music theory 1 - music scales & notes

8/6/2019 Music Theory 1 - Music Scales & Notes

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Music Scales & Notes

Frequency Notes and Octaves Tuning Notes Equal-Tempered Tuning Scales Major and Minor

Scales Major & Minor Transforms Modes Modal Transforms Pentatonics Modal-Pentatonic

Transforms Example Application of Transforms Scales Reference Conforming to Classical Notation

Frequency

Let's imagine you have a long hollow tube. If you hit it, you get a fairly constant sound because hitting it

produces a shock-wave which oscillates (travels up and down) the tube. This oscillation or vibration is what

we hear as pitch.

The speed of oscillation or vibration is called "Frequency". Frequency is measured in Hertz (Hz), which are

oscillations per second. If the hollow tube vibrates at 200 cycles per second, the frequency is 200 Hz.

When you hit a hollow tube, the shock-wave is actually traveling at a constant speed. What determines the

frequency is the length of the hollow tube. The longer the tube, the further the shock-wave has to travel,

hence, the lower the frequency... and vice versa.

Notes and Octaves

A "Note" is a given name to describe a musical frequency. It describes the pitch of a piano key or guitar

string. By convention, notes are named as:-

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

The suffix "#" denotes sharp and "b" denotes flat.

Also note that A# = Bb, C# = Db, D# = Eb, F# = Gb and G# = Ab.

The names chosen are the de facto standard for nearly all music.

"Octaves" of a note are just multiples of the original frequency. Let's say that a length of hollow tube has afrequency of 264 Hz and we'll call it "C".

1. If the length is half of the original length, the frequency will be double. This creates another "C"but one octave higher than the first (264 x 2 = 528 Hz).

2. If the length is quarter of the original, the frequency will be quadruple. This creates yet another"C" but two octaves higher than the original (264 x 4 = 1,056 Hz).

3. If the length is double, the frequency is halved. This creates "C" again but one octave lower thanthe original (264 / 2 = 132 Hz).

We can summarize the relationship between octaves and frequency as follows:

Tube Length Note Octave Frequency

Original C Original 264 Hz 264 Hz

Half C Up 1 264 x 2 528 Hz

Quarter C Up 2 264 x 4 1,056 Hz

Double C Down 1 264 / 2 132 Hz


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5 D 73.416 146.832 293.665 587.330 1,174.659 2,349.318

6 D#/Eb 77.782 155.563 311.127 622.254 1,244.508 2,489.016

7 E 82.407 164.814 329.628 659.255 1,318.510 2,637.020

8 F 87.307 174.614 349.228 698.456 1,396.913 2,793.826

9 F#/Gb 92.499 184.997 369.994 739.989 1,479.978 2,959.955

10 G 97.999 195.998 391.995 783.991 1,567.982 3,135.963

11 G#/Ab 103.826 207.652 415.305 830.609 1,661.219 3,322.438

12 A 110.000 220.000 440.000 880.000 1,760.000 3,520.000

Since this tuning is mathematically derived, a song will sound "correct" when played in a different key.

Special note - The decision to use A3 = 440 Hz, 12 notes per octave and naming them A to G was due to

historical circumstances. Any other combination would also be valid. However, the equal-tempered tuning

is now the de facto system.

Scales

Musicians compose and play songs. In order to ensure that the song is played correctly, we have todetermine which notes are valid. A Scale is a series of notes which we define as "correct" or appropriate for

a song. Normally, we only need to define the series within an octave and the same series will be used for all

octaves.

A Scale is usually referenced to a "root" note (e.g. C). Typically, we use notes from the "equal-tempered"

tuning comprising 12 notes per octave; C, C#, D, D#, E, F, F#, G, G#, A, A# & B.

For most of us, we will only probably need to know 2 scales: the Major scale; and, the Minor scale. Using a

root of "C", the Major scale comprises C, D, E, F, G, A, B while the Minor scale comprises A, B, C, D, E

,F, G. Both of these scales have 7 notes per octave.

Examples of various Scales (Root = "C")Name C Db D Eb E F Gb G Ab A Bb B C

Major 1 2 3 4 5 6 7 1

Minor (natural) 1 2 3 4 5 6 7 1

Harmonic Minor 1 2 3 4 5 6 7 1

Melodic Minor (Asc) 1 2 3 4 5 6 7 1

Melodic Minor (Desc) 1 2 3 4 5 6 7 1

Enigmatic 1 2 3 4 5 6 7 1

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

Diminished 1 2 3 4 5 6 7 8 1

Whole Tone 1 2 3 4 5 6 1

Pentatonic Major 1 2 3 4 5 1

Pentatonic Minor 1 2 3 4 5 1

3 semitone 1 2 3 4 1

4 semitone 1 2 3 1

Bluesy R&R* 1 2 3 4 5 6 7 1

Indian-ish* 1 2 3 4 5 6 7 1


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Note - The Melodic Minor is played differently when ascending (Asc) and descending (Desc).

* denotes Names conjured by myself to reflect the mood of the Scales.

For more examples of scales, see the Scales Reference section at the end of this document.

As you can see, there are many scales and there is nothing to stop you from creating your own. After all,

scales are just a series of notes. Different cultures have developed different scales because they find some

series of notes more pleasing than others.

Major and Minor Scales

The Major scale and Minor scale share many similarities. For example, the white notes on a piano concur

for both "C Major" as well as "A minor". More precisely, "C Major" comprises C, D, E, F, G, A and B

whilst "A Minor" comprises A, B, C, D, E, F and G. The difference is the starting point or root.

The Major scale will always have semitone jumps of 2 2 1 2 2 2 1 while a Minor scale has semitone jumps

of 2 1 2 2 1 2 2. Semitone means the next note so one semitone up from "C" is "C#". In any major scale, the

6th note will be the equivalent minor scale. Similarly, in any minor scale, the 3rd note will be the

equivalent major scale.

By a process called "transposition", we can workout the major or minor scale for every key (ie root).

Transposition is basically starting from another key but still maintaining the separation of notes by

following the same sequence of semitone jumps. In other words, we are shifting the scale to a different

starting note. We can calculate the "Db Major" scale as being Db, Eb, F, Gb, Ab, Bb and C. The concurring

minor for the "Db major" scale will be "Bb minor".

The Major Scale

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

C 1 2 3 4 5 6 7 1

D 7 1 2 3 4 5 6

E 6 7 1 2 3 4 5

F 5 6 7 1 2 3 4 5

G 4 5 6 7 1 2 3 4

A 3 4 5 6 7 1 2

B 2 3 4 5 6 7 1

When we transpose, we are changing key (i.e. root). The scale is always maintained. I have not included the

Major scales for Db, Eb, F#, Ab and Bb but that should be easy for you to work out.

Major & Minor Transforms

"Transform" is a general term meaning to convert something into another. Here, transform is just a way to

convert from one scale to another. It is not the same as transpose. Transpose changes the key but always

maintains the scale. A transform can change the key and/or the scale. Transforms are a convenient way to

convert a musical sequence into a different scale and/or key.

This document will concentrate on one-note transforms. If you have a song in C Major, then converting

every occurrence of F to F# will transform it into G Major. Similarly, converting every B to A#/Bb will

give you F Major.


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The table below highlights the one-note transforms for the major scale. These particular transforms only

involve Key changes (not scale).

One Note Transforms - Comparisons for the Major Scale

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

F 5 6 7 1 2 3 4 5C 1 2 3 4 5 6 7 1

G 4 5 6 7 1 2 3 4

D 7 1 2 3 4 5 6

A 3 4 5 6 7 1 2

E 6 7 1 2 3 4 5

B 2 3 4 5 6 7 1

A scale can be transformed into the one above it or below it simply by comparing the difference between

them. The difference should only be one note.

When would you use a transform? Let's say you have a nice sequenced pattern running throughout a song.You have to accommodate a big key change but transposing it doesn't sound right. Then try transforming it

instead. Transforming only a few notes will not detract too much from the original pattern and can sound

more natural.

Modes

Modes are variant-scales developed from the Major scale simply by starting from a different note. Consider

the C Major scale [C, D, E, F, G, A, B, C] which has 7 notes: If you start from D with the same 7 notes,

you get a new scale [D, E, F, G, A, B, C, D]. Basically, starting the series from any of 7 notes would give

you a different scale and these are called "Modes". Each mode also has a name taken from ancient Greece.

The table below shows the modal scales for the white notes on a piano.

Modal Scales

MODES C D E F G A B C Semitone Jumps

mC Ionian 1 2 3 4 5 6 7 1 2 2 1 2 2 2 1

mD Dorian 7 1 2 3 4 5 6 7 2 1 2 2 2 1 2

mE Phrygian 6 7 1 2 3 4 5 6 1 2 2 2 1 2 2

mF Lydian 5 6 7 1 2 3 4 5 2 2 2 1 2 2 1

mG Mixolydian 4 5 6 7 1 2 3 4 2 2 1 2 2 1 2

mA Aeolian 3 4 5 6 7 1 2 3 2 1 2 2 1 2 2mB Locrian 2 3 4 5 6 7 1 2 1 2 2 1 2 2 2

Note - this looks is a bit like transposition but is actually completely different.

In transposition, the series of semitone jumps is the same. In other words, the separation of notes of the

scale is maintained (i.e. the relative differences in frequencies between notes remains).

In modes, the series of semitone jumps changes. In other words, the separation of notes of the scale is

different (i.e. the relative differences in frequencies between notes is not maintained).


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The table below shows the same modal scales with a "C" root.

MODES C Db D Eb E F Gb G Ab A Bb B C

mC Ionian 1 2 3 4 5 6 7 8

mD Dorian 1 2 3 4 5 6 7 8

mE Phrygian 1 2 3 4 5 6 7 8

mF Lydian 1 2 3 4 5 6 7 8

mG Mixolydian 1 2 3 4 5 6 7 8

mA Aeolian 1 2 3 4 5 6 7 8

mB Locrian 1 2 3 4 5 6 7 8

What do they sound like? Well, Ionian mode is the same as the Major scale and Aeolian mode is the same

as Minor scale. The rest sound strangely familiar but not quite right. For example, Dorian mode sounds like

the band is playing in "D" but you're doing the melody in "C" instead.

Mode Transforms

We can look as the modes in terms of one-note transforms. The table below highlights the one-note

transforms for modes. These particular transforms involve scale changes but not key changes.

If there is a song in C Major (i.e. Ionian), then converting every occurrence of B to A# (Bb) will give you

Mixolydian. Similarly, converting every, F to F# will give you Lydian.

One Note Transforms - Comparisons for Modes

Modes C Db D Eb E F Gb G Ab A Bb B C

mF Lydian 1 2 3 4 5 6 7 1

mC Ionian 1 2 3 4 5 6 7 1

mG Mixolydian 1 2 3 4 5 6 7 1

mD Dorian 1 2 3 4 5 6 7 1

mA Aeolian 1 2 3 4 5 6 7 1

mE Phrygian 1 2 3 4 5 6 7 1

mB Locrian 1 2 3 4 5 6 7 1

mF^-1 Lydian 2 3 4 5 6 7 1

The prefix "m" denotes mode. Therefore "mF" is Lydian. "Carets" (^) with plus or minus signs denote

transposition up and down respectively and is enumerated in semitones. Therefore "mF^-1" is Lydian

transposed down one semitone.




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Pentatonics

A pentatonic is simply a scale of five notes. A series of any five notes per octave will qualify as a

pentatonic scale.

A Major pentatonic in "C" comprises C, D, E, G and A... which is a common scale used by most cultures in

the world. This is achieved by removing the 4th and 7th notes.

What is interesting is that if we remove the 4th and 7th notes from the modal scales, we get quite

remarkable results. The table below illustrates the modal Pentatonics. This time I'm using the "black" notes

on the piano.

Modal Pentatonics

Name from F# G G# A A# B C C# D D# E F F# Semitone Jumps

pC Ionian 1 2 3 - 4 5 - 1 2 2 3 2 3

pD Dorian 1 2 3 - 4 5 - 1 2 1 4 2 3

pE Phrygian 1 2 3 - 4 5 - 1 1 2 4 1 4

pF Lydian 1 2 3 - 4 5 - 1 2 2 3 2 3

pG Mixolydian 1 2 3 - 4 5 - 1 2 2 3 2 3

pA Aeolian 1 2 3 - 4 5 - 1 2 1 4 1 4

pB Locrian 1 2 3 - 4 5 - 1 1 2 3 2 4

What do they sound like (my interpretation)?

"pF, pC & pG" are exactly the same and as they are the entire Major pentatonic. The major pentatonic is

the mainstay of most Folk music.

"pA" is used mainly in Japanese and Balinese music.

"pE" is a popular scale in music from India (also used in Bali).

"pB" sounds like a mix of Arab and Indian music (or somewhere from Asia minor). You'll have to judge

this one yourself."pD" sounds very serious indeed. You'll have to judge this one yourself too.

Modal-Pentatonic Transforms

If we arrange the Pentatonics in the same order as the previous one-note transforms, we get the following

modal scale transforms:-

One Note Transforms - Comparisons for Modal Pentatonics

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

pF Folk 1 2 3 4 5

pC Folk 1 2 3 4 5

pG Folk 1 2 3 4 5

pD Asia-Min 1 2 3 4 5

pA Jap-Bali 1 2 3 4 5

pE Indian 1 2 3 4 5

pB Serious 1 2 3 4 5

pF^-1 Folk 1 2 3 4 5


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In addition to the above transforms, there are a further set of transforms for the modal-Pentatonics. The

table below is slightly different as it groups the possible transforms by each pentatonic. These particular

transforms involve scale changes as well as key changes.

More One Note Transforms - Grouped for Modal Pentatonics

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

pFCG Folk - - 1 - 2 - 3 - - 4 - 5

pFCG^+7 3 4 5 1 2

pFCG^+5 4 5 1 2 3

pB^+1 1 2 3 4 5

pD^+7 3 4 5 1 2

pB^+6 4 5 1 2 3

pD AsiaMin - - 1 - 2 3 - - - 4 - 5

pA^+7 3 4 5 1 2pFCG^+5 4 5 1 2 3

pB^+6 4 5 1 2 3

pA JapBali - - 1 - 2 3 - - - 4 5 -

pE^+7 3 4 5 1 2

pD^+5 4 5 1 2 3

pE Indian - - 1 2 - 3 - - - 4 5 -

pB^+7 3 4 5 1 2

pA^+5 4 5 1 2 3

pB Serious - - 1 2 - 3 - - 4 - 5 -

pD^+6 4 5 1 2 3

pFCG^+6 3 4 5 1 2

pE^+5 4 5 1 2 3

Well, there you have it... all the possible one-note transforms for the Pentatonics. If wish to transform from

one pentatonic to another but no direct one-note transform is available, then you will have to do it in two or

more steps.

Example Application of Transforms

Transforms are useful for converting from one scale and/or key to another. Of all the transforms describedin this document, the modal pentatonic transforms are the most interesting to apply because the results are

quite remarkable.

If you have a sequencer, try this modal pentatonic experiment:

- Write a short pattern using only the black notes... name it "pFCG".

- Using "pFCG", convert every "A#" into "A"... name it "pD".

- Using "pD", convert every "D#" into "D"... name it "pA".


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- Using "pA", convert every "G#" into "G"... name it "pE".

- Using "pE", convert every "C#" into "C"... name it "pB".

- Using "pFCG" again, convert every "F#" into "E"... name it "pD^+7".

- Using "pD^+7", convert every "C#" into "B"... name it "pA^+2".

- Using "pFCG" again, convert every "F#" into "G"... name it "pB^+1".

- Using "pB^+1", convert every "A#" into "C"... name it "pE^+6".

- Then delete "pFCG".

You now have 7 pentatonic patterns: 2 AsiaMins, 2 JapBalis, 2 Indians and 1 Serious.

Arrange the patterns in any order you like... you've now made one seriously ethnic-sounding new tune.

Scales Reference

Below is a table of Scales. They are arranged into 3 sections: (a) Non 7 or 5 note scales, (b) 7 note scales,

and (c) 5 note scales. They are sorted in order of distance from the root-key.

NAME C - D - E F - G - A - B C ALTERNATIVE

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

Spanish 8 Tone 1 2 - 3 4 5 6 - 7 - 8 - 1 -

Flamenco 1 2 - 3 4 5 - 6 7 - 8 - 1 -

Symmetrical 1 2 - 3 4 - 5 6 - 7 8 - 1 Inverted Diminished

Diminished 1 - 2 3 - 4 5 - 6 7 - 8 1 -

Whole Tone 1 - 2 - 3 - 4 - 5 - 6 - 1 -

Augmented 1 - - 2 3 - - 4 5 - - 6 1 -

3 semitone 1 - - 2 - - 3 - - 4 - - 1 -

4 semitone 1 - - - 2 - - - 3 - - - 1 -


Ultra Locrian 1 2 - 3 4 - 5 - 6 7 - - 1 -

Super Locrian 1 2 - 3 4 - 5 - 6 - 7 - 1 Ravel

Indian-ish* 1 2 - 3 4 - - 5 6 - 7 - 1 -

Locrian 1 2 - 3 - 4 5 - 6 - 7 - 1 -

Phrygian 1 2 - 3 - 4 - 5 6 - 7 - 1 -

Neapolitan Minor 1 2 - 3 - 4 - 5 6 - - 7 1 -

Javanese 1 2 - 3 - 4 - 5 - 6 7 - 1 -

Neapolitan Major 1 2 - 3 - 4 - 5 - 6 - 7 1 -

Todi (Indian) 1 2 - 3 - - 4 5 6 - - 7 1 -

Persian 1 2 - - 3 4 5 - 6 - - 7 1 -

Oriental 1 2 - - 3 4 5 - - 6 7 - 1 -Maj.Phrygian (Dom) 1 2 - - 3 4 - 5 6 - 7 - 1 Spanish/ Jewish

Double Harmonic 1 2 - - 3 4 - 5 6 - - 7 1 Gypsy/ Byzantine/ Charhargah

Marva (Indian) 1 2 - - 3 - 4 5 - 6 - 7 1 -

Enigmatic 1 2 - - 3 - 4 - 5 - 6 7 1 -


Locrian Natural 2nd 1 - 2 3 - 4 5 - 6 - 7 - 1 -


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Minor (natural) 1 - 2 3 - 4 - 5 6 - 7 - 1 Aeolian/ Algerian (oct2)

Harmonic Minor 1 - 2 3 - 4 - 5 6 - - 7 1 Mohammedan

Dorian 1 - 2 3 - 4 - 5 - 6 7 - 1 -

Melodic Minor (Asc) 1 - 2 3 - 4 - 5 - 6 - 7 1 Hawaiian

Hungarian Gypsy 1 - 2 3 - - 4 5 6 - 7 - 1 -

Hungarian Minor 1 - 2 3 - - 4 5 6 - - 7 1 Algerian (oct1)

Romanian 1 - 2 3 - - 4 5 - 6 7 - 1 -


Maj. Locrian 1 - 2 - 3 4 5 - 6 - 7 - 1 Arabian

Hindu 1 - 2 - 3 4 - 5 6 - 7 - 1 -

Ethiopian 1 1 - 2 - 3 4 - 5 6 - - 7 1 -

Mixolydian 1 - 2 - 3 4 - 5 - 6 7 - 1 -

Major 1 - 2 - 3 4 - 5 - 6 - 7 1 Ionian

Mixolydian Aug. 1 - 2 - 3 4 - - 5 6 7 - 1 -

Harmonic Major 1 - 2 - 3 4 - - 5 6 - 7 1 -

Lydian Min. 1 - 2 - 3 - 4 5 6 - 7 - 1 -

Lydian Dominant 1 - 2 - 3 - 4 5 - 6 7 - 1 Overtone

Lydian 1 - 2 - 3 - 4 5 - 6 - 7 1 -

Lydian Aug. 1 - 2 - 3 - 4 - 5 6 7 - 1 -

Leading Whole Tone 1 - 2 - 3 - 4 - 5 - 6 7 1 -

Bluesy R&R* 1 - - 2 3 4 - 5 - 6 7 - 1 -

Hungarian Major 1 - - 2 3 - 4 5 - 6 7 - 1 Lydian sharp2nd


"pB" 1 2 - 3 - - 4 - 5 - - - 1 -

Balinese 1 1 2 - 3 - - - 4 5 - - - 1 "pE"

Pelog (Balinese) 1 2 - 3 - - - 4 - - 5 - 1 -

Iwato (Japanese) 1 2 - - - 3 4 - - - 5 - 1 -

Japanese 1 1 2 - - - 3 - 4 5 - - - 1 Kumoi

Hirajoshi (Japanese) 1 - 2 3 - - - 4 5 - - - 1 "pA"

"pD" 1 - 2 3 - - - 4 - 5 - - 1 -

Pentatonic Major 1 - 2 - 3 - - 4 - 5 - - 1 Chinese 1/ Mongolian/ "pFCG"

Egyptian 1 - 2 - - 3 - 4 - - 5 - 1 -

Pentatonic Minor 1 - - 2 - 3 - 4 - - 5 - 1 -

Chinese 2 1 - - - 2 - 3 4 - - - 5 1 -

In general, the non-European scales have not been well documented and many of the names selected may

not be representative of their music. For example, Indian and Indonesian music use a huge range of

different scales. Arabic music also use quarter-tone tuning (there are notes in between the semitones).

Algerian music can use one scale for the first octave and another for the next. Ethiopian music can also use

the minor, Dorian and Mixolydian scales. And this is only the tip of the iceberg. Also remember that the

above table is only a guide to scales used and the actual tunings used can vary immensely. In the end, the

best source for examining scales it to hear it for your self and translate it.


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Conforming to Classical Notation

You do not have to know how to read classical notation in order to use the information in this section. This

information is provided as an additional guide to scales because of the limitations imposed by classical

notation. For example, the scale of "A# major" and "Bb major" are exactly the same but classical notation

only allows for "Bb major".

The classical notation system is well suited for instruments which are "pre-fingered" for the major scale

(e.g. keyboards) but, for "linear" instruments (e.g. guitar, violin), it requires more familiarization.

Classical Notation system:-

The Range of Notes - is represented by a pair of "Staffs" (a Staff has 5 horizontal lines) and these are

marked by "Clefs" (i.e. either treble or bass).

Note Identification - Every line or space has been pre-assigned a note "letter" (i.e. C, D, E, F, G, A, B). The

large space between the Staffs has an imaginary line which represents "middle C".

The Duration of Notes - are represented by a set of Note-Symbols (usually containing some form of

circular dot).

The Notes to be played - are the placement of Symbols either on the lines or in the spaces.

Sharp and Flat Notes - "#" and "b" can also be placed next to the Note-Symbols on the Staff.

Specific Scales - are declared by a "Key-Signature" (a set of sharps or flats on the relevant line or space) atthe beginning of the Staff (eg The scale of G major or E minor is declared by marking "#" on "F" locations

at the start).

If you are using the scale of C major or A minor (the white notes on a piano), you will not have to pre-mark

any sharps or flats as Key Signature. With any other scale, you will need to assign sharps or flats.

With classical notation, problems arises because the Staff represents notes by their "letter". This means that

every note in the scale should have a different letter. For example, the scale of F major is F, G, A, Bb, C, D,

E. You should not use A# instead of Bb, otherwise the "A#" will have to share the same line or space as

"A" (and the "B" line or space will not be used at all). This will cause problems with the Key-Signature.

The table below gives Major and Minor Scales which conform to classical notation. Note - as you count the

notes in the scale, you are also counting "letters" (i.e. In E major, the 6th note is "C#"... so counting 1, 2, 3,

4, 5, 6 is counting E, F, G, A, B, C... and "C" is letter no.6 from "E").

Major Scale R - 2 - 3 4 - 5 - 6 - 7 Minor Scale R - 2 3 - 4 - 5 6 - 7 -

C Major C - D - E F - G - A - B C Minor C - D Eb - F - G Ab - Bb -

Db Major Db - Eb - F Gb - Ab - Bb - C C# Minor C# - D# E - F# - G# A - B -

D Major D - E - F# G - A - B - C# D Minor D - E F - G - A Bb - C -

Eb Major Eb - F - G Ab - Bb - C - D Eb Minor Eb - F Gb - Ab - Bb Cb - Db -

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

F Major F - G - A Bb - C - D - E F Minor F - G Ab - Bb - C Db - Eb -

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

G Major G - A - B C - D - E - F# G Minor G - A Bb - C - D Eb - F -

Ab Major Ab - Bb - C Db - Eb - F - G G# Minor G# - A# B - C# - D# E - F# -

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

Bb Major Bb - C - D Eb - F - G - A Bb Minor Bb - C Db - Eb - F Gb - Ab -

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


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Note - F# major contains "E#" (which is "F") and that Eb minor contains "Cb" (which is "B"). This is a

small discrepancy in the system.

The table below illustrates the "letter" problems of using the non-conforming keys. Notes in brackets ()

indicate small discrepancies. Notes in square brackets [] indicate serious problems.

C# maj.: C# D# (E#) F# G# A# (B#)

D# maj.: D# (E#) [F##] G# A# (B#) [C##]

Gb maj.: Gb Ab Bb (Cb) Db Eb F

G# maj.: G# A# (B#) C# D# (E#) [F##]

A# maj.: A# (B#) [C##] D# (E#) [F##] [G##]

Ab min.: Ab Bb (Cb) Db Eb (Fb) Gb

A# min.: A# (B#) C# D# (E#) F# G#

Db min.: Db Eb (Fb) Gb Ab [Bbb] (Cb)

D# min.: D# (E#) F# G# A# B C#

Gb min.: Gb Ab [Bbb] (Cb) Db [Ebb] (Fb)

These problems do not exist physically, scientifically or mathematically. The problems arise from the

system itself. However, the classical notation system is the de facto "language" of music. Plus the system is

fairly compact and concise. So perhaps this extra "learning" is not too bad.

The table below shows the Scales of the Major and Minor Keys which conform to classical notation. This

may be easier to visualize and remember.

1. Major only - Db, Ab.

2. Both Major & Minor C, D, Eb, E, F, F#, G, A, Bb, B, C.

3. Minor only - C#, G#.

music theory 1 - music scales & notes

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