Sparky’sPages
Music Theory for Musicians
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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
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music theory for musicians and normal people by toby w. rush
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!
it’s Sparkythe music theory dog!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
Q:
A: WOOF!*
Dear Sparky:Since we are supposed to use different approaches for identifying perfect andimperfect intervals, can you summarize them all into one system?
--I.M., Staten Island, NY
& œbœ# & œœpoof
!
poof!
& œbœ#& œbœ& œœ
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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
music theory for musicians and normal people by toby w. rush
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!
it’s Sparkythe music theory dog!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
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!
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music theory for musicians and normal people by toby w. rush
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!
it’s Sparkythe music theory dog!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
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
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& œ œ œ œb œ œ œ œ
& œ œ œ œb œ œ œ œ
& 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
music theory for musicians and normal people by toby w. rush
*translation:
Hey,
kids!
it’s Sparkythe music theory dog!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
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
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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!
music theory for musicians and normal people by toby w. rush
*translation:
Hey,
kids!
it’s Sparkythe music theory dog!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
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
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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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