Notes for Second Theory Test as of 10-18-18

Notes for 2^nd Theory Test as of 10-18-18

Test Date: October 30, 2018

NOTE: In order to make sense of Minor – Major scale relationships, I have included here on page 1 the review notes on key signatures from the last 6 weeks.

I.                     Order of Sharps when used in a key signature:

a.       F,C,G,D,A,E,B    is the order of sharps.

II.                   Order of Flats when used in a key signature (reverse of the order of sharps):

a.       B,E,A,D,G,C,F   is the order of sharps.

III.                 You will need to know all of your major keys. Remember that when dealing with major keys, if the key signature has no sharps or flats then you are in the key of C Major.

a.       Order of sharps and related keys (major scales):

Key or Scale:       G             D             A             E              B             F#           C#

Order of #s:        F              C             G             D             A             E              B

b.       Order of flats and related keys (major scales):

Key or Scale:       F              Bb           Eb           Ab          Db          Gb          Cb

Order of bs:        B             E              A             D             G             C             F

As you can see from the chart above, If one has 4 sharps in the key signature, the scale or major key is E Major. The sharps in the key signature would be F, C, G, and D.

If one has 3 flats in the key signature, the scale or major key is Eb Major. The flats in the key signature would be B, E, and A.

Relative Minor

Every Major Scale has a Minor Scale that is relative to it. Relative is only a condition that exists between two scales when they share the same key signature. If a major and minor scale have the same key signature, then by definition, they are relative to each other. Relative is NOT a type of minor scale.

The 6^th step of the major scale is where the relative minor scale starts. If we consider the same pitch collection with no altered notes then we have the Natural Minor. An example of this is:

C Major = C, D, E, F, G, A, B, C. The 6^th step (in red) is A. If we use the same pitch collection starting on A we have:  A, B, C, D, E, F, G, A. This is the A Natural Minor scale and it is relative to C Major because they both have the same key signature of no sharps or flats.

It follows that if we are trying to find the relative Major scale when given a Minor scale we would use the 3^rd step of the Minor scale to find the relative Major scale as follows:

A, B, C, D, E, F, G, A is the A Natural Minor. It is related to C Major as we would use the same pitch collection starting on the third scale degree which in this case is C (in red):

C, D, E, F, G, A, B, C.

Three forms of the Minor Scale

1. Natural Minor- This is discussed above. This scale has the exact same pitch collection as its relative Major scale.
2. Harmonic Minor-This is just like the Natural Minor except we raise the 7^th degree of the Minor Scale. Using the Natural Minor scale of A, B, C, D, E, F, G, A, we would raise the 7^th step (in red). Therefore the A Harmonic Minor scale would be: A, B, C, D, E, F, G#, A.
3. Melodic Minor-This is like the Natural Minor, except we raise the 6^th and 7^th degrees while ascending. Descending the Melodic Minor is identical to the Natural Minor. So the A Melodic Minor would be:

A, B, C, D, E, F#, G#, A (ascending)  and A, G, F, E, D, C, B, A (descending).

4. Below is a chart with the Major keys and the Relative minor keys. This means that a Major key and its relative minor key share the same key signature.

MAJOR KEY                                         minor key

C Major                                                A minor

F Major                                                D minor

Bb Major                                             G minor

Eb Major                                              C minor

Ab Major                                             F minor

Db Major                                             Bb minor

Gb Major                                             Eb minor

Cb Major                                             Ab minor

G Major                                               E minor

D Major                                                B minor

A Major                                                F#  minor

E Major                                                C# minor

B Major                                                G# minor

F# Major                                              D# minor

C# Major                                              A# minor

CHROMATIC, WHOLE-TONE, DIMINISHED (aka Octotonic) AND DIMINISHED-WHOLE TONE (aka Super Locrian Mode)  SCALES

Chromatic Scale: A chromatic scale is comprised of the following notes, all ½ step away from one another (enharmonic tones are in red. These are tones that sound the same as the note written in black but are spelled differently):

C (B#),   C# (Db),   D,   D# (Eb),   E (Fb),   F,   F# (Gb),   G,   G# (Ab),   A,   A# (Bb),   B (Cb),   C (B#). 

Whole-Tone Scale. This means that every pitch is a whole step away from the previous pitch.  A whole step is equivalent to two half steps. It has 6 tones before the first one repeats one octave higher.

An example of this would be :  C,  D,  E,  F#,  G#,  Bb ,  C. Notice in the key of C , we have a b5  or #11 (F#) and a #5 or b13 (G#) as altered pitches.

                The whole tone scale is applied against a dominant 7 chord. There for a C7 chord’s whole tone scale would be C,D, E, F#,G#,Bb,C.

Diminished Scale. This scale starts with a half step and alternates back and forth with a whole step. C to Db is a half step and Db to Eb is a whole step.

An example of this would be:   C,  Db,  Eb,  E,  F#,  G,  A, Bb,  C.   Notice in the key of C , we have a b9(Db), a #9 (Eb), and  a b5  or #11 (F#) as altered pitches. This scale would be applied against a dominant 7 chord—in this case a C7 chord.

               Diminished Whole-Tone Scale (not covered yet) : This is a combination of the Diminished and Whole-Tone Scales. The bottom half is derived from the Diminished Scale and the top half from the Whole-Tone Scale.

An example of this would be: C, Db, Eb, E, F#, G#, Bb, C. .   Notice in the key of C , we have a b9(Db), a #9 (Eb),  a b5  or #11 (F#), and a #5 or b13 (G#) as altered pitches. This scale would be applied against a dominant 7 chord—in this case a C7 chord.

TRIADS AND SEVENTH CHORDS

1. Triads (3-Note chord structures)

a.       Major Triad-contains the 1^st, 3^rd, and 5^th steps of a Major Scale. For example a C Major Triad (CM) would have the following notes (C, E, G) since the C Major Scale is : C D E F G AB C.

b.       Minor Triad- contains the 1^st, flatted 3^rd, and 5^th steps of a Major Scale. For example a C Minor Triad (Cm) would have the following notes (C, Eb, G).

c.       Diminished Triad - contains the 1^st, flatted 3^rd, and flatted 5^th steps of a Major Scale. For example a C Diminished Triad (Co)would have the following notes (C, Eb, Gb).

2. Seventh Chords (4-note chord structures)

a.       Major 7^th chord- contains the 1^st, 3^rd, 5^th, and 7^th  steps of a Major Scale. For example a C Major 7^th (CM7) chord would have the following notes (C, E, G, B) since the C Major Scale is : C D E F G AB C.

b.       Minor 7^th chord- contains the 1^st, flatted 3^rd, 5^th, and flatted 7^th  steps of a Major Scale. For example a C Minor 7^th (Cm7) chord would have the following notes (C, Eb, G, Bb).

c.       Dominant 7^th chord- contains the 1^st, 3^rd, 5^th, and flatted 7^th  steps of a Major Scale. For example a C dominant 7^th (C7) chord would have the following notes (C, E, G, Bb.

d.       Half Diminished 7^th chord (also called a “minor seven flat five chord”)- contains the 1^st, flatted 3^rd, flatted 5^th, and flatted  7^th  steps of a Major Scale. For example a C half diminished  7^th (C^ø7 or Cm7(♭5) ) chord would have the following notes (C, Eb, Gb, Bb).

e.       Diminished 7^th chord - contains the 1^st, flatted 3^rd, flatted 5^th, and double flatted  7^th  steps of a Major Scale. For example a C diminished  7^th (C dim. 7th ) chord would have the following notes (C, Eb, Gb, Bbb).

  

Alterations and Extensions

1. Extensions- These are the 9^th, 11^th and 13^ths that are added on to 7^th chords.
2. A  9^th would be the equivalent of the 2^nd degree of a scale. A C Major  9^th (CM9) contains the 1^st, 3^rd, 5^th, 7^th, and 9^th of a major scale and would be constructed using the following notes (C, E, G, B, D) as per the major scale below:

C             D             E              F              G             A             B             C             D

1              2              3              4              5              6              7              8              9

               

The 11^th would be the equivalent of the 4^th , and the 13^th would be the equivalent of the 6^th.  Remember that when playing dominant or major chords that extend above a 9^th (CM11, CM13, C11 or C13), we automatically raise the 11^th scale degree by ½ step to avoid the clash between the 3^rd and the 11^th of the chord.

The CM11 chord would therefore have the following notes: C, E, G, B, D, F#. If we didn’t raise the F we would have the not so good sounding interval between the E (3^rd of the chord) and the F (11^th of the chord).

The 11^th is not raised on a minor 11^th or minor 13^th chord as there is no clash that occurs here between the 3^rd and the 11^th. The notes in a C minor 13^th chord would include C, Eb, G, Bb, D, F, and A.

Altered extensions and Altered fifths:

For the purposes of our study, we will deal with altered notes that only appear with relation to a dominant chord. The one exception to this is the chord that we have already talked about which is the minor 7 (b5) or half-diminished chord.

With respect to a C13 (C, E, G, Bb, D, F#, A) chord we have the several  possibilities for alterations. Remember that we automatically raise the 11^th of any chord that has a regular or major third. In this case the major 3^rd is the “E”. Therefore the “F” must be raised to an F# to avoid the horrible clash that would otherwise occur between the “E” and the “F”. The full list of alterations is as follows:

A (the 13^th) could be lowered one half step to Ab making it a b13.

As stated above the F (the 11^th) must be raised by one half step to F# making it a #11.

The D (the 9^th) can be raised by one half step to D# making it a #9.

The D (the 9^th) can be lowered by one half step to Db making it a b9.

The b13 and the #11 can also be written as altered 5ths. In other words the Ab could be written as G# (#5) and the F# could be written as Gb (b5).

Based on the above discussion, there are 4 basic alterations for a dominant  chord. They are:

1. b13 or its enharmonic  alteration of a #5.
2. #11 or its enharmonic  alteration of b5.
3. #9
4. b9