Muzik Study

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Scales refer to a series of notes that go in an ascending and descending manner. The major scale

is the foundation from which all other scales are formed. A C major scale begins with a C and ends with a

C. The same rule applies with the rest of the keys where a D Major Scale begins and ends with a D and so

on. The notes on a major scale is numbered from 1 to 8, this signifies the intervals.

Major Scale in Every Key

C = C - D - E - F - G - A - B - C

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

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

F = F - G - A - Bb - C - D - E - F

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

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

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

C# = C# - D# - E# (=F) - F# - G# - A# - B# (=C) - C#

Db = Db - Eb - F - Gb - Ab - Bb - C - Db

Eb = Eb - F - G - Ab - Bb - C - D -Eb

F# = F# - G# - A# - B - C# - D# - E# (=F) - F#

Gb = Gb - Ab - Bb - Cb (=B) - Db - Eb - F - Gb

Ab = Ab - Bb - C - Db - Eb - F - G - Ab

Bb = Bb - C - D - Eb - F - G - A Bb



If there are major scales there are also minor scales. The notes on a major scale sound bright

and cheerful while notes on the minor scale sound solemn and sad. There are three types of minor

scales:Natural Minor Scale - When you play all the notes in a minor key signature, you are playing the

minor scale. To guide you, here are the minor scales in every key:

C = C - D - Eb - F - G - Ab - Bb - C

D = D - E - F - G - A - Bb - C - D

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

F = F - G - Ab - Bb - C - Db - Eb - F

G = G - A - Bb - C - D - Eb - F - G

A = A - B - C - D - E - F - G - A

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

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

Eb = Eb - F - Gb - Ab - Bb - Cb - Db - Eb

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

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

Bb = Bb - C - Db - Eb - F - Gb - Ab - Bb

To simplify, you can memorize this formula to form a minor scale = whole step - half step - whole step -

whole step - half step - whole step - whole step or w - h - w - w - h - w - w.

Harmonic Minor Scale - To play a harmonic minor scale, you simply raise the seventh note of the scale

by a half-step as you go up and down the scale. For example:

Natural C Minor Scale = C - D - Eb - F - G - Ab - Bb - C

Harmonic C Minor Scale = C - D - Eb - F - G - Ab - B - C

Melodic Minor Scale - When you raise the sixth and seventh notes of a scale by a half step as you go up

the scale and then return to the natural minor as you go down the scale. For example:

Melodic C Minor Scale = C - D - Eb - F - G - A - B - C (as you go up the scale)

Natural C Minor Scale = C - D - Eb - F - G - Ab - Bb - C (as you go down the scale)



What are Interval

An interval is the difference between two pitches measured by half steps. It is also defined as the distance of one

note to another note. In Western music, the smallest interval used is the half step. Learning about intervals makes

it easier to play scales and chords.

Intervals have two characteristics: the type or quality of an interval (ex. major, perfect, etc.) and the size or

distance of an interval (ex. second, third, etc.). To determine an interval, you first look at the type of interval

followed by the size (ex. Maj7, Perfect 4th, Maj6, etc.). Intervals can be major, minor, harmonic, melodic, perfect,

augmented and diminished.

Sizes or Distance of Intervals (Using the C Major Scale as example)

When determining the interval between two notes, you need to count every line and space starting from the

bottom note going to the top note. Remember to count the bottom note as #1.

Prime/First - c to c

Second - c to d

Third - c to e

Fourth - c to f

Fifth - c to g

Sixth - c to a

Seventh - c to b

Octave - c to c

Types or Qualities of Intervals

Perfect Intervals have only one basic form. The first (or prime), fourth, fifth and eighth (or octave) are all perfect

intervals. When you lower a perfect interval by a half step it becomes diminished. When you raise it a half step it

becomes augmented.

Non-perfect Intervals have two basic forms. The second, third, sixth and seventh are non-perfect intervals; it can

either be a major or minor interval (ex. Maj7, minor6, etc.). When you lower a major interval by a half step, it

becomes a minor. When you raise it a half step it becomes augmented. On the other hand when you lower a minor

interval by a half step it becomes diminished. When you raise it a half step it becomes a major.



This table gives the most common nomenclature for each interval according to its relation to the major

scale. For example, the interval of four semitones occurs as the third note of the major scale, and thus it

is called a major third. The interval of seven semitones occurs as the fifth note of the major scale, and so

it is called a perfect fifth. Whether an interval is "perfect" or "major" depends on mathematical ratios of

frequencies as determined by the Greeks. Other possible names are given under "alternate names," and

the most common of these are emboldened. One may draw several inferences from this table:

If any perfect interval is raised by one semitone, the interval becomes augmented

If any perfect interval is lowered by one semitone, the interval becomes diminished

If any major interval is raised by one semitone, the interval becomes augmented

If any major interval is lowered by one semitone, the interval becomes minor

If any major interval is lowered by two semitones, the interval becomes diminished



What Are Harmonic Intervals

Notes that are played together or simultaneously create harmony. The interval between these

notes are called harmonic intervals. Just like melodic intervals, there are harmonic 2nds, 3rds, 4ths, 5ths,

6ths, etc. The difference is that in melodic intervals the notes are played one after another, while in

harmonic intervals you play the notes at the same time.

Notes on a chord that are played together have harmonic intervals. The most common type of chords

are major and minor chords. The triad is a type of major or minor chord that has 3 notes played either at

the same time or one after another. A major triad is played using the 1st (root) + 3rd + 5th notes of a

major scale. A minor triad is played using the 1st (root) + 3rd + 5th notes of a minor scale.

``` There are many different types of chords, the most common are major and minor

chords. For this lesson we will learn about how to form "major triads." First, let's define what a major

triad is; a triad are 3 notes either played together or simultaneously. A major triad is played using the 1st(root) + 3rd + 5th notes of a major scale. A major triad chord has a symbol of M or Maj. Here's how to

form major triads:

Difficulty: Average

Time Required: Depends on your playing level

Learn all the note names on a keyboard. The white key to the left of two black keys is always a C; now

moving to the next white keys on the right we have D - E - F - G - A - B then back to C again. These note

names just keep repeating. The names of the black keys (and some white keys as well) varies depending

on whether it's a sharp or a flat. For example, the black key next to C may either be a C# or a Db.

Learn how to play the major scales. A scale is a series of notes that go in an ascending and descending

manner. To guide you, here are the major scales in every key:

C = C - D - E - F - G - A - B - C

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

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

F = F - G - A - Bb - C - D - E - F

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

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

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

Here are the other major scales for flats and sharps:



C# = C# - D# - E# (=F) - F# - G# - A# - B# (=C) - C#

Db = Db - Eb - F - Gb - Ab - Bb - C - Db

Eb = Eb - F - G - Ab - Bb - C - D -Eb

F# = F#= F# - G# - A# - B - C# - D# - E# (=F) - F#

Gb = Gb - Ab - Bb - Cb (=B) - Db - Eb - F - Gb

Ab = Ab - Bb - C - Db - Eb - F - G - Ab

Bb = Bb - C - D - Eb - F - G - A - Bb

To simplify, you can memorize this formula to form a major scale = whole step - whole step - half step -

whole step - whole step - whole step - half step or w - w - h - w - w - w - h

Now, assign numbers to each note of a major scale, always assign number one to the root note. For

example, in the C major scale the numbers will be assigned as follows:

C = 1

D = 2

E = 3

F = 4

G = 5

A = 6

B = 7

C = 8

Now, in order to form a major triad play the notes numbered 1 + 3 + 5. In our example above, that is C +

E + G, that's the C Major Triad. Do this pattern to form all the other major triad chords.

Added Tip: To play the chords with your right hand, use your thumb to play the root, your middle finger

for the third note and your pinky to play the 5th note. For the left hand it's the other way around, with

your pinky playing the root, your middle finger still playing the third note and your thumb playing the

5th note.

Try this: Try playing the following major triads in this pattern: C major triad - A major triad - F major triad

- G major triad. You can play the notes on a chord one after the other or all at the same time. Just listen

to how it sounds.



` if you know how to form major chords, you'll find it easy to learn how to form minor chords. In

this lesson, we will learn how to form "minor triads." First let's define what a minor triad is; a triad are 3

notes either played together or pressed one after another. A minor chord is played using the 1st (root) +

3rd + 5th notes of a minor scale. A minor chord has a symbol of m or min. Here's how to form minor

triads:

Difficulty: Average

Time Required: Depends on your playing level

Here's How:

Learn all the note names on a keyboard. The white key to the left of two black keys is always a C; now

moving to the next white keys on the right we have D - E - F - G - A - B then back to C again. These note

names just keep repeating. The names of the black keys (and some white keys as well) varies depending

on whether it's a sharp or a flat. For example, the black key next to C may either be a C# or a Db.

Learn how to play the minor scales, also known as natural minor. A scale is a series of notes that go in an

ascending and descending manner. To guide you, here are the minor scales in every key:

C = C - D - Eb - F - G - Ab - Bb - C

D = D - E - F - G - A - Bb - C - D

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

F = F - G - Ab - Bb - C - Db - Eb - F

G = G - A - Bb - C - D - Eb - F - G

A = A - B - C - D - E - F - G - A

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

Here are the other minor scales for flats and sharps:

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

Eb = Eb - F - Gb - Ab - Bb - Cb - Db - Eb

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

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

Bb = Bb - C - Db - Eb - F - Gb - Ab - Bb



To simplify, you can memorize this formula to form a minor scale = whole step - half step - whole step -

whole step - half step - whole step - whole step or w - h - w - w - h - w - w. To make it easier, if you

already know how to play a major triad chord, just lower the third note (or the note being pressed by

your middle finger) a half-step to make it a minor triad. For example, a C major triad is C - E - G, lower

the E a half step (=Eb), thus, a C minor triad is C - Eb - G.

Now, assign numbers to each note of a minor scale, always assign number one to the root note. For

example, in the C minor scale the numbers will be assigned as follows:

C = 1

D = 2

Eb = 3

F = 4

G = 5

Ab = 6

Bb = 7

C = 8

Now, in order to form a minor triad play the notes numbered 1 + 3 + 5. In our example above for the key

of C that is, C + Eb + G, that's the C Minor Triad. Do this pattern to form all the other minor triad chords.

Added Tip: To play the chords with your right hand, use your thumb to play the root, your middle finger

for the third note and your pinky to play the 5th note. For the left hand it's the other way around, with

your pinky playing the root, your middle finger still playing the third note and your thumb playing the

5th note.

Try this: Try playing the following minor triads in this pattern: C minor triad - A minor triad - F minor

triad - G minor triad. You can play the notes on a chord one after the other or all at the same time. Just

listen to how it sounds.



The melodic minor scale is the same as the natural minor with the exception that the sixth and seventh

tones are raised by a semitone (half step) when the scale is ascending. When the scale is descending, the

melodic minor is the same as the natural minor, e.g.:

C, D, E-flat, F, G, A, B, C (ascending)

C, B-flat, A-flat, G, F, E-flat, D, C (descending)

SCALE STEPS (IN SEMITONES OR HALF STEPS)

SCALE STEPS (IN SEMITONES OR HALF STEPS)

1 2 3 4 5 6 7 8 9 10 11 12 13

c d eb f g a b c'

c d eb f g ab bb c'



The harmonic major scale

The harmonic major scale has just one tonally effective mode which is named after its parent

prime.

It is spelled in numerical form (relative to the major scale):

1 2 3 4 5 6 7 Notes

I ii0 iii iv V VI+ vii0 Chor ds

So if the tonic is c, then the scale consists of the following notes and chords:

c d e a b Hear these notes

C d 0 e G A + b0 Hear these chor ds

It has semitones between its 5th and 6th degrees and between its 7th and 8th degrees. It has

three types of second - major, minor and augmented, making it less melodically smooth than the

diatonic scales.

It is, however, very effective tonally, with the tonic on I being very decisive and quite

unambiguous.

Indeed this scale is often substituted for the major scale as it can strengthen the tonality. It is

from this scale that perhaps the two most common chromatic chords in the major scale are

derived - the minor subdominant (iv) and the diminished supertonic (iio

).

The harmonic major scale is not usually used for an extended period of time because of its

melodic and harmonic deficiencies compared to the major scale. But outside of the stylistic

conventions of common practice music which avoid augmented seconds and prefer major and

minor triads to augmented and diminished it can be very effective as a medium for tonally

centred expression.



The harmonic minor scale

The harmonic minor scale has just one tonally effective mode and that is the scale

conventionally known as the harmonic minor scale. It is spelled, in numerical form (relative tothe major scale):

1 2 3 4 5 6 7 Notes

i ii0 III+ iv V VI vii0 Chor ds

If the tonic is c, the notes and chords are:


c d 0 E + G A b0 Hear these chor ds

The harmonic minor scale is well known to common practice classical music because it is

the harmonic foundation of minor mode music. It is, however, avoided as

the melodic foundation because of the "unmelodic" augmented second found between its sixth

and seventh degrees.

Conventionally when the sixth degree proceeds to the seventh the sixth degree is raised by a

chromatic semitone, and when the seventh degree proceeds to the sixth the seventh degree is

lowered by a chromatic semitone. Both of these devices transform the augmented second into a

major second.

These devices are used simply to smooth the melodic line without disturbing tonal function in

the scale too drastically, although repeated use of the natural sixth will weaken the tonal

function of the scale. It is not necessary though, and the melodic leap between the sixth and

seventh degree can be used as an interesting feature.

The reason that the harmonic minor scale is used as the harmonic foundation of the minor

mode is that, despite its melodic deficiencies, its tonality is very powerful and unambiguous,

whereas the tonality of the aeolian mode is weak and easily displaced, and the tonality of the

melodic minor is even weaker and more ambiguous. In a sense the harmonic minor scale is the

"default" scale to which the melodic variations must return in order for the tonality to bemaintained. By using it as the harmonic resource for the minor mode one is emphasising its

fundamental role in maintaining tonal function.

There are, of course seven modes of the harmonic minor scale just as there are with the diatonic

scale, none of them have common names, and it is only the harmonic minor which is tonally

effective.



The melodic scales

The melodic scale can be represented by these notes: c, d, e , f, g, a, b.

The melodic scale is proper, and, like the diatonic scale, it is smooth with only two sizes of

second (major and minor second). This makes the scale particularly suitable for melodic

purposes, including improvisation. The two tonal scales which can be derived from it are,

however, amongst the least effective and convincing at providing a tonic of all the tonal

scales.

Two of the other modes of this scale are very familiar in jazz circles as melodic modes used

as the basis for improvisation (or indeed composition) over dominant seventh type chords.

These two modes are usually called the lydian dominant scale and altered scale.

These two jazz modes and the two tonal harmonic scales are listed below. They are all

taken from the same melodic scale (c, d, e , f, g, a, b) and the name of each scale is listed

next to its home note. It should be stressed here that neither the lydian dominant scale nor

the altered scale has a tonic triad on its home note, because that is the root of the

(unstable) dominant chord over which it is used. The term "home note" is used only to

indicate that this note is the most convenient reference point of the scale since it matches

the root of the chord over which it is used.

Home note Name of mode

e lydian dominant (or lydian flat 7)

c c (ascending) melodic minor (descending) melodic major

d a

b b alter ed

The melodic scale above has two triads which are capable of functioning as tonics: c minor

and G major, so these are the tonics of the two tonally effective modes of the melodic scale

- the (ascending) melodic minor scale and the (descending)melodic major scale.

Both of these scales can be understood to be melodic "improvements" of the harmonic

minor and harmonic major scales respectively, although the strength of the tonic in both

these melodic scales is weaker than in their harmonic counterparts.

The melodic minor scale

The melodic minor scale is represented numerically (relative to the



major scale):

1 2 3 4 5 6 7 Notes

i ii III+ IV V vi0 vii0 Chor ds

So if the tonic is c, the notes and chords of this scale are:


c d E + F G a0 b0 Hear these chor ds

There are semitones (minor seconds) between the 2nd and 3rd

degrees and between the 7th and 8th degrees, and wholetones

(major seconds) between all the other adjacent degrees. Using this

formula the melodic minor scale can be built on any note.

The scale is most frequently encountered as a temporary

substitution for the harmonic minor scale in order to smooth the

melodic line from the sixth to the seventh degree without disturbing

the tonic function on i.

In common practice classical it is rarely used in isolation for any

extended period of time. This is largely because its tonic is not so

effective as that of the harmonic minor scale. Repeated use

of ii or IV in a minor mode tend to make the tonic sound like a

slightly artificial alteration of a major tonic.The melodic major scale

The melodic major scale is spelled (relative to the major scale):

1 2 3 4 5 6 7 Notes

I ii0 iii0 iv v VI+ VI Chor ds

If c is our tonic then the notes and chords in this scale are:


C d 0 e0 A + B Hear these chor ds

It is so named because it is a mirror of the (ascending) melodic

minor scale. In the melodic minor scale the 6th and 7th degrees of

the diatonic aeolian mode are sharpened, in the melodic major scale



the 6th and 7th degrees of the diatonic major scaleare flattened.

What a strange, wonderful and under-used scale this is ! It has a

very usable (if a little unstable) tonic function on I. To me it evokes

Eastern European folk melodies, with its yearning flattened sixth

and its mellow and relaxed flattened seventh degree, but it has beenmostly ignored by classical composers.

Perhaps this is a reflection of the incorrect theoretical belief that the

dominant (V) chord has to be major, for the I (i) to have any tonic

function. But the melodic major scale proves this to be nothing more

than dogma. In this scale the leading tone is not the 7 (which

resolves to 1), but the 6 which resolves to fifth of the tonic triad.

This leading tone is found in the subdominant (iv), so here the

subdominant takes on the role that is usually taken on by the

dominant in the major and minor scales. Certainly, alternating

between v and I will displace the tonicity of the latter triad, butproviding that iv is interposed between them, the minor dominant is

fairly safe.

The piece of music below is set entirely within the scale of g melodic

major.

The Dance (midi file).

It's chord progression is:

I x 9 | VII | iv | I |

I x 9 | VII | ii0 | v | iv | I | - |

I | - | ii0 | - | I | - | VII | - |

I | - | iv | v | VII | v | I | - |

I x 9 | VII | iv | I | - | ii0 (over 1) | - | I | - |

G x 9 | F | c | G |

G x 9 | F | a0 | d | c | G | - |

G | - | a0 | - | G | - | F | - |

G | - | c | d | F | d | G | - |

G x 9 | F | c | G | - | a 0 (over g)| - | G | - |



Modulation

There are two fundamental forms of modulation - between different tonal centres, and

between different tonal types (major and minor tonalities). This means that we canmodulate from the major tonality of C to:

y a different tonal centre, but the same tonal type, such asG major;

y the same tonal centre, but a different tonal type, which isc minor;

y a different tonal centre and a different tonal type, such as f minor.

A modulation can be between closely related or a distantly related keys, and it can be

articulated in a manner which either smooths this transition or which highlights it as a

sudden shift. The choice is the composer's, and in this section I will describe the

relationships between the different tonalities and the methods used to move between them.

The distance between keys

There are two important ways to measure the distance between any two keys. The first is

the number of notes that they have in common - the more they share, the more similar they

are; the second is the inherent similarity of any two keys which share the same tonic note -

the only two keys which share the same tonic note are parallel major and minor keys.

Modulating between any two keys which are closely related is likely to be much less

disruptive than direct modulation between any two distantly related keys. Of course, it may

be desired for the modulation to be heard as a sudden and unexpected transition, in which

case no preparation need be made, but if we wish to modulate smoothly to a distantly related key we can do this most effectively by using a series of closely related keys as

stepping stones to the more distant key.

R elative and other note-similar keys

The most basic measure of the reltionship between keys is the

number of notes they have in common.

The most closely related keys, measured on this basis, are

therelative major and minor keys which share all seven notes. For

instance, the keys C major and a minor can be said to share all of

their notes (if we take the natural minor as the basis of the minor

scale, and consider the harmonic minor to be an alteration of it).

The relative minor of any major key is a minor third below, the

relative major of any minor key is a minor third above, and these

keys have exactly the same key signature.

The keys C major, G major, and e minor share six (out of seven)



notes - c, d , e, g , a, b. So both G major and its reciprocal F major,

and e minor and its reciprocal d minor can be considered to be the

next most closely related keys to C major.

The following table shows the number of notes shared by every key

and the key of C major (or a minor), so that we can see the mostclosely related keys at the top and the most distantly related at the

bottom:

Minor keys

onflat side

Major keys

onflat side

No. of notes

in commonwith

Major keys

onsharp side

Minor keys

onsharp side

C or a d F 6 G e

g B 5 D b

c E 4 A f

f A 3 E c

b D 2 B g

e G 1 F d

Modulation between any of these closely related keys is easy to do,

and can be achieved quickly and simply.

The most common method of making such a modulation as smooth

as possible is to use a pivot chord, which must be a chord that is

found in both keys. The pivot chord is approached as a member of

the original key but then quitted as a member of the new key whichis established with a cadential progression. For instance to modulate

from C major to e minor, we could use the progression

C - F - G - a - B - e

In this context, a is the pivot chord - it is approached as vi of C major

but quitted as iv, in the cadential progression iv - V - i, of e minor.

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