music_basic_theory

Section 1: Determining what notes are worth

• The rhythm is the pattern of regular or irregular pulses.
• A beat is a pulsation that divides time into equal lengths. A ticking clock is a good example. Every minute, the second hand ticks 60 times, and each one of those ticks is a beat.
• If you spped up or slow down the second hand, you're changing the tempo of the beat.
• Notes in music tell you what to play during each of those ticks.
• In other words, the notes tell you how long and how often to play a certain musical pitch: the low or high sound a specific note makes within the beat.
• The note value, indicated by the size and shape of the note, determines this how long a specific pitch should be held.

Recognizing Notes and Note Values

• Notes are like letters of the alphabet: they're that basic to the construction of a piece of music.
• In fact, when musicians talk about performing a piece of music "in the style of" Bach, Beethoven, or Philip Glass, they're talking as much about using the rhythm structure and pace characteristics of that particular composer's music as much as any particular chord progressions or melodic choices.
• Notes are made of up to three specific components: note head, stem, and flag.
• Head: The head is the round part of a note. Every note has one.
• Stem: The stem is the vertical line attached to the note head. Eigth (quaver) notes, quarter (crotchet) notes, and half (minim) notes all have stems.
• Flag: The flag is the little line that comes off the top or bottom of the note stem. Eighth (quaver) notes and shorter ntoes have flags.
• Instead of each note getting a flag, notes with flags can also be connected each other with a beam, which is just a cleaner-looking incarnation of the flag.

Looking at note values

• Depending on the time signature of the piece of music, the note value that's equalt o bone beat changes.
• In the most common time signature, 4/4 time, also called common time, a whole (semibreve) note is held for four beats, a half (minim) note is held for two, and a quarter (crotchet) note lasts one beat.

Extending notes with dots and ties

• augmentation dot indicates that the note's value is increased by one half of its original value.
• Another way to increase the value of a note is by tying it to another note. Thies connect notes of the same pitch together to create one sustained note instead of two separate ones.

Section 2: Giving It a Rest

• Silent "notes" are called rests.

Getting to know the Rests

• Think of rests as the spaces between words in a written sentence.
• Whole (semibreve), half (minim), quarter (crotchet), eighth (quaver) rests

Section 3: Introducing Time Signatures

Decoding Time Signatures and Measures

• The pair of numbers is called the time signature and it tells you two things:
  1. The number of beats in each measure: the top number in the time signuatre tells you the number of beats to be counted off in each measure. If the top number is three, each measure contains three beats.
  2. Which note gets one beat: The bottom number in the time signature tells you which type of note value equals one beat: most often, eighth notes and quarter notes. If the bottom number is four, a quarter note is one beat. If it's an eight, an eighth note carries the beat.
• Written music contains the following two main types of time signatures
  1. Simple: With simple time signatures, the beat of a piece of music can be broken down into two-part rhythms.
  2. Compound: In compound time signatures, the beat is broken down into three-part rhythms.
• A measure (or bar) is a segment of written music contained within two vertical lines. Each measure in a piece of music has as many beats as is allowed by the time signature.

Keeping Things Easy with Simple Time Signatures

• Simple time signatures are the easiest to count, because a one-two pulse in a piece of music feels the most natural to a listener and a performer.
• The following four requirements indicate that a time signature is a simple one:
  1. Each beat is divided into two equal components.
  2. The note that gets one beat has to be an undotted note.
  3. The top number isn't divisible by 3 except when it is 3.
  4. The number of beats is the same in every measure.
• In simple time, a slightly stronger accent is placed on the first beat of each measure.
• Here are some common examples of simple time signatures:
  • 4/4: used in popular, classical, rock, jazz, counrtry, bluegrass, hip-hop, and house music
  • 3/4: used for waltzes and country and western ballads
  • 2/4: used in polkas and marches
  • 3/8: used in waltzes, minuets, and country and western ballads
  • 2/2: used in marches and slow-moving processionals
• Counting 4/4 time: ONE two three four ONE two three four
• Counting 3/4 time: ONE two three ONE two three
• Counting 3/8 time: ONE two three ONE two three (the time signatures 3/8 and 3/4 hav almost exactly the same rhythm structure in the way the beat is counted off. However, because 3/8 uses eighth notes instead of quarter ntoes, the eighth notes get the beat.
• Coungint 2/2 time: also called cut time, the half note gets the beat. ONE two ONE two. Time signatures with a 2 as the lower number were widely used in medieval and pre-medieval music. Music from this period used a rhythm structure, called a tactus (later called a minim) that was based on the rhythm pattern of a human heartbeat.

Working with Compound Time Signatures

• The short of list of rules:
  1. The top number is evenly divisible by 3, with the exception of time signatures where the top number is 3.
  2. Each beat is divided into three components.
• One big difference between music in a simple time signature and music in a compound time signature is that they feel different, both to listen to and to play.
• In compound time, an accent is not only placed on the first beat of each measure (as in simple time), but a slightly softer accent is also placed on each successive beat. Therefore, there are two accents in a piece of 9/8 music, and four accents in a piece of music with a 12/8 time signature.
• Here are some examples of compound time signatures:

• 6/8: used in mariachi music
• 12/8: found in 12-bar blues and doo-wop music
• 9/4: used in jazz and progressive rock

• To dertermine the number of accents permeasure under a compound time signature, divide the top number by three.
• Counting 6/8 time: ONE two three FOUR five six ONE two three FOUR five six
• Counting 9/4 time: ONE two three FOUR five six SEVEN eight nine

Feeling the Pulse of Asymmetrical Time Signatures

• Asymmetrical time signatures (also called compelx or irregular time signatures) generally contain five or seven beats, compared to the traditional two-, three-, and four-beat measure groupings introduced earlier.
• Asymmetrical time signatures are common in traditional music from around the world, including in European folk music and in Eastern (particularly Indian) popular and folk music.
• Music with 5/4, 5/8 and 5/16 time signatures is usually divided into two pulses, either two beats plus three beats or vice versa.
• Counting 5/8 time: ONE two THREE four five, ONE two three FOUR five
• Counting 7/4 time: ONE two three FOUR five six seven, ONE two three four FIVE six seven

A Short Discussion about Conducting

• While the audience are positioned perfectly to hear the orcehstra as a whole, the idividual orchestra members are completely engulfed in the sound fo the instruments closest to them, which makes it incredibly easy to lose one's place when trying to follow along just reading a piece of sheet music.
• However, because of the conductor's stance in front of the orchestra, he or she can hear the entire performance as it's meant to be heard, and can keep all the musicians performing in time with one another at the volumne and speed they're supposed to be performing, almost like a studio engineer fine-tuning a mix throughout a live performance.
• Following is an interpretation of some basic conductor moves:
  • The beat: Conductors usually beat time with their right hand, which leaves their left hand free to cue various instruments or to tell the orchestra or sections of the orchestra when to play louder or softer. Most conductors use a baton to keep the beat simply. The basic movements of the baton or stick are horizontal and vertical, with the baton or right hand always counting out the beat. The underlying principle is that there is an imaginary point in the air where the beat lands: this point is referred to as the "ictus". The ictus is crtical because it indicates the time signature used in the composition, the cut-off points in the music, and where the emphasis in each measure is to be placed.
  • Phrasing, articulation, and dynamics: While the right hand maintains the beat, the left hand works independently to indicate other things about the music, such as the phrasing, dynamics, and articulation. In order to bring an orchestra to a crescendo, the conductor raises his or her left hand slowly or quickly in order to demonstrate how fast the crescendo must build, or, for a diminuendo, lower that hand to quiet the orchestra. A left bouncing in the air indicates staccato (short, clipped notes) is needed, while a smooth movement is used to indicate legato (smooth) passages. In a way, it's almost like the conductor is drawing sound waves in the air to demonstrate what he or she wants the orchestra to do. Conductor rely on body language and facial expressions to convey their directions as well (examples in Book P49).
  • Cueing: When a conductor suddenly points to a player or instrument section-generally, a section or performer that's been silent while the rest of the orchestra's been performing- that's called an entrance cue, and that player or section is to being playing immediately.

Section 4: Playing with Beat

Creating Stress Patterns and Syncopation

• The underlying rhythimic pulses of music is called the beat. It determines how people dance to music or even how they feel when they hear it. The beat influences whether people feel excited, agitated, mellow, or relaxed by music.
• When you're writing a piece of music down on paper, the way you group your notes together in a measure reflects the kind of beat the music will have.
• Placing stress: Knowing the general rules: generally, the first beat of a measure receives the strongest stress. If more than three beats are in a measure, usually a secondary strong beat comes halfway through the measure.
• Syncopation: Hitting the off-beat: Syncopation is a deliberate disruption of the two- or three-beat stress pattern. Musicians most often create syncopation by stressing an off-beat, or a note that isn't on the beat. If you had a piece of music that the quarter rest where the natural downbeat is located is considered the point of syncopation in the music. The fourth beat of the measure is accented instead of the third beat, which is normally accented, creating a different-sounding rhythm than you would normally have in 4/4 time numsic. If your perspective of where the downbeat occurs is moved, a point of syncopation results because it's shifting where the strong and the weak accents are built.

Getting a Jump on Pick-Up Notes

• Start with an odd measure at the beginning of a piece music, and the last measure "fixes" what looked wrong with that first measure, and therefore you have a piece of music written according to all the rules of music theory.

Exploring Irregular Rhythms: Triplets and Duplets

• Another way you can add rhythmic interest and variety to music is through the use of irregular rhythms (also called irrational rhythm or artificial division).
• An irregular rhythm is any rhythm that involves dividing the beat differently form what's allowed by the time signature. The most common of these divisions is called a triplet, which is three notes joined together that equal the beat a single note. The second most common type of irregular rhythm is a duplet, which is two bracketed notes with a note value of three of the same notes.
• Triplets: In 4/4 time, if you want to play an even number of notes in your sequence, you can use a couple a of eighth notes, or four sixteenth notes, or eight thirty-second notes. But what if you want to play an odd number of notes, and you absolutely want that odd number of notes to equal one beat? The answer is to play a triplet, which is what you get when you have a note that's usually divisible by two equal parts divided into three equal parts.
• Duplets: Duplets work like triplets, except in reverse. Composers use duplets when they want to put two notes in a space where they should put three.

Section 5: Music Notes (and Where to Find Them)

Meeting the Staff, Cleffs, and Notes

• Notes and rests in music are written on what musicians call a musical staff (or staves, if you're talking about two). A staff is made of five parallel horizontal lines, containing four spaces between them.
• The particular musical notes that are meant by each line and psace depend on which clef is written at the beginning of the staff. You may run across any of the following clefs (though the first two are the most common):
  • Treble Clef
  • Bass clef
  • C clefs, including alto and tenor
• Think of each clef as a graph of pitches, or tones, shown as notes plotted over time on five lines and four spaces.
• Each pitch or tone is named after one of the first seven letters of the alphabet; A,B,C,D,E,F,G,A,B,C... and it keeps on going that way indefinitely, repeating the note names as the pitches repeat in octaves.
• The treble clef: The treble clef is for higher-pitched notes. It contains the notes above middle C on the piano. On the guitar, the treble clef is usually the only clef you ever read. Most woodwind instruments, high brass instruments, and violins stick solely to the treble clef. The treble clef is also sometimes called the G clef.
• The bass clef: On the piano, the bass clef contains lower-ptiched notes, the ones below middle C, including all the notes you play with your left hand on the piano. Music is generally written in the bass clef for lower wind instruments like the basson, the lower brass instruments like the tuba, and the lower stringed instruments like the bass guitar. Another name for the bass clef is the F clef.
• Put the treble and bass clefs together and you get the grand staff. Middle C is not in either clef. Instead it's written on a ledger line. Ledger Lines are lines written above the bass clef and below the treble clef that are necessary to connect the two clefs.
• C clefs: Alto and tenor: The C clef is a moveable clef that you can place on any line of the staff. The line that runs through the center of the C clef, no matter which line that is, is considered middle C. C clefs are preferred in classical notation for instrumental ranges that hover right above or right below middle C. Instead of having to constantly switch between reading treble and bass clefs, a musician has just one musical staff to read. Today, the only C clefs commonly used are the following:
  • The alto clef: Puts middle C on the third staff line; most commonly used for writing viola music
  • The tenor clef: Puts middle C on the next-to-the-top line of the staff; most commonly used for writing cello, trombone, and basson music

Identifying Half Steps, Whole Steps, and Accidentals

• In Western music, an octave is broken up into 12 tones called half steps, or semi-tones. But a musical scale contains seven notes, meaning that some of the distance between notes in a scale spans one semitone and some spans at least two semi-tones. In other words, some half steps are skipped when building scales.
• When musicians talk about the notes A,BC,D,E,F, and G, they mean the natural notes (correspond to the white keys on a keyboard).
• Moving a whole step on the piano or guitar means you move two half steps from your starting position.
• Half steps and whole steps are intervals, which we discuss later.
• You also employ half steps when you come across an accidental, a notation used to raise or lower a natural note pitch. So when a note is sharped, you add a half step to the note; when a note is flatted, you remove a half step from the note.
• Strictly speaking, musical pitch is a continuous spectrum, because it's determined by the frequnecy of vibration. Therefore, many other microtonal sounds actually exist between consecutive half steps.
• Western musical notation recognizes only the division of pitch into half steps. In contrast, many Eastern instruments, particularly sitars and fretless stringed isntruments, use quarter tones. Quarter tones are pitches located halfway between each half step.
• Accidentals are notations used to raise or lower a natural note pitch on the staff by a half step. (Sharps, Flats, Double sharps, Double flats, Naturals)

Section 6: Mastering the Major and Minor Scales

• To put it simply, a scale(音阶) is any group of consecutive notes that provides the material for part or all of a piece of music.

Following Major-Scale Patterns

• Major scales follow the interval pattern of WWHWWWH, which means Whole step Whole step Half step Whole step Whole step Whole step Half step.
• Pitchwise, a half step is exactly 1/12 of an octave, or 1 semitone. A whole step is exactly 1/6 of an octave, or 2 semitones.
• Each of the eight notes in a major scale is assigned a scale degree according to the order it appears in the scale:
  • 1st note: Tonic（主音）
  • 2nd note: Supertonic
  • 3rd note: Mediant
  • 4th note: Subdominant
  • 5th note: Dominant
  • 6th note: Submediant
  • 7th note: Leading tone (or leadning note)
  • 8th note: Tonic
• The 1st and 9th notes, the tonics, determines the name of the scale. (Scales that share the same starting notes are called parallel scales).
• Each of these numbers represents a scale degree (音级), and their pattern of whole steps and half steps determines the key of the scale.
• The major scale, or the diatonic scale, is the most popular scale and the one that's the easiest to recognize when played. Songs like "Happy Birthday" and "Mary had a Little Lamb" are composed in the major/diatonic scale.

Discovering All That Minor Scale Patterns Have to Offer

• The arrangements and tones available in the minor scales can be much more flexible for a composer to use than the major scales alone.
• The minor scale degress all have the same names as the ones in major, except the 7th degree, which is called the subtonic.
• In the harmonic and melodic minor scales, the 7th degree is called leading tone. In the melodic minor scale, the 6th degree is called the submediant.
• Natural minor scales follow the interval pattern of WHWWHWW. A natural minor scale is taken from the major scale of the same name, but with the 3rd, 6th and 7th degress lowered by one half step.
• Harmonic minor scale is a variation of the natural minor scale. It occurs when the 7th note of the natural minor scale is raised by a half step. The step is not raised in the key signature; instead, it's raised throught the use of accidentals.
• Melodic minor scale is derived from the natural minor scale. In the melodic minor scale, the 6th and 7th notes of the natural minor scale are each raised by one half step when going up the scale. However, keep in mind that they return to the natural minor when going down the scale.

Section 7: Key Signatures and the Circle of Fifths

• The key signature tells you in what key the song is written.

Understanding the Circle Of Fifths and Recognizing Major Key Signatures

• In the sixth century B.C., the Greek scholar and philosopher Pythagoras divided a circle into 12 equal sections, like a clock. The result of his experimentation eventually became known as the Circle of Fifths, which is still used today.
• Each of the 12 points around the circle was assigned a pitch value, which roughly corresponds to the present system of an octave with 12 half steps.
• In mathematical terms, the unit of measure used in the circle is cents, with 1200 cents equal to one octave. Each half step, then, is broken up into 100 cents.
• Each of the circle's 12 stops is actually the fifth pitch in the scale of the preceding stop, which is why it's called the Circle of Fifths.
• To figure out how many sharps are in each key, count clockwise from C at the top of teh circle. The sharps always appear in a specific order in every key: F,C,G,D,A,E,B. You can easily remeber this pattern of sharps by using the mnemonic Father Charles Goes Down And Ends Battle.
• For the major scales and keys with flats, you move counterclockwise around the Circle of Fifths. The flats appear in a specific order in every key: B,E,A,D,G,C,F. The mnemonic we suggest here is Battle Ends And Down Goes Charles's Father.

Finding Minor Key Signatures and Relative Minors

• The Circle of Fifths works the same way for minor keys as it does for major keys.
• The minor keys on the inside of the circle are the relative minors of the major keys on the outside of the circle.
• The relative minor and its major key have the same key signautre.The only difference is that the relative minor's scale starts on a different tonic, or first note. The tonic, or starting point, of a relative minor is a minor third-or three half steps-lower than its relative major key.
• On sheet music, the relative minor is the note one full line or space below the major key note.

Section 8: Intervals: The Distance between Pitches

• The distance between two musical pitches is called an interval (音程).
• Scales and chords are both built from intervals. Music gets its richeness from intervals.

Breaking Down Harmonic and Melodic Intervals

• The following two types of intervals exist:
  1. A harmonic interval is what you play two notes at the same time.
  2. A melodic interval is what you get when you play two notes separately in time, one after the other.
• The identity of an interval, and this goes for both harmonic and melodic intervals, is determined by two things:
  1. Quantity
  2. Quality
• Quantity: Counting lines and spaces: The first step in naming an interval is finding the distance between the notes as they're written on the staff. The quantity, or number size, of an interval is based on the number of lines and spaces contained by the interval on the music staff. Musicians and composers use different names to indicate the quantity of intervals:
  • Unison (or prime) (two notes are the same)
  • Second
  • Third
  • Fourth
  • Fifth
  • Sixth
  • Seventh
  • Octave (two notes are exactly an octave apart)
• You determine an interval's quantity by simply adding up the lines and spaces included in the interval. You must count every line and every space between the notes as well as the lines or spaces that the notes are on. Accidentals don't matter when counting interval quantity.
• What if an interval spans more than one octave? In that case, it's called a compound interval. As with all interval quantities, you just count the lines and spaces for a compound interval.
• Quality: Considering half steps: Interval quality is based on the number of half steps from one note to another. Unlike in interval quantity, accidentals do matter in interval quality. Interval quality gives an interval its distinct sound.
• The terms used to describe quality, and their abbreviations, are as follows:
  • Major (M): A major 2nd interval contains 2 half-steps between notes, a Major 3rd contains 4 half-steps between notes, a major 6th contains 9 half-steps in between notes, and a major 7th contains 11 half-steps between notes.
  • Minor (m): A minor 2nd interval contains 1 half-step between notes, a minor 3rd contains 3 half-steps between notes, a minor 6th contains 8 half-steps between notes, and a minor 7th contains 10 half-steps between notes.
  • Perfect (P): Refers to the harmonic quality of unisons, octaves, fourths, and fifths.
  • Diminished (dim or d): Contains a half step less than a minor or perfect interval.
  • Augmented (aug or A): Contains a half step more than a major or perfect interval.
• Naming intervals: every interval gets its full name from the combination of both the quantity and the quality of the interval. For example, you may encounter a major third or perfect fifth. Here are the possible combinations that you use when describing intervals:
  • Perfect(P) can only be used with unisons, fourths, fifths, and octaves.
  • Major(M) and minor(m) can only be used with seconds, thirds, sixths, and sevenths.
  • Diminished(dim) can be used with any interval, with the exception of unisons.
  • Augmented(aug) can be used with any interval.

Looking at Unisons, Octaves, Fourths, and Fifths

• Perfect Unisons: A perfect melodic unison is possibly the easiest move you can make on an instrument. You just press akey, pluck, or blow the same note twice. In music written for multiple instruments, a perfect harmonic unison occurs when two or more people play exactly the same note, in the exact same manner, on two different instruments.
• Augmented unisons: To make a perfect unison augmented, you add one half step between the notes. You can alter either of the notes in the pair to increase the distance between the notes by a half step. The interval from B flat to B is called an augmented unison.
• Octaves: When you have notes with an interval quantity of eight lines and spaces, you have an octave. A perfect octave is a lot like a perfect unison in that the same note is being played.
• Fourths: Fourths are pairs of notes separated by four lines and spaces. All fourths on the white keys of a piano are perfect in quality, containing five half steps between notes-except for the fourth from F natural to B natural, which contains six half steps (making it an augmented fourth). If the natural fourth is perfect, adding the same accidental to both notes doesn't change the interval's quality.
• Fifths: Fifths are pairs of notes separated by five lines and space. Fifths are pretty easy to recognize in notation, because they're two notes that are exactly two lines or two spaces apart. All fifths on the white keys of the piano are perfect fifths, meaning that the interval contains seven half steps. However, the interval between B to F is a diminished fifth, which turns out to have the same sound as an augmented fourth. Only six half steps occur between those two notes whether you're going from F natural to B natural or B natural to F natural.

Recognizing Seconds, Thirds, Sixths, and Sevenths

• They all share the characteristic of using the terms major, minor, augmented, and diminished to identify their quality.
• A major interval made smaller by one half step becomes minor, whereas a major interval made larger by one half step becomes augmented. A minor interval made larger by one half step becomes major, and a minor interval made smaller by one half step becomes diminished.
• Seconds: If one half step exists between seconds, the interval is a minor second (m2). If two half steps exist between seconds, the interval is a major second (M2). An augmented second (A2) is one half step larger than a major second. A diminished second is an enharmonic equivalent of a perfect unison. An enharmonic means that you're playing the same two notes, but the notation for pair is different.
• Thirds: If a third contains four half steps, it's called a major third (M3). Major thirds occur from C to E, F to A, and G to B. If a third contains three half steps, it's called a minor third (m3). Minor thirds occur from D to F, E to G, A to C, and B to D. An augmented third (A3) is a half step larger than a major third, with five half steps between notes. An augmented third is also the enharmonic equivalent of a perfect fourth-they're the same note, but the notation is different.
• Sixths and sevenths: The notes in a sixth are always separated by either two lines and space or two spaces and a line. Sevenths always consist of a pair of notes separated by either three lines or three spaces.

Building Intervals

• The first step in building any interval when creating a piece of music is to create the desired quantity, or number size, above or below a given note. Then you determine the quality.
• Determining quantity: is easy, especially on paper. For, say, a unison interval, just pick a note. Then right next to the first note, put another one exactly like it. Want to make your interval an octave? Put the second note exactly seven lines and spaces above or below the first, making for a total interval quantity of eight lines and spaces. How about a fourth? Put the second note three spaces and liens above or below the first note, making for a total interval quantity of four lines and spaces.
• Establishing the quality: The second step to building an interval is to decide what the quality of the interval will be. (examples in P119).

Showing Major and Perfect Intervals in the C Major Scale

• A scale is really nothing more than a specific succesion of intervals, starting from the first note of the scale. Getting comfrotable with intervals and their qualities is the first step to mastering scales and chords.
• Example: intervals in the C Major Scale

Note	Interval from Tonic	Note Name
First note (tonic)	Perfect unison	C
Second note	Major 2nd (M2)	D
Third note	Major 3rd (M3)	E
Fourth note	Perfect 4th (P4)	F
Fifth note	Perfect 5th (P5)	G
Sixth note	Major 6th (M6)	A
Seventh note	Major 7th (M7)	B
Eighth note	Perfect octave (P8)	C

• In the major scale, only major and perfect intervals occur above the tonic note. Knowing this can make identifying the qualities of intervals much easier. If the top note of an interval is in the major scale of the bottom note, it must be major (if it's a second, third, sixth, or seventh) or perfect (it's a unison, fourth, fifth, or octave).

Checking Out Compound Intervals

• What distinguishes a compound interval from other intervals is that a compound interval is not confined to one octave the way a simple interval is. A compound interval can be spread out over several octaves, although the notes of the chords most often just come from two neighboring octaves.
• Creating a compound interval, you have two options:
  • Count the interval between notes by half steps, as with the tenth discussed before.
  • Take your compound interval, put both notes in the same octave, figure out the number size of that interval, and then add seven to the number size of the resulting interval.

The Nashville Number System

• One of the great thigns about mastering all the musical scales is that it makes it so much easier to play with other musicians. Most session and studio musicians use a system called the Nashville Number System, which is designed both to make playing with other musicians easier as well as to make transposing music to a new key almost effortless.
• In the NNS, all the chords in a key signature are reffered to in their diatonic number in a scale instead of their formal letter name.

Section 10: Chord Building

• A chord is simply three or more notes played together or, in the case of arpeggiated (琶音) chords, one after another. Most people don't appreciate a properly played chord until they hear the way "wrong" notes sound against each other. In most Western music, chords are constructed from consecutive intervals of a third-that is, each note in a chord is a third apart from the one before and/or after it.

Creatubg Triads with Three Pitches

• Triads(三和弦), which consist of any three pitches from the same scale, are the most common type of chord used in music. Here are the different types of triads you'll likely work with:
  • Major
  • Minor
  • Augmented
  • Diminished
• The term triad refers to chords that contain three different pitches and are built of thirds. The bottom note of a traid is called the root; many beginning music students are taught to think of a triad as being a tree, with the root of a triad being its, well, root. Chords carry the letter name of the root note, as in the root of a C chord.
• The second note of a triad is the third. The third of a chord is referred to as such because it's a third interval away from the root of the chord. The third of a chord is especially important in constructing chords, because it's the quality of the third that determines whether you're dealign with a major or minor chord.
• The last note of a triad is the fifth. This note is referred to as a fifth because it's a fifth from the root.
• The following sections walk you through building a variety of different triads: major, minor, augmented and diminished.

Building Triads by Counting Half Steps
Major =	Root position + 4 half steps + 3 half steps (7 half steps above root)
Minor =	Root position + 3 half steps + 4 half steps (7 half steps above root)
Augmented =	Root position + 4 half steps + 4 half steps (8 half steps above root)
Diminshed =	Root position + 3 half steps + 3 half steps (6 half steps above root)
Buding Triads with Major Scale Degrees
Major =	1,3,5
Minor =	1,f3,5
Augmented =	1,3,s5
Diminished =	1,f3,f5

• Major triads: Because they're made of intervals, triads are affected by interval quality. The quantities of the notes that make up the triad are intervals of root, third, and fifth, but it's the interval quality of each note that changes the voicing of the triad. A major triad contains a root, a major third above the root, and a perfect fifth above the root.
• Half-step counting method: you can count out the half steps between notes to build a major triad using the formula in the table. But it looks trickier whenyou move away from C.
• First, major third, and fifth method: the second way to construct major triads is to simply take the first, third and fifth notes from a major scale.
• Minor triads: A minor triad is made up of a root, a minor third above the root, and a perfect fifth above the root. As with major triads, you can build minor triads two different ways.
• Augmented triads: Augmented triads are major triads that have had the fifth raised a half step, creating a slightly dissonant sound.
• Diminished triads: Diminished triads are minor triads that have had the fifth lowered a half step.

Expanding to Seventh Chords

• When you add another third above the fifth of a triad, you now have a seventh chord. Seventh chord got their name because the last third interval is a seventh interval above the root.
• Several kinds of seventh chords exist. The six most commonly used seventh chords are as follows:
  • Major sevenths
  • Minor sevenths
  • Dominant sevenths
  • Minor 7 flat 5 chords (also sometimes called half-diminished)
  • Diminished sevenths
  • Minor-major sevenths
• The following sections walk through building a variety of different sevenths:

Building Sevenths by Counting Half Steps
Major =	Root position + 4 half steps + 3 half steps + 4 half steps (11 half steps above root)
Minor =	Root position + 3 half steps + 4 half steps + 3 half steps (10 half steps above root)
Dominant =	Root + 4 half steps + 3 half steps + 3 half steps (10 half steps above root)
Minor 7 flat 5 =	Root + 3 half steps + 3 half steps + 4 half steps (10 half steps above root)
Diminshed =	Root position + 3 half steps + 3 half steps + 3 half steps (9 half steps above root)
Minor-major =	Root + 3 half steps + 4 half steps + half steps (11 half steps above root)
Buding Sevenths with Major Scale Degrees
Major =	1,3,5,7
Minor =	1,f3,5,f7
Dominant =	1,3,5,f7
Minor 7 flat 5 =	1,f3,f5,f7
Diminished =	1,f3,f5,ff7
Minor-major =	1,f3,5,7

• Major sevenths (M7): A major seventh chord consists of a major triad with a major seventh added above the root.
• Minor sevenths (m7): A minor seventh chord consists of a minor triad with a minor seventh added above the root. To build a minor seventh using major scale degrees, you pick the first, flatted third, fifth, and flatted seventh degrees from the scale.
• Dominant sevenths (7 or dom7): A dominant seventh chord, sometimes called a major-minor seventh chord, consists of a major triad with a minor seventh added above the root.
• Minor 7 flat 5 chords (mi7(b5)): A minor 7 flat 5 chord (or half-diminished seventh) is a diminshed triad with a minor seventh added above the root. To build a minor 7 flat 5 chord using major scale degrees, you pick the first, flatted third, flatted fifth, and flatted seventh degrees from the scale.
• Diminished sevenths(dim7): The diminished seventh chord is a stack of three consecutive minor thirds. A diminished seventh is a diminished triad with a diminished seventh from the root tacked onto it. To build a diminished seventh using major scale degrees, you pick the first, flatted third, flatted fifth, and double-flatted seventh degress from the scale.
• Minor-major sevenths: The first part of the name telss the triad is a minor chord and the second part of the name tells you that the second part of the chord is a major seventh above the root. To build a minor-major seventh using major scale degrees, you pick the first, flatted third, fifth, and seventh degrees from the scale.

Manipulating Triads through Voicing and Inversion

• When is a triad not a perfect little stack of thirds built on top of a root? Ans: When its voicing is open, or when it's inverted. Voicing, or spacing as it's referred to in some classical circles, simply refers to the way a chord is arranged.
• Open and close voicing: Sometimes, the notes of a triad are spread out over two or more octaves, with the different parts rearranged so that, for example, the root may carry the highest-sounding note, or the third, or the fifth can carry the lowest-sounding note. When all the notes of a chord are in the same octave, the chord is considered to be in a close voicing. Open voicing means the notes in the chord aren't all located in the same octave. Chords are still considered to be in the root position when root note is still the lowest note of the triad.
• Identifying inverted chords: if the lowest-sounding pitch of a chord is not the root, the chord is considered to be inverted. Here are the possible inversions of a triad:
  • First inversion: If the third of a chord is the lowest-sounding note, the chord is in first inversion.
  • Second inversion: when the fifth of a chord is the lowest-sound note, the chord is in second inversion.
  • Third inversion: when the seventh of a chord is the lowest-soudn note, that chord is in third inversion.
• So how do you identify inverted chords? Simple: They aren't arranged in stacks of thirds. To find out which chord it is, you have to rearrange the chord into thirds again. Only one way exists to rearrange a chord into thirds, so you don't have to guess on the order of the notes.

Exploring Extended Chords

• Ninth chords:stack five thirds on top of one another.
• Eleventh chord: stack of six thirds.
• Thirteenth chords: stack of seven thirds.

Section 11: Chord Progressions

Reviewing Diatonic Chords

• In Western music, the key signature tells you which notes can be used in that piece. Therefore, if you have a song written in C major, the only seven notes that can appear in the song are C,D,E,F,G,A, and B (with the odd sharp or flat thrown in as rare exceptions allowed by accidentals).
• Chords built on the seven notes of a major key signature are called diatonic chords. Chords that are built on notes outside the key signature are called chromatic chords.
• Minor keys get a little trickier because nine notes can potentially fit under a single minor key signature when you consider the melodic and harmonic minor scales. The easiest way to think about chords built on minor keys is to recognize that each key signature has just one minor scale. One facet of minor keys is the flexible nature of the 6th and 7th degrees of the scale.

Identifying and Naming Chord Progression

• Triads strung together to form a succession of chords are called progressions. Chord progressions make up pretty much all of Western harmonic music.
• When breaking down a piece of music based on chord progressions, roman numerals represent the different scale degrees. Capitalized roman numerals represent the chords with a major third, and lowercased roman numerals represent the minor chords. Other special characters indicate whether the chord is diminished (o) or augmneted (+).
• Because the name of a chord comes from its root note, it's only natural that the root of each chord located within a scale would also carry the scale degree with its name. In other words, a chord's name tells you what the chord is, based on the root note, whereas a chord's number tells you what the chord does, based on key.

Common Major Key Chord Progressions

Chord	Leads To
I	Can appear anywhere and lead anywhere
ii	i,V, or vii^o chords
iii	i,IV, or vi chords
IV	I,ii,V,or vii^o chords
V	I or vi chords
vi	I,ii,iii,IV, or V chords
vii^o	I chord

• When dealing with minor keys, the construction of triads is unfortunately a lot more involved than it is with the major keys. The 6th and 7th degrees of the scale are variable, depending on whether the music uses notes from the natural minor, harmonic minor, melodic minor. So for nearly all minor triads, more possibilities for building chords exist in the 6th and 7th degrees than they do in the major scale.

Common Minor Key Chord Progressions

Chord	Leads To
i chords	Can appear anywhere and lead anywhere
ii^o (ii) chords	i,V (v), or vii^o (VII) chords
III (III+) chords	i,iv (IV), VI (#vi^o), or vii^o (VI) chords
iv (IV) chords	i, V (v), or vii^o (VII) chords
V (v) chords	I or VI (#vi^o) chords
VI (#vi^o) chords	i,III(III+), iv (IV), V (v), or vii^o (VII) chords
vii^o (VII) chords	i chord