My Dad Sofia Rush, Age 5 Pen and crayon on printer paper MUSIC THEORY this file is a collection of individual sheets for covering a unch of lessons on music theory MUSICIANS it s not a ook yet it might e someday! ut the more I made, ut as of right now, it s incomplete The truth is, they weren t intended to e a single volume when I started making them they were just review sheets for my own theory students and the more I realized NORMAL they could e collected into a textook of sorts eventually! so understand it s a work in progress the progress is slow sometimes, ecause I teach music theory and aural skills during the day at the university of dayton in dayton, ohio, and then head home to spend time with my wife and six kids! I still have a lot of work to do, ut 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 ut didn t want to download every file individually! PEOPLE y Toy W Rush ut if you like this, or find it useful, great! feel free to share it, copy it, and use it just don t sell it, change it, or tell others you made it!* hello! *for more info, see http://creativecommonsorg/licenses/y-nc-nd/40/ so if you ve een sent this file y someone, know that there might e a newer version or more pages at toyrushcom Rush now let s learn some music theory!
liz phair what makes you happy [melody from chorus] whitechocolatespaceegg (1998) music theory for musicians and normal people y toy w rush Notation: Pitch music notation is the art of recording music in written form gfddµdsµsdmfsµsµgf Œ modern music notation is a product of centuries of transformation and it is neither efficient nor intuitive! pitch is the highness or lowness of a sound the system of musical notation we use is essentially a stylized graph of pitch versus time for example, a flute has a high pitch, while a tua has a low pitch pitch pitch the five lines on which notes appear is called a staff a note is a written representation of a particular pitch time notation is ased on the piano keyoard; lines and spaces on the staff represent the white notes on the keyoard to display notes outside the staff, we use shortened staff lines called ledger lines the clef determines what notes each staff line corresponds to the four modern clefs are shown here; the note displayed on each staff corresponds to middle c To notate the lack notes on the piano keyoard, we use accidentals, which alter the note y one or two half steps a half step is the distance etween two adjacent keys on the piano keyoard, regardless of what color the keys are trele clef n w B w alto clef The doule sharp raises the note y two half steps The sharp raises the note y one half step The natural cancels out any previous accidental The flat lowers the note y one half step The doule flat lowers the note y two half steps F g a c d e F g a c d e the white notes on the keyoard are laeled with letters from A to G B w tenor clef? ass clef middle c is the c that is closest to the middle of the piano keyoard these symols are placed to the left of the note that they affect, and they apply to all the notes on that line or space for the rest of the measure n two notes which have the same pitch (for example, f sharp and g flat) are called enharmonics w n F g a c d e F g a c d e licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
frederic chopin nocturne in major, op 62, no 1 (1846) music theory for musicians and normal people y toy w rush Notation: Rhythm doule whole note w whole note half note quarter note eighth note while pitch is pretty clearly notated on a vertical axis, note length is indicated using a somewhat arcane system involving noteheads, stems and flags sixteenth note thirty-second note sixty-fourth note one-hundredtwenty-eighth note in this chart, each successive type of note is half as long as the note to its left none of these notes has a standard length; a half note in one piece may e the same length as an eighth note in a different piece note lengths in a piece are indicated y the tempo marking at the eginning of a piece or section doule whole rest whole rest half rest quarter rest Πeighth rest sixteenth rest thirty-second rest sixty-fourth rest one-hundredtwenty-eighth rest a rest is a period of silence that a length which corresponds to a particular note usually rests are placed on the staff at a particular vertical position as shown here the augmentation dot is a dot placed to the right of a notehead though small, this dot wields some serious power: it adds half of the original note s length! = + = + + ties are curved marks which connect two notes together to create a single, extended sound = = = + + multiple dots can also e added, each one adding half of the previously added value + to tie more than two notes together, draw ties etween each note; do not use a single, extended tie ack! Get it off! GEt it off! a tuplet is any non-standard division of a note these are usually written as a group of notes delineated with a racket and a numer showing the division eing made most tuplets are simple divisions, like the triplets to the left ut anything is possile! chopin, for example, would often go to town with these things 3 for example, these aren t exactly quarter notes; they are each a third as long as a half note wha gah! chopin, no! down, oy! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
the corrs heaven knows [drum intro] forgiven, not forgotten (1996) music theory for musicians and normal people y toy w rush Notation: Meter there are two types of eat units: those containing two divisions, called simple eat units a fundamental feature of most pieces of music is a consistent rhythmic pulse this pulse is called the eat, and a single pulse is called a eat unit and those containing three divisions, called compound eat units in music, eats are organized into patterns of accented and unaccented eat units in fact, if you listen to a sequence of repeated notes, your rain will proaly start to perceive the notes as groups of two, three, or four, even if no accents are present! these groups are called measures, and they are delineated with arlines arline measure the organization of eat units and measures in a piece is called meter Meter is descried y two numers placed at the eginning of the piece: the time signature simple TIME SIGNATURES are easy the top numer indicates the numer of eats in a measure the ottom numer indicates the type of note which serves as the eat unit the code for the ottom note is pretty easy: refers to a quarter note, to an eighth note, to a sixteenth note, and so on y looking at the top numer of the time signature, you can tell two things aout the meter: whether it s simple or compound, and how many eats are in a measure eats per measure compound TIME SIGNATURES are kind of lying to you 2 3 4 simple the top numer indicates the numer of divisions in a measure to get the numer of eats, divide it y three the ottom numer indicates the type of note which serves as the division to get the eat unit, use the note that is equal to three of these notes in a compound meter, the eat unit is always a dotted note! compound notes that have flags can e grouped together y using eams in place of flags in fact, wouldn t this e an easier way to notate compound meters? sorry the man says you have to do it the other way however, eaming is only used to group notes within eats for the most part, you shouldn t eam notes etween eats, nor should you tie notes within eats licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
Hey, kids! it ssparky the music theory dog! Q: music theory for musicians and normal people y toy w rush Dear Sparky: I understand that we re supposed to eam rhythms to show the organization of eats in the measure, ut is there an easy way to eam complex rhythms? --AY, Owatonna, MN A:WOOF!* notes should e eamed in groups that illustrate the meter for simple rhythms, this is pretty easy to do; simply group any notes that can e eamed (eighth notes and smaller) into groups that are equal to the eat unit of the current meter *translation: for complex rhythms, however, things can get complicated when a rhythm includes things like syncopations or other off-eat figures, illustrating the meter may involve dividing notes across eat units with ties fortunately, there is a step-y-step system for correctly eaming these complicated rhythms! for example, let s take this rhythm, which is written without eaming step 1: find the smallest note value used, and fill a complete measure with this type of note, eamed in groups that are equal to a eat unit in the current meter step 2: yes, i know it looks weird ut we re not done yet! step 3: if you have notes that are tied or eamed, ut not oth, then leave them alone! don t touch! add ties etween individual notes to recreate the original rhythm make sure that each tied group corresponds to a note in the rhythm you started with! original rhythm: find every group of two or more notes that are oth tied together and eamed together, and replace them with a single note of equivalent value hands off! = yes simplify it! a correctly eamed rhythm may include ties, ut it will very clearly show the eats in the measure which, in turn, makes it easier for the performer to read! DOING STUFF THE SPARKY WAY IS ALWAYS FUN! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush The Major Scale johann seastian ach Minuet in G major noteook for anna magdalena ach, 1722 one of the reasons that a particular piece of music sounds the way it does has to do with the group of notes the composer decided to use take this melody, for example let s first remove all the duplicate notes, regardless of which octave they re in next, let s put the notes in alphaetical order, starting on the note what we end up with is the palette for this particular piece that the melody sounded like it was centering on like the oard on which a painter holds the its of paint eing used in the painting eing created there are actually many different types of scales, each with a different pattern of whole steps and half steps a half step is the distance etween two adjacent keys on the piano keyoard, 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 etween steps three and four and etween steps seven and eight (or etween seven and one, since eight and one are the same note), is called the major scale a whole step whole step half step whole step whole step whole step half step (this scale, y the way, is called the g major scale, ecause it starts on g) whole step is the equivalent of two half steps knowing this formula, you can create a major scale on any note! the f major scale the major scale the d flat major scale the g flat major scale ut rememer with great power comes great responsiility! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush Key Signatures A B E A D if you start writing major scales and pay attention to the accidentals that occur, you are going to start noticing a pattern A f c g B E for example look at the flat keys, starting with the key that has one flat, all the way through the key with seven flats: the flats accrue in a specific order same with the sharp keys! so if you look for a key that has only a d flat, you won t find it: if a key has a d flat, it must also have a flat, an e flat and an a flat! since writing an entire piece in c sharp major would have een a sure-fire way to get carpal tunnel syndrome with all the sharps involved, composers pretty quickly came up with a way to simplify things: key signatures a key signature is a group of accidentals placed at the eginning of every line of music, just to the right of the clef, that instructs the performer to apply those accidentals to every corresponding note in the piece unless specified otherwise for example, this key signature indicates that every f, c, and g in the piece should e sharped, regardless of octave! c c c d d e e f f g f c g d a B E A D G C F f c g d a e B E A D G f c B E A f c g d B f c g d a e B E A D G C n oh, and another thing: the accidentals have to e placed in the correct order, and they need to follow a particular pattern of placement that varies slightly depending on the clef eing used! if you deviate from this, you, as a composer, will e mocked! tenor clef sharps! what s your prolem? you need to conform! g ha ha never! f licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush The Circle of Fifths this chart, called the circle of fifths, displays each key as a spoke on the circle, eginning with c major at the top and adding accidentals, one at a time, to the key signatures around the perimeter F 1 C 0 theorists find it convenient to organize all the possile key signatures into a chart that shows their relationship to one another we ll return to this chart as we continue learning aout how composers use keys 1 G B 2 as you move clockwise around the circle, you add sharps to the key signature as you move counterclockwise around, you add flats to the key signature 2 D E 3 A notice how that eadgcf pattern pops up all over the circle of fifths? weird! to determine the key signature for a key, look to see which spoke of the circle it s on to determine how many flats or sharps it has, and add accidentals to the key signature appropriately 4 for example, e flat major has three flats, so it should look like this: 7 5 the keys down here line up enharmonically for example, the key of d flat major will sound just like the key of c sharp major C D 6 F G 6 when adding flats to a key signature, add them in this order: eadgcf when adding sharps, use the reverse of the order aove 5 7 B C nooooo! 4 3 E A so could you continue the enharmonic deal and have the key of f flat major? yes, if you want a doule flat in your key signature: licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush Diatonic Intervals the most asic way which we identify different intervals is y counting the steps etween the two notes specifically, we count scale degrees, ut the easiest way to do it is to count lines and spaces on the staff 7 5 3 1 6 4 2 this interval is a seventh! when counting, egin with the ottom note as one and count until you reach the top note an interval is the distance in pitch etween two notes larger intervals smaller intervals when counting the lines and spaces, we can safely ignore any accidentals this interval is also a seventh we ll discuss how it s different very soon! unison second third fourth fifth sixth seventh octave two notes on the same line or space is called a unison that s latin for one sound! and that s latin for eight! the distance from a note to the next closest note with the same letter name is called an octave when we are talking aout intervals we sometimes discuss harmonic intervals and melodic intervals harmonic interval melodic interval a harmonic interval is simply two notes played simultaneously; a melodic interval is one note played after the other and when you swap the two notes (move the lower note up y an octave so it ecomes the higher note), that is called inverting the interval it s helpful to rememer that seconds always invert to sevenths, thirds to sixths, and so forth the fact that each of these pairs add up to nine is known to theorists as the rule of nines THE RULE 2nd 3rd 4th 5th 6th 7th 7th 6th 5th 4th 3rd 2nd OF NINES licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush Perfect Intervals inflection is a it harder to understand, partly ecause it depends on the type of interval so let s start y looking at unisons, fourths, fifths and octaves the distance of an interval is one part of its name, ut there s more: every interval has another quality to it, which we ll call inflection some theorists use the term quality for this that s cool too unisons and octaves are the easiest to lael: if the two notes are the same (for example, flat and flat), then the inflection is perfect: such an interval is called a perfect unison or a perfect octave an interval that is a half-step larger than perfect is called an augmented interval A8 wait why are the to f intervals different? you can go further, to douly augmented and douly diminished intervals, ut do you really want to? fourths and fifths require a little more explaining if you look at all the fourths and fifths you can create using only the white notes on the piano keyoard (in other words, using only notes without accidentals): each one is perfect except for those which use f and! well, if you were to count the half-steps that make up each interval, you d notice that all the other ones are equal in size, ut the to f intervals are not: f to is a half-step larger than a perfect fourth, and to f is a half-step smaller than a perfect fifth which raises the question: if the interval is not perfect, than what is it? A augmented d5 d4 d8 P and there s no such thing as a A5 A4 diminished unison perfect just like two things can t e negative two feet A1 away from each other! d an interval that is a half-step diminished smaller than perfect is called a diminished interval licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
music theory for musicians and normal people y toy w rush Imperfect Intervals We ve talked aout unisons, fourths, fifths and octaves, ut what aout the rest? are these other intervals somehow imperfect? well, yes, ut not ecause they are somehow inferior to perfect intervals seconds, thirds, sixths and sevenths just work a little differently! A augmented for one thing, the inflection for these intervals is never perfect; it will e either major or intervals are a half-step smaller than major intervals like perfect intervals, though, they can also e augmented or diminished; augmented intervals are a half-step larger than major, and diminished intervals are a half-step smaller than M m major d diminished how do we know if an interval is major or? we can actually use the major scale to find out notice that, in the major scale, intervals from the tonic up to another scale degree are major major second likewise, intervals from the tonic down to another scale degree are second major third third major sixth sixth major seventh seventh knowing this, when you are confronted with a second, third, sixth or seventh, you can find its inflection y thinking aout the key signature of the top and/or ottom note we know this is a major sixth ecause d, the top note, is in the key of f major (the ottom note) and this is a seventh ecause, ottom note, is in the key of a major (the top note) if the top note is in the major key of the ottom note, the interval is major if the ottom note is in the major key of the top note, the interval is when the notes of the interval have accidentals, the associated key signatures can e more complicated so it s easiest to temporarily ignore the accidentals, determine the interval, and then add the accidentals ack one at a time and track how the interval changes! ack! what is that? let s first hide the accidentals poof! poof! M6 e is in the key of g, so we know this is a major sixth m6 adding ack the flat makes the interval smaller, so it s now a sixth d6 adding ack the sharp makes it even smaller a diminished sixth! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
Hey, kids! it ssparky the music theory dog! Q: music theory for musicians and normal people y toy w rush Dear Sparky: Since we are supposed to use different approaches for identifying perfect and imperfect intervals, can you summarize them all into one system? --IM, Staten Island, NY A:WOOF!* STEP 1: STEP 2: STEP 3: if it is a unison or octave: the following chart shows an approach for identifying any interval a similar approach can e used when you need to write a particular interval aove or elow a given note: first, add a note aove or elow 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 *translation: determine the distance of the interval y counting lines and spaces cover up all accidentals determine the inflection of the interval in front of you (the one without accidentals!) as follows: if it is a fourth or fifth: 7 5 3 1 6 4 2 count the ottom note as one, and continue until you reach the top note poof! if it is a second, third, sixth or seventh: poof! the interval shown is a perfect unison or perfect octave really it just is if the interval uses the notes f and, it is either an augmented fourth or a diminished fifth otherwise, the interval is perfect if the top note is in the major key of the ottom note, the interval is major if the ottom note is in the major key of the top note, the interval is STEP 4: diminished perfect d P perfect intervals augmented A rememer: accidentals can never affect the distance of an interval all they can ever do is change the inflection! add the original accidentals ack, one at a time, and track how the interval changes inflection imperfect intervals diminished d Mmajor A augmented This method may seem complicated at first, ut it ecomes easier and faster with practice and it gives you the correct answer every time! DOING STUFF THE SPARKY WAY IS ALWAYS FUN! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more M6 m6 d6
music theory for musicians and normal people y toy w rush The Minor Scales this key is defined y a key signature of no sharps and flats, ut also y the fact that it centers around c There are actually two things that define a key: the key signature is the most ovious one, ut another important part of a key is the tonic the note around which the key centers ut what if we change the tonic? what if we use the same notes for the key signature, ut 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 scale the natural scale the thing is, common practice period composers weren t all that crazy aout this scale, ecause it lacks something the major scale has: a half-step from seven to one the whole step here didn t have the tension they liked going into the tonic! the harmonic scale so here s what they did: they raised the leading-tone y a half-step with an accidental This gave them the tension they were looking for! halfstep! this scale is great for uilding chords, so we refer to it as the harmonic scale however, composers didn t use it for writing melodies, ecause it had a prolem: an augmented second etween the sixth and seventh scale degrees so, for melodies, they made another change: they added another accidental to raise the sixth scale degree y a half-step the melodic scale now we only have whole steps and half-steps! now, rememer the reason we raised the leading tone in the first place was to create tension from the seventh scale degree to tonic ut in a melody, if the seventh scale degree is followed y 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 y differentiating etween ascending melodic and descending melodic ; for descending melodic, we don t raise anything! licensed under a creative commons BY-NC-ND license - visit toyrushcom for more
Triads music theory for musicians and normal people y toy w rush although a chord is technically any comination of notes played simultaneously, in music theory we usually define chords as the comination of three or more notes secundal harmony chords uilt from seconds form tone clusters, which are not harmonic so much as timral tertial harmony chords uilt from thirds (MORE SPECifically, from major thirds and thirds) form the asis of most harmony in the common practice period quartal harmony chords uilt from perfect fourths create a different sound, used in compositions from the early 1900s and onward quintal harmony chords uilt from perfect fifths can e respelled as quartal chords, and as such they do not create a separate system of harmony sextal harmony? septal harmony? as with quintal harmony, these are the same as tertial and secundal harmony, respectively? is the chord still tertial if it is uilt from diminished thirds or augmented thirds? when we stack the chord in thirds within one octave, we get what is called the simple form of the chord let s get started on tertial harmony with the smallest chord possile: the triad well, diminished thirds sound just like major seconds, and augmented thirds sound just like perfect fourths, so no the lowest note in the chord when the chord is in simple form is called the root the fifth names of the other notes third are ased on root their interval aove the root a triad is defined as a three-note chord, ut in practice it is almost always used to refer to tertial three-note chords incidentally, four-note chords are technically called tetrads, ut we usually call them seventh chords, since they add a seventh the diminished triad there are four ways to create a triad using major and thirds: the triad the major triad the augmented triad two thirds stacked together a major third on top a third on ottom a third on top a major third on ottom two major thirds stacked together min 3rd min 3rd c c maj 3rd min 3rd C min 3rd maj 3rd C + we lael triads using their root ( a c triad ) the areviations shown aove, which use upper case, lower case, and symols to show chord type, are called macro analysis licensed under a creative commons BY-NC-ND license - visit toyrushcom for more maj 3rd maj 3rd
what are you snooping around here for? he already told you what the piece was Triads in Inversion ladies and gentlemen, it s franz joseph haydn! music theory for musicians and normal people y toy w rush and he s rought a movement from his 1767 sonata in g major ooh! let s see em! thank you for having me in this piece I use quite a few triads haydn?? f 8 3 8 3 j f this one is g,, and d a g major triad! ut it sounds different, somehow j here s one: it has the notes c, e and g it s a c major triad! very nice p j j F thank you see how the notes are spread out, and not just stacked in thirds? it s still a triad, though that s ecause the third of the chord is in the ass when that happens, we say the chord is in first inversion j f? first inversion? what is it called when the root is in the ass, like the first chord we looked at? ƒ that s called root position U n n? M p M M M? F n so this one with d, f, and a is a d triad in second inversion! exactly! ecause the fifth is in the ass n p so the thing that makes a triad root position, first inversion or second inversion is simply which note is in the ass? it s hard to elieve that the sound of the chord can change so much just ecause of the ass note that s right! and each one has its own character I know, right? it s awesome haydn licensed under a creative commons BY-NC-ND license - visit toyrushcom for more