Music Notation and Theoryfor Intelligent BeginnersbyJono KornfeldCover art byJason Dullack 2001, revised 2005 Jono KornfeldAll rights reserved. No part of this book may be duplicated in any form without written permission of the author.Artwork 2004 Jason Dullack: all rights reserved
Music Notation and Theory for Intelligent Beginners 2001, revised 2005 Jono KornfeldTable of ContentsNotes, The StaffThe KeyboardClefsLedger LinesThe Grand Staff, AccidentalsSimple IntervalsEnharmonic EquivalenceDouble AccidentalsNote ValuesBeamingStem DirectionStem LengthMeasure, Bar LineTime SignaturesBeat EmphasisPutting Notes into PracticeCounting Eighth NotesCounting Sixteenth NotesRestsThe DotTiesSlursOther Time SignaturesCompound Time SignaturesThe Triplet, SyncopationTempo ITempo II, Tempo ChangesDynamicsArticulationEconomical Devices IEconomical Devices IIEconomical Devices ExercisesThe Major Scale, KeysScales Using FlatsScales Using SharpsKey Signatures, The KeyThe Circle of FifthsTranspositionScale Degrees, Note NamesThe Minor ScaleThe Three Minor onIntervalsSpelling IntervalsIn the scaleDetermining Intervals IDetermining Intervals IIInversionCompound IntervalsHearing IntervalsIdentifying in ContextTriadsIn the ScaleRoman NumeralsHarmonizationMinor Key HarmonizationTerminology7th ChordsInverting ChordsFigured Bass NotationApplication to AnalysisPosition of Upper NotesVoicing a ChordContemporary ContextCadences and PhrasesThe PeriodMelodic AspectsAnalysisMelodies and Voice LeadingExamplesCombining Melody and HarmonyThe ProcessNon-Chord TonesPassing ToneNeighbor ToneSuspensionModulationAppendix /ReviewScalesKeys & Key SignaturesCircle of 5ths ReferenceMajor Scales ReferenceIntervals & Figured 6A-7
XNOTESOne of the most basic elements in music is the note.In written music, it might look like this:h qeSome free-standing notesOr this (if there are more than one):orTHE STAFFThe five horizontal lines on which the notes sit are called a staff.a staff with no notes on itEach line or space on the staff is for its own note.Notes represent sounds called pitches. Because music employs a set of pitches (ranging from low tohigh), the staff acts like a map for the notes--allowing us to hear, read or write them as:Higher(higher on the staff)Lower(lower on the staff)We read the sequence of notes from left to right.Another way to understand the idea of pitches being lower or higher is to compare it to bears and birds.A bear's voice is low-pitched, while the voice of a bird's is high (this explanation works well for children!).A less musically specific term for pitch is frequency, which is also referred to as low or high.11
THE KEYBOARDIn Western music, pitches and notes are specific and have specific names. We use the first sevenletters of our alphabet: A through G.To see these notes in connection with a music making device, let's look at a standard keyboard:A modern keyboard has a total of 88 keys (black and white combined) asopposed to the 60 in this illustration.etcetc.lower registermiddle registerhigher registereach white key is a different noteRegister refers to high or low pitch range and is more often a relative term.Since there are obviously more than seven pitches on the keyboard, the A to G series repeats itself manytimes. Above we have C to C in brackets for reasons that will soon be obvious.You will notice that the pattern made by the white and black keys also repeats with the series.Because there are also more than seven combined lines and spaces on a staff, we can begin to see how astaff, or two staffs, could accommodate all these notes.N.B. in these examples we will see how music notation connects with the keyboard. It should be understoodthat this notation works with all instruments.22
CLEFSThe clef, a symbol that sits at the leftmost side of the staff, specifies which lines and spaces belong to whichnotes. In a sense, the clef calibrates or orients the staff to specific notes.The three most common clefs are:The Treble clef for high range notesThe Bass clef for low range notesThe Alto clef for middle range notesThe Treble clef (also called the G Clef because it looks like a calligraphic "G") works as follows:Notice that the curl ofthe clef circles the linethat will be the note G(the 2nd line from the bottom).The G note on the G lineThe Bass clef (also called the F Clef because it looks like an "F") works as follows:The F note on the F lineThe two dots surround theline that will be the note F(the 4th line).The Alto clef (also called the C Clef):The two curls pinch theC line (the 3rd line).The C note on the C lineAlthough it is importantto know about the AltoClef, we will spend moretime talking about andworking with the Trebleand Bass Clefs.33
The staff itself is flexible with regard to which notes the lines and spaces represent. But once aclef is put on a staff (and we always put one on), the notes become assigned and fixed.Here is how it works in relation to the keyboard:The C in the middle of the keyboard is called Middle Cetc.etcThe Treble StaffThe Bass StaffThe Alto StaffThe three staffs and the basic ranges they cover as seen on a keyboardAgain, notice that: the notes on the Bass Staff refer to the lower notes (below Middle C) on the keyboard the notes on the Alto Staff refer to the middle notes (surrounding Middle C) on the keyboard the notes on the Treble Staff refer to the higher notes (above Middle C) on the keyboardREMEMBER: every instrument uses the staffs and clefs in the same way as the keyboard. Most instruments,however, do not have as wide a range as the keyboard. An instrument like the flute plays relatively highernotes (like the birds in our earlier analogy) so we say it has a "high range". Accordingly, the flute only readsfrom the treble staffs (and NOT the other staffs) because most of its playable notes fit nicely (in a visual sense)onto the treble staff. In fact, a regular flute cannot go as low as the top line of the bass staff, so the bass staff isuseless for a flute player!Likewise, a low-sounding instrument like the tuba only reads from the bass staff (and let's not forget our bear!).The range of notes on the treble staff are too high for what the tuba can play, so it has no use for the treble staff.44
LEDGER LINESOften we need to write notes that are outside the range of the staff. Remember, the range between thetreble and bass staffs is relatively narrow as compared to the possible range of the keyboard's 88 notes:Middle C.etcetc.The top and bottomlines of the Bass StaffThe top and bottomlines of the Treble StaffFor situations where we need to go beyond the outer limits of either staff, we use short lines calledLedger Lines which are placed above or below that staff. In effect, ledger lines extend the range of thestaff(s).In the diagram below, we see upper and lower ledger lines in both the bass and treble staffs. Note that thefirst ledger line above the bass staff and the first ledger line below the treble staff represent the same C inthe same register: Middle C.The upper ledger lines of the bass staff and the lower ledger lines of the treble staff share the same notes.They overlap.This A is on thefirst ledger lineThis C is on thesecond ledger lineMiddle CNotice that the ledgerlines follow the samespacing as the staff linesThis C is on thesecond lower ledgerline55
Pianists read from the Grand Staff!THE GRAND STAFFOften it is necessary to use notes that are far above the bass staff or far below the treble staff, such aswhen we use a wide range insrument like the piano. Rather than use many, many ledger lines on onestaff (which can be hard to count), we can combine two staffs at once to cover this wider range.When we combine the bass and treble staffs into one larger staff, we connect them with a line and abrace on the left-hand side. This new concoction is appropriately called the Grand Staff.These are theexact same noteson each staff!The Grand Staff, which combinesthe bass and treble staffs.Here we see how the middle notes overlap so thatin certain cases, there would be two ways to writethe same exact note on a grand staff.C# D#Db EbACCIDENTALSAn accidental is a symbol that raises or lowers anote. In practice, this usually means raising orlowering a white note to the adjacent black note.F # G# A #G b Ab B bFinally, we will investigate the black notes!If we raise a note, we use a sharp sign: #. if we lower a note, we use a flat sign: b.To cancel or deactivate a previous sharp or flat, we use a natural sign: n.In music notation, the accidental sign is placed to the left of the notehead. When we speak or write aboutsuch notes, the words "flat", "sharp", or "natural" go after the note name.A flat (A b)#The three accidentalsbnA flat A b SharpFlatD sharp D # D sharp (D #) Natural66
ACCIDENTALS continuednThe Natural signTo cancel an accidental with the natural sign:A b becomes AnD# becomes DnNotice that each accidental is centeredon the lines or spaces of the staff exactlyas is its corresponding note.To put it another way, the natural sign changes the note in the opposite direction to that of the previousaccidental. A natural raises a note that had been previously flat, or lowers a note that had been previouslysharp.SIMPLE INTERVALS: half step, whole stepAn interval is a way of describing the distance between two notes. On the keyboard, it is the distancebetween two keys. While there are many ways to determine and label intervals, we will focus on the mostbasic elements: the Half Step (H) and the Whole Step (W).C # to DHC to D E to F #G to A b B to CHWHWB b to CWThe distance from any key to the secondkey above or below is a whole step.The distance from any key to the next on thekeyboard, above or below, is a half step. Thisgoes for white to black, black to white, and intwo cases, white to white.77
ENHARMONIC EQUIVALENCECombining our knowledge of half and whole steps with our knowledge of accidentals, we encountera new idea: Enharmonic Notes:C# D#Db EbThese notes areenharmonicallyequivalentF # G# A #Gb Ab B bF b E#C# D#Db EbC b B#The note a half step above G is G#. But that black note is also a half step below A, so it is also A b.Therefore, it is possible (and often) that one note can be referred to by two different names. Contextwill often be the determinating factor as to which is the more appropriate name. So A b and G # areenharmonic notes. We can also say that they are enharmonically equivalent: A b is harmonicallyequivalent to G #. To put it simply: THEY SOUND THE SAME.is enharmonically equivalent toAbG#(they sound the same)Another enharmonic possibility on the keyboard is that we can apply an accidental to any note. So,strange as it seems, the note above E (normally called F) could also be E sharp (E #). And the notebelow F (normally E) could also be called F flat (F b). Similarly, this applies to the notes B and C,where C can be enharmonically named B sharp (B #), and B can be enharmonically named C flat (C b).sounds thesame asCsounds thesame asandB#CbBAt first glance, it seems more complicated to have more than one note name for the same soundingpitch, but there will be situations where it will seem more logical to have a B sharp rather than a Cnatural.88
‹double sharpDOUBLE ACCIDENTALS double flatTo make matters even more complicated, it is also possible to have double accidentals. A doubleaccidental raises or lowers a pitch by two half steps (or one step). A double flat looks like this: while a double sharp looks like this: ‹.D double sharpB double flatIn terms of enharmonic equivalency, D double sharp is played and sounds like E.B double flat is played and sounds like A.D double sharpsounds thesame asD double sharpB double flatsounds thesame asandE naturalB double flatA natural99
NOTE VALUESSince not all notes sound for the same length of time (some notes sound short or fast while otherssound long and slow), we use note values to indicate the duration of a note.Note values are expressed as relative lengths to one and other by a factor of two:A whole note is writtenas an open ovalA quarter note isa closed oval witha stemA half note is an openoval with a stem attachedto one side of itAn eighth note is a closedoval with a stem and a flagxXSixteenth noteshave two flagsAs their fraction-like names imply, the relative values (relative durations) of the notes are:wequals the duration of1 whole noteh2 half notesequals the duration of1 half noteqqq2 quarter notesequals the duration of1 quarter noteehhee2 eighth notesequals the duration of1 eighth notexx2 sixteenth notes1013
NOTE VALUES ContiuedLikewise:whh HalfWhole qqqqQuarter eeeeeeeexxxxxxxxxxxxxxxx EighthSixteenthOrwh h1 whole note 2 half notes q q q qeeeeeeee4 quarter notes 8 eighth notes xxxxxxxxxxxxxxxx16 sixteenth notesBEAMINGWith eighth notes and sixteenth notes (and other small values that we will discuss later), twoor more stems can be conveniently beamed together. This is a visually comfortable alternativeto writing multiple flags. We just replace the flag(s) with a beam(s) at the end of the stems.can becomecan becomeThe beamed stems canhelp represent a feelingof connectednessAs usual, different contexts will dictate a better choice between these two possibilities.1411
STEM DIRECTIONNow that we know what stems are and what they do, let's look at how we must draw them.Stems extend downward and are on the left side of the note head when the note is on or above thethird line of any staff.Stems extend upward and are on the right side of the note head when the note is below the third lineof any staff.In order to see them in a more real context, here is a random mix of of up and down stems.notice that the third line notes have their stemspointing downwardHowever, when notes are beamed together, such as with eighth and sixteenth notes, we consider all thenotes joined by a given beam to act as one note. The note that is farthest from the middle line determinesthe overall stem direction.It is as if this "note" were abovethe middle lineBecause the lowest note is below themiddle line, the stems point upAnd when the outermost notes are equidistantfrom the middle line, it is as if the "note" were onthe middle line so the stems point downward.1216
STEM LENGTHHere is another situation where we have to be sticklers about the rules. The length of the stem must beexactly long enough to reach up or down to the next line or space that represents the same note. For thoseof you who know the term, the stem must be an octave long.BUT.Once a note is on or above the second upper ledger line, or on or below the second lower ledger line, thestem must reach all the way to the middle line (making it longer than usual).All the stems touch the middle lineThe same idea applies to beamed notes. We just need to make sure that the beam is thick enough so thatit does not get confused with (or obscured by) the staff line.There is no way to get thesethick beams confused withthe staff line!When multiple notes are beamed together, the stems should be at least an octave long (meaning thatsome of the stems may be longer). Not every scenario or combination of notes will be explored here.These are only some of the most basic stem direction examples.13
MEASURE, BAR LINEMusic, and the music staff is usually divided into equal parts by vertical lines called Bar Lines. By equal,we mean equal in length of time. The space created by two bar lines is called either a Measure or a Bar.In jazz, classical, or rock music, either term is acceptable and interchangeable.Bar lines go all the way through the staff. On the grand staff, the bar lines go through the entire staff.Measure or BarNotice that the bar lineruns all the way throughon the grand staffBar LinesBar Line(when we hear about a "12-bar blues" for example, it means that the songis 12 measures long, and then it repeats those 12 measures as many times as necessary)The distance between bar lines may vary depending on the number of notes:a wider measure to accommodatemore notesNotice that the sums of the note valuesare the same in each measure. This reinforcesthe notion that each bar "measures" the sameamount of time equally, regardless of howwide it is. Within each measure is an equalnumber of beats.There is never a bar line at the beginning of a single staff (unlike the grand staff, which has the line).When a piece of music ends (or when a movement ends), the final bar line is a Double Bar:a thin line followed by a thicker line.Double Bar14
TIME SIGNATURELike a clef, a Time Signature goes at the left side of the staff, but to the right of the clef. It consistsof two numbers arranged vertically.44Unlike this clef, the time signaturedoes not extend beyond the topand bottom lines of the staffA clef calibrates the notes ona staff. The time signaturecalibrates the beats in eachmeasure.The upper number indicates how many beats (or counts, or pulses) are in each measure.The lower number indicates which type of note value counts for one beat.Four "beats" in each measure4In 4 time, the quarter note (as in 1/4th) counts for one beat (we say "gets" the beat)and there are four beats per measure.again, 4 beats in the measureThe values could be mixed!But two half notesequal four quarter notes,so two half notes couldfit into a 44 measureOne whole notefits into a "whole"4 measure because4it is just as longas four quarter notesThe same goes foreighth notes because4eight fit into a 4 measureIf we were to vocalize this idea, we could attach a "Ta" to each beat (quarter note) and "sing":The attack of each "Ta" is perfectly even,like the even ticking of a clock.or we could use numbers (EVENLY!):Notice that we start counting over when we cross the bar line.1520
TIME SIGNATURES ContinuedThe same time signature concept applies to other situations:3If we have a 4 time signature, it means that there are three quarter notes per measure and that the quarternote gets the beat.Three bars of 34 . The note values add up to three quarter notes in each bar.(a whole notew is too big to fit into a 34 measure!)2If we have a 4 time signature, there are two quarter notes per measure and the quarter note gets the beat.2A mixture of notes values in 4 time. Again, notice that the note values in each measure always addup to two quarter notes, even the 8 sixteenths at the far right.4 32While we will limit our discussion for the moment to the 4 , 4 & 4 time signatures, many time signaturesare possible. Just remember that the bottom number symbolizes a note value, which is either 1, or a multipleof two (1, 2, 4, 8, 16, 32, 64). We rarely get to 64th notes, but they are theoretically possible. As far as thetop number is concerned, it could be any odd or even number.BEAT EMPHASISIn classical music, the first beat of the measure in any time signature usually receives more emphasis thanthe other beats in the measure. We often use the word Accented to refer to something being emphasized.The first beat of each measure is slightly accentedHence the reason for different time signatures! Each time signature has its own rhthmic characteristicand feel. The relationship between the more and less emphasized beats (often called strong and weak)will vary depending on the time signature. Above, the strong (or accented) 1 is separated by a differentnumber of weak beats according to the time signature.16
PUTTING NOTES INTO PRACTICEAs we begin to apply notes and time signatures to performance practice, there are a few standard labels andmethods with which to familiarize ourselves.As seen earlier, we can sing rhythms by either the "Ta" methods or the counting method. Both approachesare useful, so it is recommended that all rhythm exercises be practiced both ways.When we Ta, we reite
3 CLEFS The clef, a symbol that sits at the leftmost side of the staff, specifies which lines and spaces belong to which notes. In a sense, the clef calibrates or orients the staff to specific notes. The three most common clefs are: The Treble clef for high range notes The Bass clef for low range notes The Alto clef for middle range notes The Treble clef (also called the G Clef because it .
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Scientific Notation (SN)- A shorthanded way of writing really large or really small numbers. In SN a number is written as the product of two factors. !Ex: 280,000,000 can be written in scientific notation as 2.8!!!10. First Factor Regular Notation ! Scientific Notation Regular Notation How to Change Scientific Notation 420,000.
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