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------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
Music and Engineering:
Review of the Western Music system for Engineers
Tim Hoerning
Fall 2008
(last modified 9/01/08)
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quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
Outline
•<= /span>Twelve Tones of Equal Temperament
•<= /span>Clefs
•<= /span>The Staff
•<= /span>Pitch & Rhythm
•<= /span>Notes & Rests
•<= /span>Measure & Rhythm
•<= /span>Intervals
•<= /span>Scales
–<= /span>Major
–<= /span>Minor
•<= /span>Chords
–<= /span>Major
–<= /span>Minor
–<= /span>7th
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Twelve= Tones of Equal Temperament
•<= /span>In the modern western Equal Tempered system of musical notation there are 7 letters that are used= to represent the notes
•<= /span>In between some of the letters are enharmonics.= 3;
–<= /span>These are indicated with a sharp (    ) or flat (    ) sign next to the note letter
–<= /span>Each enharmonic has two names.  The key signature <= span style=3D'position:absolute;top:91.25%;left:18.35%;width:75.84%;height:4.5%= '>determines which name is used.
C
D
E
F
G
A
B
C
D
F
G
A
D
= = = = = = = = = =
E
G
A
B
C
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Twelve= Tones of Equal Temperament
•<= /span>The distance between any two adjacent notes is a half step.   Two half steps make a whole= step
•<= /span>The same notes names are reused for each octave in the musical scale
C
D
E
F
G
A
B
C
D
F
G
A
D
= = = = = = = = = =
E
G
A
B
C
Half step
Whole step
Half step
Half step
Whole step
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Clefs
•<= /span>Western music uses a notation of special character= s called notes written on a set of lines called the staff.
•<= /span>There are multiple mappings of note names to lines= .
–<= /span>Treble Clef (shown above in stylized form at upper= left) is used for high freq= uency instruments.  Middle C (~261 = Hz) is located below the lines of the treble clef staff
–<= /span>Bass clef (shown below in stylized form at left) i= s used for low frequency instruments.<= span style=3D'mso-spacerun:yes'>  Middle C is located above the lines of the bass clef staff =
–<= /span>There is another clef, called C clef which will lo= cate Middle C on any one of the 5 lines of the staff.   This is less common and typically only used for certain instruments that would otherwise live between the = staffs (such as trombones and certain = vocal parts)
•<= /span>For notes above or below any given staff, ledger l= ines are used to indicate their height relative to the = staff
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Staff
C
F
A
C
E
E
G
B
D
F
A
C
E
G
G
B
D
F
A
•<= /span>The full staff above shows the locations of notes = around the note known as middle C
•<= /span>The clefs have other mnemonic names
–<= /span>The treble clef is called the G clef since the bot= tom loop circles the line for G
–<= /span>The bass clef is called the F clef since the two d= ots are around the line for F
•<= /span>There are other mnemonics for remembering the line notes
–<= /span>Every Good Boy Deserves Fudge
–<= /span>Good Boys Do Fine Always
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Notes
•<= /span>Whole notes indicate that the tone should be playe= d for the whole measure (4 b= eats in common time). 
–<= /span>The whole note is drawn as an oval.
•<= /span>Half notes indicate that the tone should be played= for half of the duration of a whol= e note (2 beats in common time).  &#= 13;
–<= /span>The half note is basically a whole note with a ver= tical line.
•<= /span>Half notes indicate that the tone should be played= for one quarter of the dur= ation of a whole note (1 beat in common time).
–<= /span>The quarter note is a half note with the center fi= lled in.
•<= /span>Eight notes indicate that the tone should be playe= d for one eighth of the durat= ion of a whole note (1/2 beat in common time)
–<= /span>The eight note is like a quarter note with a flag = on top. 
–<= /span>When an eighth note is by itself, the flag is wavy= .  When there are multiple eight notes, the flags are bridged together
•<= /span>Similarly there are 16th and = 32nd= notes that scale their durations as expected
–<= /span>For each division by 2 in duration, an extra flag = is added.
–<= /span>The same rules for bridging flags apply
–<= /span>Flags between 8ths, 16th and = 32nd=  note= s can be bridged as well.
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Notes (cont)
•<= /span>These notes work well, but what if you need someth= ing ¾ of a whole note?
•<= /span>The dotted note extends the duration of the note by 50%.
–<= /span>A dotted half note is 3 beats
–<= /span>A dotted quarter note is 1.5 beats
Besides dots, it is also possible to “tie= 221; notes together.
–<= /span>The diagram at the left indicates that the note sh= ould be held for 2.5 beats
This gives multiple ways of presenting the same no= te duration
•<= /span>A dotted half note is the same duration as a half = note tied to a quarter note&#= 13;
•<= /span>A dotted quarter note is the same duration as a qu= arter note tied to an eighth note
•<= /span>Ties are only for notes of the same pitch.  If the notes under the = curved line are different pitches, it is called a slur.
How a slur is implemented physically depends on the instrument.
•<= /span>With a wind or brass instrument, a slur can be pla= yed when a musician change= s the keys being played without “tongueing” the note
•<= /span>On a string instrument, a slur can be executed by a hammer-on or pull-off.  Basically moving the “fretting” hand while not plucking or bowing with the other hand.
=  
=  
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Rests
•<= /span>Rests are used to indicate that the musician shouldn’t play anythi= ng.
•<= /span>A Whole Rest looks like a small filled in box hang= ing below a line in the middle of the staff.  It has = the same duration as a whole note.
•<= /span>A Half Rest looks like a small filled in box resti= ng on a line in the middle = of the staff.  It has the same durat= ion as a half note.
•<= /span>A Quarter Rest looks kind of like a seagull flying sideways.  It has the same duration as a quarter note.
•<= /span>An Eighth Rest looks like a slash with a ball on top.  It has the same duration as an eighth note.
•<= /span>The division can be further divided by 2 by adding= extra balls to the rest.
•<= /span>All the same rules of dotting and tieing that appl= y to notes also apply to rests.
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file:///C:/11A15E56/music_review_v16_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
Time Signature
or Meter
•<= /span>Besides pitch and duration of individual notes, th= ere is also rhythmic organization in the music
•<= /span>In music, most songs are broken down into <= /span>measures. 
•<= /span>The rhythm of the piece is indicated by the “= ;time signature”
•<= /span>The time signature is generally represented by two= numbers, one above another, right after the clef a= t the beginning of a musical piece
–<= /span>The lower number tells you how which note “g= ets one beat”
–<= /span>The upper number tells you how many notes are in a= measure.
4
4
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Common Time Signatures
•<= /span>Of all the time signatures, 4/4 is probably the mo= st common in the modern era.  Most rock songs are in 4/4
•<= /span>It is so common, it has been called “common time” and a symbol is often used to represent it.
•<= /span>A common variation of 4/4 is 2/2 or “cut time” This also has a special symbol that looks like the common time symbol with a line through it.
•<= /span>Other common times include 2/4, ¾ and 6/8 &= #13;
–<= /span>6/8 is actually a Compound Time Signature.  In component Time <= span style=3D'position:absolute;top:73.25%;left:18.35%;width:75.84%;height:4.0%= '>Signatures, each beat is divided into three equal parts.
–<= /span>The previous time signatures are considered Simple= Time Signatures, where the beat is divided into two parts
•<= /span>Other time signatures (called complex time signatu= res) are sometimes used in = more “progressive” music (7/8, 5/8, etc)
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Some Ti= me Signature Examples
Them Bones (verse) – Alice in Chains
Compl= ex
Progr= essive
7/8
̶= 0;Money” (except break)– Pink Floyd
Limel= ight - Rush
Compl= ex
Progr= essive
7/4
̶= 0;Take Five” – Dave Brubeck
Compl= ex
Progr= essive
5/4
Compo= und
Compo= und
Simpl= e
Simpl= e
Simpl= e
Type
Fligh= t of the Valkries - Wagner
Slip = Jigs
9/8 <= /span>
Manic Depression - Hendrix
Certain types of jigs
6/8
Polkas or Marches
2/4
Waltz= es
&frac= 34;
Any r= ock song
4/4
Examples
Description
Meter
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Other Notation
•<= /span>Measures are divided by a simple vertical line.= 3;
•<= /span>Measures that are to be played multiple times are = surrounded by repeat signs
•<= /span>The tempo is given at the beginning of the song (o= r at each temp change) in Beats Per Minute <= /span>
•<= /span>Dynamic markings are given below the scale and range from pianissimo (quietest) to fortissimo (loudest)
<= span style=3D'font-size:367%'> 
<= span style=3D'font-size:367%'> 
<= span style=3D'font-size:367%'> 
<= span style=3D'font-size:367%'> 
4
4
104 bpm
ppp        = ;   fff
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Accidentals
Notes can be specified as their natural values, or as modified with accidental notation
•<= /span>There are three common accidental markings = and 2 double markings
Flat – (       ) m= eans drop the pitch from the letter value by one half step
Sharp – (       ) indicates the raise the pitch by one half step
–<= /span>Natural – (       ) c= ancels a previous sharp or flat sign.
–<= /span>There are also double flat and double sharp which = indicate alteration of the tone by a whole step= 3;
•<= /span>Any accidental only lasts for the duration of the = measure. &nb= sp; If a sharp is to be applied to only one note out of a series, a natural must be used to cancel it.
= =
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Interv= als
The distance between notes is referred to as an interval
The intervals are typically taken from the note order in the major scale. 
The 2nd 3rd 6th=  and = 7th=  are = = called major intervals
The 1st 4th 5th=  and = octave are called perfect
C
Octave=
12
B
Major = 7th
11
A
Major = 6th
9
G
Perfec= t 5th
7
F
Perfec= t 4th
5
E
Major = 3rd
4
D
Major = 2nd
2
C
Union<= /span>
0
Note in C major<= /div>
Name
Number of half steps
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Interv= als
If flattened by one half step
The 2nd 3rd 6th and 7th are called minor
The 4th and 5th are called diminished
= 226;If raised by one half step
The 4th and 5th are called augmented
C
Octave=
12
B
Minor = 7th
10
A
Minor = 6th=
8
G
Diminished 5th=  (Tri= -tone)
6
F
Diminished 4th<= /div>
4
E
Minor = 3rd
3
D
Minor = 2nd
1
C
Union<= /span>
0
Note in C major<= /div>
Name
Number of half steps
= <= ![endif]> = <= ![endif]> = <= ![endif]>
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Key signatures
Sometimes a note is supposed to always be played <= /span>as sharp or flat
•<= /span>These modifications are shown in the key signatures.  These are shown as flats or sharps at the beginnin= g of the piece or key change.
•<= /span>There are only 15 given key signatures =
–<= /span>No key signature combines sharps and flats
There is a fixed order in which sharps or flats ca= n be added.
•<= /span>Accidentals (such as the natural) can be used to <= /span>temporarily over ride the key signature within a <= /span>measure.
•<= /span>The key of no sharps or flats is the key of C
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Flat key signatures
•<= /span>The first flat major key is called F
All subsequent major keys are named after <= /span>the next to last flat added
F
B
= = = = = = =
E
= = = = = =
A
<= ![endif]>
D
=
G
=
C
= = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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R0lGODlhFAAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAQ ACgAgAAAAAAAAAJRTICpauvZnouSnWpx1ohqj4GVKJGPOV0curDbqn5xB8yUgefdlffN7wvqdkJQ cUYEjnwlHYn57NWQU9wuZb1astqk5zbcSFNVU3D5C7kgHEQBADs= ------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
Sharp key signatures
•<= /span>Sharp major keys are named after the note just above the last sharp in the key signature
G
D
A
E
B
F
C
= = = = = = = =
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Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
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Circle of Fifths (major keys)
The circl= e of fifths gives a convenient = method of remembering the relation of the ke= ys
Increasing
Sharps
Increasing
Flats
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Relative Minors
= 226;Thus far we’ve considered keys based on their Major scale names
= 226;Each major scale also has a Relative Minor key
R= 11;These have the same number of sharps or flats as their relative major, but are named after the 6th note in the major scale
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Circle of Fifths (minor keys)
The minor circle is the major circle <= /span>rotated to the left by 90 degrees (3 positions)
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Scales
= 226;Scales are series of musical notes strung together.
&#= 8226;Some Scales don’t belong to a key
There is Chromatic scale is the simply all of the 12 notes in a row. = ;
= 211;There are two whole tone scales which have a whole tone between intervals
&#= 8226;One beginning on C and another C
=
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Diatonic Scales
•<= /span>Most scales belong to notes within a key
•<= /span>The tetra chord is actually a simple 4 note scale.=
–<= /span>It is specified completely by the intervals whole = step, whole step, half step.&#= 13;
•<= /span>In the major key of F, this translates to F G A B&= #13;
•<= /span>In the major key of C this translates to C D E F&#= 13;
•<= /span>In the major key of G, this translates to G A B C&= #13;
•<= /span>In the major key of D, this translates to D E F G
The major scale is simply two tetra chords separat= ed by a whole step. (interval pattern: whole whole ha= lf whole whole whole half)
•<= /span>In the major key of F, this translates to F G A B<= span style=3D'mso-spacerun:yes'>   C D E F <= /div>
•<= /span>In the major key of C this translates to C D E F G= A B C
•<= /span>In the major key of G, this translates to G A B C = D E F G
•<= /span>In the major key of D, this translates to D E F G A B C D
•<= /span>Notice that the major scale is the first tetra cho= rd of the key and the first tetra chord of next key to t= he right on the circle of fifths
= =
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Diatonic Scales (cont)
The natural minor scale is the same pattern as the= major scale, but rotated to start on the relative = minor (the 6th position). (interval pattern: whol= e half whole whole whole half whole)
•<= /span>In the minor key of Dm, this translates to D E F G= A B   C D
•<= /span>In the minor key of Am this translates to A B C D = E F G A
•<= /span>In the minor key of Em, this translates to E F G A B C D E
•<= /span>In the minor key of Bm, this translates to B C D E F G A
•<= /span>In addition to the Natural Minor Scale, there are = two other minor scales
–<= /span>Harmonic Minor (natural minor with a raised 7th= )
•<= /span>In the minor key of Dm, this translates to D E F G= A B   C D
•<= /span>In the minor key of Am this translates to A B C D = E F G A
•<= /span>In the minor key of Em, this translates to E F G A B C D E
•<= /span>In the minor key of Bm, this translates to B C D E F G A
–<= /span>Melodic Minor (natural minor with a raised 6th=  &= ; 7th=  when= = ascending and natural 6th and = 7th=  when descending)
<= ![endif]>
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Modes
•<= /span>In addition to the Major and Minor scales there are other scales that have o= ther flavors
•<= /span>These are called the Modes and are based around the intervals of the major = scale, but starting on different root notes
–<= /span>Ionian – starting on 1st=  note= (same as major scale)
C D E F G A B C
No sharps or flats relative to the major scale wit= h the same tonic
–<= /span>Dorian – starting on 2nd=  note=
D E F G A B C D
Flat third and flat sixth relative to the major sc= ale with the same tonic
–<= /span>Phrygian – starting on 3rd=  note=
E F G A B C D
•<= /span>Flat second, flat third and flat sixth and flat se= venth relative to the major scale with the same tonic
–<= /span>Lydian – starting on 4th=  note=
F G A B C D E F
Augmented fifth relative to the major scale with t= he same tonic
–<= /span>Mixolydian – start on 5th=  note=
G A B C D E F G
Flat 7th relative to the major scale with the same tonic
–<= /span>Aeolian – start of 6th note= (same as natural minor scale)
A B C D E F G A
•<= /span>Flat second, flat third and and flat seventh relat= ive to the major scale with the same tonic
–<= /span>Locrian – start of 7th note=
B C D E F G A B
•<= /span>Flat second, flat third, diminished fifth, flat si= xth and flat seventh relative to the major scale with the same tonic
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Chords
Scales are a group of notes played in sequence, a = Chord is a group of notes played simultaneously.  (a chord can also be played in sequence, which is cal= led an arpeggio)
•<= /span>The simplest chord has two notes: the Diad.
–<= /span>The Root and 5th  pla= yed together is called the Power Chord and is the most common 2 note chord. 
•<= /span>Many musicians are famous for their use of the pow= er chord (Link Wray, Black Sabbath, SLAYER!)
•<= /span>It is a good chord for very distorted guitar becau= se there are fewer notes to int= eract in the non linear distortion product generator.
–<= /span>Other diads are often played by string players suc= h as the fourth (inverted f= ifth), major and minor 3rds.
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Triads
•<= /span>After Diads, the next set of more complex chords i= s Triads (or three note chords)
•<= /span>The most common combination of notes is the Major = Triad.  This is formed from the 1st, 3<= /span>rd=  and = 5th=  note= s of the major scale
•<= /span>In the major key of F, this translates to F A C= 3;
•<= /span>In the major key of C this translates to C E G = ;
•<= /span>In the major key of G, this translates to G B D= 3;
•<= /span>In the major key of D, this translates to D F A
The next most common chord is the Minor chord.  This is formed from the 1st, 3rd and 5th note= s of the minor scale =
•<= /span>In the major key of F, this translates to F A   C
•<= /span>In the major key of C this translates to C E   G
•<= /span>In the major key of G, this translates to G B   D
•<= /span>In the major key of D, this translates to D F A= 3;
= <= ![endif]> =
------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0039_image240.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBgAMAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgAAAAAAAAAIMDI5ombbhwFuyTlQAADs= ------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0039_image241.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBQALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAF AAoAgAAAAAAAAAIMDI5ombbgIHwhUlQAADs= ------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0039_image242.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBQALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAF AAsAgAAAAAAAAAIMhB2ny5CJnAyQvmYKADs= ------=_NextPart_01C90D43.72CBF970 Content-Location: file:///C:/11A15E56/music_review_v16_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Music and Engineering: Amplifier and Vacuum Tube basics
•<= /span>Another type of chords are called suspended.  In these chords, the third is suspended and replaced = by it’s neighbor (the 2nd or t= he 4th= )
•<= /span>The suspended second chord is formed from the 1st= , 2nd=   and= 5th=  note= s of the major scale
•<= /span>In the major key of F, this translates to F G C= 3;
•<= /span>In the major key of C this translates to C D G = ;
•<= /span>In the major key of G, this translates to G B D= 3;
•<= /span>In the major key of D, this translates to D E A= 3;
•<= /span>The suspended fourth chord is formed from the 1st= , 4th=   and= 5th=  note= s of the minor scale
•<= /span>In the major key of F, this translates to F B   C
•<= /span>In the major key of C this translates to C F G = ;
•<= /span>In the major key of G, this translates to G C D= 3;
•<= /span>In the major key of D, this translates to D G A= 3;
Suspended Chords
<= ![endif]>
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7th Chords
•<= /span>After Triads, the next group of chords includes fo= ur notes.
•<= /span>The most commonly used chords are the 7th=  chor= ds.  Named because they include the major or minor tria= d plus a 7th from the scale <= /div>
•<= /span>The Dominant 7th chor= d is formed from the 1st, 3<= /span>rd=  and 5th   and flattened 7th notes of = the major scale
•<= /span>In the major key of F, this translates to F A C E&= #13;
•<= /span>In the major key of C this translates to C E G B&#= 13;
•<= /span>In the major key of G, this translates to G B D F&= #13;
•<= /span>In the major key of D, this translates to D F A C
•<= /span>The minor 7th is formed from the 1st= , 3rd and 5th note= s of the minor scale
•<= /span>In the major key of F, this translates to F A   C E
•<= /span>In the major key of C this translates to C E   G B
•<= /span>In the major key of G, this translates to G B   D F
•<= /span>In the major key of D, this translates to D F A C&= #13;
= = <= ![endif]> <= ![endif]> = <= ![endif]> <= ![endif]>
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Other Chords
•<= /span>The previous few slides showed just some of the basic chords.
There are many other chords that can be created by
–<= /span>Altering the degree of a note in the triad
Diminished triads (1 flat 3rd=  , di= m 5th= )
Augmented triads (1 3 aug 5th=  )= 3;
–<= /span>Adding 9ths or 11ths (or various other intervals)&= #13;
–<= /span>Adding a defined bass note.
–<= /span>A countably infinite number of other combinations.=
•<= /span>A chord inversion is when the tonic is not the lowest note in the chord.
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Chords and Keys
•= It is possible to create chords = only from the key signature
•= These are called diatonic chords
To figure out what type of chord starts on a given note,start with the interval as a root, then find the other parts of the chord and compare them to the major key that would start with that note =
–= For instance, in the key of C, the triad beginning with D would be D F A.&n= bsp; Comparing that = to D major shows that it is a minor triad (the third is flat)
•= The chart at right shows the chords from a major key.
–= Also included are diminished chords on the 7th of t= he major scale.
–= Diminished chords are like minor chords with a diminished 5th
Bdim, B dim7=
dim 7t= h
min
7
A, Am7<= /span>
min 7t= h
min
6
G, G7
dom 7t= h
maj
5
F, Fmaj= 7
Maj 7t= h
maj
4
Em,Em7<= /span>
Min 7t= h
min
3
Dm, Dm7
min 7t= h
min
2
C, Cmaj7
maj 7t= h
maj
1
In the key of C
Seventh
Triad
Interval
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