symmetric harmony

8/13/2019 Symmetric Harmony

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Shai Cohen*

The Language Of Modern Jazz Music

KEYWORDS: GUAGUANCO; Afro Cuban Rumba

The Guaguancois an Afro Cuban rhythm which forms part of the rumbafamily that also comprises

Yambu an Columbia. There are se!eral styles foun throu"hout Cuba with the most influential bein" the

#$a!ana# %feature in this article& an #'atan(as# styles) The #'atan(as# style iffers in the

interpretation of the supportin" rums* the tumbadoraansegundoma+e use of !ariations in which they

#con!erse#)

The rhythm is usually performe with three rums* tumbadora, segundo an quinto, a pair of harwoostic+s that mar+ the -./ rumba claverhythm +nown as clavesan a hollowe piece of bamboo playe with

two stic+s calle cat. The names of the rums an stic+ parts !ary throu"hout Cuba) The role of the

rums calls for the tumbadora ansegundoto carry the rhythm while the quintointeracts between the lea

sin"er, supportin" rums an bac+in" sin"ers utilisin" short phrases an at times #two or four bar

patterns#) At a specifie point in the arran"ement the quintois "i!en a #solo feature#)

0 ha the opportunity to stuy with master percussionists 'ilton Carona an 1ohn Amira %amon" others&

in 2ew Yor+ urin" my 3445 research tour an foun that the parts presente here are the most common

in use toay) The parts are written in -./ clave) 6erformance arran"ement: Start with claves,then low

rum tumbadora %come in with an open tone on beat four&, mile rumsegundo %start with open tones on

the #two sie of the cla!e#&, catan finally the hi"h rum quinto.

Con"a Key: O7 Open Tone 676alm 878in"ers S7Slap 979ass
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Specially recommene recorin"s featurin" Guaguancoare:

AfroCuba* A 'usical Antholo"y

Various Artists %Rouner CD3;


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an the listeners are able to eMperience the tension that is bein" forme, between the traitional harmony

an the symmetric one) $owe!er the harmonic rhythm chan"es, an playin" lon" phrases mi"ht be too

much for the listener to process) As a result, the best way to a!oi that stress, is to use the ternary form, a

threesection form: A 9 A) The A parts are in the traitional or bebop lan"ua"e %or somethin" else&, an

the 9 section to employ the new symmetric approach) The form can be in any si(e, small or lar"e)

)

$! %i&iding The Oc#a&e

J/)3 The symmetric $armony theory eals with i!iin" the octa!e into symmetric tonal centers) An

octa!e can split into the neMt cate"ory: %Chors are spelle accorin" to common La(( terminolo"y&

3& C8NC Triton

/& CE=NC 'aLor Thir

-& CEb=b9bb%A&C 'inor Thir

5& CDE8N=NANC Wholetone

& CCNDDNE88N==NAAN9C Semitone

0n orer to form a tonal center, we nee to a the ominant before each chor so that the new succession

is eMpane)

3& =GC CNG8N =G C

/& =GC 9GE DNG=N =GC %8i"ure 3)&

-& =GC 9bGEb DbG=b EGA =GC

5& =GC AGD 9GE CNG8N DNG=N 8G9b =GC

& =GC =NGCN AGD 9bGEb 9GE CG8 CNG8N DG= DNG=N EGA 8G9b 8NG9 =GC

8i"ure 3)%9ase on 'aLor Thir&
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J/)/ The new meloy is now a succession of linear chors ) Accorin" to this metho, if a new meloy

line is playe simultaneously with the ori"inal, it creates a new polytonal color) 6olytonality may be

consiere partly as an eMtension of contrapuntal practice a sharpenini" of the e"es of ini!iual lines

an partly as a form of tonal or"ani(ation) %4& The pre!ious harmony, always be"in from the same

area that the symmetric meloy line starts, but they "o in separate ways an meet at the en of the musical

phrase) A new harmonic entity is create)

J/)- 0n the Coltrane metho, there is a chan"e in the succession orer wich is calle 6ermutation,

% chan"e the seuence of pitches an chors&) The ori"inal line is: =GC 9GE EbGAb =GC an

Coltranes cycle alteres it =GC EbGAb 9GE =GC %5&

0n 8i"ure / we can obser!e the ifferences between the chromatic lan"ua"e of the 9ebop an Coltranes

cycle) The altere eMtensions that 0 use on the ominant are %N4 th, b4th, Nth&) %-&

'igure $!
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(! The Triad Come Ou# As A Ma)or me#hod

J-)3 When the harmony is simple, sometimes the meloies are complicate, but when we eal with

complicate symmetric harmony, it is eMpecte that the tria will come out as a maLor metho of builin"

musical lan"ua"e) 'any twentieth century composers ha!e presuppose the theory that symmetry !ia

repetition is important for clarity)%3&An in orer to emphasi(e that principle, Coltrane uses simple

repetiton moti!es in his meloies)

8i"ure -)

J-)/ 0n 8i"ure - we can notice that the use of the tria with an eMtra passin" note forms 5 swin"in" notes)

An on the ominant there is a repetiti!e 9ebop moti!e) %This emphasi(es the connection between 9ebop

an the new lan"ua"e&) 8reuently, the new meloies ma+e use of close inter!als that lea the notes one

into another smoothly, so the meloy line cur!e is chan"in" up an own)
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J-)- 0n orer to eMpan the cycle, we can use a chromatic approach) 9ecause of the similarity between the

ominant an trisubF chor all ominant can be replace by the these substitutes) As a result, the new

arran"ment of the chors that is built on the maLor thir can be: C AGAb 8GE DbGC

8i"ure 5)

! Changing chords +ua,i#ies

J5)3 The uality of a chor %maLor, minor, ominant, iminishe, etc)& can be chan"e into another

uality) This can raically chan"e the atmosphere of a piece or a phrase) 8or eMample, we can ta+e the

ominant uality an apply it to the whole seuence) The meloy line can match the first 5 bars of a HC

9luesI because it has a sustaine ominant soun)

8i"ure )
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J5)/ We can eMperience a symmetry chan"e in the chors uality) 8or eMample when the chor is 'aLor

an the neMt iminishe)

8i"ure )

J5)- A seuence that is bein" constructe from minor thir, e!elops into lon"er musical 6hrase because

of i!ision the octa!e into 5 tonal centers) As a result we can lea!e behin the ominant an concentrate

on the tonic) A possibility for the new phrase can be: CEb=bA%9bb&C
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8i"ure G)

J5)5 0n the minor fiel, it is best to use minor structure) EMcept on the last ominant) %=G& 0n a symmetric

minor mo!ement each chor has at list on note ientical to the neMt chor) That stren"thens the harmony

line)

8i"ure


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J)3 9y applyin" the concepts liste, one is able to create new scales or moes that can be play in any

situation) %a"ainst any chor pro"ression&) The scales are lon"er than an octa!e, an one must maintain

the orer of the nots) Yet one can chan"e the irection of the meloy line an create an interestin"

contour)

8i"ure 4)

/! Gian# S#e0s and o#her

J)3 The main feature of Coltrane chan"es is tonality mo!ement by maLor thirs) The pro"ression to

H=iant StepsI is:

PP 1ma)2 DG P Gma)2 9bG P 3bma)2 P AmG DG P

P Gma)2 9bG P 3bma)28NG P 1ma)2 P 8mG 9bG P

P 3bma)2 P AmG DG P Gma)2 P CNmG 8NG P
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P 1ma)2 P 8mG 9bG P 3bma)2 P CNmG 8NG PP

The first +ey center here is 1, then G, then 3b, an it continues to cycle throu"h these three +eys, which

are a maLor thir apart)

Coltrane was able to e!elop this iea in many ways) 8or eMample, he use it as a substitute for an

orinary iiF pro"ression) The pro"ression to HCountownI is loosely base on that to the 'iles Da!is

composition HTuneupI) The latter tune be"ins with the fourmeasure pro"ression:

P EmG P AG P DmaLG P DmaLG P

this pro"ression is a iiF0 pro"ression in D maLor) The first four bars of HCountownI are:

P EmG 8G P 9bmaLG DbG P =bmaLG AG P DmaLG P

Coltrane starts with the same ii chor, an then moulates to the ominant se!enth chor one half step

hi"her) 8rom there, he launches into the cycle of maLor thirs, "oin" from the +ey of 9b to =b an finally

bac+s to D) The neMt four bars of the tune are ientical harmonically, eMcept they are base on an iiF in

the +ey of C* the neMt four bars are the same in the +ey of 9b)

J)/ An eMample that is eMamines the cycle on well+nown son" H0 =ot RhythmI presente in fi"ure 3;)

The basic chor pro"ress 0F000F has chan"e accorin"ly to the coltrane iea)

'igure 4!
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2! 5a,6ing u0 and do.n

JG)3 0n the matriM that is presente beneath, we can ma+e chors succession in any irection) 0f we

ecie to "o in the !ertical irection we meet the minor thir, an if we "o in the hori(ontal we meet the

maLor thir) We can "o up an own an ma+e any chors seuences)

Chor succession matriM

C Ab E C

A ' %b A

8N % 1b 8N

Eb 1 G Eb

C Ab E C
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$ere Are some possibility :

8i"ure 33

7! Chroma#ic diminished 8a##ern

J


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9! Me,odies in 'our#hs

J4)3 Tria lac+s complete efinition if its thir is omitte, an the resultant inter!al, a perfect fifth in root

position or a perfect fourth in in!ertion, has bare effect which soun asserti!e in en!ironment of classical

harmony with its interplay of !arie inter!als) %4& Chors which are intentionally

constructe of inter!als of fourth or secons, for eMpress purpose of Hbrea+in" freeI from functionality

associate with it) %


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J3;)3 The i!ersity of the styles in 1a(( is reflecte in its many stylistic resources for creatin" meloies)

0n the early ays of 1a(( the meloy was the bassis of impro!isin") When 9ebop arri!e, compleM

harmony was the moti!e of the meloy lan"ua"e) Coltrane an his symmetric system, opene the oor to

new concepts that su""este a theoretical framewor+ with a new philosophy) The aoption of the new

metho by youn" players emonstrates a "rowin" awareness to the re!olution that Coltrane create)

0mpro!ise music usually e!elops in a wie ran"e of ways) 0t is eMpecte that the youn" players, with the

intention of ealin" with the new ?an"ua"e Of 'oern 1a(( 'usic, woul create new ieas in the future)

0n my opinion, the preferable way is to fin an inte"rate techniue that combines traition approach an

inno!ation)

symmetric harmony

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