http://library.thinkquest.org/15413/theory/theory.htm

 BEST FOR: explanations of Intervals, Triads and Inversions of both


INVERSIONS OF INTERVALS     Intervals can be inverted, which basically means you turn them upside down. The lower note is raised up an octave so that the top note/bottom note relationship is reversed. The chart below shows the inversions of intervals.

Qualities Major becomes Minor Minor becomes Major Perfect remains Perfect Augmented becomes Diminished Diminished becomes Augmented

Size 2 becomes 7 3 becomes 6 4 becomes 5 5 becomes 4 6 becomes 3 7 becomes 2

Interval Identification
     It is important to be able to hear and identify intervals. This is a very important thing for musicians to do. Here is a list of familiar songs that will help you to identify the intervals.

m2- Stormy Weather	m2
M2- Happy Birthday	M2
m3- The Impossible Dream	m3
So Long, Farewell from The Sound of Music
M3- Halls of Montezuma	M3
P4- Here comes the bride	P4
A4- Maria from West Side Story	A4
P5- Star Wars	P5
Twinkle, Twinkle, Little Star
M6- NBC theme music	M6
m7- Somewhere from West Side Story	m7
M7- Bali Hai from South Pacific	M7
Octave- Over the rainbow	Oct.

Triads and Chords

David Loberg Code, Western Michigan University

Chords are collections of 3 or more pitches sounding at the same time.  They are usually used to accompany a melody.  If the notes of a chord are played separately (one after another) it is called an arpeggio (or broken chord).   A triad is a special type of chord made of three notes: a root, third, and fifth.  You can form a basic triad from three consecutive lines or spaces on a staff (i.e., stacking 3 doughnuts or a triple scoop of ice cream).   Like intervals, triads come in different qualities (flavors).  A major triad is formed by taking the 1^st, 3^rd, and 5^th scale degrees (Do, Mi, and So) of a major scale.  (That is why it is called a major triad.)

                  Spell a G major triad.

                  The G major scale is: G A B C D E F# G

                  G, B, D spells a G major triad.

A minor triad is formed by taking the 1^st, 3^rd, and 5^th scale degrees of a minor scale (Do, May, and So).

                  Spell a C minor triad.

                  The C minor scale is: C D Eb F G Ab Bb C

                  C, Eb, G spells a C minor triad.

An augmented triad is like a major triad but with an augmented 5^th.

A diminished triad is like a minor triad but with a diminished 5^th.

Minor Scales and Keys

David Loberg Code, Western Michigan University

Minor scales come in three variants: natural, harmonic, and melodic.  It is probably easiest to compare them with the major scale.

                           1       2       3       4       5       6       7       8

D major               D      E       F#     G       A       B       C#     D

D natural minor     D      E       F       G       A      Bb       C       D

D harmonic minor    D      E       F       G       A      Bb      C#     D

D melodic minor    D      E       F       G       A       B       C#     D   (descend with natural minor C     Bb  A  etc.)

To form the natural minor scale, we can lower scale degrees 3, 6, and 7.  This will change these intervals to a minor 3^rd, minor 6^th, and minor 7^th.  (That is why this is called a minor scale.) 

The harmonic minor scale uses the same leading tone as the major scale (C#), but a minor 3^rd and 6^th.  The melodic minor scale is more unusual because it is different going up then it is going down.  Notice how the 6^th and 7^th scales degrees change from B and C# to Bb and C natural.  Going up, melodic minor is almost the same as major, except for the minor 3^rd.  Going down it is exactly the same as minor.

Minor key signatures are formed from the natural minor form of the scale.  Therefore, the key signature for D minor has only one flat: Bb.  If a piece is using the harmonic or melodic forms of the minor scale, the "extra" accidentals are NOT included in the key signature.  They are written in separately each time they are needed in the music.  It may seem silly, but that is how it is done.   As a result, the order of sharps and flats in minor key signatures is the actually the same as for major keys.

To determine the name of a minor key from the key signature, first find the major key using the tricks for sharps or flats described earlier.  Once you know the major key, go to the 6^th scale degree.  This is the starting note for the relative minor, that is the minor key with the same key signature.  For example:

                  The key signature has 3 sharps (F#-C#-G#).

                  The last sharp is G#, a  minor 2^nd above that is A.

The major key is A major.  The 6^th scale degree of
A major is F#.  The minor key is F# minor.

WARNING: When looking at a piece of music, do not automatically assume that it is in a major key.  The key signature could be for either major or minor.  You need to look for additional clues to determine which one is correct.  What note does the piece start on or end on?  Often, but not always, this will be the tonic (Do).  Are there any "extra" accidentals?  Remember, harmonic and melodic minor will have extra accidentals which are not included in the key signature.

Key Signatures

David Loberg Code, Western Michigan University

Keys come from scales.  People sometimes make the mistake of thinking that keys come from key signatures.  They might say that A major has 3 sharps because of the key signature.  This is backwards.  It is like saying that deer like to cross the road at particular spot because there is a Deer X-ing sign there.  Key signatures are signs.  They help remind us of the key and save us the trouble of writing the same sharps or flats over and over again.  The easiest and best way to determine a key signature is to think of the scale.  When you play a D major scale, you use an F# and a C#, therefore the key signature for D major has 2 sharps (F# and C#).  For uniformity, the sharps or flats in a key signature are always written in the same order (regardless of what order they appear in the scale.)

For example, an A major scale is: A B C# D E F# G# A.  In the key signature, however, the order of the sharps is rearranged: F#, C#, G#. 

The order of sharps is always as follows:

F#              C#              G#             D#            A#              E#              B#    

Fat             Cats            Go              Down       Alleys             Eating         Birds

Father              Charles               Goes                    Down           And                        Ends                 Battle

The order of flats is coincidentally the same sequence but backwards:

Bb              Eb              Ab              Db              Gb              Cb              Fb     

Big              Elephants   Always        Do              Great          Circus         Feats

Battle                  Ends                And                 Down                  Goes                 Charles'             Father

(or) BEAD---------------------------------------------------->                  Glass                 Crystal                Falls

There are other tricks you can use to determine the name of the key from looking at the key signature.  For Major keys, the last sharp in the key signature is always Ti (the seventh scale degree).  To find the key, simply go up a minor second (to Do).  For example:

                  The key signature has 5 sharps (F#-C#-G#-D#-A#).

                  The last sharp will be A# (Alleys)

                  A minor 2^nd (half step) above A# is B.

                  The major key is B major.

For Major key signatures with flats, the second to last flat is always Do. 

                  The key signature has 4 flats (Bb-Eb-Ab-Db).

                  The second to last flat is Ab.

                  The major key is Ab major.

Obviously, these tricks will not work for C major (no sharps or flats), or F major (1 flat).  You will just need to memorize these.  Also, these tricks do not work for minor keys.

INTERVALS

David Loberg Code, Western Michigan University

 The space between any two pitches is called an interval. Whole steps and half steps are two types of intervals.  A whole step can also be called a major 2^nd, and half steps are sometimes called minor 2^nds.   Major simply means BIG; minor means little.  The number 2 (2^nd) comes from counting the number of letters from one note to another.  Bigger intervals can also be identified by their interval count (or size) and quality (major, minor, etc.).  

When counting, always start on 1 (never zero).  For example, the interval count from D to B is a 6^th:

D (1) – E (2) – F (3) – G (4) – A (5) – B (6) 

Instead of counting letter names, you can also count the number of lines and spaces on the staff (still starting with 1).  The answer should be the same.  By the way, a count of 1 is called a unison or a prime, and a count of 8 is called an octave (instead of an 8^th).  Also, when counting, it doesn't matter whether or not there are any sharps or flats.  D# to B is also 6^th; so is D to Bb, or Db to B#, and so on.  The differences between these various kinds of 6^ths is called the interval quality.  You might think of them as different flavors of 6^ths.

As another example, A to C has the same interval count as A to C#: they are both 3^rds.  However A to C# is a BIGGER 3^rd than A to C, so they have different interval qualities.  Not surprisingly, the BIG 3^rd is called a major third and the little 3^rd is called a minor third (just like with major and minor 2^nds).  Unfortunately, there is more than just major and minor.  Other interval qualities include perfect, augmented, and diminished.

Finding the interval count is easy enough, but how do you figure out what the interval quality is supposed to be?  The simplest way is to go back to the major scale.  Taking the intervals from the starting note (Do) to each successive scale degree we get the following intervals:

     From Do to�

           

    Do           Re            Mi            Fa               So            La            Ti             Do 

Perfect 1   Major 2^nd    Major 3^rd    Perfect 4^th    Perfect 5^th Major 6^th   Major 7^th  Perfect 8ve

    

Notice that the second, third, sixth, and seventh are all major intervals.  (That is why it is called a major scale.)  The unison, fourth, fifth, and octave are all perfect.   You can find out why they are these qualities another day, but for now just remember:

         In a major scale 1,4, 5, and 8 are always Perfect

                                    2, 3, 6, and 7 are always Major

(There is NEVER such a thing as a Major 5^th or a Perfect 3^rd.)

So, to figure out the interval between two notes:

1. Pretend that the bottom note is the first note (Do) of a major scale. (Write out the scale if you need to or finger it on your instrument.)

2.  Is the top note already in the scale?  If yes, then you already know what the interval is.  Just count up the number of notes and add the name of the quality (either major or perfect). 

Let's try the interval from G up to E.
The G major scale is: G A B C D E F# G

E is in the scale.  It is the 6^th scale degree.

The 6^th scale degree is always major.

G to E is a Major 6^th.

3. If the exact note is not in the scale, you will need to adjust the interval quality.  If your note is a half step lower than the major interval in the scale, the quality will be minor.  For example:

Let's try the interval from D up to F.
The D major scale is: D E F# G A B C# D

D to F# is a major 3^rd.  F is a half step lower.

D to F is a Minor 3^rd.

For other qualities, use the following adjustment chart starting from either a perfect or major interval:

           Diminished  <  Perfect   <   Augmented

                                      or

Diminished  <   Minor       <  Major     <   Augmented

                  -2 half steps  - half step                              + half step

Let's try the interval from F to B.
The F major scale is: F G A Bb C D E F

F to Bb is a perfect 4th.  B is a half step higher.

F to B is an Augmented 4^th.

4. What if I can't make a major scale using the bottom note?  No problem, you can use the same method of adjusting the quality in reverse.

 Let's try the interval from C# to E.
I don't like C# major, so I'll spell a C major scale instead.

The C major scale is: C D E F G A B C.  C to E is a major 3^rd.  C# to E will shrink the size by a half step. 

C# to E is a minor 3^rd.

SCALES

David Loberg Code, Western Michigan University

The point of music theory is to help you understand how music works, so you can be a better player.  Playing the notes without understanding how or why they are put together is like reading a book by sounding out the words without knowing what they actually mean.

Most of what you need to know about how pitches are put together you can learn straight from the scales you play (or are supposed to play) every day.  A major scale has seven different notes arranged in order like going up or down a set of stairs.  If you repeat the first note when you reach the top there are actually eight notes.  The stairs are a little uneven because they are made up of two different sizes of steps. 

C

       B       B

       A                              A

      G                                                       G

      F                                                                                 F

E                                                                                            E

D                                                                                                                     D

C                                                                                                                                             C

This is why sometimes you need a bigger space between some adjacent notes and other times they are close together.  The big steps are usually called whole steps; and the little ones half steps.  All major scales follow the same pattern of whole and half steps:

    whole          whole          half            whole         whole         whole       half_

 G               A                B       C                D                E                F#     G

 D               E                F#     G                A                B                C#     D

 A               B                C#     D                E                F#              G#     A

etc

Even though your fingerings may change for different major scales, the spacing between notes will always be the same: W-W-H-W-W-W-H

Each step in a scale is called a scale degree.  Scale degrees can be identified by numbers, solfege syllables, or function names:

 1         2          3     4             5         6              7       8

Do       Re        Mi    Fa            So        La            Ti      Do

               Tonic    Supertonic    Mediant  Subdominant   Dominant      Submediant    Leading Tone  Tonic

http://quizlet.com/subject/music-theory/

BEST FOR: People who learn through flash cards!!

Contains pre-made flash card sets for theory topics ranging from scales and key signatures to chords, harmonies and intervals.

http://www.flashcardexchange.com/flashcards/list/616411

BEST FOR: vocabulary

Pre-created flashcards of all AP music theory from the 2008 AP Exam.

http://www.musictheory.net/lessons

TOP WEBSITE!

Has understandable explanations of concepts with awesome, uncomplicated practice exercises.
Utilizes great tools such as a staff paper generator and an online piano.

http://www.emusictheory.com/practice.html

BEST FOR: note identification, intervals, aural skill practice using listening drills
 
Can select options for drills such as which notes or keys to include or focusing on major or minor.
Excellent to improve speed of identifications by telling your average answer time.
Great for instrumentalist too!