela t ive dura t ion a s

expr essed by fract iona l names. A given note or rest va lue is equa l in dura t ion to

two notes or r est s of the next sma ller value.

Fig u re 2.20: N ot e a n d R est E q u i v a l en t s.

T i ed N ot es

Since on ly mult iples of two a re possible with basic note and rest symbols,

devices a re used to extend dura t ion. One symbol used to extend the dura t ion of a

note is the t ie. A ti e is a curved line join ing two or m ore successive notes of

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iden t ica l pit ch . Tied notes sound as one note. Ties a re not u sed with r est s because

r est va lues ar e cumula t ive.

Figu r e 2.21: T ied N ot es .

Dot t ed N ot es a n d R es t s

Another symbol u sed to extend the du ra t ion of a note or rest is the dot . A d ot

placed after a note or rest in creases du ra t ion by one half the or iginal va lue. A

dot ted note or rest has a value equa l to th r ee of the next smaller value.

Figu r e 2.22: Dot t ed N ot es a n d R es t s.

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Note a nd rest dura t ion may be fur ther increa sed by addit iona l dot s pla ced

a fter the or iginal dot . Each addit iona l dot increa ses the dura t ion of the note or

rest by one ha lf the va lue of the previous dot .

Fi g u r e 2.23: Mu l t ip l e Dot t ed N ot es.

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CH AP T E R 3

M E T E R

Music exists in t ime. Sounds, int er sper sed with silence, occur with specific

dura t ion and a re replaced by more sound or silence of the same or different

dura t ion . These dura t ions of sound a nd silence must be measured before it is

possible to nota t e them.

TH E BE AT

The st anda rd of measurement in most musica l t ime is the bea t . Regular ly

recur r ing pu lsa t ions in music a re known a s beats. Bea t s in music a re not of fixed

dura t ion ; they a re of longer or shor ter dura t ion as determined by the cha ract er of

the music. The slower the music, t he longer the dura t ion of the bea t ; t he fa st er

the music, t he shor t er the dura t ion of the bea t .

Tempo r efer s to the ra t e of progression of bea t s and bea t combina t ions. Slow tem pia re compr ised of bea ts of long dura t ion; fa st t empi a re compr ised of bea t s of shor tduration.

B ea t Grou p in gs

In most music, cer ta in bea t s t end to assum e more rela t ive impor t ance than

other s. These st ronger , m ore accented bea t s may recur with regula r it y,

establishing groups of two, th ree, or four bea ts. This recur r ing pa t tern of

accen ted a nd unaccen ted pu lsa t ions is known a s meter.

T h e te rm m etrical stress descr ibes these bea t groupings. If t he meter

establishes groups of two, the metr ica l st r ess is duple; if t h re e, triple; and if four ,

quadruple.

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Fig u re 3.1: B ea t Gr ou pin gs .

Div id ed B ea t s

In addit ion to grouping of bea ts, m ost music has bea t s regula r ly divisible by

two or th ree. M etrical stress a lso descr ibes the division of the bea t . When the bea t

is norma lly divisible by two, the metr ica l st r ess is simple. When the bea t is

norma lly divisible by th ree, t he met r ica l st r ess is compound.

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Fi gu r e 3.2: Di v isi on of B ea t .

ME T E R OR T IME S IGNAT UR E

Th e m eter or tim e signatu re is a musica l symbol which indica tes metr ica l

st r ess (meter ) and unit of bea t (not a t ion). The unit of bea t is the va lue tha t get s

one bea t . The meter or t ime signa ture is represen ted by two arabic numera ls

a r ranged vert ica lly a t the beginning of a st a ff or rhythm line (single line used for

nota t ing rhythm). The upper numera l indica tes the metr ica l st r ess; the lower

numera l indica tes the un it of bea t or division of bea t .

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In nota t ion, the st ronger , more accen ted bea t in a bea t grouping is indica ted

by placing a bar line vert ica lly on a sta ff or th rough a rhythm line. The ba r line

precedes the note tha t begins the bea t group. The spa ce between any two

adjacen t ba r lines is known a s a measure. The word ba r is commonly used tomean measure.

Fi g u r e 3.3: B a r L i n es a n d M ea su r es.

S i m p l e T i m e S i g n a t u r es

Any note divisible by two may be used as the un it of bea t in sim ple tim e.

Since una ltered note a nd rest va lues a re norma lly divisible by two, any undot ted

note, except the sixty-four th, may be used as the un it of bea t (dividing the sixty-

four th is impract ica l). The lower numera l in a t ime signa ture is a lways 1, 2, 4, 8,

16 or 32, cor responding to the note va lue/name, a nd specifies the unit of bea t .

The most commonly used numera ls, in order of frequency, a re: 4, 2, 8, and 16.

Duple, t r iple, or quadruple simple metr ica l st r ess is indica ted by an upper

numera l in a t ime signa tu re of 2, 3, or 4 respect ively.

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Fig ur e 3.4: s im p le T im e sig na tu r es .

Note tha t figure 3.4 l ist s two symbols (C a nd ~) as abbrevia t ions for simple

t ime signa tu res. The symbol C, called com m on tim e, funct ions a s 4/4. Thesymbol @ ca lled cu t tim e or alla breve (according to the breve or ha lf not e),

funct ions as 2/2.

Fig u r e 3.5: S i m p l e T i m e E x a m p le.

In figure 3.5, the 2 indica t es tha t the music is in simple duple t ime with each

bea t divisible by two. The 4 indica tes tha t the qua r t er note is the un it of bea t with

the division of bea t r epresent ed by eighth notes.

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Com p ou n d T im e S ig n a t u res

Any note divisible by thr ee ma ybe used as the un it of bea t in compoundtime. Since dot ted n ote and r est values a re normally divisible by th ree, anydot ted note, except the dot ted sixty-four th , may be u sed as th e un it of bea t(dividin g t he dot ted sixt y-fou rt h is im pr act ica l). In com pou nd t im e, t he lowern um er al of a t im e sign at ur e will a lwa ys be 2, 4,8, 16,32 or 64, cor respon din g t ot he n ot e va lu eln am e. Th ese n umer als u su ally specify t he division of bea t. Th eu nit of bea t is der ived by fin din g t he dot ted n ot e va lu e t ha t is equ al t o t h ree of t henotes indica ted by the lower numera l. The most common ly used numera ls, in or der of fr equ en cy, a re: 8,4,2, a n d 16. D uple, t riple or qu a dr u ple m et r ica l st ress isin dica ted by a n u pper n um er al in a t im e sign at ur e of 6 (2 x 3 division s of bea t), 9(3 x 3 division s of bea t), or 12 (4 x 3 division s of bea t) r espect ively.

Unit of Beat Divided Beat Duple Triple Quadruple

O* clt4ci :;y

I J 6 9 12d : d d 64 64 64Figu re 3.6: Com p ou n d Tim e S ign atu res.

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Fi gu r e 3.7: Com p ou n d T i m e E x a m p l e.

In figure 3.7, the 6 indica t es tha t the music is in compound duple t ime with

each bea t divisible in to three pa r t s. The 8 indica tes tha t the eighth note is the

division of bea t with the un it of bea t repr esen t ed by the dot t ed qua r t er .

Some con tempora ry com posers indica t e compound t ime signa tures with the

actual number of bea ts a s the upper numera l and a note va lue below.

Fig u re 3.8: Con t em p or a r y Com p ou n d E x a m p les.

COMP OSITE ME TE R

When music is composed of bea ts of unequa l bea t lengths, the metr ica l

st r ess is composite or complex. The bea t s in composit e meter s will be divisible by

two or th ree with the divided bea ts having the sa me dura t ion .

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Fi gu r e 3.9: Com p osi t e Di v i s i on of B ea t .

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Com p osi t e T im e S i gn a t u r es

Notes divisible by two and th r ee are r equ ir ed for the r epr esen ta t ion of the

beat in com posite tim e. The un it of bea t will be r epresen ted by u ndot ted and

dot ted notes of the same value. Composit e t ime signa tu res may be n ota ted in

th r ee ways:

the lower numer al as the divided bea t and the u pper numera l as the

sum of divided bea t s in the measu re, or

the lower numer al as the un it of bea t and the u pper numer al as a

mixed numeral, or

the lower numer al as the divided beat and the upper numera ls as the

bea t com posit es.

Figu r e 3.10: Com p osi t e T im e S ig n a t u r es .

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Fi g u r e 3.11: Com p osi t e T i m e E x a m p l e.

In figure 3.11, the 5 indica tes tha t the music is in com posit e duple t ime with

one bea t divisible in to two pa r t s a nd the other divisible in to th ree pa r t s (2+3 in

ba r 3 a nd 3+2 in ba rs 1 & 2). The 8 indica t es the eigh th note is the division of bea t

with un it of bea t represen t ed by the qua r t er and dot t ed qua r t er .

ME TR ICAL STR E SS E XCE P TIONS

If t em po is fa st , a t ime signa tu re with an upper numera l of 3 may ca ll for a

coun t of one bea t per m easur e, which m ay require compound int erpret a t ion .

Th is metr ica l st r ess is refer red to a s com pou n d single.

If tem po is slow, a t im e signa ture with a n upper numera l of 6, 9, or 12 may

call for a count of 6, 9, or 12 bea t s per m ea sure, and may require simple

interpretation.

If t empo is slow, a t ime signa tu re with an upper numera l of 2, 3, or 4 may ca ll

for a coun t of 4, 6, or 8 bea t s per measure.

A t ime signa tu re with a n upper num era l of 7, 10, 14, 15, 21, et c. ma y requ ire

simple or com pound in terpret a t ion.

A t ime signa ture with an upper num era l of 2, 3, 4, 6, 8, 9, or 12 may require

com posit e in ter pr et at ion .

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CH AP TE R 4

RHYTHM

Rhythm is t he occur rence of va rying lengths of sound a nd silence. Meter is

t he pa t tern of bea t groupings and the na ture of the divided bea t . Rhythm does

not a lways coincide with meter . The two must not be confused.

The sum of note and rest va lues in each measure equa ls the number of bea t s

indica t ed by the t ime signa ture, Rela t ionsh ips between rhythm and meter can

be shown in two ca tegor ies: regular rhythm a nd irregular rhythm.

R E GULAR R H YTH M

R egular rh ythm occurs:

when long notes coincide with st rong bea ts and shor t er notes (when

presen t) occur a s non-syncopa ted divisions of weak bea t s; or

when repea t ing non-syncopa ted divisions occur on all bea t s.

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Figu r e 4.1: R egu la r R h yt h m .

Uniform rhyth m is regu lar rhythm tha t occu rs:

when the measu re is filled by one note; or

when the measu re is filled by two equa l notes in quadruple meter ; or

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when the measu re is divided equally in to un its of bea t s; o r

when the measu re is divided in to equa l divisions of the un it of beat .

Figu r e 4.2: Un i for m R h yt h m .

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All un iform rhythms ar e regu la r bu t not all regu lar r hythms ar e uniform.

IR R E GULAR R H YTH M

Irregu lar rhythm occurs:

when long notes coincide with weak beat s or weak par t s of bea t s; or

when the rhythm h as been syncopa ted.

Figu r e 4.3: I r r egu l a r R h yt h m .

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S yncopated rhyth m occu r s when notes alt er the normal or expected pat t er n

of rhythm, accen t , or meter by appear ing on weak bea t s or weak par t s of beat s.

Syncopat ion may be crea ted:

when a weak bea t or weak par t of a bea t is accen ted; or

when a weak bea t or weak par t of a bea t is t ied to the st r ong beat

wh ich follows it ; or

when a rest occu rs on a beat a ft er a note on a weak beat or when a

rest occu r s on any beat aft er a weak par t of a beat .

Fig u re 4.4: S yn cop a ted R hyt h m .

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All syncopa ted rhythms ar e ir regu lar , bu t not all ir regu la r rhythms are

syncopated.

R H YTH MI C P H R ASE I NITI ATIO N AND C OMP LE TION

The fir st beat in a measu r e is ca lled the thesis. A phrase (a sh or t musical

though t , normally two to fou r measu r es long) tha t begins on the fir st bea t has a

thetic beginning; the ph rase is said to begin thetically. The thesis is a lso ca lled

the down-beat. Down-beat der ives it s name from the down war d st roke of a

conductor indicat ing th e pr incipally accen ted note of the measu r e.

An unaccen ted beat in a measu re is called an arsis. An anacrusis, a lso ca lled

upbeat or pick-up, con sist s of one or mor e notes tha t precede the fir st down-bea t

of a musical ph r ase. Normally, when a composit ion begins with an anacr usis,

the last measu re con ta in s on ly the r hythmic values tha t will complete the fir st

measu re. However , some composers an d ar ranger s en d their composit ions with

a complete measu re regar dless of the mater ial con tained in the fir st (incomplete)

measure.

When the last a t t ack of a ph rase coincides with th e thesis, the ending is

called a m ascu line ending. If the last a t tack does not coincide with the th esis, theending is ca lled a fem in ine end ing.

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Figu r e 4.6: R ela t ed Met er s (r h yt h m ic t r a n scr ip t ion ).

E QUIVALE NT ME TE R S

Equ ivalen t m eters ar e two differ en t meters, one simple an d one compound,

tha t have the same beat gr ouping and the same note to r epresen t the divided

bea t . The un it of bea t in simple t ime is an un dot ted note and in compound t ime is

a dot ted note.

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Figu r e 4.7: Eq u iva len t Met er s .

By making use of equivalent meters, it is possible to use the compou nd

division of bea t in simple t ime and the simple division of bea t in compou nd time.

These borr owed divisions of the bea t ar e nota ted as the triplet in simple meter

and the duplet in compound meter .

Figu r e 4.8: E q u i va l en t M et er s (m et r i c con ver s ion ):

d u p let s a n d t r ip l et s .

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CH AP T E R 5

SCALE S AN D TE TR ACH OR DS

SCALES

A sca le (fr om the Lat in scala - ladder or staircase) is a gr adua ted ser ies of

musical tones ascending or descending in or der of pit ch according to a specified

in terval scheme. An interval is the difference in pit ch between tones. Music

depends on the succession of pit ches and cer ta in measu r able pa t t ern s of

in tervals used with regu lar ity. These pa t t ern s may be ext r acted from musica l

examples, a r ranged in or der , an d expressed as sca les.

The basic in terva ls used for sca le analysis ar e the half st ep (sem itone) an d

whole step (whole tone). Any two adjacen t keys on the keyboard soun d a half

st ep. The in terval of two half st eps soun ds a whole step. A whole step (two half

st eps) occu r s between C an d D, D and E, F an d G, G and A, an d A an d B. Observetha t ther e are no keys between E and F, and B and C; these in terva ls a re half

steps.

Figu r e 5.1: Keyboa r d H a l f S t ep s a n d Wh ol e S t ep s .

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The note a whole step above E is F # , n ot F. The note a whole step above B is

a re both whole steps below F an d C respectively.

Figu r e 5.2: W h ole S t ep s.

TETR AC HOR DS

The tet r achord is a device used in the const ruct ion and ana lysis of scales. A

tetrachord is a ser ies of fou r tones on successive degr ees of the sta ff with an

in terval of five half st eps between the fir st and last tones. Tet rachords used are

the major (M), minor (m) , na tu ra l (N), and harmon ic (H). Any tetr achord may be

const ructed on any pitch and will r eta in the in terval rela t ionsh ip of the

tetrachord.

Ma jor T et r a ch or d (M )

Th e m ajor tetrach ord is composed of two half st eps, two half st eps, and one

half st ep ascending on fou r successive staff degrees.

5-2Figu re 5.3: Ma jor T et r a ch or d s.


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M in or T et r a ch or d s (m )

Th e m in or tetrach ord is composed of two half st eps, one half st ep, and two

half st eps ascending on fou r successive sta ff degrees.

(m - 212)

Fi gu re 5.4: M in or T et r a ch or d s.

N a t u r a l T et r a ch or d (N )

Th e n atu ral tetrach ord is composed of one half st ep, two half st eps, and two

ha lf st eps ascending on fou r successive sta ff degr ees.

(N - 122)

Fi gu re 5.5: N a tu ra l T et r ach or ds .

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H a r m on ic T et r a ch or d (H )

T he harm on ic tetrachord is composed of one ha lf st ep, th r ee ha lf st eps, and

one half st ep

(H - 131)

ascending on fou r successive staff degr ees.

F ig u r e 5.6: H a r m o n i c Te tr a c h or d s .

SC ALE C ONSTR UC TION USING TE TR ACH OR DS

Sca les const ru cted with tet r achor ds combine two tet r achords and a link

(abbreviated L). The link is always composed of two half st eps (a whole step) on

adjacen t sta ff degrees. The link may be placed at th e bot tom, in th e middle, or a t

the top of the sca le. The combina t ion of two tet rachor ds and a link form a scale

tha t encompasses an octave. An octave is an in terva l con ta in ing twelve half

st eps. I t is the distance from any pitch of a given let t er name to the next h igher or

lower pit ch with the same let ter name.

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F ig u r e 5 .7 : Te t r a ch o r d sn d L in k in S ca le Con s t r u c t ion .

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CH AP TE R 6MAJ O R SCAL E S

The for mula for the major scale is MLM.

The scales half st ep/whole step in terval relat ionsh ip cor responds, on a

keyboard, to a w h ite k ey scale from C to C.

S ca le F or m ula : ML M

Fi g u re 6.1: C M a jor S ca le .

SH AR P SCALE S

To const ruct a sca le other than C major , ch romat ic signs must be u sed to

main ta in the scale formu la. The addit ion of ch romatic signs in major sca lesfollows specific, recogn izable pat t ern s, When a major scale is const r ucted on the

fifth scale degree ascending in the C major sca le, the scale formed is a G m ajor

scale an d has one sharp:


Fi g u re 6.2: G Ma jor S ca le.

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When a major scale is const r ucted on the fifth sca le degree in the G major

sca le, the sca le formed is a D m ajor scale and has two sharps:


Figu r e 6.3: D Ma jor S ca le.

When a major scale is const ructed on the fifth scale degree in the D major

sca le, the sca le for med is an A m ajor scale and has th ree shar ps:

G#.

S ca le F or m ula : MLM

Figu re 6.4: A Ma jor S ca le.

The pat t er n con t inu es thr ough the

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C# m ajor scale with all seven pitch n ames sh arped:

F#, C#, G#, D#, A#, E$, an d B#.

S ca le F or m u la : ML M

Fi gu re 6.5: C# M a jor S ca le.

Althou gh a G# major scale (fifth degree ascen din g in C8 major) is possible,

th e, scale requ ir es a dou ble sh arp an d is con sider ed a th eoret ical sca le. Th erefore,

major (seven sh arps) is th e last pr act ical sh arp

making a tota l of seven major scales with sh arps.

F L AT SCAL E S

sca le to be con sidered,

Wh en a major scale is con st ru cted on th e fifth sca le degree descen din g (th e

fou r th degree ascen din g is th e same n ote) of th e C major scale, th e scale formed

is an F m ajor scale an d h as on e fla t : Bb.

S ca le F or mu la : ML M

Fi gu re 6.6: F Ma jor S ca l e.

Wh en a major scale is con st ru cted on th e fifth degree descen din g (fou r th

degree ascen din g) of t he F major sca le, th e sca le formed is a ~b m ajor scale an d

h as two flat s: Bb an d ~b.


Fi gu re 6.7: Bb M a jor S ca l e.

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The pa t t ern cont inues th rough the


Fi g u r e 6.8: M a jor S ca l e.

Although an ma jor sca le (fifth degree descending

possible, t he, sca le requires a double fla t and is considered a

in ma jor ) is

theoret ica l sca le.

Therefore, ma jor (seven fla ts) is the la st pract ica l fla t sca le, making a tota l of

seven ma jor sca les with fla t s.

KE YS AND MAJ OR KE Y SIGNAT UR E S

In most music, one pit ch becomes more impor tan t than any of the other

pitches in mot ion a round it . Th is pr imary pitch to which the other pitches rela t e

is known as the ton ic. Key is the t erm which refer s to int erva l rela t ionships

within a piece of music which establish one pitch as the tonic. A key involves a

network of rela t ionships, while a sca le is an a r ranged list of the pitches of a key.

In most music, r a ther than nota t ing the chroma t ic signs for each pitch , the

chroma t ic signs are extracted from the sca le and placed a fter a clef sign to

indica te the key. This a r rangement of chromat ic signs is a k ey sign atu re.

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The sca le of E ma jor con ta ins four sha rps: F# , C#, G#, and D# in or der of

their addit ion to sha rp sca les. Ar ranged as a key signa tu re it is nota t ed:

Fi g u r e 6.9: K ey S i g n a t u r e.

Achroma t ic sign in a key signa tu re a ffect s a ll not es of tha t let t er name in a ll

oct aves th roughou t the dura t ion of the key signa tu re un less cancelled with in a

measure by a different chrom a t ic sign. The key signa ture is a lways in effect

a fter a ba r line except for a note t ied from an a lt ered note in the previous

measure .

Fig u r e 6.10: S h a r p M a jor Key S i g n a t u r e s .

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Fig u r e 6.11: Fla t M a jor Key S ign a t u r es .

CIR C LE OF MAJ OR KE YS

Major keys ar ran ged in a cir cle sta r t ing with C an d progr essing th rough the

sharp keys clockwise and the fla t keys coun terclockwise, for m the circle of m ajor

keys or the circle of fifth s.

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Fi g u r e 6.12: Cir cl e of M a jor Keys.

E NH AR MONIC KE YS

Keys tha t have different names but sound the same a re enh arm on ic k eys.

The enha rmonic ma jor keys a re

It is possible to sta r t on C major and travel a round the circle of fifths in

either direct ion and retu rn to C major by using one of the enha rmonic keys to

cont inue a round the circle.

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NAME S O F S CAL E DE GR E E S

Tradit iona l names a re used for ident ifica t ion when reference is ma de to

specific sca le degrees. The tonic is t he fir st sca le degree. The pit ch a fifth above

the tonic is ca lled the dominant and is the fifth sca le degree. The pitch a fifth

below the tonic is ca lled the subdominant (meaning the dominan t below the

tonic) and is the four th sca le degree. The pitch midway between the ton ic a nd the

dominant is ca lled the mediant (occurr ing in the middle) and is the third sca le

degree. The pitch midway between the tonic and the subdominant is ca lled the

submediant a nd is the sixth sca le degree. The pit ch immedia tely above the tonic

is ca lled the supersonic and is the second sca le degree. The seven th sca le degree

is ca lled a lead in g tone or subtonic depending on whether it is one ha lf st ep or

two ha lf st eps (a whole st ep) below the tonic.

Fi g u r e 6.13: N a m es of S ca le Degr ees .

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SCALE DE GR E E ACTIVITY IN MAJ OR

Some sca le degrees serve as poin ts of stability or rest ; other s a re more act ive,

r anging from a rest less sound to a t endency to move to a specific pitch .

S table T ones show a tendency towards being a t rest .

Active T ones want to move.

T en den cy T ones a re act ive tones tha t exhibit a st rong pull t oward a

specific pit ch.

STABLE

Tonic

Mediant

Dominant

ACTIVE

Supersonic

Subdominant

Submediant

Lea din g Ton e

Te n d e n c y

Subdomin an t (pu lls t o Median t)

Leadin g Ton e (pu lls t o Ton ic)

Fi g u r e 6.14: S ca l e Deg r ee A ct i v i t y i n M a jor .

Normally, in ma jor keys, the act ive tones will move to one of the two

adjacen t notes in the sca le. Tha t is, t he supersonic will move to the tonic or

mediant ; t he submediant will move to the dominan t or leading tone. Th is does

not mean act ive tones a lways move in th is manner bu t t end to do so regu la r ly.

Tendency tones t end to move a ha lf st ep to an adjacen t sca le degree. The

leading tone will most oft en move to the tonic un less it is pa r t of sca lewise

mot ion in the opposite direct ion . Simila r ly, the subdominan t will most often

move to the mediant unless it is pa r t of sca lewise mot ion in the opposite

direct ion. Note tha t t endency tones pu ll to stable sca le degrees.

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C H AP TE R 7MIN OR SCALE S

Thr ee comm only used form s of minor sca les a re: natural (a lso ca lled pure),harmonic, and melodic minor sca les. The ha rmonic and melodic minor sca les

der ive from the na tu ra l minor sca le.

NATUR AL MINOR SCALE

The form ula for the na tura l minor sca le is m L N . The sca les ha lf st ep/whole

st ep in terva l rela t ionsh ip cor r esponds, on a keyboa rd, to a wh ite k ey sca le from

A to A.

S ca le F or mu la : m LN

Fi g u r e 7.1: T h e a N a t u r a l M i n or S ca l e.

N a t u r a l M i n or S h a r p S ca l es a n d Keys

When a na tu ra l minor sca le is const ruct ed on the fifth sca le degree

ascending in the a na tu ra l m inor sca le, t he sca le for med is an en at u ra l mi n or

sca le and has one sha rp: F#.

S ca le F or mu la : m LN

Fi g u r e 7.2: e N a t u r a l M i n or S ca le.

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When a na tu ra l minor sca le is const ruct ed on the fifth sca le degr ee

a scending in the e na tur a l minor sca le, the sca le form ed is a b n atu ral m inor

scale and has two sha rps: F ~ a nd C#.

S ca le F or m ula : m LN

Fi gu r e 7.3: b N a t u r a l M i n or S ca l e.

This pa t tern con t inues thr ough the

If the pa t t ern is con t inued, double sha r ps will r esult . Therefor e, a # na tu ra l

minor (seven sha rps) is the la st pract ica l sha rp sca le, making a tot a l of seven

na tu ra l minor sca les with sha r ps. Although the ton ics in na tu ra l m inor differ

from major , t he or der of sha rps rema ins the sam e.

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Fi gu r e 7.4: S h a r p N a t u r a l M i n or Key S i gn a t u r es .

N a t u r a l M i n or Fl a t S ca l es a n d Keys

Wh en a n a tu r al min or sca le is con st ru cted on th e fifth sca le degree

descen din g (fou r th degree ascen din g) of t h e a n atu r al min or scale, th e sca le

formed is a d n atu ral m inor scale an d h as on e fla t : Bb.

S ca le F or m ula : m L N

Fi gu re 7.5: d N a t u r a l M i n or S ca l e.

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Figu r e 7.7: Fla t N a t u r a l M in or Key S ign a t u r es .

S ca le Deg r ee Act iv i t y in N a t u r a l Min or

The na tu ral minor sca le has a lowered median t , lowered submedian t , an d a

subton ic when compar ed to the major sca le const ructed on the same ton ic.

Fi gu r e 7.8: C om p a ri son of M a jor a n d N a t u ra l Mi n or .

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Since the sca le degr ee rela t ionsh ips in natu ra l

major , the act ivity of sca le degrees is also differen t .

STABLE ACTIVE

Tonic SupersonicMediant SubdominantDominant Submediant

Subtonic

T E N D E N C Y

minor are differen t fr om

Submediant (pulls t o Dominant )

Figu r e 7.9: S ca le Deg r ee Act iv i t y in N a t u r a l M in or .

H AR MONIC MINOR SCALE S AND KE YS

The formula for the har mon ic minor sca le is m L H . The sca les ha lf

st ep/wh ole step in terval rela t ionsh ip does not cor respond to any wh ite key

scale.

S ca le F or m ula : m LH

Fig u r e 7.10: T h e a H a r m on ic M in or S ca le.

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Harmonic minor sca les der ive from na tu ra l minor sca les. When const ruct ed

on the sam e ton ic, t he na tu ra l minor sca le ha s a subton ic while the ha rmonic

minor sca le ha s a leading tone.

Fi g u r e 7.11: Com p a r i son of N a t u r a l a n d H a r m on ic M i n or .

Harmonic minor sca les sha re the key signa tures of na tu ra l minor sca les.

They a re formed by a chroma t ic a lt era t ion of the subton ic upward to a leading

ton e. Ch rom at ic signs used ou tside the key signa ture a re ca lled accidentals.

Fi g u r e 7.12: H a r m on i c M i n or S ca l es w i t h Key S i g n a t u r e.

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S ca le Deg r ee A ct i v i t y i n H a r m on ic M i n or

The ha rmonic minor sca le evolved because of the rela t ive lack of tendency

tones in the natura l minor . Using the ha rmonic form of the sca le develops a

bet t er ba lance of tendency tones in minor keys.

STABLE ACTIVE

Tonic Supersonic

Mediant Subdominant

Dominant Submediant

Leading Tone

T E N D E N C Y

Submedian t (pu lls to dominan t )Leading Ton e (pu lls to Ton ic)

Fig u r e 7.13: S ca l e Degr ee Act i v i t y in H a r m on ic Mi n or .

Although the ha rmonic form of the sca le has desirable ha rmonic fea tu res,

the th ree-half-step interval on two successive st a ff degrees (augmented second)

has been found to be melodica lly object ionable. Therefore, a third form of the

sca le has been developed to avoid the effect of this interval.

ME L ODIC MINOR SCAL E S AND KE YS

The melodic minor sca le has two formula s, one ascending and one

descending. The formula for the ascending melodic minor sca le is m L M . Th e

formula for the descending melodic minor sca le is N L m , which is the same as

the na tura l minor sca le.

F ig u r e 7.14: T h e a M el od i c M in o r S c a le .

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Melodic minor sca les der ive from na tura l minor sca les. The ascending

melodic minor sca le has a ra ised submediant and leading tone (which

elimina tes the object ionable melodic interval) tha t retu rn to a subtonic a nd

lowered submediant when descending to achieve a more minor sound.

Fi gu r e 7.15: Com p a r ison of N a t u r a l a n d Melod i c Mi n or .

Melodic minor sca les sha re the key signa tu res of natura l minor scales. They

a re formed by chroma t ic a ltera t ions of the submediant upwards a ha lf st ep and

the subtonic upward to a leading tone.

Fig u re 7.16: M el od i c Mi n or S ca les w i t h Key S i gn a t u r es.

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S ca le Deg r ee A ct ivi t y i n M elod ic M in or

STABLE ACTIVE

Tonic Supersonic

Mediant SubdominantDominant Raised Submediant (passes t o Lea ding Tone)

Subt onic (pa sses downwa rd t o lowered Submediant )

T E N D E N C Y

Lower ed Submediant (pulls t o Dominant )

Lea ding Tone (pulls t o Tonic)

Figu r e 7.17: S ca le Degr ee A ct ivi t y i n Melod ic Min or .

C IR CLE OF MINOR KE YS

Since the na tu r al, ha rmon ic, and melodic minor scales sh ar e the same group

of key signatu r es, it is possible to const ruct one cir cle of fifth s for all th ree forms

of th e sca le.

Figu r e 7.18: Cir cl e of M in or Keys.

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The enharmon ic minor keys are

It is possible to star t on a minor an d travel a roun d the circle of fifth s in either

direct ion and retu rn to a minor by using one of the enharmon ic keys to con t inue

around the cir cle.

R E LATIVE AND P AR ALLE L KE YS

R ela t ive Keys

Keys having the same key signa tu r e are called relative. Rela t ive keys will

not have the same ton ic. The keys of a minor an d C major have no shar ps or

flat s. Ther efore, the relat ive major of a minor is C major , and the relat ive minor

of C major is a minor.

To find the rela t ive minor of any major key, descend th ree ha lf st epson th ree

successive sta ff degr ees, or deter mine the sixth degree (submedian t ) of the major

scale.

Fi gu r e 7.19: R ela t ive M in or Fr om Ma jor .

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To find the rela t ive ma jor from any minor key, a scend three ha lf st eps on

th ree successive sta ff degrees, or determine the third degree (mediant ) of the

minor sca le.

Fi gu re 7.20: R el a t i v e Ma jor Fr om M in or .

P A R A L L E L KE Y S

Keys having the same ton ic a re parallel. Para llel keys do not have the same

key signa ture. The keys of C major a nd c minor have the same ton ic: C.

Therefore, t he pa ra llel ma jor of c minor is C major , and the pa ra llel minor (or

tonic minor ) of C major is c minor . Note that their key signa tures differ (no #s or

bs and 3 ~s).

Fi g u r e 7.21: P a r a l lel Keys.

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CH AP T E R 8MOD AL S CALE SSca les of eight tones conta ining ha lf st eps and whole st eps in specified

posit ions a re ca lled modes or m od al scales. Histor ica lly, the modes have been

used in many per iods and styles of music. They a re a lso ca lled chu rch m odes,

ecclesiastical m odes, and m edieval m odes. Although the techniques for their use

have changed, they reta in their interva l pa t t erns and their t r adit ional Greek

names.

Most modes can be cla ssified genera lly a s ma jor or minor . The modes with a

predominantly

lydian

ionian

major sound a re

mixolydian

The modes with a

dorian

aeolian

phrygian

Th e locrian mode

predominant ly minor sound a re

sounds neither ma jor nor minor ; it tends t oward minor and

will be discussed with minor m odes.

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MA J OR M ODE S

LYDIAN

The formula for the lyd ian m od e (sca le) is LMM. The sca les ha lf st ep/whole

st ep interva l rela t ionship cor responds, on a keyboa rd, to a wh ite k ey sca le from

F t o F. The link (L ) occurs a t the beginning of this sca le.

Fig u re 8.1: F L yd i a n S ca l e.

The rema in ing lydian sca les a re const ructed on fifth sca le degrees

a scending and lowered fift h sca le degrees descending from F lydian through

seven sha rps and fla ts. This crea t es fift een lydian keys tha t can be represent ed

in a circle of lydian keys (circle of fift hs). Although lydian ton ics differ from

major and minor , the order of sha rps and fla t s rema ins the same.

Fig u r e 8.2: Ci r cle of L yd ia n Keys.

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C major and F lydian a re rela t ive keys. Likewise, C lydian a nd G major ; ~b

lydian and F major; A lydian and E major ; and Db lydian and Ab major a re

examples of rela t ive keys. The rela t ive lydian tonic is the four th sca le degree

(subdominant ) of the ma jor sca le.

S ca l e Deg r ee A ct i v i t y i n L yd ia n

The lydian sca le ha s a ra ised subdominant when compared to it s

pa ra llel (same tonic) ma jor sca le.

Fig u r e 8.3: P a ra l l el M a jor a n d L yd ia n .

STABLE ACTIVE

Ton ic Superson ic

Mediant Subdominant

Domin an t Subm edian t

Lea din g Ton e

T E N D E N C Y

Su bdominan t (pu lls to Dominan t )

Leading Ton e (pu lls t o Ton ic)

Fi g u r e 8.4: S ca l e Deg r ee A ct i v i t y i n L yd i a n .

IONIAN

The formula for the ion ian m ode is MLM, making the ion ian mode iden t ica l

to ma jor sca les.

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MIXOLYDIAN

The formulas for the m ixolyd ian m ode ar e MM L or M L m . The scales ha lf

st ep/whole step in terval rela t ionsh ip cor responds, on a keyboard, to a white keyscale fr om G to G.

Figu re 8.5: G Mix olyd ia n S ca le.

The remain ing mixolydian sca les a re con st r ucted on fifth scale degr ees

ascending and descending from G mixolydian th rough seven sh arps and flat s.

Th is crea tes fifteen mixolydian keys tha t can be r epresen ted in a circle of

mixolydian keys (circle of fifth s). The or der of sh arps and flat s remains the same

as in pr evious key signatu res.

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STABLE ACTIVE

Tonic

Mediant

Dominant

Supersonic

Subdominant

Submediant

Subtonic

T E NDE NCY

Subdominant (pulls t o Media nt )

Media nt (ca n pull t o Su bdom in an t)

Su bt on ic (pu lls t o Su bm edia nt

Fi g u r e 8.8: S ca l e Degr ee A ct i v i t y i n M i x ol yd i a n .

M I N OR M O DE S

DORIAN

Th e formu la for th e dorian m ode is m L m . Th e sca les h alf step/wh ole step

in terval r elat ion sh ip cor r espon ds, on a keyboard, to a wh ite key sca le from D to

D.

Fi gu re 8.9: d Dor i a n S ca l e.

Th e remain in g dor ian sca les ar e con st ru cted on fifth scale degrees

ascen din g an d descen din g from d dor ian th rou gh seven sh arps an d fla t s. Th is

cr ea tes fift een dor ian keys th at can be represen ted in a circle of dor ian keys

(circle of fift h s). Th e order of sh arps an d fla t s r emain s th e same as in previou s

key sign at ur es.

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Fi g u r e 8.10: Cir cle of Dor i a n Keys.

C major and d dor ian a re rela t ive keys. The rela t ive dor ian tonic is the

second sca le degree (super son ic) of the ma jor sca le.

S ca le Deg r ee A ct i v i t y i n Dor i a n

The dor ian sca le has a lowered median t (~3) and a subton ic (~7) when

compared to it s pa ra llel ma jor sca le. When compared to it s pa ra llel na tura l

minor sca le, t he dor ian sca le has a ra ised submediant

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AEOLIAN

The formula for the aeolian m ode is m L N , making the aeolian m ode

iden t ica l t o na tura l m inor sca les.

PHRYGIAN

The formula for the ph rygian m od e is NLN. The sca les ha lf st ep/whole

st ep interva l rela t ionsh ip cor responds, on a keyboa rd, t o a w hite k ey sca le from

E to E .

Fi g u re 8.14: e

The rema ining phrygian sca les

P h r yg i a n S ca le.

a re const ruct ed on fift h sca le degrees

a scending and descending from e phrygian through seven sha rps a nd fla t s.

This crea t es fift een phrygian keys tha t can be represen ted in a circle of phrygian

keys (circle of fifths). The order of sha rps and fla ts rema ins the sam e as inprevious key signa tur es.

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Figu r e 8.15: Cir cl e of Ph r yg ia n Keys .

C major and e phrygian are relat ive keys. The relat ive ph rygian ton ic is theth ird scale degree (median t ) of the major scale.

S ca le Deg r ee A ct ivi t y in Ph r yg ia n

The phrygian sca le has a lower ed superson ic (b2), lowered median t (~3),

lower ed submedian t (~6), and subton ic (~7) when compared to it s parallel major .

When compared to its para llel natu ra l minor sca le, the ph rygian scale has a

lower ed su per son ic (bz).

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Figu r e 8.16: P a r a l l el Ma jor a n d P h r yg ia n .

Figu r e 8.17: P a r a l l el M in or a n d Ph r yg ia n .

STABLE

Tonic

Mediant

Dominant

Figu re 8.18: S ca le d eg r ee A ct iv i t y in Ph ryg ia n .

ACTIVE

Supersonic

Subdominant

Submediant

Subtonic

T E N D E N C Y

Supersonic

Submediant

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LOC R IAN

The formula for the locrian m ode is NNL. The sca les half st ep/whole st ep

in terva l r elat ionsh ip cor responds on a keyboar d, to a wh ite key scale, from B to

B. The link (L ) occu rs a t the end of th is scale.

Figu re 8.19: b L ocr i a n S ca le.

The remain ing locr ian scales ar e con st r ucted on raised fifth scale degrees

ascending an d fifth sca le degrees descending fr om b locr ian thr ough seven

sh arps and fla t s. Th is crea tes fift een locr ian keys tha t can be r epresen ted in

circle of locr ian keys (circle of fifth s). The or der of shar ps and flat s remain the

same as in previous key signa tu res.

Figu re 8.20: Ci r cl e of L ocr i a n Keys .

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C major a nd b locr ian a r e rela t ive keys. The rela t ive locr ia n ton ic is the

leading tone of the m a jor sca le.

P a r a l l el A n a l ysis of M a jor a n d I .ocr i a n

The locr ian ha s a lowered superson ic (b~), lowered media n t (b;]), lowered

dominan t (bh), lowered subm edian t (b(j), a nd subton ic (~7) when com pa red to it s

pa ra llel ma jor sca le. Only the subdom inan t rema ins una lt ered when com pared

to the pa ra llel m a jor sca le.

Fi g u r e 8.21: P a r a l l el M a jor a n d L ocr i a n .

As a sca le, t he locr ian mode is unst able. It exhibit s st rong tendencies for

movement . Sca le degree act ivit y in locr ian mode is not ea sily ana lyzed. The

mode is used pr imar ily a s a per for mance tool.

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COM P A R IS ON OF M ODAL S CA L E DE GR E E S

T O M A J OR S CA L E DE GR E E S

Char t ing the seven modes th rough their a ltera t ions as they rela te to thesame tonic (pa ra llel) shows their sca le degree rela t ionsh ips to the ma jor sca le.

Fi g u r e 8.22: Com p a r i son of M od a l S ca l e Deg r ees t o M a jor S ca le Deg r ees .

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CH AP TE R 9CH R OMAT IC, WH OLE TONE ,AND P E NTATONIC SCALE S

Chromat ic, whole tone, and pen taton ic sca les cannot be analyzed usingtet rachor ds. These sca les do not form regu lar keys; therefore, none have r egula r

key signatu r es. Chromat ic and whole tone sca les requ ir e acciden tals when they

are u sed with key signatu res.

C H R OMATIC SCALE

Th e chrom atic scale consist s ent irely of half st eps. Ther e ar e twelve half

st eps (th ir t een pitches) in an octave. If all th ir teen pitches (twelve half st eps)

with in an octave are repr esen ted in an ascending or descending order , the r esu lt

is a ch romat ic scale. The name of the ch r omatic sca le is the fir st note of the sca le

regardless

When

wr it t en as

of the key signa tu re.

notat ing ch romat ic sca les, any pitch requ ir ing an acciden ta l is

a ch r omat ic alt erat ion of the previous pitch.

Figu r e 9.1: Ch r om a t i c S ca le.

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Double sha rps a nd double fla ts should be a voided when nota t ing chroma t ic

sca les. Therefore, na tura l signs on adjacent st a ff degrees a r e used to avoid

double sha rps a nd double fla t s.

Fi g u r e 9.2: a n d A Ch rom at i c S ca l es .

The sam e chroma t ic sca le ca n be nota t ed severa l ways. The key signa ture

determ ines the nota t ion of the chrom a t ic sca le.

Fi g u r e 9.3: E Ch r om at i c S ca l es.

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WH OLE TONE SC ALE

Th e whole tone scale, as it s name implies, is a sca le a r ranged to sound in

whole st eps. The whole tone sca le is nota ted using acciden ta ls to cr eate whole

steps.

The same whole tone sca le can be notated severa l ways. The key signatu r e

often deter mines the notat ion of the whole tone scale.

Since the whole tone scale consist s of seven pitches in stead of eight

(including the octave), one of the sta ff degrees with in the sca le will not con tain a

note. The whole step tha t is

anywher e in the sca le.

indica ted by non-adjacen t sta ff degrees may occu r

Figu re 9.4: C a n d 13b W h ole T on e S ca les .

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P E N TATONIC SC ALE S

A pen taton ic scale con sist s of five tones (six pit ch es including the octave).

Two common pen taton ic scales a re the pen ta ton ic major and the pen taton ic

minor . No half st eps occu r in either of these sca les.

P en t a t on i c M a jor

When const r ucted on the fir st degr ee of a major sca le, a pen taton ic m ajor

scale con ta in s the ton ic, super son ic, median t , dominan t , and submedian t of that

scale. The pen taton ic major sca le cor responds, on a keyboar d, to a black key

scale fr om Gb to Gb.

Fig u r e 9.5: P en t a t on i c M a jor S t a t es .

The tones omit t ed ar e the tendency tones in major : the subdominan t an d

leading tone.

Pen t a t on ic M in or

When const ructed on the fir st degree of a na tu r al minor sca le, a pentatonic

m inor scale con tain s the ton ic, median t , subdominan t , dominan t , and subton ic

of that minor scale. Th is cor r esponds to the fir st , lowered th ir d, fou r th , fifth , and

lower ed seven th scale degrees of the parallel major scale. The

pen ta ton ic minor scale cor r esponds, on a keyboar d, to a black key sca le from

Eb to Eb.

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Fig u r e 9.6: P en t a t on i c M i n or S ca les.

The tones omit t ed a re the act ive tone and the tendency tone which form ha lf

st eps in natura l minor: the supersonic and submedian t .

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CH AP T E R 10INTERVALS

An interval is t he difference in pit ch between two tones. In terva ls a re named

according to the number of let ter names, or the number of successive st a ff

degrees, encompassed by the interva l.

Fi gu r e 10.1: N a m es of In t erv a l s.

When interval tones sound simult aneously, the interva l is a harmonic

interval. When int erva l tones sound in succession , the in terva l is a melodic

interval.

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Figu r e 10.2: H a r m on ic a n d M elod ic In t er va l s .

When in terval tones en compass an octave or less, the in terval is a simple

interval. When in terval tones encompass a n in th or mor e, the in terva l is a

compound in terva l.

Figu r e 10.3: S im p le a n d Com p ou n d In t er va l s .

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QUALITIE S OF INTE R VALS

To iden t ify a specific in terval both it s name an d quality must be sta ted. The

quality of an in terval may be descr ibed by one of five terms: perfect, m ajor,m inor, augm en ted , or d im in ished .

P er fec t In t er va l s

A perfect prim e (PI) con sist s of two notes of the same pitch on the same sta ff

degree. A perfect fou rth (P4), a perfect fifth (P5), and a perfect octave (P 8) con sis t

of the in tervals for med between the ton ic and the subdominan t , dominan t , and

octave of a major or minor sca le.

The perfect pr ime con ta in s no half st eps; the per fect fou r th con ta in s five

half st eps; the per fect fifth con tain s seven ha lf st eps; and the per fect octave

con tain s twelve half st eps.

F ig u r e 1 0.4 :er fect In ter va ls .

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M a jor In ter v a l s

A m ajor secon d (Ma j 2), m ajor th ird (Ma j 3), m ajor sixth (Ma j 6), a nd major

seventh (Ma j 7) consist of the int erva ls form ed between the ton ic and

supersonic, m edian t , submedia n t , and leading tone of a ma jor sca le.

The m a jor second conta ins two ha lf st eps; the m a jor third con ta ins four ha lf

st eps; t he m a jor sixth con ta ins n ine ha lf st eps; and the m a jor seventh con ta ins

eleven ha lf st eps.

Fi g u re 10.5: M a jor In ter v a ls .

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Mi n or In ter va l s

A major in terva l made smaller by a ha lf st ep becomes minor . A m inor 2nd

(min 2), m inor 3rd (min 3), m inor 6th (min 6), and m inor 7th (min 7) consist of the

in tervals formed between the tonic and lowered superson ic (b2), median t

and submedian t (b6) of a major sca le, and between the ton ic and subton ic

The minor second con tain s one half st ep; the minor th ird con tain s th r ee half

st eps; the minor sixth con ta in s eigh t half st eps; and the minor seven th con ta in s

ten half st eps.

Fig u r e 10.6: M in or In ter va l s .

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A u gm en t in g Per f ec t In t er va l s

A per fect in terval made greater by a half st ep becomes au gmen ted. The

augm en ted prim e (Aug 1) con ta in s one half st ep; the augm en ted fourth (Aug 4)

con tain s six ha lf st eps; the augm en ted fifth (Aug 5) con ta in s eight half st eps;

and the augm en ted octave (Aug 8) con ta in s th ir t een half st eps.

Figu r e 10.7: A u g m en t ed In t er va l s f r om P er fec t In t er va l s .

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Dim in i sh in g P er fec t In t er va l s

A per fect in terva l made smaller by a half st ep becomes dimin ished. The

d im in ished fourth (dim 4) con tain s fou r ha lf st eps; the d im in ished fifth (dim 5)

con tain s six half st eps; and the d im in ished octave (dim 8) con tain s eleven half

st eps. There is no dimin ished pr ime because it is impossible to make a pr ime

smaller.

Figu r e 10.8: Dim in i sh ed In t er va l s f r om P er f ec t In t er va l s .

A u gm en t in g Ma jor In t er va l s

A major in terva l made greater by a half st ep becomes augmen ted. The

augm en ted second (Aug 2) con tain s th ree half st eps; the au gm en ted th ird (Aug

3) con ta in s five half st eps; the augm en ted sixth (Aug 6) con ta in s ten half st eps;

an d the augm en ted seven th (Aug 7) con ta in s twelve half st eps.

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Minor int er va ls ma de grea t er by a ha lf st ep becom e ma jor ; m a jor in terva ls

ma de grea t er by a ha lf st ep become augm ented; therefore, a m inor int erva l m ade

grea ter by a whole st ep becom es augmented.

Fi g u r e 10.9: A u g m en t ed I n t er v a ls f r om M a jor In t er v a ls .

D im i n i sh i n g M i n or In t er v a l s

A m inor in terva l ma de sm a ller by a ha lf st ep becomes dim inished. The

d im in ish ed secon d (dim 2) con ta ins no ha lf st eps beca use the two pit ches sound

the same; the dim in ish ed th ird (dim 3) con ta ins two ha lf st eps; t he

d im in ish ed sixth (dim 6) conta ins seven ha lf st eps; and the dim in ish ed seven th

(dim 7) con ta ins n ine ha lf st eps.

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Major in t erva ls made smaller by a h alf s tep become min or ; min or in tervals

made smaller by a h a lf st ep become dimin ish ed; th er efor e, a major in terval

made smaller by a wh ole st ep becomes dimin ish ed.

Fi g u r e 10.10: Di m i n i sh ed In t er va l s f r om M i n or I n t er va l s .

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INT E R VAL QUAL IT Y R E L AT IONSH IP S

Th e followin g diagram illu st r ates th e r ela t ionsh ips of var iou s in tervals

when moved by h alf st eps.

Fi gu re 10.11: I n ter va l Qu al i t y R el a t i on sh i p s .

E NH AR MONIC INTE R VAL S

In tervals th at h ave differ en t n ames bu t sou n d th e same are enharmonic

intervals. En harmon ic in terva ls will a lways have th e same n u mber of ha lf st e ps

bu t differen t nota t ion . For example, th e Au g 5 an d min 6 sh own in Fig. 10.12 are

en h armon ic in tervals. Both in tervals con ta in eigh t h a lf st eps.

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Fi gu r e 10.12: E n h a r m on i c In t erv a l s.

INVE R SION OF SIMP L E INT E R VAL S

Inversion is a change in the rela t ive posit ion of the notes in a simple

interval. When the upper note in a simple interval becomes the lower note, or the

lower note becomes the upper note, t he interva l has been inver ted. Inversion is

accomplished by moving the lower note up an octave or the upper note down an

octave.

Fig u re 10.13: In v er si on of S im p l e In t er v a l (P 5).

Three simple int erva ls do not invert : the perfect pr ime, per fect octave, and

augmented oct ave.

The per fect pr ime will not inver t because there is no upper or lower note.

The per fect octave will not inver t because this would crea t e a per fect pr ime,

which has no upper or lower note.

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The augmented octave will not inver t because the upper note would rema in

the upper note and the lower note would rema in the lower note.

The names of inver ted simple int erva ls a re predictable. The sum of a simple

interva l and it s inversion is a lways N I N E :

1 becomes 8 (when inver table)

2 becomes 7

3 becomes 6

4 becomes 5

5 becomes 4

6 becomes 3

7 becomes 2

8 becomes 1 (when inver table)

The qua lit ies of inver ted simple intervals a re a lso predictable:

per fect remains perfect (when invertable)

major becomes minor

minor becomes ma jor

augmented becomes diminished

diminished becomes augmented

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Fi gu r e 10.14: S i m pl e I n t er va l I n v er s i on s .

COMP OUNDING AND R E DUCING INT E R VAL S

Compounding an d reducing in terva ls a r e ot h er meth ods of ch an gin g th e

relat ive posit ion of th e n otes in an in terval. Compou n din g a simple in terva l is

accomplish ed by movin g th e u pper n ote u p an octave or t h e lower n ote down an

octave. Movin g th e u pper n ot e down an octave or t h e lower n ote u p an oct ave

redu ces a compou n d in terval. Compou n din g in tervals may con t in u e in defin ite-

ly, bu t r edu ct ion can con t in u e on ly u n t il t h e in t erva l becomes simple, t h en

in version ru les con t rol fu r th er movemen t . Wh en compou n din g or r edu cin g

in terva ls, t h e n ame of t h e in terval ch an ges wh ile th e qu ality remain s t h e same.

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Com p ou n d i n g In t er v a ls

When compounding a simple or compound int erva l, the number S E V E N is

added to the name of the in terval for each octave displacement . The qua lit y of

the interva l rema ins the sam e.

Fig u re 10.15: Com pou n d in g In t erv a ls .

The per fect pr ime, which is not inver ted, maybe com pounded. The per fect

pr ime compounds to a per fect octave (P 1+7 equa ls P8).

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R ed u cin g In t er v a l s

When reducing a compound interva l, t he number S E V E N is subtracted

from the name of the interva l for each octave displacement . The qua lit y of the

interval rema ins the same.

Fig u re 10.16: R ed u cin g In t erv a l s.

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Two simple int erva ls may be reduced. The augmented octave reduces to an

augmented pr ime (Aug 8-7 equa ls Aug 1) and the per fect octave reduces to a

per fect pr ime (P8 -7 equals P1).

CO NSO NANT AND DIS SON ANT INT E R VAL S

The basic sound of int erva ls may be genera lly descr ibed as consonant or

dissonant. Consonant interva ls t end to rema in st able. Dissonant intervals t end

to be unstable, r equir ing movement to a consonance. Per fect pr imes, thirds,

per fect fift hs, sixths, and per fect octaves are genera lly consonant int erva ls.

Seconds, per fect four ths, seven ths, augmented, and diminished interva ls a re

genera lly dissonant interva ls.

C on s on a n t I n te r va ls D is so n an t I n te r va ls

P1, P5, P8, P4,

Maj 3, Maj 6 Maj 2, Maj 7

min 3, min 6 min 2, min 7

All a ugm en ted in ter va ls

All dim in ish ed in ter va ls

Fig u r e 10.17: Con son a n t a n d Di sson a n t In t erv a l s.

Although the minor third (3 ha lf st eps) and the augmented second (3 half

st eps) a re enha rmonic, one is classified as a consonance, the other a s adissonance. Th is is t rue of severa l enha rmonic interva ls (Ma j 3 and dim 4, dim 2

and P1, dim 6 and P5, Aug 5 and min 6, etc.). The musica l context determines

consonance and dissonance when the int erva ls a re enha rmonic.

The diminished fift h (dim 5) and augmented four th (Aug 4) conta in six half

steps, are dissonant , and a re enha rmonic. Since both these interva ls con ta in

three whole st eps, both a re commonly refer red to as the tritone (abbrevia ted TT).

DIAT ONIC AND CH R OMAT IC INT E R VAL S

Pitches tha t belong to a sca le or key a re ca lled diatonic. Pit ches foreign to a

sca le or key a re called chromatic. The pitch C is dia tonic to the keys of C major

(tonic), eb melodic minor a scending (ra ised submediant ), and ~b minor

(superson ic). However , t he pitch C is chroma t ic (not dia tonic) to the keys of D

m ajor (subt onic), G lydian (lowered subdominan t), and minor (ra ised

mediant).

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In tervals ar e diat on ic wh en bot h th e u pper an d lower n ot es of th e in terva l

ar e fou n d in th e key. In tervals a re ch romat ic wh en on e or both n otes of t h e

in terval a r e for eign to th e key. Th e simple in terval formed by th e pit ch es G u p t o

~b is a dia ton ic in terva l in ~b Major , mixolydian , an d c n atu ra l min or , bu t it

is a ch romat ic in terva l in Gb major , e min or , an d D lydian.

Fi gu r e 10.18: Di a t on i c a n d Ch r om a t i c I n t er va l s .

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CH AP TE R 11TR IADIC CH OR DS

A chord is a combin a t ion of th ree or more differen t ton es sou n ded simu ltan eou s-

ly or in su ccession (broken chord ). Ch ords in mu sic ar e oft en spelled in th irds.

Fi g u r e 11.1: Ch or d .

A t r iad is a ch ord of th r ee ton es spelled in t h irds. It maybe con st ru cted of

any combin a t ion of t wo su per imposed major an d min or th irds. Th e lowest of

t h ese ton es is called th e root of t h e t r iad. Th e middle t on e is called th e third of th e

t r iad becau se it is a th ird above t h e root of th e t r iad. Th e h igh est of th e th r eet on es is called th e fifth of th e t r iad becau se it is a fifth above th e root of th e t r iad.

Th e writ t en t r iad u ses alterna te st aff degrees in it s n otat ion , Th a t is, th e

t r iad is n ot at ed on adjacen t lin es or spaces, depen din g on wh eth er t h e root is on a

lin e or a space.

Fou r combin a t ion s of major an d min or th irds a r e possible in t h e

con st ru ct ion of t r iads:

a major th ird as th e lower in terval with a min or th ird as t h e u pper

interval,

a min or th ird as t h e lower in terval with a major th ird as th e u pper

interval,

major th irds as both u pper an d lower in terva ls,

min or th irds as bot h u pper an d lower in tervals.

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Tr iads have the following qua lit ies:

Ma jor (Ma j)

minor (min)

Augmented (Aug)

diminished (dim)

Fi g u re 11.2: T r i a d q u al i t i es .

MAJ OR T R IAD

Th e m ajor triad has three tones on a lterna t e st a ff degrees with a ma jor third

(4 ha lf steps) a s the lower interva l and a minor third (3 ha lf steps) a s the upper

interval. The interva l between the root a nd fifth is a per fect fift h (7 half st eps).

When const ruct ed on the fir st degree of a ma jor sca le, a ma jor t r iad conta ins the

ton ic, median t , and dominan t of tha t sca le. This cor responds to the fir st , t hird,

and fift h (1, 3, and

us navy course navedtra 10244 - basic music

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