Scales: theory

This page tells you how scales are built and the relationships between different scales. It is being written as I learn about music theory: namely scales and harmony. Please feel free to correct or advise through the comments or email.

Contents of this page:

• Pitch and notes
• What is a scale?
  • Major scale
  • Natural minor scale
  • Harmonic minor scale
  • Melodic minor scale
  • The modes
  • The Andalusian or Phrygian dominant mode
  • The others

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Pitch and notes

The note A or La has a frequency of 440Hz. This note is sometimes called “concert A” by classical musicians because it is used as an absolute reference for all the instruments. If you remember your school physics lessons, you might remember that frequency is the number of waves in a given time. What will happen if we double this frequency? So instead of 440 Hz, we hear 880Hz. The note will be exactly the same – it will have the same pitch, but it will sound higher than the 440Hz original. This is known in music as an octave.

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What is a scale?

A scale is a series of notes that go up or down in pitch until they reach their octave. The simplest scale is the: Chromatic Scale The chromatic scale uses each and every note. So, starting a chromatic scale on the bass E [Mi] string, you will have to play 12 notes to get to the octave higher:

E-F-F#-G-G#-A-A#-B-C-C#-D-D#-E’

Each of these intervals are known as semitones. So, E-F# is two semitones, that is, one tone. Notice – and this is important – notice how there is only one semitone between the notes E – F and B – C.

The chromatic scale is pretty difficult to listen to and is very rarely used for music. There is no structure and to my (feeble) mind, just far too many notes! Taking some notes out gives some more interesting and musical results.

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Major Scale

Major scales are one of various types of scales used in Western music. It contains seven notes, the eighth being the octave. Which notes should we include? To know this, we should use a musical template. Here is the template for the major scale:

Tone -Tone-Semitone-Tone-Tone-Tone-Semitone

that is:

T – T – S – T – T – T – S

Starting from the note A [La], we get

A – B – C – D – E – F – G – A’

The notes A to B is a full tone, so no problems there. Next, B to C is only a semitone and that does not fit our major scale template. The solution to this problem is to raise the C note by semitone. Do to this, use a sharp:

A – B – C# – D – E – F – G – A’

Continuing, C# to D is a semitone, but it is not necessary to raise the D to D# because the template says that this interval should be a semitone. Next, D to E is a tone, no problems there then, but E to F is a semitone and should be a full note. The solution is to raise the F.

A – B – C# – D – E – F# – G – A’

the final interval should be a semitone also, so we need to raise the G to G#:

A – B – C# – D – E – F# – G# – A’

This is known as the scale of A Major [La Mayor]. Every major scale that starts on A will always need every C, F and G raised by a semitone to fit the template. This is annotated at the start of musical scores and is known as a key signature.

If we had started the example above with the note C (do), then there would have been no need for raising notes a semitone because the intervals fit the major template perfectly:

C – D – E – F – G – A – B – C’

Strting on G, we will need one raised note:

G – A – B – C – D – E – F# – G’

and so on:

D – E – F# – G – A – B – C# – D’

Notice how our starting notes C, G and D are all five notes distance from each other. This is known as the circle of fifths. See the Wiki for more information and here for a diagram.

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Natural Minor Scale

The minor scale works in exactly the same way as a major scale does, but with a different template. Here it is:

T – S – T – T – S – T – T

A minor would therefore be:

A – B – C – D – E – F – G – A’

Notice that there are no raised (or lowered) notes, just like the major scale that starts on C – see above. Because of these shared notes, A minor is known as the relative minor of C major.

The template for major and minor keys is the same, but starting in a different place:

T – T – S – T – T - T – S

or,

T – S - T – T – S – T – T

Minor starts in blue and major starts in orange.

Because this is the same pattern starting in a different place, it is easy to predict what the relative minor of a major is going to be:

a relative minor is always three steps lower than its relative major.

For example, C minor has the same key signature as E flat major, since E flat is a minor third higher than C.

The minor scale above is a natural minor scale. There are two other minor scales which use other scale templates.

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Harmonic Minor Scale

Here is the template and two examples:

T – S – T – T – T½ – S – T

A – B – C – D – E – F – G# – A’

E – F# – G – A – B – C – D# – E

“The harmonic minor is also occasionally referred to as the Mohammedan scale due to its similarity to a common Arabic maqam, a scale that does not require quarter tones (and thus can be played on instruments in Western fixed tunings).”

Wikipedia

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Melodic Minor Scale

Here is the template:

↑: T – S – T – T – T – T – S

↓: T – T – S – T – T – S – T

The sixth and seventh notes of the scale are each raised by one half step when going up the scale, but return to the natural minor when going down the scale.

A – B – C – D – E – F# – G# – A’ and then

A – G – F – E – D – C – B – A’ respectively

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The Modes

We saw that the relative minor of a major key was the same template as the major, but one that started in a different place. I am beginning to see that the modes follow this pattern. If I am wrong, please correct me.

Here is a template:

T – T – S – T – T – T – S

The template for our major keys. Also known as the Ionian mode. If we move the first tone interval in the above template, we will get another mode:

T – S – T – T – T – S – T

… the Dorian mode. The next is Phrygian:

S – T – T – T – S – T - T

And this is the one that is of special interest to us aficionados of flamenco.

If you followed the section on the natural minor scale above, you will now realise that the natural minor scale is in fact a mode: the Aolean mode.

If you wish tro study mode further and if you wish to do some ear training go here to the musical interval tutor.

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The Andalusian Phrygian Dominant

I don’t know what else to call it, but it has given me a real headache trying to fit this very common scale into the my understanding of music. Some people call it the Greek Dorian Mode (Manuel Granados), other people call it a Dorian Mode, others a Phrygian Mode. There are several references on the internet calling this scale the Spanish gypsy scale and the phrygian dominant.

Here are the notes:

E – F – G# – A – B – C – D – E’

A very commonly heard scale usually known as “por arriba” position as opposed to the “por medio” position which chords fall in the centre of the fretboard.

Here is the template derived from an analysis of the scale:

S – T½ – S – T – S – T – T

To my mind this is the Phrygian mode with a raised third note. This is the scale that has such a characteristic flamenco sound.

To start on A (that is “por medio”), the scale is:

A – Bflat – C# – D – E – F – G – A’

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The other modes

For the sake of completeness, here are the templates for all seven modes.

• Ionian – T-T-S-T-T-T-S
• Dorian – T-S-T-T-T-S-T
• Phrygian – S-T-T-T-S-T-T
• Lydian – T-T-T-S-T-T-S
• Mixolydian – T-T-S-T-T-S-T
• Aeolian – T-S-T-T-S-T-T
• Locrian – S-T-T-S-T-T-T

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What scales?

There are many different types of scale, including:

• The diatonic scale (seven notes)
• The melodic and harmonic minor scales (seven notes)

In the nineteenth and twentieth century, additional types of scale are explored:

• The chromatic scale (twelve notes)
• The whole tone scale (six notes)
• The pentatonic scale (five notes)
• The octatonic or diminished scales (eight notes)

A large — indeed, virtually endless — variety of other scales exists:

• The Phrygian dominant scales (actually, a mode of the harmonic minor scale)
• The Arabic scales
• The Hungarian minor scale

For a full and excellent treatment of musical theory the following link is recommended:

• Dolmetsch Online

Scale jargon

Each note of a scale has a name – irrespective of the scale being played: The first and last notes are always called the tonic notes. These note are the notes that give the scale its name. So, the tonic of C major is C and A major is A and so on.

First = Tonic (I) = do

Second = Supertonic (II) = re

Third = Mediant (III) =mi

Fourth = Sub-dominant (IV) = fa

Fifth = Dominant (V) = sol

Sixth = Sub-mediant (VI) = si

Seventh = Sub-tonic =do

Do not confuse the solfege names (do, re, mi etc.). In the list given above, the solfege names DO NOT refer to absolute notes. In flamenco parlance Do is always the note C. Re is its turn is always D and so on. From a classical perspective I have been informed that this is a nonsense because do is always the tonic, that is the first note of a major scale. There is an excellent Wiki on this subject for those who are interested.

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