hello!

this file is a collection of individual sheets MUSICcovering a bunch of lessons on music THEORY theory.

for it’s not a book... yet. it might be someday! but as of right now, it’s incomplete.

The truth is, they weren’t intended to be a single volume when I started making them... they were just review sheets for my own theory students.

but the more I made, MUSICIANSthe more I realized they could be collected into a textbook of sorts... eventually! and I still have a lot of work to do, but I’ve collected the ones I’ve made so far into a single document to make it easier for the folks who wanted them all... but didn’t want to download every file individually!

I still have a lot of work to do, but I’ve collected the ones I’ve made so far into a single document to make it easier for the folks who wanted them all... but didn’t want so if you’ve been sent this file NORMALto download every file individually! by someone, know that there might be a newer version — or more pages — at tobyrush.com.

but if you like this, or find it useful, great! feel free to share it, copy it, and use it.

now let’s learn some music theory! just don’t sell it, change it, or tell others you made it!*

PEOPLERush by Toby W. Rush *for more info, see http://creativecommons.org/licenses/by-nc-nd/4.0/ music theory for musicians and normal people by toby w. rush

music notation is the art of Notation: Pitch recording music in written form.

liz phair “what makes you happy” [melody from chorus] whitechocolatespaceegg (1998) #¶#g#F#d#DµD#SµS#d#Mf#SµSµg#F œ œœœ œœ œ œœœ œ œœ Œ modern music notation is a product œ of centuries of transformation... the system of musical notation and it is neither efficient nor intuitive! we use is essentially a stylized graph of pitch versus time.

pitch is the highness or lowness of a sound. œ œ œ & œ œ œ œ œ for example, a flute has the five lines on which notes a high pitch, while a tuba appear is called a staff. has a low pitch. pitch pitch time a note is a written representation of a particular pitch.

notation is based on the piano keyboard; lines and spaces on the staff represent F g a b c d e F g a b c d e the white notes on the keyboard. the white notes on the keyboard are labeled with letters from A to G.

to display notes outside the staff, we use shortened staff lines & called treblew clef B w B w w alto clef ledger lines. tenor clef ? bass clef the clef determines what notes each staff line corresponds to. the four modern middle c is the c that is closest to clefs are shown here; the note displayed the middle of the piano keyboard. on each staff corresponds to middle c.

these symbols are placed to The double sharp raises the To notate the the of the note that they note by two half steps. left black notes affect, and they apply to all the on the piano ‹ notes on that line or space keyboard, we use for the rest of the measure. accidentals, The sharp raises the which alter the note by one half step. note by one or two half steps. # & bœ œ nœ #œ ∫œ œ nœ ‹œ The natural cancels out a half step is any previous accidental. the distance n between two adjacent keys The flat lowers the on the piano note by one half step. keyboard, F g a b c d e F g a b c d e regardless b of what color The double flat lowers two notes which have the same the keys are. the note by two half steps. pitch (for example, f sharp and g flat) are called enharmonics. licensed∫ under a creative commons BY-NC-ND license - visit tobyrush.com for more Notation: Rhythm as thenoteto itsleft. noneofthesenoteshasastandard a numbershowingthedivisionbeing made. which corresponds to a note. theseareusually writtenasagroup length; ahalfnoteinonepiecemay bethesamelengthas in thischart, eachsuccessivetypeofnoteishalfaslong a tupletisanynon-standard divisionofa silence that alength a restisperiodof double whole rest double whole note the augmentation dotisaplacedto the length ofthenoteby150%.Inotherwords, of notesdelinated withabracketand wields someseriouspower:itchangesthe W right ofanotehead. thoughsmall,thisdot œ q „ particular note. = œ 3 it makesthenotehalfagainaslong! ties arecurvedmarkswhichconnect œ j œ e two notestogether to create a single,extendedsound. + œ for example, thesearen’t j exactly quarternotes; they areeach athirdas e

whole rest an eighthnoteinadifferentpiece. whole note long as ahalfnote. w ∑ = licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more œ q. music theoryformusiciansandnormalpeoplebytoby w. rush

= half rest half note h ∑ e + œ e œ + j

e quarter rest quarter note = q Œ œ .

) ederic chopin 1 (1846 fr jor, op. 62, no. nocturne in b ma q.. eighth rest eighth note e = ‰ vertical axis,notelengthisindicated using a e the tripletsto theleft. butanythingis while pitch isprettyclearly notated ona possible! chopin,forexample,would most tuplets aresimpledivisions,like often goto town withthesethings. + to tiemorethantwo notestogether, e draw tiesbetweeneachnote;donot somewhat arcane system involving noteheads, stemsandflags.

+ sixteenth rest sixteenth note multiple dotscanalsobeadded, x e œ ≈ each oneaddinghalfofthe + use asingle,extendedtie. œ x previously addedvalue. œ thirty-second rest thirty-second note œ x are indicated bythe tempo ® q... marking at thebeginning placed onthestaff at a position asshownhere. K note lengthsinapiece of apieceorsection. = particular vertical usually restsare e

+ sixty-fourth rest sixty-fourth note x Ù e K K œ + chopin, no! down, wha... gah! e œ + one-hundred- one-hundred- œ x twenty-eighth rest twenty-eighth note boy! + x  œ x K K K K music theory for musicians and normal people by toby w. rush a fundamental feature of most pieces of music is a Notation: Meter consistent rhythmic pulse. this pulse is called the beat, [drum intro] the coors knows” “heaven (1996) forgotten not forgiven, and a single pulse is called a beat unit.

there are two types of beat units: ...and those containing those containing two divisions, q q. three divisions, called simple beat units... E E E E E called compound beat units. in music, beats are organized into patterns of accented and unaccented beat units. in fact, if you listen to a sequence of repeated notes, your brain will probably start to perceive the notes as groups of two, three, or four, even if no accents are present! Q Q Q Q Q Q Q Q Q Q Q Q Q Q> Q Q Q Q> Q Q Q >Q Q Q Q Q Q Q Q Q Q Q Q these groups are called measures, barline measure and they are delineated with barlines.

the organization simple TIME SIGNATURES are easy. of beat units and measures in the top number a piece is called indicates the number meter. Meter is of beats in a measure. described by two 3 Q Q Q Q Q Q numbers placed the bottom number the4 code for the bottom note at the beginning indicates the type of is pretty easy: 4 refers to of the piece: note which serves as a quarter note, to an eighth the beat unit. note, to a sixteenth8 note, the time signature. 3 16 4 and so on. compound TIME SIGNATURES are stupidly complicated.

the top number indicates the number of divisions in a measure. to get the 6 . . . . number of beats, divide it by three. 8 Q Q Q Q the bottom number indicates the type of in fact, wouldn’t this be note which serves as the division. an easier way to notate to get the beat unit, use the note that compound meters? 6 is equal to three of these notes. 2 in a compound meter, the beat unit is always a dotted note! sorry... the man says you have to do it 8by looking at the top the other way. number of the time signature, you can tell two things about the meter: whether it’s simple notes that have flags can or compound, and how many be grouped together by using beats are in a measure. beams in place of flags.

simple compound

2

2 6 however, beaming is only used to group notes within beats. 3 for the most part, you shouldn’t beam notes between beats, 3 9 nor should you tie notes within beats. 4 beats per measure beats 4 12

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush Hey, it’s Sparkythe music theory dog! kids! Dear Sparky: Q: I understand that we’re supposed to beam rhythms to show the organization of beats in the measure, but is there an easy way to beam complex rhythms? --A.Y., Owatonna, MN A: WOOF!*

*translation: 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) into groups that are equal to the beat unit of the current meter.

3 œ œ œ œ œ œ 3 œ œ œ œ œ œ &4 J J J J J J &4 for complex rhythms, however, things can get complicated... when a rhythm includes things like syncopations or other off-beat figures, illustrating the meter may involve dividing notes across beat units with ties. fortunately, there is a step-by-step system for correctly beaming these complicated rhythms! for example, let’s take this rhythm, which is written 4 œ. œ œ œ œ œ œ œ œ without beaming. &4 J J R R R J R R find the smallest note value used, and fill a complete measure with this type of step 1: note, beamed in groups that are equal to a beat unit in the current meter.

&44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ add ties between individual notes to recreate the original rhythm. make sure that step 2: each tied group corresponds to a note in the rhythm you started with!

yes, i know it looks weird... but we’re not 4 done yet! &4œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

original rhythm: 4 œ. œ œ œ œ œ œ œ œ 4 J J R R R J R R find every group of two or more notes that are both tied together and step 3: beamed together, and replace them with a single note of equivalent value. if you have notes that are tied or beamed, but not 4 . . . both, then leave &4œ œ œ œ œ œ œ œ œ œ them alone! a correctly beamed rhythm may include ties, but it will œ œ œ œ œ œ = œ very clearly show the beats in the measure... which, in don’tJ J hands yes... turn, makes it easier for the performer to read! touch! off! simplify it! DOING STUFF THE SPARKY WAY IS ALWAYS FUN! licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush one of the reasons that a particular piece of The Major Scale music sounds the way it does has to do with the group of notes the composer decided to use.

2 2

, 17

bach

na e

bachr a magdal

ian jo t a ann

bas m

G for se n i

ann ook

oh eb inuett j M no œ#œ œ œ œ œ œ &43 œ œ œ œ œ œ œœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ˙. take this melody, for example... let’s first remove all the duplicate notes, regardless of which octave they’re in. œ#œ œ &43 œ œ œ œ next, let’s put the notes in alphabetical order, œ #œ œ starting on the note œ #œ œ œ œ œ that the melody sounded œ œ œ œ like it was centering on. œ œ

what we end up with there are actually many is the for “palette” different types of scales, this particular piece... each with a different pattern of whole steps and half steps. œ œ œ #œ œ œ œ œ a half step is the distance between like the board on which a painter holds two adjacent keys the bits of paint being used in the painting on the piano keyboard, being created. regardless of color.

in music, this “palette” is called a scale. though we usually write scales from low to high, the order is actually unimportant; it’s the notes contained in the scale that help make a piece sound the way it does. this particular arrangement, where half steps occur between steps three and four and between steps seven and eight (or between seven and one, since eight and one are the same note), is called the major scale.

half a whole step is the whole whole stepœ equivalent of step#œ half whole stepœ two half steps. whole stepœ step whole œ stepœ œ stepœ (this scale, by the way, is called the g major scale, because it starts on g.)

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

the f major scale the d flat major scale œ but remember... œ bœ œ œ œ bœ bœ œ bœ with & œ œ & bœ bœ œ bœ great power the b major scale the g flat major scale comes great bœ bœ œ bœ responsibility! & #œ #œ œ & bœ bœ bœ bœ œ #œ #œ œ #œ licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush

A B E A D Key Signatures b b if you start writing major scales and pay attention to A f c g the accidentals that occur, # you are going to start noticing a pattern... B E b b b

for example look at the flat keys, starting with the key b f c g d a that has one flat, all the # way through the key with seven flats: the flats accrue c B E A D G C F in a specific order. b b same with the sharp keys!

c so if you look for a key that n has only a d flat, you won’t find it: if a key has a d flat, f c g d a e b it must also have a b flat, c # # an e flat and an a flat!

d B E A D G since writing an entire piece in b b c sharp major would have been a sure-fire way to get f c carpal tunnel syndrome with d # all the sharps involved, composers pretty quickly came up with a way to simplify things: e B E A key signatures. b b a key signature is a group of accidentals placed at the e f c g d beginning of every line of music, # just to the right of the clef, that instructs the performer to apply those accidentals to f B every corresponding note in b the piece unless specified otherwise. f f c g d a e for example, this key # # signature indicates that every f, c, and g in the piece should be sharped, regardless of octave! g B E A D G C b b oh, and another thing: the accidentals have to be placed g f in the correct order, and # they need to follow a particular pattern of placement that varies slightly depending on the clef being used! if you deviate from this, you, as a composer, will be mocked! tenor clef sharps! what’s your problem? you need to conform! ha ha... never!

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theorists find it convenient to The Circle of Fifths organize all the possible key signatures into a chart that shows their relationship to one another. this chart, called the circle of fifths, displays each key as a spoke on the circle, beginning with c major at the top and adding accidentals, one at a time, to the key signatures around the perimeter. we’ll return to this chart as we continue learning about how composers use keys. C F 0 G 1 1b # b #

as you move clockwise around the circle, you add sharps to the key signature. as you move counterclockwise around, B you add flats to the key signature. D b 2b 2#

to determine the key signature for a key, look to when adding flats to see which “spoke” of the circle a key signature, add them it’s on to determine how many in this order: flats or sharps it has, and add accidentals to the key b E 3b signature appropriately. beadgcf 3# A b # for example, when adding sharps, e flat major use the reverse has three flats, of the order above. so it should look like this: 4 4 b the keys down here line up # A enharmonically... for example, E the key of d flat major will sound b just like the key of c sharp major. so could you 7# 5# continue the 5 7 enharmonic b 6 b deal and have # the key of C B f flat major? notice how that 6 b yes, if you want beadgcf pattern # a double flat pops up all over C D in your the circle of F key signature: fifths? b # b weird! G b nooooo! licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush

an interval is Diatonic Intervals the distance in pitch between two notes. smaller the most basic way which we intervals identify different intervals is œ by counting the steps between œ œœ the two notes. & œ larger œ œ intervals specifically, we count scale degrees, but the easiest way to do it is to count lines and spaces when counting on the staff. the lines and spaces, we 7 can safely when counting, 6 ignore any begin with the 5 accidentals. as 4 bottom note one and count 3 this interval until you reach 2 is also a the top note. 1 seventh... we’ll discuss b how it’s this interval different is a seventh! very soon!

octave fourth fifth sixth seventh third unison second

two notes on the distance from the same line or a note to the next that’s latin for and that’s latin space is called closest note with “one sound”! for “eight”! a unison. the same letter name is called an octave.

and when you swap the two notes when we are talking about (move the lower note up by an octave intervals we sometimes discuss so it becomes the higher note), harmonic intervals and that is called inverting the interval. melodic intervals. œ THE RULE & œ œ œ œ œ 2nd 7th & œ œ it’s helpful to remember 3rd 6th harmonic melodic that seconds always invert 4th 5th interval interval to sevenths, thirds to sixths, and so forth... 5th 4th a harmonic interval is simply 6th 3rd two notes played simultaneously; the fact that each of a melodic interval is 7th 2nd one note these pairs add up to nine played after the other. is known to theorists as “the rule of nines.” OF NINES

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush the distance of an interval is the first part of its name, but there’s more: every interval has another Perfect Intervals quality to it, which we’ll call its inflection.

inflection is a bit harder to understand, partly because it depends on the type of interval. so let’s start by looking at unisons, fourths, fifths and octaves.

& œ œ œ œ œ œœ œ œ œ œ œ œ

unisons and octaves are the easiest to label: if the two notes are the same (for fourths and fifths example, b flat and b flat), require a little more explaining. then the inflection is perfect: if you look at all the fourths and fifths you such an interval is called a can create using only the white notes on the perfect unison or a piano keyboard (in other words, using only notes perfect octave. without accidentals):

œ œ œ œ & œ œ œ œ œ œ each one is œ œ œ perfect except for those which use f and b! œ œ & œ œ œ œ œ œ œ œ œ œ œ well, if you were to count the that make up wait... half-steps each interval, you’d notice that all the other ones are why are the equal in size, but the b to f intervals are not: f to b is b to f intervals a half-step larger than a perfect fourth, and b to f different? is a half-step smaller than a perfect fifth. which raises the question: if the interval is not perfect, than what is it?

an interval that is a half-step larger than perfect is called augmented œ bœ an augmented interval. & #œ & ∫œ & d5 œ A d4 d8 œ #œ and there’s & bœ & œ no such thing as a A5 A4 diminished unison... perfect #œ œ bœ just like two things & œ & can’t be negative two feet A1 P away from each other! A8 you can go further, to doubly augmented and an interval that is a half-step doubly diminished intervals, diminished smaller than perfect is called but... do you really want to? a diminished interval. licensed under a creative commonsd BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush We’ve talked about unisons, fourths, fifths Imperfect Intervals and octaves, but what about the rest? are these other intervals somehow imperfect?

& œ œ œ œ œ œœ œ œ œ œ œ œ

well, yes, but not because they are somehow inferior to perfect intervals... seconds, thirds, sixths and sevenths just work a little differently!

for one thing, the inflection for these intervals is never perfect; it will be either major or minor. minor intervals are a half-step smaller augmented than major intervals. like perfect intervals, though, they can also be augmented or diminished; augmented intervals are a half-step larger A than major, and diminished intervals are a half-step smaller than minor. how do we know if an interval is major or minor? we can actually use the major scale to find out. notice that, in the major scale, Mmajor intervals from the tonic up to another scale degree are major. œ œ & œ œ œ œ œ œ majorœ majorœ œ œ majorœ majorœ œ minor second third sixth seventh likewise, intervals from the tonic down to another scale degree m are minor. œ œœ œ œ œ œ œ œ diminished & œ œ œ œ minor minor minor minorœ œ d second third sixth seventh

knowing this, when you are confronted with a second, third, sixth or seventh, you can find its inflection by thinking about the key signature of the top and/or bottom note.

we know this is a major sixth and this is a minor seventh because d, the top note, is in because b, bottom note, is in the key of f major œ œ the key of a major (the bottom note). & œ & œ (the top note).

if the top note is in the major key of the bottom note, the interval is major. if the bottom note is in the major key of the top note, the interval is minor.

when the notes of the interval have accidentals, the associated key signatures can be more complicated... so it’s easiest to temporarily ignore the accidentals, determine the interval, and then add the accidentals back one at a time and track how the interval changes!

adding back adding back e is in the ack! what is the flat makes the sharp key of g, so that? let’s poof! the interval makes it even poof! we know first hide the smaller, so smaller... bœ œ this is a bœ bœ accidentals... it’s now a a diminished & # œ & œ major sixth. & œ & # œ M6 m6 minor sixth... d6 sixth!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush Hey, it’s Sparkythe music theory dog! kids! Dear Sparky: Q: Since we are supposed to use different approaches for identifying perfect and imperfect intervals, can you summarize them all into one system? --I.M., Staten Island, NY A: WOOF!*

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

count the bottom determine the distance of the interval note as one, and by counting lines and spaces. continue until you STEP 1: reach the top note.

poof! cover up all accidentals. bœ poof! œ STEP 2: & # œ & œ

determine the inflection of the interval STEP 3: currently shown as follows: if it is a if it is a if it is a second, third, unison or octave: fourth or fifth: sixth or seventh:

if the top note is if the interval uses in the major key of the interval shown the notes f and b, the bottom note, is a it is either an perfect unison the interval is augmented fourth major. or or a perfect octave. diminished fifth. if the bottom note is in the major key of really. otherwise, the the top note, it just is. interval is the interval is perfect. minor.

add the original accidentals back, one at a time, and track how the œ bœ STEP 4: interval changes inflection. & œ & # œ

remember: accidentals can never affect This method may seem complicated at first, the distance of an interval... distance is but as you use it, you’ll internalize it and determined solely by the number of become faster... so get out there and lines and spaces between the two notes! identify some intervals! DOING STUFF THE SPARKY WAY IS ALWAYS FUN! licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush There are actually two things that define a key: the key signature is the most obvious one, but The Minor Scales another important part of a key is the tonic... the around which the key this key is defined note centers. by a key signature of no sharps and flats, but also by the fact that it œ œ centers around c. œ œ & œ œ œ œ but what if we change the tonic? what if we use the same notes for the key signature, but change the note that the key is centered around?

if we center the key around the sixth scale degree of the major scale, we get a new scale: the minor scale. the œ œ œ natural œ œ œ minor œ œ scale & the whole step the thing is, common practice period composers here didn’t have weren’t all that crazy about this scale, because the tension it lacks something the major scale has: they liked going a half-step from seven to one. into the tonic!

so here’s what they did: they raised the leading-tone by a half-step with an accidental. This gave them the tension they were looking for!

the œ œ #œ œ harmonic œ œ half- minor œ step! scale & œ

this scale is great for building chords, so we refer to it as the harmonic minor scale. however, composers didn’t use it for writing melodies, because it had a problem: an augmented second between the sixth and seventh scale degrees.

so, for melodies, they made another change: now we only they added another accidental to raise have whole steps the sixth scale degree by a half-step. and half-steps! #œ œ the œ #œ & œ œ œ œ melodic minor scale œ Nœ Nœ œ & œ œ œ œ now, remember... the reason we raised the leading tone in the first place was to create tension from the seventh scale degree to tonic. but in a melody, if the seventh scale degree is followed by the sixth scale degree, we don’t need that tension, so we don’t need to raise the leading-tone at all. the way we illustrate this is by differentiating between ascending melodic minor and descending melodic minor; for descending melodic minor, we don’t raise anything!

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although a chord is technically any combination of notes Triads played simultaneously, in music theory we usually define chords as the combination of three or more notes.

secundal tertial quartal quintal harmony harmony harmony harmony œ œœ œ œ œœ œ œ œ chords built from chords built from chords built from chords built from seconds form thirds (MORE perfect fourths perfect fifths tone clusters, SPECifically, from create a different can be respelled as which are not major thirds and sound, used in quartal chords, harmonic so much minor thirds) compositions from and as such they as timbral. form the basis of the early 1900s do not create a

most harmony in and onward. separate system of are the same as tertial and as with quintal harmony, these harmony, as with quintal

the common harmony. respectively. secundal harmony, practice period. harmony? harmony? septal sextal

well, diminished thirds sound is the chord still tertial just like major seconds, and if it is built from diminished augmented thirds sound just thirds or augmented thirds? like perfect fourths, so... no. œ œ let’s get started the lowest note in the chord & œ on tertial harmony when the chord is in simple œ with the smallest form is called & œ chord possible: the root. the œ the triad. fifth ? œ when we stack names of the œ the chord in other notes third thirds within one octave, are based on root we get what is called the their interval simple form of the chord. above the root. œ a triad is defined as a œ three-note chord, there are four ways to create a triad but in practice it is almost always used using and to refer to tertial three-note chords. major minor thirds:

the the the the minor major diminishedtriad triad triad augmentedtriad

two minor thirds a major third on top a minor third on top two major thirds stacked together a minor third on bottom a major third on bottom stacked together

min 3rd maj 3rd min 3rd maj 3rd & bbœ min 3rd & bœ min 3rd & œ maj 3rd & #œ maj 3rd c°œ cœ Cœ Cœ+ we label triads using their root (”a c minor triad”). the abbreviations shown above, which use upper case, lower case, and symbols to show chord type, are called macro analysis.

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Triads in Inversion and he’s brought a ladies and gentlemen, it’s movement from his 1767 franz joseph haydn! sonata in g major.

thank you for having me. in this piece I use quite a few triads. ooh! let’s see ‘em! haydn

here’s one: it has the notes # j œ c, e and g. it’s a jc major œ 3 œ œ œ œ œ triad!œ œveryœ nice.œ œ œ œ œ œ. . & 8 œ œ œ œ œ œ œ œ œ œ œ . œ œ. œ œ œ œ œ œ œ. œ. œ f . thank you. see how the notes . . œ. œ œ œ . œ. œ œ œ. œ ? # 3 ‰ œ œ areœ spreadœ œ out,‰ œand not just œ œ. œ . 8 œ œ œ stackedJ in œthirds?œ it’sœ stillœ œ J J a triad, though. J J œ # œ. œ œ œ ´ œ œ œ ´ œ œ œ œ´ œ œ œ œ œ´ j & this. one is g,œ b, œandœ œ d...œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ a g majorJ œ triad!œ but it soundsœ œ œ . different,f somehow. p that’sF because the third of the f œ . j œ . chordj is in the .bass...œ when. .that happens, ? # œ œ œ œ œ œ œ œ œ œ œ. œ. . ‰ œ œ œ œ we say theœ chordœ œis in firstœ inversion.œ ‰ J œ œ J œ œ. J J œ

œ œ œ . U # œ œ œ œ. œ œ œ œ œ œ œ œ œ œ . n b & œ œ firstœ œ œ œinversion?œ œ œ whatœ is itœ œ œ œ œ. œ . b called when the root isœ œinœ the. J bass, like the first chord ƒthat’s called we looked. at? . . . œ œ œ root position. œ œ. œ ? # œ œ œ. œ œ œ. œ . œ . n b œ œ œ œ J ‰ J J œ . b œ J J œ œ œ œ so this one with d, f, and a M M is a d minorœ triad... in M M #œ œ second inversion!œ œ œ bb . ‰ œ ‰‰ œ ‰‰ J #œ ‰‰ œ ‰‰ nœ œ #œ œ ‰ . & . J J J ‰‰ ‰‰ J J J . p F p exactly!nœ becauseœ œ theœ ? œ fifth? isœ inœ the bass.œ œ œ œ bb . ‰ & ‰œœ ‰ œ ‰ œ ‰œœ ‰ ‰ œ œ . œ œ so the thing that makes a triad root position, first inversion that’s right! or second inversion is simply and each one which note is in the bass? has its own character. it’s hard to believe that the sound of the chord can change so much just because of the bass note. I know, right? it’s awesome. haydn

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more musical works written in the baroque era would often include a part called the basso continuo which would Figured Bass consist of a single bass clef melodic line with various numbers and accidentals printed beneath the notes. no, no, no... there wasn’t an actual instrument called a basso continuo! the part was played by two instruments: a bass clef instrument like cello or bassoon, and a keyboard instrument like a harpsichord. music theory for musicians and normal people by toby w. rush in performances, the bass clef instrument would simply play the given notes, but the keyboard player would improvise a part based on the notes and the symbols below the part!

j.S. Bach: brandenberg concerto no. 5, bwv 1050 ?# œ #œ œ œ œ œ #œ œ œ œ œ so this...# œ œ œ #œ œ œ œ œ œ 6 6 #6 6 #6 6 6 #6 6 9 5 6 # Figure 1. e Basso Continuo # 5 5 5 could be played as this!

the numbers and symbols # j printed below the basso # œ œ œ œ œ & œ œ œ œ œ #œ œœ œ œ œ œ continuo part are called œ œ œ #œ œ œ œ œ #œ œ œ œœ œ œ #œ the figured bass. So how J J do you turn figured bass into chords? ? # œ #œ œ œ #œ œ œ œ # œ œ œ œ #œ œ œ œ œ œ œ œ first of all, it’s important to know that the note given on the bass clef part is always the bass note of the chord. and remember: the bass is not necessarily the root!

second, the numbers represent intervals ?# w ?# w ?# w above the bass, even # w # w # w though some numbers (5) 6 w6 are usually left out. (3) (3) 4 if there are a six by itself a six and a four note that the intervals no numbers, indicates a sixth indicate a sixth are always diatonic. add a third and and a third above and a fourth don’t worry about a fifth above the the bass, which above the bass, inflection... just use bass... you get a creates a first giving you a second the notes from the root position triad! inversion triad! inversion triad! key signature!

lastly, accidentals are applied to the interval nw they appear with. if you ?# #w ?# #w ?# w have an accidental by # w # w # w itself, it applies to the w third above the bass. #6 # n 6 don’t overthink these: here, the sharp here, there is no note that there is if the composer wants applies to the number next to the a natural, not a flat, a note raised by a half- sixth above the sharp, so we apply next to the six... bass, so we add a it to the third above if it were a flat, we step and it’s flatted in sharp to the g. the bass note. would write a c flat. the key signature, the figured bass will have a natural, not a sharp.

by the time the classical period got realizing figured bass (writing chords going, composers stopped including a given a figured bass line) makes for an basso continuo part, and so figured excellent exercise for students to learn bass fell out of use... with only one how to write in the common practice exception: music theory classes! period style! wooo!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush now that we’re familiar with how Triads Within Tonality triads work, it’s time to put them into the context of a key.

since writing music in a particular key means using the notes in that key signature, it stands to reason that most of the chords will be built from those same notes! chords which use notes from a particular key signature are said to be diatonic to that key. diatonic means “from the key.” that means no accidentals!

we can quickly show all the diatonic triads in a particular key by writing a scale in that key and building triads on each note, using only the notes in that key. œ œ œ œ & œ œ œ œ œ œ œ we refer to œI œii iiiœ IV V vi vii° these chords œ with roman numerals as shown here.

notice how chord type is shown by capitals or lower case? tonic

these chords are also mediant sometimes referred to by their official names! dominant Supertonic submediant subdominant this pattern of leading-tone and major, minor diminished why is the sixth chord called the submediant? triads is the in same every major key! well, just as the mediant chord is halfway the is always subdominant triad major, between the tonic and dominant chords, and the is always leading-tone triad the submediant chord is halfway between the whether you’re in diminished, tonic... and the subdominant a fifth below! c major or f sharp major! because the dominant and leading-tone triads both have a strong tendency to resolve to tonic, we say they have a “dominant function.” the subdominant and supertonic chords both tend to resolve to the dominant, so we say they both have a “subdominant function.”

the diatonic triads in minor work the same way... since we’re dealing with chords, we use the harmonic minor scale. however, it’s important to note that common practice period composers raised the leading tone only over dominant function harmony: the dominant and leading-tone triads! œ œ same names œ œ œ œ and roman & œ œ œ #œ œ #œ numerals... œ œ œ different œ œ œ œ capitalization! œi ii°œ III iv V VI vii° licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Introductionmusic theoryto for Part-Writing musicians and normal people by toby w. rush as we look ahead, we’re confronted with an ugly truth:

there is a lot of music in the history of the world that is worth studying...

much more than we can hope to cover in the span of a few semesters. since we can’t cover it all, we have to choose a specific musical language to study in depth. let’s start by narrowing things down to the common practice period. 1700 1500 1600 1900 1800 2000

early 20th renaissance baroque classical romantic century contemporary

the common practice period is the music of the baroque, it’s especially worth classical and romantic eras in europe and america. studying because the name comes from the fact that most composers used most of the pieces a common musical language during this time. commonly performed in concert are from this period... but there is a ton of common practice period music...... and the language more than we can hope to cover. is there a forms the basis for we can sink our representative style the most popular academic teeth into? musical styles today.

leipzig, germany

st. thomas church

four-voice chorale writing is a good style to study for several reasons:

chorales have a fast a large percentage of the cantatas of j.s. bach harmonic rhythm, allowing common practice period music provide us with a tremendous for a larger number of can be easily reduced to amount of consistently-written chords per exercise. four-voice counterpoint. four-voice chorales.

one of the changes to the catholic church more than two hundred years later, j.s. bach proposed by martin luther was appointed musical was to allow members of director at the st. thomas the congregation to church in leipzig, germany participate in the singing and, in the spirit of luther, of the liturgy. wrote five years’ worth of liturgical music. of course, luther was branded a heretic for each of these works, his proposals, and began called cantatas, were built his own church in which around a hymn melody to implement his ideas. harmonized in four parts l j. uther for congregational singing. s. bach

by analyzing bach’s cantatas, we can construct a set of “rules” for writing in four-voice common practice period musical style, allowing us to study it in depth.

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Part-Writing:music theory The for musicians Vertical and normal people by tobyRules w. rush to best understand how it’s wrong to think these were common practice period composers “rules” for the composers... wrote music, we are going to they were just writing what learn how to write music using sounded good to them. their musical style. nor should we treat these as rules so the patterns we see in their music, for writing music in general... the things they consistently did each style of writing has it’s or didn’t do, are going to become own set of patterns, and thus “rules” for us in our writing. it’s own “rulebook.” as a composer, you get to write your own rules for your own style!

we’re going to start with the vertical rules... that is, the rules that pertain to building a single soprano chord in four-voice harmony.

first, the distance between soprano and alto and between a lto alto and tenor must be an octave or less.

the tenor and bass can be as œ as you & far apart want! second, the voices must be kept in their proper order; for example, œ the tenor shouldn’t be higher than the alto. (Bach did this now and then, but it was only when he wanted to incorporate some special melodic shapes.)

tenor third, since we have four voices and only three notes in a triad, one of the notes should be doubled. for triads in root position, we typically double the bass root of the chord unless forced ? œ (by other rules) to do otherwise. lastly, each voice should stay in its range. these are conservative ranges œ œ for modern singers, but œ & tenor bass remember that bach’s œ chorales were really soprano a lto written for amateurs: œ œ the common people who œ attended church in leipzig! ? œ licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more œ Part-Writing:music theory The for musicians Horizontal and normal people by toby w. Rules rush

the supreme goal of part-writing is good voice leading... making each individual voice part easy to sing by avoiding awkward intervals or large leaps!

before we get to the specific dos and don’ts, let’s take a look at some important characteristics of four-voice part-writing:

in some cases, the voice note how each voice moves can simply stay on the same as little as possible, going note. This is called to the nearest chord tone in each subsequent chord! keeping the common tone, and it’s always cool!

cantata bwv “ich armer

mensch, ich

55

s

undenknech..

t”

it’s common for the bass to move in the opposite direction the bass line, since it provides of the upper three voices. the foundation of the harmony this is called contrary motion in each chord, tends to include and it helps maintain larger leaps than the other voice independence. three voices, but that’s okay. voice independence?

there are also a few other four-voice harmony is a form of counterpoint, rules that apply to this style: which is the combination of more than one melody played simultaneously. in counterpoint, when you have the leading tone each voice is equally important; no voice is in an outer voice (soprano or given a role of accompaniment to another voice. bass) it must resolve to the in counterpoint, it is important for each voice to tonic in the next chord. be independent; that is, no two voices should be doing the exact same thing. if two (or more) you may not move any voice voices were moving in parallel, the richness by an interval* of an of the texture would be reduced. augmented second as a result, common practice composers were or an augmented fourth. very consistent in avoiding two or more voices that moved in parallel perfect octaves, parallel perfect fifths, or parallel perfect unisons! the *good news: you can avoid all three of these by doing the following whenever possible:

1. keep the common tone! 2. move to the parallel parallel parallel octaves! fifths! unisons! nearest chord tone! 3. use contrary motion!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Part-Writing:music theory Using for musicians andInversions normal people by toby w. rush when common practice composers used inverted chords in four-voice writing, they followed some general patterns regarding which note of the chord should be doubled.

root position first inversion second inversion

the doubling of first inversion triads depends on the type of the chord being written. in root in second position triads, in major first in minor first in diminished inversion triads, composers usually inversion triads, inversion triads, first inversion composers usually doubled the root, composers composers triads, they doubled the fifth, which is in the doubled the doubled the doubled the which is in the bass soprano bass bass bass or of the chord. of the chord. of the chord. of the chord. soprano of the chord.

here’s another way to think of it: the only time you can’t double the bass is in first inversion major triads, where you should double the soprano instead.

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

the only “rule” regarding other than that, you can use root position triads 6 root position and first inversion and first inversion triads essentially whenever you want! is that diminished triads are vii° 6 it’s second inversion triads that always placed in first inversion. ii° have the big restrictions. 6 6 the cadential 4 chord the passing 4 chord is a tonic triad in is a chord placed in second inversion second inversion followed by a where the bass is root-position treated like a dominant chord passing tone. at a cadence.

6 6 6 F: I4 V I F: I V4 I

6 the pedal 4 chord if you write a is a second inversion second inversion triad and chord where the it’s not one of these three situations, bass is treated like then you are not writing in the common a pedal tone. practice period style! the composers of the style just didn’t use these chords willy-nilly.

6 F: I IV4 I

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in the common Part-Writing: Melodic Minor practice period, composers used so anyway, harmonic minor after we got by default. but him transposed attention! attention! when augmented back to tonic, he we need assistance seconds occurred, began to modulate with a new patient they turned to a again, and... in emergency treatment hero for help: X B room 3b... stat! melodic minor!

what seems to be well, I thought I’d transpose to the sir? problem, minor, you know, to surprise the family... so I did, and then I raised all my leading tones, because I’m a common practice period progression, right? X B okay, sure. so what’s wrong? i’ve got augmented B seconds!

X B *gasp* paging... dr. melodic minor! doctor, what can we do? for this case of ascending augmented seconds, I prescribe a raised sixth scale degree! X B ooh... a major iv chord! IV6

and for these descending augmented seconds, we’re going to use B an unraised seventh! and that makes a X minor v chord! v

all in a day’s work, my good man. my now let’s turn to augmented the unpleasant matter Bseconds... of the bill. they’re X cured! cure your augmented seconds with melodic minor today!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more The Harmonicmusic theory Cadences for musicians and normal people by toby w. rush A cadence is generally considered to be the last two chords of a phrase, section or piece. there are four types of cadences, each with their own specific requirements and variations.

an authentic cadence consists of a dominant function chord (v or vii) moving to tonic. to be considered a perfect authentic cadence, a cadence must meet all of the following criteria: it must use a v chord if the cadence (not a vii) doesn’t meet *both chords must be all of those in root position criteria, it’s considered to *the soprano must perfect be an imperfect end on the tonic authentic imperfect imperfect authentic authentic *the soprano must authentic move by step cadence! 6 6 * G: V I G: vii° I G: V4 I a plagal cadence consists of a subdominant function chord (iv or ii) moving to tonic. to be considered a perfect plagal cadence, a cadence must meet all of the following criteria: it must use a iv chord if the cadence (not a ii) doesn’t meet *both chords must be all of those in root position criteria, it’s considered to *the soprano must perfect be an end on the tonic plagal imperfectplagal imperfectplagal imperfect *the soprano must authentic keep the common tone cadence! * G: IV I G: IV6 I G: ii I6

a half cadence is any cadence that ends on the dominant chord (v).

a specific type of half cadence is the phrygian cadence, which must meet the following criteria: it occurs only in minor half it uses a iv chord moving to v * phrygian phrygian *the soprano and bass move by step in contrary motion G: I V *the soprano and bass both e: iv6 V e: iv V *end on the fifth scale degree a deceptive cadence is a cadence where the dominant chord (V) resolves to something other than tonic... almost always the submediant chord (vi).

really, it’s the psych-out cadence, in that you expect it to resolve to tonic, but it doesn’t.

deceptive and, in fact, it’s more common to see this in the middle of the phrase rather than the end... where you might call it a “cadence-like structure”! G: V vi

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush how did composers of the common Harmonic Progression practice period decide which order to put chords in? did they just throw them down on paper haphazardly?

as a matter of fact, there are certain chord progressions that appear more frequently, and there are others that are avoided pretty consistently. while the choices were always based on what sounded good to the composer, as theorists there is a pattern in their choices that we can use to easily remember which chord progressions work and which ones don’t. to understand this pattern, we need to think in terms of root movements. a root movement is the basic interval between the root of one chord and the root of the next chord. you don’t have to worry about the interval’s inflection, just its distance and direction. for example, to determine the root movement ˙ it’s down a seventh, but here, we look at the root (not bass) of each ˙ ˙ since octaves don’t matter, chord and figure the between them. & ˙ we invert it to up a second. interval ˙

so here’s the pattern: common practice period composers generally used root movements of up a second, down a third, and down a fifth! that’s not say that they never used other root movements, but it didn’t 2 happen very often.

sequences of chords that remember... since don’t follow this pattern inflection doesn’t are called retrogressions, matter, we can and they are considered ignore accidentals 3 unstylistic. when we figure the root movements.

so, for example, a g chord to an 5 e chord is down a third, but so is g to e flat, and g sharp to e flat!

there are also four simple exceptions to this pattern: I I V vii° I any chord can tonic can move any chord can and the leading-tone move to tonic, to any chord, move to dominant, triad must move to tonic.

let’s try it... say you have œ œ a supertonic œ œ œ & œ chord and œ œ œ you are trying œ to decide what chord... chord to use œ œ

œ can move you can move you can move you ? to follow it. œ œ

œ a leading-tone up a second to down a fifth to œ down a third to œ œ a mediant chord... first exception and or you can use the or you

6 a dominant chord... C: ii iii vii° V chord! a tonic go to I

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Diatonic Commonmusic theory for musicians Chord and normal peopleModulation by toby w. rush modulation is the process of changing to a different key within a piece of music.

there are several different ways to modulate; perhaps the common practice period composers, simplest is the unprepared however, preferred a particular type modulation, where the music of modulation that required a little pauses and suddenly changes more planning: the diatonic common key, often up a half-step. chord modulation. as the name suggests, this uses a chord which is diatonic in both the outgoing key hey... what is this and the new key. portrait doing here? m anilow

let’s say we’re starting off in c major... here is a list of all the keys which have chords in common with c major (the specific chords are highlighted):

G: I ii iii IV V vi vii° a: i ii° III iv V VI vii°

F: I ii iii IV V vi vii° e: i ii° III iv V VI vii°

notice how these keys are all close to one keys which have another on the chords in common circle of fifths. like this are called related keys.

D: I ii iii IV V vi vii° d: i ii° III iv V VI vii°

b: i ii° III iv V VI vii° B b: I ii iii IV V vi vii°

to use this type of note that the pivot modulation, a composer chord is always the would pivot the harmony last chord that can around the chord that be analyzed in the fit into both keys. old key... the first As theorists, we show accidentals will always this pivot chord by occur in the chord analyzing the chord in C: I ii V I vi immediately following both keys. e: iv V VI iv V i the pivot chord!

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a non-harmonic tone is a note that Non-Harmonic Tones doesn’t fit into a chord. we classify non-harmonic tones by how they are approached and resolved!

name abbreviationapproach resolution notes example

passing resolves by continuing in pt step step the same direction as the tone approach.

neighboring resolves by returning to Nt step step the note preceding the tone non-harmonic tone.

resolves in opposite appoggiatura app leap step direction from approach.

resolves in opposite Escape tone et step leap direction from approach.

changing two non-harmonic tones ct any step on either side of the tones note of resolution.

common a chord tone played anticipation ant any before the rest of tone the chord arrives.

common a note held over from suspension sus step a previous chord and tone resolved down.

common a note held over from retardation ret step a previous chord and tone resolved up.

common common a chord tone which pedal tone ped temporarily becomes tone tone a non-harmonic tone.

suspensions are typically further identified by number. The first number represents the interval between the note of suspension and the bass. The second number represents the interval between the note of resolution and the bass.

the exception to this rule is the 2-3 or bass suspension, where the numbers 7-6 2-3 represent the intervals between the bass sus (bass) (where the suspension occurs) and sus whichever voice has the note which is a second (not counting octaves) above the bass. 4-3 9-8 sus sus

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush Hey, it’s Sparkythe music theory dog! kids! Dear Sparky: Q: Can you elaborate on why suspensions are identified by numbers? Also, what should one watch out for when writing suspensions in four-part harmony? --S.S., Detroit, MI A: WOOF!*

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

this a is the in almost every case, note of suspension... the suspension is it doesn’t belong in then labeled using this g major triad. two intervals: the interval between the note of suspension this is it resolves to and the bass, and the a 7th! this g, which does interval between the this is fit in the chord. a 6th! note of resolution 6 it’s the note of and the bass. C: IV V resolution! ...so it’s a 6 C: IV V 7-6 suspension!

when writing an example which the only exception to this includes a suspension, it is very this is is the 2-3 suspension, where often useful to begin by writing this is a 3rd! the suspension occurs in the the chord that is going to contain a 2nd! bass. for this one, we look the suspension, then adding the at the interval between the suspension, and finishing by writing notes of suspension and the chord of approach. resolution and the nearest chord tone, whichever voice C: vi V it may be in. ...so it’s a 2-3 suspension!

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

for the 7-6 suspension, the suspension resolves for the 4-3 suspension for the 9-8 suspension,6 to an sixth above the and 2-3 suspension, you the suspension resolves bass. that means you 6 4 6 need a chord with a to an octave above the can’t use a chord in 6 third above the bass... bass... that’s I since root position,6 because4 easy, which means you can any chord can include they have a fifthI and a I use anything except a an octave. third above the bass. I I I second inversion triad. you need a first or I second inversion triad! DOING STUFF THE SPARKY WAY IS ALWAYS FUN! licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush

I’ll tell you what’s Motivic Development going on: I’m grumpy! I bet archduke rudolph we’re going to take a little break 20 gulden that I from the usual stuff and... hey, could write it’s ludwig van beethoven! 500 measures of music this week and so far I’ve only what’s going , maestro? on come up with

bee four stinkin’ notes! thoven

hey, it’s cool, mr. b... original motive we can use these notes ‰ as a motive, and create & œ œ œ b˙ a ton more music based on them. watch!

the simplest form of motivic development: repeating a phrase repetition immediately gives you twice as b œ œ œ ˙ œ œ œ œ ˙ œ much music! & b b ‰ motive J repetition J

repeating a motive at a higher or lower level pitch. as with œ œ œ sequence œ all of these, the intervals b nœ œ œ #œ œ œ œ don’t have to match exactly. b ‰ J œ & b motive sequenceJ sequenceJ flipping the motive upside-down: inversion if the original motive leaps b œ œ downward, an inversion will & b b Œ‰œ œ œ Œ leap upward. inversion of original motive

interval contraction making the intervals within the motive smaller (contraction) or œ œ interval expansion b œœœ œ ˙ larger (expansion). b ‰ ˙œ & b motive int. expansion

diminution changing the speed of the motive augmentation so it is played faster (diminution) b œ œ œ or slower (augmentation). b b Œ ˙. &augmentation of original motive

rhythmic any change of the motive’s rhythm . . . (other than just changing the . œ. œ . œ œœœ. œ œ œœ metamorphosis tempo, as described above) b œ œ nœ œ & b metamorphosisb ‰ of original motive‰

an “echo” effect between different voices b j œ œ œ & b b Ó ‰ œ œ œ œ œ Œ imitation (between instruments in an ensemble, for imitation example, or between registers on the piano) bbb ‰ Œ & motiveœ œ œ ˙ ˙.

so, heh heh.... aw, dang! let’s go that gets us to 253 measures... double or nothing! you sly fox... wait... we are in 506 measures! 4/4 time, right? woooot! uh, yeah... read it and weep, rudy! so let’s use 2/4 time instead! bee thoven

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when we talk about the form of a piece, Binary Form we are referring to the large-scale layout of the piece... specifically, the arrangement of sections of music, how and when they are repeated, and what keys are being used.

010101110110111101110111001000010010000001011001011011110111010100100000011

One of the simplest forms is binary form, which consists of two contrasting sections. we refer to these two sections as a and b.

the sections might be contrasting in mood, tempo, key, or even in a A B combination of these characteristics. binary form

000010111001001100101001000000111001001100101011000010110110001101100011110

binary form is used in baroque dance suites in a very specific way. In these pieces, both sections are repeated. the A section begins in the primary key and modulates to the key of the dominant, and the B section begins in that key and modulates back to the A B original key. performers of the time I V V I would typically improvise ornamentation when repeating each section. baroque dance form

010010000001101001011011100110001101110010011001010110010001101001011000100

baroque dance suites were written for varying instrumentation; many were written for keyboard (usually harpsichord or clavichord), others were written for chamber groups, and some were even written for full orchestra. each movement of these suites would be written in the style of a particular baroque dance: allemande, gavotte, bouree, courante, sarabande, louree, gigue, and others, each of which had a specific character.

because baroque dance form is so common in baroque instrumental music, when theorists and musicologists are talking about baroque music and say “binary form,” they are actually referring to baroque dance form.

11011000111100100100000011001110110010101100101011010110111100100101110

another somewhat rare variation of binary form is rounded binary form, where the A section returns after the end of the b section. this reprise of the a section, however, is shortened, so we refer to it as “a prime.” A B A rounded binary form

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Ternary Form ternary form is a three-part form. rather than using three completely different sections, most pieces in ternary form consist of two sections, the first of which is reprised.

in ternary form, the a section appears both at the beginning and at the end; like binary form, the b section is contrasting in character.

the reprised a section may be an exact repeat of the first A, or it may be slightly different, but the of A B A length the a sections should be similar. ternary form

this is different from rounded binary, where the reprised a section (which we called a prime) is significantly shorter than the first a section.

Fine Da capo the minuet and trio is a variation on al Fine ternary form used for instrumental music. instead of writing out the reprised a section, the score will place the minuet instruction “da capo al fine” after the trio b section, which means to return to the A B beginning, play through the a section, minuet & trio form and end the piece.

this same form is commonly used in baroque and classical opera, where it is called a da capo aria. In both minuet & trio and da capo aria, any repeats are ignored when playing through the reprised a section.

it’s worth mentioning that there is a common form that is descended from minuet and trio form: the military march form favored by john philip trio sousa and other american fanfare march composers. 1stA & 2nd B (dogfight) strains I IV

military march form

in the military march form, the a section is split into two subsections, called the first strain and second strain. the trio adds a flat (or removes a sharp) from the key signature, modulating to the key of the subdominant. most marches begin with a short fanfare, and repeat the sousa trio, placing a short, intensely dramatic passage between repetitions called the dogfight or breakstrain.

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sonata allegro form is a specific form Sonata Allegro Form first used by early classical composers in opening movements of multi-movement the form itself is based from works for solo, chamber or large groups. ternary form, in that the first large section is reprised it was eventually adopted by other composers at the end of the form, of the classical and early romantic eras.

exposition development recapitulation

Afirst second B firstAsecond theme theme theme theme development major of main themes keys: I V I I minor keys: i III i i

sonata allegro form

one of the most important features of sonata allegro form is the two primary themes that make up the exposition. THese two themes will be constrasting in character and, at least in the exposition, will be in different keys. in a major work, the second theme will be in the key of the dominant; in a minor piece, the second theme will be in the relative major. in the recapitulation, however, both themes are played in the tonic!

the diagram above shows the required elements of sonata form; in the diagram below, several other elements, which are optionally included, are also shown.

exposition development recapitulation

Afirst second B firstAsecond coda theme theme theme theme development

introduction major of main themes keys: I V addition of I I minor others keys:

i III codetta i i transition

sonata allegro form (with optional elements)

bear in mind that composers did what they wanted to... some of the greatest pieces written in sonata allegro form feature places where the composer artfully broke these “rules”! licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush

Remember, diatonic Diatonic Seventh Chords means “from the key.” so a diatonic chord is one What are they? that only uses notes in diatonic seventh chords are the the key signature. seventh chords you can create using No accidentals! only the notes in a particular key. Here they are there are eight possible types of in major and w seventh chords in tertial harmony, minor. w w w w w but the composers of the common & w w w w w w w practice period only used five: w7 w7 w 7 w 7 7 7 7 remember: C: wI wii iii IV V vi vii° we only major 7th raise the the above root leading-tone major w w major triad seventh w over w w w dominant- w w w w w w function & w w w w #w w #w w7 w 7 w 7 w7 7 7 7 minor 7th harmony! a: wi wii° III iv V VI vii° the bw above root w major triad in harmonic progressions, diatonic sevenths can major-minorseventh w be used anywhere you can use a diatonic triad with the same root. minor 7th the above root ˙ ˙ minor bw ˙ ˙ ˙ ˙ ˙ seventh b w minor triad ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ w & ˙ ˙ ˙ ˙ ˙ ˙ V I IV vii° iii7 pending pat. vi7 ii7 V7 I7 the minor 7th the add-a-seventh-inator b bw above root half-diminishedseventh b w diminished triad 2 in fact, these chords can

be approached and resolved the diminished 7th 3 using any of the same three above root root movements b ∫w seventh b w diminished triad 5 as triads use. fully diminished w

we use “07” for With the diatonic seventh chords, we add a half-diminished sevenths and “07” for fourth root movement: 1 the common root. fully diminished sevenths. However, this root movement can only be used to increase tension, so going from a seventh chord to a triad is avoided. seventh chords have four notes, so doubling in four-part 7 7 harmony is not an issue... but if you need to use irregular V V V V doubling, double the root and omit the fifth.

when using these chords in four-part writing — in The seventh of the chord fact, when you use any seventh chord in four-part is always resolved down writing, you must always, always remember to... by step. always!

the seventh of the chord no, i’m serious. don’t ever is most often approached respect the seventh! resolve the seventh of a by the common tone. seventh chord any other way. however, it is okay to approach the seventh doing so will cause you from below by a step certain death! or a leap, or from above by a step.

You must never approach the seventh by a leap from above! www w licensed under a creative commons wBY-NC-ND license - visit tobyrush.com for more The Dominantmusic theory Seventh for musicians and normal people by toby w. rush The dominant seventh is the diatonic seventh chord built on the fifth scale degree. we already discussed diatonic seventh chords... why give this one all this special attention? for one thing, the but the primary reason dominant seventh is, for spending a little extra 77 by far, the most common time with it is the fact that seventh chord used by there are a few things the composers of the that apply to it that don’t common practice period. apply to the other diatonic seventh chords.

first, a note on terminology: it’s just a major-minor seventh... the reason these are often VVconfused is that in popular the terms “major-minor seventh” bw and jazz theory, the term and “dominant seventh” are not w “dominant” is used to label interchangeable! “Major-minor & w the chord type as well as until it’s placed in a particular key! seventh” is the chord’s type, and the chord’s role. “dominant seventh” is the role the chord plays in the context b w of a particular key. & b w the other important thing to know about the dominant seventh chord is that common practice period composers would sometimes use some non-standard ways of resolving the seventh!

theornamental resolution thetransferred resolution in this resolution, the seventh is still this is the “hot potato” resolution: instead of resolved down by step, but it takes an being resolved down by step in the same voice, ornamental before getting there. “detour” the seventh is passed to another voice in another dominant seventh chord. the ornament # can be any œ œ œ œ œ ˙ the seventh still # & seventh˙ ˙ shape or œ œ œ resolution needs to resolve & œ œ transferredœ ornament length, but it by to tenor must resolve down by step ˙ ˙ to the note whatever voice is œ the last to have it. œ œ ? # ˙ ˙ down a step ? # œ œ œ from the 7 7 6 V I seventh of the V V5 I seventh chord. If the bass voice gets it, he resolves it immediately, ending the fun for everyone.

thedelayed resolution thebass resolution Here, the resolution of the seventh is in this resolution, the seventh of the chord delayed by moving to some other chord is still resolved down by step, but the note (usually the subdominant) and having the it resolves to appears in the bass voice. seventh of the chord hold out until the dominant seventh returns. the voice that # had the seventh after the V7 œ œ œ resolves up, # the & seventh œ œ œ œ œ returns, resolution usually by step. & seventh œ resolutionœ voice that has the seventh œ œ œ œ œ œ should still ? # ? # œ œ œ resolve it œ œ œ appropriately! V7 I6 V7 IV V7 I

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so far, we’ve talked about two Extended Harmonies types of tertial chords: triads and seventh chords. remember, tertial chords are chords constructed by stacking major and minor thirds!

now, there are four types of triads bbw bw w #w and eight types of seventh chords, diminishedw triad minorw triad majorw triad augmentedw triad even though common practice period composers only used five of them.

∫w bw bw w b # bb w bb w b w bw w w #w # w diminished diminishedw diminishedw minor minorw minor minorw major majorw minor majorw major augmentedw major augmentedw augmented seventh chord seventh chord seventh chord seventh chord seventh chord seventh chord seventh chord seventh chord

so that makes for twelve chord types so far... but what if we keep going? what other chord types can we make by stacking major and minor thirds? tertial chords with five, six and seven notes are called ninth chords, eleventh chords and thirteenth chords respectively.

suddenly the possibilities increase from twelve...... to 124! ∫w bw bw w bw w w #w bw w w #w w #w #w ‹ w b∫thew bb w b bw commonb w bw w w b w bw w w #w # w ## w ## diminished bdiminishedw diminishedb diminishedw gooddiminishedb minorw minor news:diminishedb minorw major minorb minorw minor minorb minorw major minorb majorw major minorbw major major minorw minor major minorw major major majorw major majorw major augmentedw augmentedw major augmented augmentedw augmented augmented diminishedw minorw ninth chordw ninth chordw ninthw chord ninthw chord ninthw chord augmentew d ninth chordw ninthw chord ninthw chord augmentedw majorw major augmentedw augmentedw doubly-augmented ninth chord ninthpractice chord period composers ninth chord ninth chord ninth chord # ninth chord ˙ ninth chord ninth chord only used these “extended ˙ harmonies” as diatonic & ˙ ∫∫w chords∫bw bbw on thebw dominant.bbw bw w #w bbw bw w #w w #w ˙ ##w #‹w bw ∫ bw ∫ bw b∫ w b bw bb w b bw bbw b w b w b#w ˙ b w w w ˙13 w w diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb w minor diminishedbw minor diminishedb w minor diminishedb w minor minor minorbw minor minorb minorw minor minorb minorw major ˙minor bminorw major minorb majorw major minorb majorw major minorb majorw minorb wmajor diminished diminished diminished minor diminishedw minor perfectw minor diminishedw minor perfectw major perfectw major augmentedw diminishedw perfectw perfectw augmentedw perfect G:augmented V augmented augmented augmented w w eleventh chord eleventhw chord eleventhw chord eleventhw chord doubly-augmentedw doubly-diminished eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord eleventh chord ˙ eleventh chord & ˙ # ˙ G: V11 bw bw w #wthese ware the#w #w ‹w w˙ #w ##w #‹w #w ‹w ‹w # w b wseriously:bw b w w w only# w # w #w˙ #w #w #w ###w ###w #‹#w #‹ major minorw minor major minorw minor major wminor major major minorw major major majorw major major majorw major majorw major major&w major augmentedw major augmentedw major augmentedw major augmentedw major augmented augmentedw augmented augmentedw augmented augmentedw augmented augmented diminishedw perfectw extendedperfectw augmentedharmoniesw perfect usedaugmented byaugmented augmented augmented majorw perfect˙ major waugmented augmented waugmented augmentedw augmented augmented augmented doubly-augmented doubly-augmented eleventh chord eleventh chord eleventh chord eleventh chord eleventhw chord eleventhw chord eleventhw chord doubly-augmentedw eleventh chord eleventh chord eleventh chordwhatdoubly-augmented about aeleventh fifteenth wchord doubly-augmentedw chord?doubly-augmentedw triply-augmented eleventh chord ˙9 eleventh chord eleventh chord eleventh chord eleventh chord common practice period composers. G: V try it: if you add another third 11 13 in fact, the v and v weren’t used on top of a thirteenth, you b∫w ∫muchw before∫w bthew romantic∫w bw era.bw w ∫w bw bw are wjust doublingbw thew root.w # w ∫∫ w ∫b w ∫b w bb w bb w b w bw bb w bb w b w so tertialbw harmonyw stopsw at#w 13! # ∫w b∫w b∫w b∫w b∫w b∫w b ∫w b∫ w b bw bbw b bw bb w bbw b bw bbw bb diminished diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb diminishedw diminishedb MINORw MINOR diminishedb MINORw MINOR diminishedb MINORw MINOR diminishedb MINORw MINOR diminishedb MINORw MAJOR diminishedb MINORw MAJOR diminishedb MINORw MAJOR diminishedb MINOR MAJOR diminished w diminishedw diminished diminishedw diminished diminishedw minor diminishedw minor diminishedw minor minor perfectw minor minor perfectw MAJOR DIMINISHED DIMINISHEDw DIMINISHEDw MINOR PERFECTw MINOR PERFECTw MAJOR PERFECT MINOR PERFECT MAJOR AUGMENTED MAJOR AUGMENTED AUGMENTED thirteenthw chord thirteenthw chord thirteenthw chord thirteenth chord doubly-diminished doubly-diminished diminished minor diminished thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord doubly-diminished diminished thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord

∫w bnow,w whenbw we wput thesebw chordsw intow #w bw w finally,w the#w ninth,w eleventh#w #orw ‹ w bb w b w bw w we’vew got #aw # w w w #w # w of the##w chord## w is what#‹ w #‹ bw bfour-partw bw harmony,b w bw bw b w bw w w thirteenthw w w w w MINOR MINORw MINOR MINORb MINORw MINOR MINORb MINORw MINOR MINORb MINORw MINOR MINORb MINORw MAJOR MINORb MINORw MAJOR MINOR bMINORw MAJOR MINORb MINORw MAJOR MINORb MAJORw MINOR MINORb MAJORw MAJOR MINORb MAJORw MAJOR MINOR MAJORbw MAJOR MINOR MAJORbw AUGMENTED MINOR MAJORbw AUGMENTED MINOR MAJORbw AUGMENTED MINOR MAJORb AUGMENTED DIMINISHED DIMINISHEDw DIMINISHEDproblem:w MINOR PERFECTw MINOR theyPERFECTw MAJORall havePERFECT MINOR morePERFECT MAJOR thanAUGMENTED MAJOR AUGMENTED AUGMENTED PERFECTw MINOR PERFECTw MAJOR AUGMENTEDdefinesw MAJOR AUGMENTED w AUGMENTEDit asAUGMENTED a MAJORninth,AUGMENTED AUGMENTEDeleventhDOUBLY-AUGMENTED DOUBLY-AUGMENTED thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord AUGMENTEDw DOUBLY-AUGMENTED thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord THIRTEENTH CHORD thirteenth chord thirteenth chord thirteenth chord thirteenth chord four notes. So we have to make or thirteenth chord. thirteenth ∫w bthew toughbw call:w whichbw onesw do w #w bw w w #w w #w #w ‹ w bb wew cutb wfrom bthew team?w w #w # w w w #w so how# w do #youw put# wthese‹ win ‹# bw bw bw b w bw bw b w bw w w w w # w # w # w MAJOR MINORw MINOR MAJOR MINORw MINOR MAJOR MINORw MINOR MAJOR MINORw MINOR MAJOR MINORw MAJOR MAJOR wMINOR MAJOR MAJOR MINORw MAJOR MAJOR MINORw MAJOR MAJOR MAJORw MAJOR MAJOR MAJORw MAJOR MAJOR MAJORw MAJOR MAJOR MAJORw MAJOR MAJOR MAJORw AUGMENTED MAJOR MAJOR wAUGMENTED MAJOR MAJOR wAUGMENTED MAJOR MAJOR AUGMENTED DIMINISHED DIMINISHEDw DIMINISHEDw MINOR PERFECTw MINOR PERFECTw MAJOR PERFECT MINOR PERFECT MAJOR AUGMENTED MAJOR AUGMENTED AUGMENTED PERFECTw MINOR PERFECTw MAJOR AUGMENTEDw MAJOR AUGMENTED wAUGMENTEDfour-partAUGMENTED MAJOR AUGMENTED harmony? AUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord thirteenthw chord AUGMENTEDw DOUBLY-AUGMENTED thirteenth chord THIRTEENTH CHORD thirteenth chord thirteenth chord thirteenth chord THIRTEENTH CHORD thirteenth chord thirteenth chord thirteenth chord thirteenth chord omit the fifth and use only third w wew needw to keep#w the wroot#w #w &‹w w #w #w the‹w ninth,#w eleventh‹w or‹w # w w #w # w #w # w ‹ w ‹ w œ##w ## w #‹ w thirteenth#‹ w ‹‹ w as ‹necessary.‹ w ‹#‹ w ‹#‹ w #becausew #w it defines#w the##w chord.# #w # #w # #w #œ#w ##w ##w ##w ##w ##w ##w # AUGMENTEDw MAJOR MAJOR AUGMENTEDw MAJOR MAJOR AUGMENTEDw MAJOR MAJOR AUGMENTED MAJORw MAJOR AUGMENTEDw MAJOR AUGMENTED MAJORw MAJOR AUGMENTEDw MAJOR AUGMENTEDw MAJOR AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTED PERFECTw MINOR PERFECTw MAJOR AUGMENTEDw MAJOR AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTED AUGMENTEDw AUGMENTEDw AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTED AUGMENTEDw AUGMENTEDw AUGMENTEDw DOUBLY-AUGMENTEDw DOUBLY-AUGMENTEDw DOUBLY-AUGMENTEDw DOUBLY-AUGMENTED thirteenth chord THIRTEENTHsimilarly, CHORD thirteenth chord thethirteenth chord isMAJOR whatAUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED MAJOR AUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED TRIPLY-AUGMENTED TRIPLY-AUGMENTED thirdthirteenth chord thirteenth chord AUGMENTED DOUBLY-AUGMENTED thirteenth chord THIRTEENTH CHORD AUGMENTED DOUBLY-AUGMENTED AUGMENTED DOUBLY-AUGMENTED DOUBLY-AUGMENTED TRIPLY-AUGMENTED makes the chord tertial. thirteenth chord thirteenthseventh chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord oh, and if you’re worried about inversions: stop. ? œ in the common practice the seventh acts as a bridge root to the extended harmony, period, extended harmonies preventing the chord from œ13 are almost always found coming across as two separate C: V in root position. harmonies played at the same time.

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Altered Chordsmusic theory for musicians and normal people by toby w. rush up to this point, all the chords we’ve been talking about have been built using only the notes in the current key.

essentially, this means no accidentals, with the exception of the raised sixth and seventh scale degrees diatonic in minor, which we consider to be now that we’ve covered all theory 27 part of the key. the possible diatonic chords in tertial harmony, it’s time to open the door to notes outside the key...

8 altered (chromatic)

15 diatonic triads 88 these add a diatonic sevenths “altered chords” extended harmonies certain richness to the harmony by using one or more notes # b 50next that are not in the key signature miles we’ll be covering and thus require accidentals. several categories of altered chords, each of which have their own unique rules for use. Secondary NEAPOLITAN Subdominants however, there are BORROWED d V a few things that CHORDS $ they all have in SECONDARY common! 26 DOMINANTS AUGMENTED SIXTHS

first, every altered chord has to have at least one accidental... second, altered chords can be easily used in place of their if it doesn’t have any accidentals, diatonic counterparts. in other words, you can add some pizazz then by definition it’s a to a composition by replacing a diatonic chord with an diatonic chord! altered chord that has the same root. & c œ œ œ œ œ œ œ œ œ ˙ b b œ œ œ b b ? c œ œ œ ˙ ˙ b˙ & n˙ & ˙ œ œ œ œ ˙ b ˙ V˙ ˙ii 6 7 VI /V I IV IV V b vi altered diatonic b ˙ ˙ avoid cross relations. & ˙ ˙ a cross relation occurs when a note appears with two different accidentals ˙ ˙ in two consecutive chords, in two ? ˙ n˙ different voices. b 2 with few exceptions, lastly, when you use these chords altered chords can use in part-writing, you should, 3 the same basic root & b ˙ ˙ 1 whenever possible, resolve the ˙ ˙ movements that we’ve altered notes in the direction been using. of their alteration. 5 b˙ ˙ like the diatonic sevenths, so if a note has a flat, try to ? however, the common root resolve it down by step or by leap. b ˙ ˙ should only 6 increase tension... ii°5 V don’t move from an altered chord and we generally avoid doubling altered tones, to it’s diatonic counterpart. since doing so would tend to cause parallel octaves.

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Borrowed Chords how does a composer decide which altered notes to use? in a major key, altered chords use notes outside one possibility is using notes and chords the scale as a means of adding a from the parallel minor. different “color” to the chord.

for example, the following chords are diatonic chords in c minor: w “borrowed”? b w w why call them b w w w w nw that when major & b w w w w w never brings w w7 w 7 them back? c: ii° ii° III iv VI vii°

but if we use them in a major key, they require and are hey, minor! accidentals I’ll have them therefore altered chords. we call these borrowed chords because they back by tuesday are from the this time, I borrowed parallel minor. promise! bw w w bw w & bw bw bbw bw b w Nw some theorists C: wii° ii°w7 III iv VI vii°7 refer to the use b b of these chords as mode mixture. two of these chords, and, in fact, these six chords the “flat three” and “flat six,” are the six most commonly used have altered tones as roots. we place a full-sized flat symbol borrowed chords in the common before the roman numeral itself practice period. (One of them, the to indicate this altered root. major triad on the lowered mediant, or “flat three,” was not used much by composers before wait... since we the romantic era.) why? double the root, ˙ ˙ moving both roots & b˙ ˙ all the usual part-writing rules apply to these the same direction 5 chords. for example: can often result in parallel octaves. ? b˙ 8 ˙ b˙ ˙ VI V the borrowed supertonic is a b 6 diminished triad, and is therefore ˙ ˙ it’s more important to ii° always used in first inversion. & b˙ ˙ avoid parallelism than to resolve the notes a certain way, so this ? b˙ ˙ use of contrary the borrowed seventh chords 7 b˙ motion is better. can be used in any inversion, but the ˙ ii° VI V seventh must be approached 7 b and resolved properly. vii° there’s another chord that is often erroneously called a borrowed chord: used in minor, taken from the parallel it’s usually best to resolve altered major. it’s the picardy third: a tonic notes in the direction of their III chord with a raised third used as the b alteration, but doing so in the two final chord altered root chords won’t work. of the piece. U VI œ #œ w bb œ œ œ œ b named for & ˙œœ#œ œ œ œ œ œ œ œ w the leading-tone fully diminished 24th-century seventh is the king of dominant explorer j j U 7 œ œ‰ œ ‰ œ œ œ n w function. don’t even think of jean-luc ? b œ œ œ œ œ œ picard!* b œ w resolving it to anything but tonic! vii° 7 6 g: i V i VI ii° V I *Nope. licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more The Neapolitanmusic theory forSix musicians and normal people by toby w. rush in addition to the altered root borrowed chords, there is another altered root chord that fits well since it’s not a borrowed with the borrowed chords, even though it is not chord, this chord can be used actually borrowed from the parallel minor. in both major and minor. that chord is a ***** major triad there are a couple of interesting built on the things about this chord. one is lowered second the fact that it is almost scale degree. exclusively used in first inversion.

seriously! although this chord is extremely common in the common practice period, there are very few examples of it used in root position. second inversion is bw even rarer. the second interesting thing about 6 the chord is its name: you might expect b w it to be called a in keeping &C: N “flat two,” w with the other altered root chords. The Neapolitan six chord, since it is but, in fact, this is the first of a few chords built on a form of the supertonic, that have special names. This particular one has some characteristics of a is called the neapolitan chord. subdominant function chord in that it often resolves toward a “neapolitan” means “from naples,” dominant function. in fact, it is very referring to the city of naples, common to see the neapolitan chord italy. the chord isn’t actually resolve to a dominant seventh in from naples, though; it was third inversion, or to a cadential just associated with the operas six-four chord. written by neapolitan composers like alessandro scarlatti. & b˙ ˙ ˙ b ˙ b˙ ˙ scar ˙ ˙ Naples latti

? ˙ b˙ ˙ funny thing is, this chord was used pretty ˙ commonly before scarlatti’s time, in ˙ ˙ ˙ ˙ compositions far from the courts of italy. 6 4 6 6 C: N V2 N I4 (even though the neapolitan chord it’s also worth noting that although nearly has a lot in common with other every theorist and theory textbook calls the subdominant function chords, it is chord a “neapolitan sixth chord,” it is more most often referred to as part of properly called a “neapolitan six chord.” that’s a larger group of chords called because in the rare situations where it is used predominants, and the label of in root position, it is simply called the neapolitan subdominant function is generally chord, and when it is found in second inversion, limited to the subdominant and it’s called the neapolitan six-four. supertonic chords and their variants.) since we don’t pronounce I6 as “one sixth,” we shouldn’t say “Neapolitan sixth” for N6!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Secondarymusic Dominants theory for musicians and normal people by toby w. rush there is a duality at the heart of common that duality, of course, is the relationship practice period harmonic progression. of dominant function and tonic. like the ancient conflict of jedi and dominant harmony typifies tension sith, it consists of forces that, in the common practice period, and at one level, work against each the tonic represents release. other... but at another, higher V its simplest form, the authentic level, work together, creating cadence, has been ubiquitous energy that drives all else. in western music for centuries.

the progression of dominant but that’s crazy talk, though, moving to tonic is so strong, it isn’t it? I mean, how could we would be nice to be able to use control that magic and make it it to provide motion to chords I obey our compositional whim? other than tonic.

the answer, of course, is with secondary dominants.

let’s say we wanted to what if we wanted to use approach this vi chord. we could use one of the usual that dominant-tonic magic? diatonic chords, the tonic, the ? subdominant, the mediant... but ? ˙ what if we’re looking for a bit ˙ & ˙ more tension and release? & ˙ vi vi

if we pretend for a moment that the chord we’re resolving to is a tonic chord, what would the corresponding dominant chord be? altered, yes, but we’re not afraid of those anymore:

˙ ˙ ˙ & #˙ ˙ & #˙ ˙ & #˙ ˙ a: V i V a C: V vi a vi

while we might have once called this a now, we’re not just limited to the v chord: short modulation, it is really more like there are five chords with a dominant function! borrowing another key’s dominant chord. if we think of the V chord in the key as the primary dominant, V chords of 7 7 7 related keys are secondary dominants. V V vii° vii° vii° dominant function chords that gives us 7 7 7 a huge list of V V vii° vii° vii° possibilities! x x x x x the secondary dominants these chords often resolve to the in major keys, the “x” above can be any chord “under the slash,” but they can diatonic chord other than tonic (obviously) actually be approached and resolved or the leading-tone triad. why? because using the basic root movements! a diminished triad has a hard time acting like a temporary tonic chord. 2 the basic root movements 3 rock! in minor keys, the composers generally 1 only used secondary dominants 5 of iv and of V. yes. yes they do.

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like that moment of incredible tension just before the hero finally kisses the leading lady, the half-step is the go-to interval for creating tension in music of the common ˙ practice period. it drives the entire style! ˙

if one half-step can create such strong tension, how about two half-steps sounding simultaneously? Let’s get creative here for a minute to find a cool new way to approach a diatonic chord. in this case, we’ll use them to approach the dominant triad.

...and approach that first, we’ll start with octave with a half step the doubled root of a below the top note, V chord... #˙ ˙ #˙ ˙ ˙ ˙ & b ˙ ˙ & b ˙ ˙ V & ˙ V ...and, finally, add the V ...and a half step above tonic as the third note. the bottom note...

the result is a new chord, one we call the augmented sixth chord, after the interval created by the top and bottom notes.

augmented sixth chords are predominant chords, meaning they are used to approach dominant chords. if we just use they are usually used to approach dominant triads, three notes not dominant sevenths, because of the doubled and double the roots present in dominant triads. tonic, we get the #w italian ww however, they also often augmented sixth. b w & approach tonic chords & #˙ ˙ It.6 in second inversion, ˙ ˙ which also contain a doubled fifth scale degree. ? b˙ n˙ b ˙ ˙ if we add the 6 Ger.6 I4 second scale degree instead ˙ ˙ rarely, augmented sixth chords of doubling the # w & ˙ ˙ are found transposed down tonic, we get the ww a perfect fifth, analyzed as french b w ˙ ˙ “on flat two,” and used to augmented sixth. & ? b˙ ˙ approach a tonic chord in Fr.6 root position. Fr.6 I on 2 b and if we and, finally, when resolving replace the the german augmented sixth second scale chord to a dominant triad, & #˙ ˙ degree with the you might find yourself ˙ ˙ lowered third # w writing parallel fifths... scale degree, b w w but it’s perfectly okay! we get the b w mozart did it all the time! ? 5 german & b˙ ˙ augmented sixth. Ger.6 b ˙ ˙ Ger.6 V

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Altered andmusic Enharmonictheory for musicians and normal people Modulation by toby w. rush œ œ w b œ œ œ nœ w Altered common chord modulation & œ œ is easy: remember diatonic common F: I IV V chord modulation, where we used a C: I V I chord that was diatonic in both the old and new keys?

altered common chord modulation is the same thing, only using the œ œ pivot chord as an altered chord & b œ œ œ #nw in either the old key, the new key, œ # #œ w or both. F: I IV V n œ E: bVI V I Now, in both diatonic modulation and altered modulation, we have one chord that plays two different roles, one for each key. But the chord type doesn’t change... if it was a major chord in the old key, it’s still a major chord in the new key. ...but...but whatwhat ifif thethe chordchord typetype did change?

this technique is in enharmonic modulation, we respell a chord so — well, odd — that so the enharmonically chord type itself there are only is different in the old and new keys. two specific ways to do it. ever notice that the german augmented sixth chord is just like fully diminished seventh chords are a major-minor seventh chord cool for a lot of reasons, and one of with the seventh respelled them is that they are equidistant chords: enharmonically? inverting a fully diminshed seventh yields another root-position fully dimished seventh chord. # w bw beethoven b ww b w did! & b w bw bw bww b ∫w 7 b w C: Ger.6 D : V b w b w w b & w7 invert & 6 & 7 a° a°5 respell c° we can take advantage of this and use it meaning that a fully diminished as a pivot chord... where it acts like a leading tone seventh chord german augmented sixth in one key can be a pivot chord into but like a 7 (or a 7 secondary dominant) V V /x three other possible keys: in the other key!

which can be # œ bœ respelled as # œ & œ œ œ #œ b œ 7 œ 7 œ b b G: I vii° vii° & b b œ œ nœ œ 6 œ œ n œ œ E: vii°5 I which can be # œ bœ respelled as œ œ & œ œ b∫œœ n bœ ? b œ nœ 7 7 b œ b b œ nœ œ G: I vii° vii° b 6 œ7 4 b n œ D : vii°3 I D b : IV V b C: Ger.6 V I which can be note that the pivot chord above is # nœ œ bœ respelled as œ b œ approached like a dominant seventh, & œ œ bœœ but resolved like an G: I vii°7 vii°7 augmented sixth chord! 4 B b : vii°2 I

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after learning about secondary dominants, you might wonder if it’s possible to extend the concept to other chords.

for example, if we can use a dominant function chord from a related key, what about a subdominant function chord from a related key, like IV of V?

well, the answer is yes, and the chords that result are called secondary subdominants. but before we talk about them, you need to understand a few things.

first of all, the very existence of these chords is debatable. what one theorist might call second, the only place a secondary subdominant: we find chords that we can call secondary subdominants is in the œ music of thex œ œ romantic era.x & bœ #œœ œ nœ œ 7 4 œ 6 C: C: ii° V2 V I V V

another might call a short modulation. iv Lastly, since these chords are already pushing the limits of tonality, composers œ IV would only use secondary subdominants & œ #œ œ œ iv from closely related keys. In bœ œœ œ nœ other words, secondary subdominants œ 7 4 œ6 G: ii° V2 I should only be “of IV” and “of V.” C: V6 I V

keeping these things in mind, let’s look at the possibilities: what are all the subdominant function chords we’ve encountered? first, there are next, the diatonic and, lastly, a few the diatonic triads: seventh chords: borrowed chords: ii IV ii7 IV7 ii° ii°7 iv

so a secondary subdominant can 7 have any subdominant function 7 chord above the slash, and ii° a IV or V below the slash. ii° however, the most commonly found secondary subdominants are those that use the half- IV diminished supertonic seventh. V to approach these chords, the most common way to use any of the basic root resolve 7 7 secondary subdominants is to movements. ii° V the corresponding secondary which are awesome. dominant. V V

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early 20th renaissance baroque classical romantic century contemporary however, the music of the romantic the music of the baroque, classical era employed some interesting and romantic eras share a consistent use techniques that set it apart from of harmony and counterpoint, enough to cause the baroque and classical eras... theorists and historians to group them together as the “Common Practice Period.” ...and foreshadow some of the big changes coming in 11 ii° the twentieth century! V we’ve already mentioned a few chords IV that were specific to the romantic era: 13 dominant eleventh and ii° V thirteenth chords, V the “flat three” borrowed chord, III and secondary subdominants. iv b IV & #˙ n˙ another technique that is unique to the romantic era is the resolution of an augmented sixth chord to a ? dominant seventh chord rather than a dominant triad, b˙ ˙ causing the interval of the augmented sixth to resolve b ˙ ˙ obliquely instead of moving outward to the octave. Ger.6 V7 finally, romantic era composers would sometimes use a particular type of chord progression that had the effect of suspending tonality for a portion of the piece. By temporarily removing the feeling of being in a certain key, the composer could easily modulate to a distant key! if you think of ...third relations tonality like are like turning off the gravity this technique is called being in a room... in the room third relations because it for a bit... involves moving by root movements of a major or minor third without respect to key signature.

for example... here, we’re in F major...... here, we’re just moving down by Major thirds... œ œ b œ œ œ œ ˙ & œ œ #˙ n˙ F: I IV V I DM b B˙ M b ...which obscures any *whump* sense of key we had...... and then turning the gravity back on ... but in a b # #˙ b˙ œ #œ different & # ˙ ˙ œ #œ œ œ direction! b ˙ #n#œ œ œ F M E M B: I IV V I # b and then we land in b major!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more music theory for musicians and normal people by toby w. rush modern? wait, isn’t this stuff, like, The Modern Modes 100 years old? yes, but we only call them “modern” because we need to differentiate between a bunch of unrelated things across music history that, ever so inconveniently, use the same names!

the modern which were, in and those modes’ names turn, named in used the same came from the honor of the names as scale various “keys” lute ranges used tunings discussed used in medieval in later ancient by plato in church music greek music 380 bc!

v. wil hilde aris pl liams gard toxenus ato

and, to make matters worse, each of these things use the names to represent different concepts! fortunately, right now, we’re only worried about the modern modes. these modes are used a lot... one of the primary characteristics of especially in folk music. as for these english modalists is that they standard western repertoire, tended to avoid the strong tensions they are first prominently featured of the common practice period...

in the post-romantic music britain! for example, they avoided chords of the early twentieth century that used a tritone... and avoided british isles. raising the leading tone in minor keys! so what are they? well, remember when we created the natural minor scale by starting with a major scale, but using the sixth note of the scale as the tonic? it gave us a new pattern of whole steps and half steps... a new scale. keeping the same key signature, we use this note as our new tonic!

major œ minorœ œ œ œ œ œ œ & œ œ œ œ œ & œ œ œ in fact, these are two of the seven modern modes: major is the ionian mode, and natural minor is the aeolian mode. by starting on the other notes of the major scale, we get the other five modes. because it has B to B the locrian mode a diminished tonic, locrian is a theoretical G to G: the mixolydian mode mode... it’s not used in actual practice. F to F: the lydian mode œ œ œ œ œ œ œ & œ œ œ the modes here all share œ œ E to E: the phrygian mode the same key signature... œ œ they are related, like D to D: the dorian mode c major and a minor! c ionian a more effective œ œ œ œ œ method of keeping œ œ œ œ & œ œ œ œ the modes straight & œ a aeolian œ œ involves memorizing minor + raised 6th c mixolydian each mode’s œ œ œ color tone: œ œ œ #œ œ bœ the scale degree œ œ a dorian & œ majorœ œ + lowered 7th & œ œ that makes it minor + lowered 2nd c lydian unique from the major or minor œ œ œ œ œ œ scale with the bœ œ œ a phrygian & #œ majorœ œ+ raised 4th & œ œ œ œ same tonic. licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Introductionmusic theoryto for Species musicians and normal peopleCounterpoint by toby w. rush in 1725, an austrian composer and theorist named johann joseph fux it’s wrote a theory textbook called gradus ad parnassum, in which he pronounced outlined his method of teaching how to write good counterpoint. “fooks”!

Gradus ad parnassum means counterpoint is the combination “Steps to parnassus.” Parnassus of two or more melodies, each referred to the highest peak in one as important and interesting greece, and was used as a as the other. metaphor for perfection.

Gradus ad parnassum was a big hit, used (or at least praised) by composers like Mozart, beethoven, and haydn. the system that fux used is referred to as species counterpoint, because it involves going through increasing levels of rhythmic complexity f which are labeled* as species I, Species II, *and so forth. ux

1660-1741 1750 1550 1650 1450 1950 1850 1700 1500 1600 1900 1800 1525-1594

interestingly enough, the language fux was advocating was not the counterpoint of the common practice period to which he belonged, but the more strict rules of counterpoint used by composers of the renaissance more than a century earlier.

specifically, fux was a starry-eyed admirer of the italian renaissance composer giovanni pierluigi da palestrina, who he considered to represent the peak of compositional artistry... something he felt was being lost or even squandered by his baroque and classical contemporaries. pal estrina

right. so the language fux is teaching is really of course, an interesting ideal: based partly on his it’s worth pointing out that perceptions of palestrina’s musical language fux didn’t actually have access as delivered to him through italian theorists, and to much of my music! partly on his own ideas of what he thought the language should be.

but let’s cut fux some slack here: as theorists, we’re all guilty of this to some degree.

anyway, let’s get started! going through fux’s steps for learning counterpoint gives us a glimpse of how the masters learned their craft and a feel for the environment in which they developed their own musical languages.

hurray! Let’s go, giovanni, and bring the beautiful light of perfect composition to these eager students!

yeah, Joe, about that... you do realize that your idea of perfect composition is just a blissfully awesome thing? f pale ux yes, that’s just what I was thinking! strina

no, I mean that it’s super fun? yayyyy!!!!!

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and really, to be Species Counterpoint: Melody fair, these are good guidelines before we start combining melodies, we need for any melody... to understand what constitutes a good melody it’s just that fux in the system of species counterpoint. is a little more strict about it. in general, melodies should be primarily stepwise, with a single, definite high point or low point. effective melodies tend to progress slowly toward the high or low point and then move back toward the starting pitch. high point w ww & w w w w w w w w w oh, and don’t like this. yeah, yeah, Palestrina, we know repeat notes BUT contrapuntal melodies need to be you repeated notes all the But fux was pursuing an interesting, not boring. time. ideal. Maybe he felt you could do... better? as you can see above, occasional are okay... leaps why, I SHHHH. let’s just move on. but they come with a bunch of restrictions.

pal first, leaps should be no larger than a perfect fifth,estrina with two exceptions: leaping by a perfect octave, and leaping upward by a minor sixth. don’t do these very often, though!

second, for heaven’s sake, avoid the tritone! this interval (an augmented fourth or diminished fifth) was actually considered evil to musicians of w w the time and was called the diabolus in musica... the “devil in music!”

leaping by a tritone is bad, but it’s also important to avoid the tritone in other ways... for example, this pattern, where w w w a tritone is outlined in the melodic line, & w w w would be considered inappropriate. tritone

third, leaps of a perfect fourth need to be preceded or followed by stepwise motion in the opposite direction, to counterbalance the leap. and if a leap is larger than a perfect fourth, it needs to be counterbalanced both before and after!

m2 P4 m2 P5 M2 & w w w & w w w w This perfect fourth is counterbalancedw This perfect fifth is counterbalanced by the step that occurs before the leap. by steps on both sides of the leap.

P4 P5 w w & w w & w w This perfect fourth is surrounded by steps, This perfectw fifthw has steps on both sides, but they aren’t in the opposite direction. but the first one isn’t in the opposite direction.

lastly, don’t write three or more leaps in a row. You can write two leaps in a row, but they need to outline a major or minor triad. no diminished triads... they have tritones in them! evil!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Species Counterpoint:music theory for musicians and normal Species people by toby w. rush I “first species” counterpoint is the most rhythmically simple type of counterpoint: both voices have the exact same rhythm. as a result, it’s all about the intervals! and that takes us to the first rule: only use consonant intervals. and it’s see how the important number of the to know interval is written that to the in between the two & & w & voices? you should sixteenth- w4 w2 7 century do that too. ear, the w w perfect w it’s how ? ? fourth ? rock stars was also do it! no seconds! no sevenths! dissonant! no fourths!

next rule: voices can’t cross or overlap. and then: thirds and sixths are fine, but no more than three in a row. voice crossing: top note is lower than bottom note to much consonance, and & & w the natives get restless. -3?w voice overlap: 3 w top note is lower 6 & w w w w w6 6 w than the previous w 6 6 6 bottom note w ? ? w ? w w w w wooooooooooo

the next rules have to do with perfect intervals (P1, P5, and P8... remember, P4 is dissonant!), which play important roles and require some special treatment.

because they are such a strong sonority which can stop the counterpoint in its tracks, unisons can only be used on the first or last notes of an exercise.

all perfect intervals must be approached with care in order to preserve voice independence. & 1 w3 w3 w1 w3 first of all, never repeat a perfect interval! w w w w w w ? these are called first note: in the middle: & parallel fifths... no problem no way w5 w5 and they’re just awful! in fact, each exercise must begin ? w w and end with a perfect interval with the tonic in the lower voice. in fact, approaching perfect intervals with both wait... why is that voices moving in the same direction is bad, even last bit important? if it’s from an imperfect interval. plus, it’s not okay to approach a perfect also for these exercises, you’ll be interval with in leaps both voices! writing a melody above or below so it’s easiest to remember what you can do: an already-written melody, called approach perfect intervals using contrary motion, a cantus firmus. with at least one voice moving by step. the cantus firmus will always start and end on the tonic note... so if you are writing counterpoint & w & w w below the cantus firmus, you can’t 8 w5 6 8 start with a perfect fifth, because you’re lower voice won’t w w w be the tonic. You’ll have to start ? w ? with a unison or octave instead!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Species Counterpoint:music theory for musicians and normal Species people by toby w. rush II second species counterpoint adds a C Ó touch more & ˙ ˙ ˙ ˙ complexity: ˙ ˙ ˙ there are two notes against every one in w the cantus firmus. ? C w w w

fortunately, that doesn’t make it twice as difficult: in fact, most of the previous rules still apply without any changes. there are only a few exceptions: species i species ii rule: rule:

leaps are still fine, but don’t leap to a new high point on a downbeat.

no leaps the a in the third measure is a larger than C ˙ new high point for the line, a perfect & ˙ ˙ ˙ ˙ ˙ so leaping to it on the fifth* downbeat puts a lot of weight on that one note, making it ? C w w w stick out of the texture.

*excepting, of course, ascending minor sixths and perfect octaves, but you already knew that.

still true... for downbeats. for the unaccented beats, dissonant intervals C only use are fine, as long as they happen as & ˙ ˙ ˙ ˙ 6 7 10 8 consonant passing tones: notes that fill in a intervals. third created by surrounding notes. ? C w w oh, and notice how dissonant intervals have their numbers circled? nice, huh. You should do it too.

unisons can only & C ˙ ˙ unisons can be used on unaccented be used 8 7 ˙3 ˙1 notes... just be careful about on the crossing or overlapping voices! first and w w last notes. ? C

this rule still applies: if you use a perfect interval on a downbeat, you need to use contrary motion from the immediately preceding approach notes, and at least one voice must move by step. perfect intervals however, you must also be careful not using to have the same perfect interval on contrary & C ˙ ˙ ˙ ˙ two successive downbeats. This is motion 8 10 8 6 called parallel perfect intervals with at least and it’s going to be a no-no for a one voice ? w w good long time. moving C by step. (in fact, it’s also not okay to have parallel perfect intervals from the unaccented beat to the downbeat, but if you are approaching with contrary motion, that wouldn’t happen anyway.)

not too bad, is it? yeah! bring on third species!

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third species, as you might have guessed, involves four notesœ againstœ one. & C œ œ œ œ œ œ œ œ œ œ and, compared to the other species, it’s easy peasy! in fact, the differences can be ? C w w w summed up into four rules.

first: don’t leap more than once SECOND: all intervals larger than a third, in the same direction. including perfect fourths, must be counterbalanced by steps on both sides. œ & œ œ œ & œ œ œ œ

third: As usual, the first note in each measure must be consonant. The third note in the measure is also usually consonant, but it can be dissonant... as long as it’s the only dissonant note in the measure. wait, dissonances as for the second and fourth notes, they can be dissonant, as long on beat two? but i never as they are or passing tones neighbor tones. quiet, & C œ œ œ œ Palestrina. a neighbor tone is a note approached by step, 8 9 8 9 which resolves back to the note it came from. ? C w

fourth: there are two special figures which act as exceptions to the rules above. Hey, that makes five rules! no fair! well, they’re kind of similar...

the double neighbor tone the nota cambiata (or involves an upper neighbor changing tone) follows and a lower neighbor played the pattern of a step down, one after another, then a third down, then returning to the note that two steps up. the middle note approached it. of this five-note figure must be consonant.

can be & C œ œ œ dissonant! 3 œ2 4 3 œ ? C w can be & C œ œ œ œ dissonant! 8 7 5 5 6

this figure can be inverted, w w so the upper and lower ? must be neighbors switch places. C consonant!

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more Species Counterpoint:music theory for musicians and normal Species people by toby w. rush IV with the fourth species, we stop using smaller note values and back up a bit to species I. But instead of having the notes move at the same time, species IV involves the voices being offset from one another.

The biggest difference with species IV is the & C Ó ˙ ˙ ˙ ˙ ˙ ˙ fact that dissonances ˙5 ˙3 6 7 ˙6 ˙7 ˙6 ˙3 6 7 6 4 3˙ are permitted on the downbeat. but as you w w might expect, they have ? w w w w w to follow certain C specific rules. dissonances in species IV must be in the form of suspensions. A suspension is a dissonant note that is approached by being oh you held over — suspended — from the previous note. don’t say.

another important defining in this case, the suspension characteristic is that the is the F on the downbeat of C the it’s suspension resolves down & ˙ ˙ second measure. by step. if it doesn’t resolve 6˙ 8 7 ˙6 prepared by the F in the down by step, it’s not a previous measure, and resolves suspension! w down to the E. ? C w suspensions are great, by the way, we label suspensions by the intervals of the but don’t use the same one more suspension and resolution, so this one than three times in a row, or 7-6would be called a 7-6 suspension. fux will release the hounds. the only suspension fux allows when writing counterpoint below the cantus firmus is the similarly, in C 2-3 suspension, in which the suspended note & forms a second with the cantus firmus, then this example, ˙ ˙ ˙ the suspended 8 6 4 ˙3 resolves down to a third. (when this suspension note is the D, is written an octave lower, it is sometimes called which forms a ? w w a 9-10 suspension.) fourth with C see how we resolve to the A. it moves to a C, a third above the a larger interval, unlike C bass, making it a 4-3 suspension. the 7-6 or 4-3? we’re & below the cantus firmus, 5w 3 w2 3 the 7-6 and 4-3 suspensions so we move away from it. are the only ones fux allows because suspensions when writing counterpoint ˙ ˙ always resolve down! ? ˙ ˙ 4-3above the cantus firmus. 2-3 C in species IV, you’re dealing with a lot of limitations with melody and counterpoint, so you will sometimes get trapped in a situation where nothing will work. when this happens, you are allowed to “break species”: forget the tie and slip into species II for a couple of notes. species breaker! for example, here we break species so we & C Ó ˙ ˙ ˙ ˙ can avoid writing a 8 4 3˙ ˙4 ˙3 ˙4 3˙ ˙6 ˙5 ˙6 8 6 fux-enraging four 4-3 suspensions w in a row! w w w ? C w w w don’t go crazy with this, though... species IV counterpoint should embrace suspensions, not avoid them. it’s best to break species only rarely. unfortunately, sometimes that means backing way up and choosing a different starting pitch for your counterpoint!

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fifth species counterpoint is the culmination of all the other species, and it’s the closest fux gets to palestrina’s style of florid counterpoint that fux thought was so amazingly awesome.

there aren’t a lot of new rules for this species, and they mainly and they’re all deal with combining about rhythm! the other species.

First, aim for a good when you’re using a particular note value, mix of different follow the rules of the corresponding species. don’t stay Species V Casserole species. so when you are using half too long with any ½ cup first species make sure you’re obeying the 2 cups second species 3 tsp ties (fresh or frozen) notes, (optional) particular note value 2 cups third species dash eighth notes rules of species II. If you tie two half before switching to 1-½ cups fourth species notes together, keep the laws of something else, so Combine all ingredients in a grand staff and mix well. fourth species. your counterpoint Heat through to prevent unjustified dissonances from forming. Let cool and serve on period instruments. remains rhythmically interesting. Leave the whole notes out, though, until you get to the end of your exercise. if you go all species I in the middle, things get real boring real fast.

C Ó ˙ œ œ ˙ ˙ œ #œ w & œ œ œ ˙ wZ ˙ œ œ oh yeah! ? C w w w w w w w

next, species III and IV can be combined lastly, you can include eighth notes to add by using dotted half notes, which always more rhythmic interest, as long as you have to start on a strong beat. follow a few restrictions:

they have to occur & C & C C ˙ in pairs on weak 6˙. œ5 ˙ œ œ & œ œ beats, ˙6 8 7 6 ˙5 œ * both notes must ? C w ? C w w be approached and resolved by step, any dissonances involved with this kind of ? C w figure have to follow the rules of * fourth only one pair species counterpoint: that is, they need eighth notes? should be used to be suspensions prepared and executed I love those in any given by the dotted half note and resolved guys! measure! immediately afterward. *

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