Vladimir Jovanović
THEORY OF MUSIC
PREFACE This Theory of Music is originally conceived to be one big practicum of examples, practices and exercises. Over 2.800 examples show clear author’s intention to prioritize a practical instead of a verbal part of the theory. The author has been engaged in practical theory all of his working years. Experimenting, he has always been searching for the new, better and easier solutions, as well as new ways of thinking, new explanations and definitions. This book is intended for the students of elementary and secondary music schools, as well as for all the students of Music Academy that are yearning for a new knowledge, new approaches and definitions and want to learn about new solutions and a different way of thinking.
To my daughter Olja, with love
THE METHODICAL INSTRUCTIONS This Theory of Music is very comprehensive with the number of pages, covered fields, as well as practicing examples. Two thirds of the written material is covering three most important fields: intervals, scales and chords. The methodical instructions apply to these three fields.
INTERVALS Intervals cover majority of this book (40 pages). Methodical instructions are identical for all intervals. First we have a summary of all intervals on the basic notes. Out of it, the author classifies all the intervals of the same size and type into two groups: major and minor intervals for all the seconds, thirds, sixths and sevenths and on the other side perfect and augmented /diminished fifth for fourths and fifths. Then you should practice fast pronunciation of chromatic semitones and tones of all of the seven, alphabetically different tones, using the model of an augmented unison (page 31). That will help you later on with the quick pronunciation of all the intervals by its name and type, using written models. Models will be multiplied – pronounced alphabetically numerous times, as many times as there are visually similar intervals given in each model. This study already contains examples of visually similar intervals. These are intervals same by name and type, but also visually similar, as both tones have the same tonal image (meaning sharp and flat symbols -accidentals). Written models are including all the possible intervals by its name and type, in total of 25 (13 + 12) models of fourths and fifths and 32 (16 + 16) of remaining ones. All of the models are to be used in oral training. There are 90 fourths and fifths, each and112 of others (each).
MODELS THE TYPES OF INTERVALS
GROUP А
THE TYPES OF INTERVALS
GROUP B
NUMBER OF MODELS
INTERVALS
MAJOR-PERFECT
VISUALLY SIMILAR INTERVALS
MINOR (DIMINISHED AUGMENTED)
VISUALLY SIMILAR INTERVALS
32
SECONDS
C-D
5
E-F
2
32
ТHIRDS
C-E
3
D-F
4
25
FOURTHS
C-F
6
F-B
1
25
FIFTHS
C-G
6
B-F
1
32
SIXTHS
C-A
4
E-C
3
32
SEVENTHS
C-B
2
D-C
5
Oral training of the seconds, for example, means that every C-D model (of the 16 differently written) is used for alphabetical pronunciation of 5 different, but visually similar seconds, and models E-F (16 different models) is to be pronounced within two different seconds. You should incorporate in your training all intervals in the same manner, only changing the number of visually similar intervals (groups A and B). Practices and exercises are to be used both orally and for written work. They contain many different exercises and have a number of new and interesting ideas. Written comments above the practice examples are there to clarify all of the possible methods.
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SCALES In this chapter of theory most attention is paid to diatonic major and minor scales, as well as different types of major and minor. The basics are natural major and natural minor scales. Numerous starting exercises are used to check basic knowledge of scales: key signatures, scales degrees, finding relative keys. Further practices and exercises are including consecutive notes within the scale that do not begin from the first degree. Enclosed useful charts in this book are a result of the author’s rich and long practice within this topic. Especially is interesting the chart which, by using only two chords (I5 - VII7) in a computer manner gives you all of the notes 3 in the scale (page 86). It’s very important to compare, using methodical thinking, scales that are mutually similar (relative, parallel, chromatic scales). Especially useful is to compare chromatically similar scales that often discover characteristic tones helpful in identifying the scale. That resulted with the idea of writing symbols for the scales, making new definitions (for scales with 5 and 6 accidentals) and also discovering new knowledge considering difficult scales. Surely innovation is in a way that all tetrachords could be constructed over well learned major tetrachords (page 74, 75). “Computer way of thinking” again could be unbelievably helpful for rapid pronunciation (and playing) of all the tetrachords. At the end of this chapter, once you mastered all the modes, author recommends playing 5 different consecutive notes from the “major accordance”, and the same amount of the scales of “minor accordance”, revealing and recognizing them.
CHORDS Best ideas are used from the authors Practicum: a) classification of all the triads into three visually similar groups b) construction of all the triads based on well learned major triads Of course, there is a lot of a new material: construction of a descending chord, triads within the scale, useful charts ect. There is a very interesting method used in practices and exercises. Using a well known model you’ve been asked to write down groups of the same intervals, which are visually similar. Chapter ‘Intervals’ contains the identical assignments. Another innovation is discovery of all the intervals and inversions given in the music stave, by double – different solutions, considering the clef. Part of the book including dominant seventh chords and its inversions, as well as the other seventh chords have a lot of examples for practice (over 350). We consider that methodic of the practical theory of music is constantly involved trough the practice examples. Exercises and practice are the biggest assets of this Study. With perfect knowledge of basic elements of theory (chromatic semitones and tones, major and minor second, major triad, major tetrachord...) we can almost as easy as a computer find out new information. Connecting topics, merging and comparing, classifying into visually similar groups, using the familiar for mastering the unknown, all of the above is written a long time ago in the author’s Practicum. This Study has grown out of the seed of the Practicum of the Theory of Music, which has been written back in 1985. Author
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BASIC CONCEPTS Music is an art about notes which can be understood and comprehended by listening to it. It expresses the thoughts and feelings using the tones. It is also a “time art” because it develops and lasts trough the passing of time. Elementary material, without which there will be no music, is sound. Sound is appearance that arises by flickering of air particles from various sound sources. Sound with certain pitch produces notes, and with uncertain pitch it’s pure noise. Sound has four major characteristics: duration, volume, pitch and colour. Duration is determined by length of the flickering sound source. Volume depends on the magnitude – expanse of the flickering. Higher pitched tone has a bigger frequency and lower pitched tone has a smaller one. Tone pitch depends on the speed and number of flickering, sampling rate of the frequencies, bigger or smaller. Regular flickering produces tones, and irregular one produces noise (speech, clamor, squeak, thunder). So, the difference in the flickering decides if we hear the tone or the noise. Speaking of the tone colour, tones of the same pitch although coming from different sound source, are distinctly different (flute from oboe, violin from cello, within human voice – soprano from alto, alto from tenor, tenor from the bass...). Musical tone represents a complex musical phenomenon consisted from fundamental tone, the one you can really hear and barely recognizable aliquot tones that are not played but sound “in sympathy” with the same note. Aliquot tone is always perfect row of tones that influence its colour. The order of the aliquot tones is always the same. Here is the order of the first 16 aliquot tones on the tone C (tones marked with () do not sound clear).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Following the order of intervals, second aliquot tone is an octave of the first one, third is a fifth of the second tone, fourth aliquot tone is a fourth of the third tone, fifth is a third of the previous one and so on... Only after you’ve mastered intervals, you should practice aliquot tones, first by the groups: 1-4, 4-7, 8-12, 12-16, and then the whole sequence from different notes, as an example: D, A, E, B, F sharp... You should also remember that first, fourth, eight and sixteenth tone are the same, but in a different octaves. Second, third and fifth are the tones of the major triad. Here we have two examples of aliquots of 16 tones divided into groups a) from the tone B flat, and b) from the tone E. a)
b)
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MUSICAL NOTATION With exception of the color we can write down the other three characteristics of the tone: duration, volume and pitch. Duration of the tone is written as notes of different shapes. The basic is whole note (semibreve), consisted of two half notes (minims), four quarter notes (crotchets) or eight eight notes (quavers), 16 sixteen notes (semiquavers) etc... This is a normal even partition of the basic unit.
whole note (semibreve)
= = = =
half note (minim)
= = =
quarter note (crotchet)
= =
eight note (quaver)
sixteen note (semiquaver)
= = = =
All of the notes above have their corresponding rest.
whole (semibreve) rest half (minim) rest quarter (crotchet) rest eight (quaver) rest sixteen (semiquaver) rest thirthy-second (demisemiquaver) rest
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It’s expected to connect the notes that have “tails” (eights, sixteens…) with a beam, into a figure.
= =
=
Duration of notes and rests can be increased by using a dot, for the half of its original value. In that case uneven partition of all dotted notes on 3, 6 parts is considered as normal. If the note is increased using two dots, length of the tone is than increased by one-half of the value of the first dot. A dot could be added to the rests as well, increasing its length.
=
+
=
+
+
= + + = + = + + + = = + + 6 = + It has already been said that note values can be minimized by an even partition into two, four, eight parts.
But it could be also divided into three, five, six, seven parts. On contrary, in case of an uneven partition on three or six, it’s possible to divide note into two, four parts. This results in irregular rhythmic division of note values.
Triplet
Quintuplet
= =
Duplet
= =
Quadruplet
6
Sextuplet
= =
11
= =
= =
Volume of the tone is written with different acronyms, taken from the Italian language, as well as with graphic symbols. Here are some of the most used dynamic symbols (from the Greek dynamis = force, strenght, volume): f (forte) - loud, ff (fortissimo) - very loud, p (piano) - soft, pp (pianissimo) - very soft, mf (mezzo forte) moderately loud, mp (mezzo piano) - moderately soft. For graduate transition from soft to louder we use the term crescendo , for transition from loud to quiet we use the term decrescendo or diminuendo . Every tone has its name. Seven basic tone pitches are named by alphabetical letters: C-D-E-F-G-A-B. Using different pronunciation called solmization, these notes could be also named as Do-Re-Mi-Fa-Sol-La-Ti-Do. Tones are written with signs called notes. Notes are written on a set of parallel lines called a staff or stave, consisting of five lines and four spaces between them. Sequence of all the tones, from the lowest one to the highest is called tonal system, divided by octaves (sequence of eight tones C-D-E-F-G-A-B). The eighth tone has the same name as the first one, only one octave higher. The whole tonal system has a range of eight octaves: subcontra, contra, large, small, first, second, third, fourth.
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C
C
Sub contra
C
Contra Large
c
c1
Small
c2
First
c3
Second Third
c4
8
c5
Forth
As musical staff is restricted to five lines and four spaces, only limited amount of notes of the huge tonal system is possible to write. That’s why leger lines are used to extend the staff.
CLEFS Names of notes couldn’t be read without a sign at the beginning of each musical staff called clef. Clef indicates the place of certain tones in the staff. Although there are several different clefs, most common are the treble or G clef (it begins on a second line of the staff and gives a name to a note G) and bass clef or F clef (it starts on a fourth line of the staff and gives a name to a note F). Treble clef is used to mark the high pitched notes, while bass clef is used for lower pitched tones.
g
f
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Here are some notes and their names in the treble and bass clef.
g
f
a
g
h
a
c
h
d
c
g
f
f
e
e
d
d
c
c
e
h
g
g
h
h
d
d
f
f
a
f
a
a
c
c
e
e
g
In earlier times many different old clefs called “vocal” C clefs have been used: soprano, alto, tenor and mezzo soprano clefs. Although nowadays mostly used clefs are a treble G clef and a bass F clef, some old clefs as alto and tenor are also regularly used.
Here is a summery of all the clefs, using the note C1.
treble
bass
alto
tenor
soprano
mezzo soprano
Here are some examples comparing notes in treble, alto and tenor clefs.
a1
a1
baritone
basso profondo
a1
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Following examples are showing us tones of the same pitch in different clefs.
Practices, exercises Rewrite given examples from the treble into alto and tenor clefs.
Rewrite given melody from the alto into treble clef. (You should first transpose melody for one descending seventh and then add the accidentals).
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Rewrite given melody from the tenor into treble clef. (You should first transpose melody for one ninth downwards, then add the accidentals).
ACCIDENTALS In addition to basic notes in the tonal system, there are also raised and lowered notes. Every basic note can be raised with a sharp sign () or lowered using a flat sign () for a semitone. These signs are either written in front of the note, where it stands in the staff or at the beginning of the musical staff, right after the clef. Other signs are a double sharp (x) and double flat ( ) that are raising or lowering a note for a tone. Sign that is cancelling previous accidental, thus returning the note to its original pitch is called a natural ().
g
-
g
g sharp
-
g -
g flat
g
double sharp
-
g double flat
Here is the chart of basic notes and its chromatics changes.
C
D
E
F
G
A
H
C
15
c sharp
c flat
d sharp
d flat
e sharp
e flat
f sharp
f flat
g sharp
g flat
a sharp
b sharp
a flat
b flat
Oral training
First (semibreve) note is named by teacher, following ones
(••), (•••) by students.
c double sharp
c double flat
d double sharp
e double sharp
d double flat
e double flat
f double sharp
f double flat
g double sharp
a double sharp
g double flat
a double flat
b double flat
To practice, pronounce alphabetical notes from double flats to double sharps and vice versa (follow given examples). Repeat the exercise from all notes with double flats and double sharps.
b double sharp
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RHYTHM To be able to call something music we must rhythmically formulate and organize a sequence of tones. From all the factors of music: melody, harmony, key, musical form – rhythm is the most important and only independent category in the music. Rhythm is defined like a flow of sounds or notes of different time duration. Sequence of notes of the same duration is sometimes used, although very rear in longer episodes. Besides duration rhythm is characterized by emphasized beats - accents. They are noted and measured by a constant repeat of the pulse – beat, and can be also shown in constant change of non accented and accented notes. That flow of change between stressed and unstressed sounds called music meter is explained by science of metric structure. Rhythm and meter are closely connected – rhythm is based on the duration, while meter is focusing on the accents. Meter is organizing music notes into bars, or grouping the beats into measures, with their recurring accents. Every metrically defined group that has at least one meter accent is called a bar. Bar is a smallest part of a music composition defined by meter. A vertical line is placed on the staff, called a bar line. To determine the time, we use a time signature at the beginning of the composition, right after the clef (and possible accidentals). The upper figure in the time signature tells us how many beats there are in each bar, and lower figure represents what kind of note is a beat. A beat is usually a quarter (crotchet) or eighth (quaver) note, less commen is a half note (minim), and in rear cases a whole (semibreve) or sixteenth note. The type of bar is determined therefore by a number and type of beats. Number of beats could be from 2 to 12. Upper figure explains time signatures us duple, triple, quadruple… compound duple, triple…. time.
2 3 4 4 2 8
…
6 7 8 8
…
9 8
…
12 16
The lower figure shows that note representing the beat is a quarter note, a half note, an eighth note, a sixteenth note. The upper figure shows us how many beats there are in one bar. Duple and triple times with only one accent are called simple times. First part of the bar is always accented. Other times occur when at least two categories of simple time signatures unite. These are mainly simple 4 4 4 6 6 quadruple time 4 8 2 and compound duple time 8 4 . There are other compound time signatures, as well as irregular times that consist of mixture of duple and 5 5 7 triple times (they can also be called mixed meter signature): 8 4 (2 + 3, 3 + 2), 8 (two duple and one triple), 8 9 8 (two triple and one duple), like compound time (3 + 3 + 3) or irregular time (three duple and one triple). 8
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It’s very interesting that in compound time 8 we conduct on three, because there are three strikes – accents, while irregular time 98 has four strikes (three duple and one triple) so it’s conducted on four. Other distinctive rhythmic groups include: syncopation, anacrusis and upbeat. Syncopation occurs by connecting unstressed note with the accented one. That way accent gets switched on beginning of the syncopation, so unstressed part of the bar becomes the stronger one. The easiest way to notice syncopation is connecting the second and third note with a tie, in a sequence of four identical notes.
You should notice the same syncopation even if written differently.
=
=
=
We should also notice more complex forms (with a rest at the beginning).
=
=
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=