Music Theory for Musicians and Normal People Sparky’s Pagesmusic theory for musicians and normal...

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Music Theory for Musicians

tobyrush.com

and Normal People

music theory for musicians and normal people by toby w. rush

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

for complex rhythms, however, things can get complicated... when a rhythm includes thingslike syncopations or other off-beat figures, illustrating the meter may involve dividingnotes across beat units with ties. fortunately, there is a step-by-step system for correctlybeaming these complicated rhythms!

*translation:

step 1:

Hey,

kids!

it’s Sparkythe music theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN!

Q:

A: WOOF!*

Dear Sparky:I understand that we’re supposed to beam rhythms to show the organization ofbeats in the measure, but is there an easy way to beam complex rhythms?

--A.Y., Owatonna, MN

& 43 Jœ Jœ Jœ Jœ Jœ Jœ & 43 œ œ œ œ œ œ

& 44 .Jœ Jœ œ Rœ Rœ Rœ Jœ Rœ Rœ

for example, let’stake 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: find every group of two or more notes that are both tied together andbeamed together, and replace them with a single note of equivalent value.

a correctly beamed rhythm may include ties, but it willvery clearly show the beats in the measure... which, inturn, makes it easier for the performer to read!

yes, i know itlooks weird...but we’re not

done yet!

if you have notesthat are tied orbeamed, but not

both, then leavethem alone!

=

don’ttouch!

handsoff!

yes...simplify it!

original rhythm:

& 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

& 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

44 .Jœ Jœ œ Rœ Rœ Rœ Jœ Rœ Rœ

& 44 .œ œ œ .œ œ œ œ œ .œ œ

œ œ œJœ œJ œ œ

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more


the following chart shows an approach for identifying any interval. a similar approach can be used when youneed to write a particular interval above or below a given note: first, adda note above or below the given note at the correct distance, then followsteps 2 through 4 of this chart to identify it. Then, if necessary, alter thenote you added with an accidental to create the interval called for.

determine the distance of the intervalby counting lines and spaces.

count the bottomnote as one, andcontinue until you

reach the top note.

*translation:

STEP 1:cover up all accidentals.STEP 2:determine the inflection of the interval in front of you(the one without accidentals!) as follows:

if it is aunison or octave:

the interval shownis a

perfect unisonor

perfect octave.

if the interval usesthe notes f and b,

it is either an

augmented fourthor a

diminished fifth.

if the top note isin the major key ofthe bottom note,

the interval is

major.

if the bottom note isin the major key of

the top note,the interval is

minor.

otherwise, theinterval is

perfect.

really.it just is.

if it is afourth or fifth:

if it is asecond, third,

sixth or seventh:

STEP 3:

add the original accidentals back, one at a time, and track howthe interval changes inflection.

remember: accidentals can never affectthe distance of an interval... all they can

ever do is change the inflection!

This method may seem complicated at first,but it becomes easier and faster with

practice... and it gives you the correctanswer every time!

Hey,

kids!



Q:

A: WOOF!*

Dear Sparky:Since we are supposed to use different approaches for identifying perfect andimperfect intervals, can you summarize them all into one system?

--I.M., Staten Island, NY

& œbœ# & œœpoof

!

poof!

& œbœ#& œbœ& œœ


12

34

56

7

STEP 4:dd i m i n i s h e d mm i no r Mma jo r Aaugm en t e ddd i m i n i s h e d Pp e r f e c t Aaugm en t e d

M6 m6 d6pe

rfec

t

inter

vals

impe

rfec

t

inter

vals


4 I6 4IV V6C:

vi VC:

this a is thenote of suspension...

it doesn’t belong inthis g major triad.

it resolves tothis g, which doesfit in the chord.it’s the note of

resolution!

when analyzing suspensions, it is important to identify both the note of suspension (the non-harmonic toneitself) and the note of resolution (the note that comes right after thenon-harmonic tone in the same voice).

in almost every case,the suspension isthen labeled usingtwo intervals: theinterval between thenote of suspensionand the bass, and theinterval between thenote of resolutionand the bass.

the only exception to thisis the 2-3 suspension, wherethe suspension occurs in thebass. for this one, we lookat the interval between thenotes of suspension andresolution and the nearestchord tone, whichever voiceit may be in.

when writing an example whichincludes a suspension, it is veryoften useful to begin by writingthe chord that is going to containthe suspension, then adding thesuspension, and finishing by writingthe chord of approach.

*translation:

Hey,

kids!



Q:

A: WOOF!*

Dear Sparky:Can you elaborate on why suspensions are identified by numbers? Also, whatshould one watch out for when writing suspensions in four-part harmony?

--S.S., Detroit, MI

IV V6C:

this isa 6th!

this isa 7th!

...so it’s a7-6 suspension!

this isa 2nd!

this isa 3rd!

...so it’s a2-3 suspension!

I6 II6 I6

the real trick, though, is to plan ahead... if you are planning to write a particular typeof suspension, you need to think about the interval that needs to be present in thechord that includes your suspension.

for the 9-8 suspension,the suspension resolvesto an octave above thebass... that’s easy, sinceany chord can include

an octave.

I6 I

for the 4-3 suspensionand 2-3 suspension, you

need a chord with athird above the bass...which means you can

use anything except asecond inversion triad.

for the 7-6 suspension,the suspension resolves

to a sixth above thebass. that means youcan’t use a chord in

root position, becausethey have a fifth and athird above the bass.you need a first or

second inversion triad!



F major

F major

F minor

the

circleof

fifths

related

parall

el

Since D minor has the samekey signature as F major,we say that D minor is the

relative minor of F major.

So F minor is the parallel minor of F major!

it’s convenient to add minor keys tothe circle of fifths; they’re usuallyplaced on the inside of the circlein lower case.

because relative keys share thesame key signature, they alsoshare the same position onthe circle of fifths!

parallel keys have differentkey signatures, but seeingthem on the circle of fifthsillustrates their consistentkey relationship: minor keysalways appear three degreescounterclockwise from theirparallel major key.

So to find the key signature fora minor key, start with the majorkey signature with the same tonic andeither add three flats, subtract threesharps, or some combination of both!

d minor

*translation:

Hey,

kids!



Q:

A: WOOF!*

Dear Sparky:What does it mean when music theorists talk about “relative minor” and“parallel minor”? In what ways can major and minor keys be connected?

-M.T., Canton, OH


& œ œ œ œb œ œ œ œ



#& œ œ œ œ œ œb œ œ

sure, d minormight use ac sharp asa raised

leading-tone,but we don’t

consider that aspart of the

key signature.

b bb

F

A

E

B

D

GC

e

b

f

ad

g

c

Bb

E b

Ab

DbGb

C bC#F#

0

1b

2b

3b

4b

5b

6b

7b

1#

2#

3#

4#

5#

6#7#

a bbb

eb

f #

c#g #

a # d #

related. when two keys that have the same key signature but different tonic notes, we say they’re related.

parallelparallel keys, on the other hand, arekeys that have the same tonic note, but

different key signatures.

&## &

#& &po

of!

poof! bb# +-#-D major... ...D minor!

2# 1# 0 1b


*translation:

Hey,

kids!



Q:

A: WOOF!*

Dear Sparky:What does it mean that certain instruments are “transposing instruments”?Does that affect how I should music for them?

-A.M., Dana Point, CA


transposing instruments are instruments which play play in a different key than what is on the page.

the reason depends onthe type of instrument!

woodwind instruments come in different sizes to

cover a larger range. rather than learn new fingerings for each

size of instrument, it’s easier to have oneset of fingerings that works on all of them!

brass instruments, like woodwinds, were built in many different keys...especially since early brass instruments didn’thave valves, and thus could only play theharmonic overtones of a single note!

Even after valves became common,instruments were still available in a

variety of keys... and it made senseto write their music so that fingerings

were consistent across the board!

why?why?

for example, when a clarinetistsees and plays a G,

it actually sounds like an f!& œ & œ

co

ntrabass s

axo

pho

ne

bass s

axo

pho

ne

barito

ne s

axo

pho

ne

teno

r s

axo

pho

ne

alt

o s

axo

pho

ne

so

prano

saxo

pho

ne

so

pranin

o s

axo

pho

ne

& œ

& œb & œ & œb? œ ? œb ?

œ?

œb

& wb w wb w w wb

Eventually, of course, instruments incertain keys were preferred for theirtimbre and range, and became much

more common!

trumpet in b flat horn in f

first, figure out if your instrument transposes... and if it does, how:

so what does all this mean if youjust want to write some music?

then, account for it!if an instrument sounds a perfect fifth lower,

tranpose their part a perfect fifth higher!

twooctaveshigher

glockenspie

l

piccolo

xylophone

e f

lat c

larin

et

b f

lat c

larin

et

soprano s

ax

trumpet

cornet

flute

oboe

trombone

tuba

violin

viola

cello

alto

flute

alto

clarin

et

alto

sax

englis

h h

orn

french h

orn

contrabassoon

double b

ass

bass c

larin

et

tenor s

ax

bari s

ax

oneoctavehigher

minorthird

higher

aswritten

Majorsecondlower

perfectfourthlower

perfectfifthlower

majorsixthlower

oneoctavelower

P8+M2lower

P8+M6lower

when you play a

written note

on:

it will sound:

& bb Œ œ.>̇

& b Œ œ. >̇

want this? write this!

the good news:most music notationsoftware can handleall this automatically!


*translation:

Hey,

kids!



Q:

A: WOOF!*

Dear Sparky:I understand pitch class sets, normal form and prime form, but are there otherways to describe a chord using set theory?

-G.L., Corona del Mar, CA


because set theory is primarily interested in the intervals which make up a chord, prime form isusually the best way to categorize chords using set theory... but thereare other ways theorists use to describe sets in their prime form!

howard hanson, one of the first proponents of set theory, came up with a code which counted each type of basic interval, ordered from consonance to dissonance:

nowadays,most theorists

express this conceptin a more mathematical

way, using what we call aninterval vector:

twentieth- century theorist Allen Forte figured that since there was a finite number of possible sets, someone ought tocatalog them all!

of course, that someonewas Allen Forte, who cameup with the system offorte numbers: a uniquenumber for each andevery possible set.

in his chart, forte labeled sets which haddifferent primeforms but the sameinterval vector with a “z”. like 4z-15 and 4z-29, which are both called all-interval tetrachords... since they both have the interval vector (1,1,1,1,1,1)!

how do you figure out aset’s forte number?

step one: look it upon the chart.

there isno step

two!

to figure out the hanson analysis, list theletters in this order, omitting any intervals

not present and using superscriptednumbers to show duplicates.

you could use amnemonic toremember theorder... like

“please makenick stop

doing that”!hansonanalysis:

hanson

&œœœb b

[0,1,6]

[0,3,4,7] = PM2N 2D[0,1,2,6] = PMSD 2T

[0,3,4,7] = (102210)[0,1,2,6] = (210111)

PDT

fortenumber:

3-5intervalvector:

(100011)

P M N S D T

P4P5

M3m6

m3M6

M2m7

m2M7 TT

#( # # # # # )

P4P5

M3m6

m3M6

M2m7

m2M7 TT

deyoewait...doingwhat?

forte

Fortenumbers

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