Theory for Musicians and Normal People Diatonic Harmony

tobyrush.com for musicians and normal people by toby w. rush

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.

tertial quartal quintal harmony harmony harmony harmony and

œ harmony? œœ œ œ œ œœ œ œ tertial œ œ œ septal 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 respectively. harmony, which are not major thirds and sound, used in quartal chords, harmonic so much minor thirds) compositions from and as such they harmony? 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 as with quintal harmony, these harmony, as with quintal

the common harmony. secundal practice period. 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 the lowest note in the chord & œ let’s get started when the chord is in simple on tertial harmony form is called œ the the & œ with the smallest . œ chord possible: names of the œ ? œ when we stack the triad. other notes œ the chord in are based on root thirds within one , their interval we get what is called the above the root. œ simple form of the chord. œ a triad is defined as a three-note chord, incidentally, four-note chords are technically but in practice it is almost always used called tetrads, but we usually call them to refer to tertial three-note chords. chords, since they add a seventh.

there are four ways to create a triad using thirds:

the the the the minor major diminishedtriad triad triad augmentedtriad

two minor thirds a on top a 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

c, e and g. it’s a c major

re for? re

ce was. ce

ound he ound

hat the pie the hat

oping ar oping

d you w you d

eady tol eady

re you sno you re he alr he what a what # j œ j 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 lookedœ. at?œ . œ. . 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 !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, 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 . I know, right? it’s awesome. haydn

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 musical works written in the baroque era would often include a part called the which would 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.

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. Te 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 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 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 sometimes referred to by their official names! dominant this pattern of leading-tone and major, minor diminished why is the 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 . however, it’s important to note that 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 its or didn’t do, are going to become own set of patterns, and thus “rules” for us in our writing. its 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 alto 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 alto 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 ... 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 ,

and it’s always cool!

”

undenknecht

ensch, ich s ich ensch, 55

..

“ich armer m armer “ich

cantata bwv bwv cantata J.S. Bach J.S.

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. as a result, common practice composers were or an augmented fourth. very consistent in avoiding two or more voices that moved in parallel perfect , parallel perfect fifths, or parallel perfect ! 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 . the middle note of a stepwise line 6 6 6 moving or F: I4 V I F: I V4 I up down.

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 a note preceded and the style just didn’t use these chords followed by the willy-nilly. same note. 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... it makes 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 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 plagal 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, theorists can find a pattern in their choices that we can use to easily remember which chord progressions work and which ones don’t. one way to understand this pattern is 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 ˙ A to B is down a seventh, here, we look at the root (not bass) of each ˙ ˙ but 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 that’s not say that they third, and down a fifth! 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. “Unstylistic” is a polite way of saying “The composers didn’t do it so you shouldn’t so, for example, a g chord to an 5 do it either”! 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... to to say you have to chord! œ œ a supertonic œ chord... chord... œ œ & œ chord and œ œ œ you are trying œ to decide what tonic chord... chord to use œ

leading-tone œ œ can move you œ can move you can move you œ

? to follow it. mediant

œ a up a second dominant down a fifth œ down a third œ œ a first exception and or you can use the or you

6 a C: ii iii vii° V a 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):

for instance, the I chord in G major G: I ii iii IV V vi vii° is G-B-D... a: i ii° III iv V VI vii° ...which is the V chord in C major!

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 . 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 a 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

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 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 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 another 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-... the reason these are often VVconfused is that in popular the terms “major-minor seventh” bw and theory, the term and “dominant seventh” are not w “dominant” is used to label interchangeable! “Major-minor & w the chord type instead of 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 & Vw7 the other important thing to know about the 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 bb w bb w b w bw bw w #w ##w diminished diminishedw diminishedw minor minorw minor minorw major majorw minor majorw major augmentedw major augmentedw 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 chords, chords and 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 major major augmented augmented doubly-augmented ninthw chord ninth chordw ninth chordw ninth chord ninthpractice chord period composers 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 diminished minor perfect minor diminished minor perfect major perfect major augmented diminished perfect perfectw augmented perfect G:augmented V augmented augmented augmented w w w w w w w w w w w eleventh chord eleventh chord eleventh chord doubly-augmented doubly-diminished eleventh chord w w w w 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 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 diminished diminished diminishedw diminished diminished minor diminished minor diminished minor minor perfect minor minor perfect MAJOR DIMINISHED DIMINISHED DIMINISHED MINOR PERFECT MINOR PERFECT MAJOR PERFECT MINOR PERFECT MAJOR AUGMENTED MAJOR AUGMENTED AUGMENTED w w w w w w w w w w thirteenth chord thirteenth chord thirteenth chord thirteenth chord doubly-diminished minor diminished thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord thirteenth chord w w w doubly-diminished diminished 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 DIMINISHED DIMINISHEDproblem: MINOR PERFECT MINOR theyPERFECT MAJORall havePERFECT MINOR morePERFECT MAJOR thanAUGMENTED MAJOR AUGMENTED AUGMENTED PERFECT MINOR PERFECT MAJOR AUGMENTEDdefines MAJOR AUGMENTED AUGMENTEDit asAUGMENTED a MAJORninth,AUGMENTED AUGMENTEDeleventhDOUBLY-AUGMENTED DOUBLY-AUGMENTED w w w w thirteenth chord thirteenth chord thirteenth chord thirteenth chord w w w w thirteenth chord thirteenth chord AUGMENTED DOUBLY-AUGMENTED thirteenth chord thirteenth chord thirteenth chord thirteenth chord w w w w thirteenth chord THIRTEENTH CHORD thirteenth chord thirteenth chord w w w 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.

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