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THEORY OF MUSIC (I)

Tutorial about theory of music: basic knowledge of timing and scales.

Timing

Albeit it might not be necessary to read music for being able to create a musical composition in a computer, there is some fundamental knowledge which should not be skipped. To begin with, it is essential to learn how musical elements (notes or samples) are distributed along time. In a music sheet notes are written along ensembles of five horizontal lines known as staff or stave, which in turn are divided by vertical lines into sections known as measure or bar. Every measure represents an equal value of time but in a music staff measures are depicted with varying lengths, unlike what happens in the piano roll of a modern sequencer.

At the beginning of a staff there is a fraction known as time signature. The upper number indicates how many beats a measure has whereas the lower number indicates which length of note is equivalent to the length of one beat. More notorious than the time signature is the symbol drawn next to it, which is either a treble clef (upper staff) or a bass clef (lower staff). Music clefs indicate which are the notes of higher or lower pitch in a composition; according to their nature, some instruments can play the notes written in both staffs whilst others might be limited to only one of the two staffs.

Musical notes vary in length according to standard sizes; whole note (1/1), half note (1/2), quarter note (1/4), eighth note (1/8) and sixteenth note (1/16) are the most common lengths used. In the following example the time signature indicates that the length of measures is equivalent to four quarter notes. The first measure is occupied by a whole note, the second one is occupied by two half notes and the third one is occupied by four quarter notes, being the last one a sharp note. In the lower staff we can see a whole silent note placed at the beginning of each measure. For each musical note there is an equivalent silent note for indicating silences of diverse durations.

Music score note lengths

The following pictures compare the beginning of a classical staff with its equivalent in a modern piano roll; we can see two eighth notes, one half note and one quarter note. We should remember that, albeit modern music is generally written in 4/4 measures, along space and time diverse types of measures have been used in the rich world of music. In Europe, apart from the 4/4, a well known measure was the 3/4 which defines not only classical waltz music but also the traditional music of many places in the world. It is to be expected that many versions of sequencers and virtual music studios do not have the capability of displaying a measure format other than the typical 4/4.

Music score measure Piano roll measure

Scales

The importance of musical scales lies in that they are sets of notes that will work well when played together, avoiding dissonances. If we look at a piano keyboard we will see that there is a pattern of keys that repeats itself every twelve keys; this is like this because music in the western civilization works with twelve notes, what is called the chromatic scale. Taking as starting point any key on a piano keyboard, counting up or down twelve keys would lead to the same note located in an octave higher or lower. Playing the chromatic scale only requires to choose a note and then play every consecutive note until reaching the equivalent note in an adjacent octave.

Musical notes are named as letters from A to G in the Anglo-Saxon tradition, whereas in Latin tradition they are called do, re, mi, fa, sol, la and si. Five of the seven notes have inflections which are known as flat (b) or sharp (#); these derivative notes correspond to the black keys on the keyboard. A sharp corresponds to one note up in the chromatic scale whereas a flat corresponds to one note down. As we can see in the following picture, all the five black keys have two names for the same note; the name is relative to the direction (up or down the scale) from which a key is reached.

Piano keyboard octave

If we move upward along the keyboard the complete chromatic scale would be C, C#, D, D#, E, F, F#, G, G#, A, A#, B; if otherwise we move downward the scale would be B, Bd, A, Ab, G, Gb, F, E, Eb, D, Db, C. The twelve notes of the chromatic scale are called octave; in each successive octave each note doubles its pitch in respect of its equivalent in the previous octave. Since keyboards are built with several octaves keyboard-based instruments have wider tonal ranges than the largest part of non-keyboard instruments.

If, for example, we play the white keys of a keyboard in consecutive order starting and ending in C, the resulting sequence (C, D, E, F, G, A, B, C) would be a major scale, and because we started at C it would be the C major scale. In the following examples asterisks represent notes which are not played. The eighth note of the scale, which is always the same than the starting note, is generally included in the representation.

C * D * E F * G * A * B C

If we switch to a D major scale the interval between the played and unplayed notes remains the same, but since we start at D now two black keys are played.

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

Does it seem confusing to memorize all the notes in the twelve scales? To simplify this, many musicians tend to think in terms of the intervals between notes rather than the names of notes. For this purpose, a roman numeral is assigned to each note on the scale. When starting scales on different notes we have to think in numbers and play the same intervals. Here is the recipe for a major scale:

I
I#
II
II#
III
IV
IV#
V
V#
VI
VI#
VII
I

Note how the scheme of the recipe matches the scheme of white and black keys in a piano keyboard. The following examples show how the recipe is used for building different major scales (C major, C# major and D major). Note how the roman numerals and the intervals between them stay the same regardless of the starting note.

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

I
I#
II
II#
III
IV
IV#
V
V#
VI
VI#
VII
I

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

I
I#
II
II#
III
IV
IV#
V
V#
VI
VI#
VII
I

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

I
I#
II
II#
III
IV
IV#
V
V#
VI
VI#
VII
I

Major scales are of very common utilization because their combinations of notes sound pleasing to our hearing. But minor scales, which are slight variations from major scales, are not less pleasing. It is widely acknowledged that major keys are more suitable for confering an optimistic feeling to melodies, whereas minor keys have the opposite effect; this, however, is a subjective concept. Here is the recipe for a minor scale:

I
I#
II
IIIb
III
IV
IV#
V
VIb
VI
VIIb
VII
I

The recipe of minor scales differs from that of major scales in that three of the sharp (#) notes have been replaced by flat (b) notes; II#, V# and VI# become IIIb, VIb and VIIb, respectively. The following example shows how the recipe is used for building the C minor scale.

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

I
I#
II
IIIb
III
IV
IV#
V
VIb
VI
VIIb
VII
I

Once we have chosen a key and scale we are ready to compose or improvise melodies. In the section called REFERENCE MATERIAL there is a compilation of all the heptatonic scales including both major and minor keys, along with subjective descriptions of their personality. There are as well long lists of scales which have been traditionally used throughout the world and are suitable for composing melodies with an exotic taste. Of course, only a part of those scales are heptatonic, whereas the rest range from ditonic to decatonic. It is a good idea to compose melodies based on these scales and discover what they can contribute. Music is an abstract art and scales are the key to open its secrets.

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