The Arithmetic of Music by Nestor S. Pareja

The Arithmetic of Music

Nestor S. Pareja, M.D. 1

The Arithmetic of Music. Copyright by Dr. Nestor S. Pareja. Parts of this book may be reproduced solely for personal use. For information, telephone and fax no. (632) – 5527911; mobile phone no. 09162571055; address 30-G RPR I, Padre Faura, Ermita, MetroManila, Philippines; e-mail,[email protected],[email protected],or [email protected]

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PREFACE This booklet is a synthesis of information gathered from more than 30 years of experience in learning to play musical instruments without much help from formal training. Of the informal training received from some “naturally talented” musicians, curiosity in how they seem to have learned and retained knowledge easily spurred me to study the dynamics of music and translate these to practical ways that could be used by people like me who had the interest to play music but lacked the “natural talent” for it. Data were culled from available printed articles, books, encyclopedias on music and from informal talks with musicians, professional and otherwise

and

sporadic

playing

of

various

musical

instruments. Inasmuch as writing this book was not the original intent of the author, references were not documented but nevertheless gathered from reliable printed sources. This is a revised edition of the first that never got to be published because of time and financial constraints, as the author would like to believe. As the information and ideas were interesting and very clear, the translation and transfer did not seem to be a problem at the time of first writing. Copies of the original manuscript were shared with knowledgeable 3

people assumed to be interested. There was no response from most. Of the few who did, it was most probably out of kindness and was only meant to be polite. This was however taken by the author as an affirmation. Upon review of the original manuscript which has been kept in hibernation for several years, the truth behind the earlier response was revealed. The author himself discovered that contrary to the intent of simplifying the presentation, the medium used could barely be understood. The author strongly believes that these ideas are useful and worth sharing. Revisions have been undertaken to make the book simpler and easier to understand. Principles of tone/sound

production,

its

physical

attributes

and

appreciation by the receiver have been integrated to add to an easier and better understanding of music. The Author

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The Arithmetic of Music Table of Contents Introduction

1

Chapter One: Music, Sounds and Silences

11

Chapter Two: Music Intervals

21

Chapter Three: Reading and Writing

43

Chapter Four: Musical Scales An Overview

55

Chapter Five: Diatonic Scale, Major and Minor

65

Chapter Six: Modal Scales

75

Chapter Seven: Pentatonic and the Whole Tone Scale

83

Chapter Eight: Music Chords

89

Chapter Nine: Melody, Musical Form and Design

119

Chapter Ten: Cadence

125

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Option: Music may be defined as the art and science of transmitting emotions or ideas with the use of sounds (of varying pitches) and silences that are considered pleasing to the listener. Musical sounds or notes are produced by strings, tubes or percussed suitable materials. A musical note is defined or characterized by its pitch (high, low or anything in between). The pitch of a note is determined by the frequency with which the string or the column of air in a tube vibrates. Together with the pitch, a musical note is also defined by its timbre. The timbre allows us to differentiate the sound of a guitar from that of a violin. The timbre is determined by final sound a musical instrument produces. The final sound is influenced by the interplay of the primary tone and its overtones. Let us take for example a guitar string vibrating at a frequency of 264 cycles per second. This string does not only vibrate at 264 cps on its whole length ( called the primary length. It also vibrates 528 cps (264 X 2) on ½ of its length. 528 cps is an overtone of 264 cps (the primary tone of the example guitar string). This string also vibrates at 792 cps (264 X 3) on !/3 of its length. 792 cps is also an overtone of 264 cps. This string vibrates at 1056 cps (264 X 4) on ¼, 1320 cps (264 X 5) on 1/5 its length and so on down the line. These simultaneous vibrations influence how the final sound of that string will be produced by tha particular string. That final sound is the timbre.

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THE ARITHMETIC OF MUSIC By Dr. Nestor S. Pareja INTRODUCTION Music is primarily an art. This booklet deals with another side: the measurable, easily identifiable and easy to grasp but vital feature of music. This is neither the mathematics nor the physics of music. Rather this is reading, writing and the Arithmetic of Music for those who appreciate music but feel a need to understand how it works. Understanding how something works can help us better appreciate, further explore and put to use the potentials of many of its wonders. For those who can hum a tune, can sing a song but have confined these activities where others may not hear, applying the simple guidelines this booklet offers will increase their love for and involvement in music. It can open new doors to a bigger world of music. Lord William Thomson Kelvin, an English physicist, said that one’s knowledge of a thing is meager and unsatisfactory if that thing can not be expressed in numbers and can not be measured. This booklet 7

subscribes to this idea. This will introduce numbers that will allow us to measure and to describe music understandably and easily. This knowledge will enable us to read and write music sheets/scores and begin to play our favorite music instrument or yet be able to compose songs. This is primarily for those with little or no background in music but who are willing to learn the essentials to understand how it works. These essentials will help us understand music articles, many of which presume such knowledge. This knowledge will make us understand what Key of C or C Scale and the other Keys or Scales mean. This will make us understand why a symphony or a song is a B flat minor or a D flat composition. We will understand what Ionian Mode, Dorian Mode or Lydian Mode mean. This is also for those who already are into music, the professionals, those with advanced knowledge and the “gifted”. This book presents a simple complementary view that will help those with advanced knowledge in music further grasp/comprehend/internalize and make the most of their present concepts and know-how. Music teachers may find practical ways of teaching the basics of music.

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WHAT THIS BOOK CONTAINS The first two chapters deal with simple principles that are applied in music. They are explained even the “nongifted” in the Sciences can understand. Waves, overtones and intervals are explained in layman language. The third chapter introduces the language of music, symbols used by musicians to convey emotions and ideas, the same way we use letters of the alphabet, punctuation marks, words, sentences and paragraphs to transmit ours in the print media. A complementary view to the present concepts of music is offered in the fourth chapter. For the novice this can advantageously be the primary view because it is simple and easy to use. For the advanced this view hopes to significantly strengthen their concepts, abilities and knowhow. The fifth to seventh chapters talk about music scales: how the different scales are created, why they project certain moods/ambiance/atmosphere and how and when they are used presently. The eighth chapter discusses music chords: their uses, how they are built, and a simple and easy method of building chords in all scales, by memory! 9

The ninth chapter touches briefly on melody, musical form and design. This will introduce terms that will help us better understand and appreciate music. STRATEGY The basic strategy of this book is repetition, saying the same idea in different ways. The ideas are presented from different points of view, so that we may acquire a 3 (even a 4?) dimensional picture of the concepts. This is to ensure that concepts are well understood. They are important building blocks in our understanding of music. As is true in many disciplines, concepts in music are simple when taken individually/separately but seem complicated when taken all together at one time. Chapters are arranged mainly to facilitate explanation. They are intended to stand alone and could be understood even without having full comprehension of the others. Although

ideas

understood

are

without

interrelated, reading

other

a

chapter chapters.

may

be

Chapters

generally refer to the same ideas but are taken from different views/perspectives. Music concepts are basically simple but are prone to many different and complex interpretations, because of

10

mysteries/confusions created by vague statements. The use of numbers avoided such statements and has facilitated definition and explanation of concepts. Sentences in this book are meant to be simple and direct but inevitably repetitious because of the basic strategy. Learning these concepts and keeping them at our fingertips will allow us to devise our own learning exercises for our chosen musical instruments and/or music activities. This will allow us to determine our own pace and our own level of involvement. We will not be limited by availability of specific learning materials because hopefully we will be able to devise our own. We are offered choices. Numbers are liberally used so ideas can be measured, can be easily described or defined and stated in no uncertain way. The importance of practice and of guidance by a competent music teacher can not be overemphasized. When we students are ready, the teacher in this book will appear.

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SYNOPSIS Music is the rhythmic, melodic, harmonious and colorful arrangement of sounds and silences that communicates emotions and/or ideas. Frequencies and timbres distinguish musical sounds and tones. Differences in timbre are due to differing overtones present. The timbre allows us to distinguish the sound of a violin from that of a trumpet or the voice of a friend from another’s. The timbre makes us like or be pleased with certain sounds. As beauty is in the eyes of the beholder, how pleasing and how harmonious sounds are is personal and relative. Recurrence and interval are the measuring sticks or parameters used to assess how pleasing sounds are. In this book it is assumed that sounds which are heard more often are more pleasing. Interval in music is the ratio or relation of the frequency of a note to the frequency of another. Dividing the frequency of a note with the frequency of another will 12

give us that ratio or interval. In Western music two kinds of intervals are identified. One measures the interval created by notes with a common reference note, the tonic. The other measures the interval between nearby or adjacent notes. In the first kind, the most pleasing interval is the unison. It is created by notes with the same frequency as the tonic. Almost as pleasing are those created with the octaves (the 8th natural note or semitone 13). The octaves are notes whose frequencies are either ½ or 2 times the frequency of the tonic. The next pleasing intervals, after the unison and the octaves, in descending order, are created by notes whose frequencies are 3 times, 4 times, 5 times, 6 times and so on, that of the tonic. These frequencies are correspondingly produced by the (1/2), 1/3, ¼, 1/5, 1/6 and so on the other secondary lengths of a vibrating string. The shorter the secondary length, the higher the frequency of the note/sound the vibrating string produces and the note produced is less harmonious with the tonic. The frequencies of the notes within an octave (a group of 8 natural notes) are partials of the frequencies produced by the secondary lengths. This is explained further from another view and in a more easily digestible form in Chapter

13

Two. The second kind of interval is that created between adjacent notes. There are 2 types that are identified, the semitone (or half tone, half step, a 16/17 or its reciprocal 17/16, interval) and the whole tone (or whole step, a 16/18 or its reciprocal 18/16, interval). If we divide the frequency of one

note

with

the

frequency

of

the

next

higher

adjacent/nearby note and get the ratio 16/17 or 0.94, the interval is a semitone. If the ratio between the frequency of the lower note with the frequency of the higher adjacent note is 16/18 or 0.89, the interval is a whole tone. In the chromatic scale there is only one kind of interval, the semitone. Dividing the frequency of the lower semitone with the frequency of the higher gives us the ratio of a semitone interval. The inverse/reciprocal (frequency of the higher divided by the frequency of the lower note), likewise defines a semitone interval. Musical scales with 2 types of intervals between adjacent natural notes, whole tones and half tones, are called diatonic scales. The notes of a melody may sound lacking in fluidity, rhythm and unity if played without other sounds. The notes of music chords correct these. They supply additional

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“color” and character to the melody. They serve as the framework and body to a set of melodic notes. Silences between notes play a significant role as well. Tryreadingasentencewithoutspacesinbetweenwords. The character, personality, atmosphere, ambiance or mood of a set of melodic and harmonic notes depends on the location of the semitone and whole tone intervals. Thus we have the emergence of the different scales: the diatonic, the modal, the pentatonic, the whole tone and the major and the minor scales. These scales on analysis are derivatives and/or modifications of the mother scale, the chromatic scale. Dr. Nestor S. Pareja Author

15

CHAPTER ONE MUSIC, SOUNDS AND SILENCES

Music is the arrangement of sounds and silences to express emotions and/or ideas. This is achieved through the use of rhythm, melody, harmony and “color” of sounds. Rhythm is the uniform or patterned recurrence of a beat, accent, or the like. Melody is how the musical notes of varying frequencies or pitches are arranged one after another while harmony is how pleasing two or more musical notes sound together. “Color” is the quality, the timbre, the mood, the atmosphere, the personality or the character of the melody or harmony of sounds/notes. “Color” is determined by what overtones are present. Overtones will be explained later.

16

Sounds are waves that are heard. Other waves are seen. Others are felt. The ripples created by a stone thrown into a quiet body of water are waves. Waves that are seen are those coming from a light bulb and those that are reflected/bounced back from objects. Reflected light waves give color to the objects. Objects that bounce off all light waves of natural light will look white. Objects that do not bounce off light waves will look black. Light waves are energy and energy is heat. Dark colored clothes do not reflect most of the light waves they receive. Most are absorbed. Light colored clothes bouncing off most of the light waves they receive explains why they feel cooler than are dark colored ones. Ultraviolet waves are felt. These waves can warm or burn. Taste buds in the mouth and nerve endings in the nose possibly respond to waves coming/emitted from what is tasted or smelled. The frequency of the wave determines whether it will be heard, seen, felt, tasted (?) or smelt (?). The function of the receiving sense organ also determines how a stimulus will be interpreted or translated. 17

To illustrate; the function of the eye is to see light. Stimulation of the eye, other than by light, will still be interpreted as light. As an example, touch your eye with your eyelid closed. The eyelid will feel your finger. A dark spot with a halo of light about the area of the finger that is in contact with the eyelid will be sensed or “seen”. WHAT IS A WAVE? A wave is a rhythmic/regular/patterned movement of energy. A guitar string when plucked will vibrate and produce waves. We hear some of these waves. The other waves we feel as we hold the guitar close to our chest. Imagine and trace the up and down movements of a point, the midpoint of the whole length of the vibrating string. The whole length of the string is called its primary length. From position A, it moves up to position B, bounces down to position C (passing through position A) and bounces back to position A, completing a cycle. The string completes many more cycles with diminishing loudness until the energy transferred to it by plucking is used up.

18

If the up and down movement of this point is plotted on paper that is behind and moving horizontally (across) at an even speed, the vertical distance AB (also equal to AC) traveled by the midpoint on the paper is called the amplitude of the wave. The amplitude of a wave determines its loudness, volume or intensity. The horizontal distance traveled by the midpoint on the paper during one cycle is called the length of the wave or wavelength. The number of cycles completed during/within a unit of time is called the frequency of the wave, example, cycles per second (cps or Hertz, Hz). The frequency determines the pitch/key of a note, the higher the frequency, the higher the pitch/key. Joseph Fourier, a French physicist, discovered that any complex wave could be broken down into its 19

component simple sine waves. Waves are simple or complex. A sine wave is the simplest waveform. It has a constant amplitude and frequency.

He discovered that a complex wave like the sound wave produced by a performing orchestra is but a combination of many simple sine waves of different amplitudes and frequencies produced by the different musical instruments. Have you wondered how the sounds of all the music instruments are heard from a single speaker, further considering that all those sounds are picked up from a single record disc by only one laser beam or one phonographic needle? The complex wave on the disc is picked up by the laser beam/needle and transmitted to the speaker. The speaker reproduces the complex wave. The ear “breaks” the complex wave into its recognizable component simpler 20

waves allowing us to recognize the sound of each instrument. How then do we distinguish the sound of a clarinet from that of an oboe? They are distinguished by the difference in the shape of the wave each produces. The shape of the wave depends on what overtones are present and predominate.

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WHAT ARE OVERTONES? A vibrating guitar string produces a complex wave. It does not produce only one sound wave. Sound waves are simultaneously produced by the whole length, by the ½ length, by the 1/3, by the ¼ length, by the 1/5, 1/6, 1/7 and on the other secondary lengths of the string. They have different frequencies. Let us take for example, a guitar string 1-meter long (its primary length), vibrating at 264 Hertz (its primary tone) on its primary length. At ½ meter, this string is also vibrating at 528 Hertz which is 2x the frequency of the primary tone. The ½, 1/3, ¼, 1/5, 1/6 meter and so on are called the secondary lengths of the 1-meter primary length. On its 1/3 meter, it will be vibrating 3x that of the primary tone, 3x 264 =792; on the ¼ meter, 4x 264 = 1056; on the 1/5 meter, 5x 264 = 1320, and so on. These statements say that the frequency of the wave produced on a secondary length is equal to the frequency of the primary tone multiplied by the reciprocal or inverse of the secondary length. The reciprocal or inverse of ½ is 2/1 or 2; that of 1/3 is 3/1 or 3; ¼ is 4 and so on.

22

On the other hand, the volume of the sound produced diminishes in direct proportion with the secondary length. The volume of the wave produced by the ½ secondary length is ½ that of the primary length. The volume and intensity of a wave is determined by the wave’s amplitude. The amplitude is directly proportional to the secondary length of a vibrating string. Each of the secondary lengths is producing overtones of their own on so-called tertiary lengths. Likewise these tertiary lengths are producing overtones of their own on the quaternary lengths and so on down the line. The overtones produced on the secondary lengths are called harmonic overtones: on the ½, the 2nd harmonic overtone, on the 1/3, the 3rd harmonic overtone, on the ¼, the 4th harmonic overtone and so on down the line. In summary, a vibrating string produces a sound, which is the result of the combination of its primary tone, harmonic and other overtones. These different waves influence and/or interfere with each other before producing the final waveform. This combination

23

of overtones and the resulting final wave form will give this particular vibrating string its timbre. When a string vibrates, it makes surrounding objects vibrate/resonate on their natural frequencies. The string also initiates forced frequencies on these objects. The presence of two or more waves or the socalled superposition of waves creates interference (reshaping of the wave). The compactness/density and shape of the vibrating material, force in stretching or the tension or pressure applied, surrounding atmosphere, humidity and many other factors determine what overtones will prevail and thus define the final shape of the wave produced, its timbre, its “color”. “Color” of Sounds For some people, sounds of musical instruments are easily distinguishable from one another. It is not that easy for others. This is due to varying levels of sensitivity to small differences in the shapes of the wave. This ability to distinguish subtle differences in the “color” of a sound can be acquired and developed. To support this statement an interesting and

24

revealing scientific experiment is worth mentioning. A group of kittens was raised in an environment whose lines were mainly horizontal and another group in an environment whose lines were mainly vertical. When they matured and were released to normal environments, the “horizontal group” kept running into legs of chairs, tables and objects whose lines were mainly vertical They “could not see” vertical lines. Those in the vertical group would bump on object whose lines were mainly horizontal. On microscopic examination, differences in their brain cell structures were identified and authenticated, verified and/or validated. This experiment demonstrates that light waves influence brain cell development. Light and sound are waves. Waves share common properties. It can be inferred that sound waves influence brain structure as well.

25

CHAPTER TWO Music Intervals We learned about overtones, how they affect the shape of the final wave, the “color” of sound. We learned how resonance, interference and other factors affect the shape of the final wave. When a string vibrates, it does not produce only one wave. It produces waves of different frequencies on its primary, on its secondary, tertiary and other lengths. The waves/overtones produced on the secondary

lengths

are

specifically

called

harmonic

overtones. Overtones produced on the lengths other than the secondary lengths are referred to simply as overtones. Both the secondary and the other overtones are among the factors that influence the final shape of the wave. The waves initiated from among surrounding materials, their interaction and superposition also modify the shape of the final wave. The resulting wave give the sound produced by the vibrating string or any vibrating material its timbre or “color”. The next concept is music interval. A good grasp of these concepts is important in our study. They are basic blocks on which we will build a clear understanding of how music works and how we can make this knowledge work

26

with us. Music interval is the ratio of the frequency of a note with the frequency of another note. Ratio is the proportional relation of one frequency to another. Dividing the frequency of a note with that of another will give us this ratio/interval. Ex: The frequency of note C is 264 Hz. The frequency of note G is 396. The interval between these notes can be stated either as 264/396 or its inverse 396/264 (2/3 or 3/2, if 264 and 396 are divided by 132, a number common to both, the greatest common number/divisor). Music intervals are defined 2 ways: (1) intervals produced by notes with a common reference note, the tonic and (2) intervals produced between adjacent/nearby notes. The consecutive natural notes of the Key of C are given letter names: C, D, E, F, G, A, B, C’. Examples of the first kind of interval are those between notes C and D, notes C and E, notes C and F, notes C and G, notes C and A, notes C and B and finally notes C and C’. Note C is the reference note, the tonic note of the Key of C. Examples of intervals between adjacent notes are, those between notes C and D, notes D and E, notes E and F, notes F and G, notes G and A, notes A and B and finally notes B and C’. The interval C and D belongs to both kinds

27

of intervals. The interval between adjacent notes in a diatonic scale is either a whole tone or a semitone (half tone or half step). The whole tone interval is practically or essentially equal to 16/18 (or 0.89), if we divide the frequency of the lower note with the frequency of the higher note. If we divide the frequency of the higher note with that of the lower note we get the reciprocal 18/16 (or 1.125). The semitone interval is essentially equal to 16/17 (or 0.94) or its reciprocal 17/16 (or 1.0625). In the popular Key of C whose notes are assigned letter names C, D, E, F, G, A, B, C’, note D is the 2nd natural note and its interval with the tonic C is called a 2nd interval. Note E is the 3rd natural note and its interval with C is called the 3rd interval. The interval with the 4th natural note is called the 4th interval and so on. There are other special names for all these intervals as we shall see later. They are more descriptive and specific but somehow tend to muddle and confuse the issue for others. These names will however be discussed later for whatever purpose they may serve. The most popular musical scale is the major diatonic scale. This scale is associated with the familiar do-re-mi sound. Let us take an example the C major diatonic scale,

28

also called Key of C, Scale of C or the C Scale. It has 7 easily distinguishable and convenient to remember tones or notes that are assigned the letters C, D, E, F, G, A, B. For purposes of practice and convenience these letter notes may be sung do-re- mi- fa- sol- la- ti. If you tried to sing that, how did the scale end? Did it feel that something more was to come after the note -ti? The feeling that the –ti sound gave, describes what a leading note does. Next, instead of singing the scale ending in -ti, sing do- re- mi- fa- sol- la- ti- do. Doing so creates an atmosphere of finality. These feelings are evoked, elicited or produced if one is familiar with the do-re-mi sound. The C major diatonic scale is usually written C, D, E, F, G, A, B, C’. Notice the prime sign (’) on the 2nd C. The interval C to C’ is an octave. The term octave may also refer to the 8th natural note of a scale, in this case, note C’. Octave can also refer to a group of 8 natural notes.

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INTERVALS WITH THE TONIC The frequency of tonic C (264 Hz) divided by that of C’ (528 Hz) is ½. The inverse ratio, the frequency of C’ divided by that of C is equal to 2/1 or 2. These intervals are called octaves. The note that creates an octave interval with the tonic is also called an octave. The octave note is also called the 8th natural note or the 8th degree. In this book, every now and then, we will refer to the octave note and the octave interval as semitone 13. The natural notes of a Scale are also known as degrees, 1st, 2nd, 3rd and so on. The frequency of note C’ is equal to the frequency of the 2nd harmonic overtone of note C. The 2nd harmonic overtone is produced by the ½ length (one of the secondary lengths) of a vibrating string and its frequency is 2x that of note C. Notes C and C’ being octaves produce essentially the same overtones; their timbres and “colors”

30

are essentially the same. Notes D and D’ are essentially the same notes, as they produce essentially the same overtones; but D’ belongs to the next higher octave, scale or key. The same is true with the other octave intervals (semitone13). The interval between the tonic note C and the 2nd natural note D is called a 2nd interval or a Major 2nd or M2 interval. The interval between the tonic C and the 3rd natural note E is called a 3rd interval or a Major 3rd or M3. The interval between the tonic C and the 4th and the 5th natural notes are respectively referred to as Perfect 4 or P4 and Perfect 5th or P5. The interval between the tonic and the 6th natural note is called a Major 6th or M6. The interval with the 7th natural note is called a Major 7th or M7. After the octave are the 9th, 10th, 11th, 12th, 13th intervals.

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The harmonic overtones produced on the secondary lengths (½, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9 and so on) are progressively and proportionately increasing in frequency. Harmony

with

the

tonic

however

proportionately

diminishes with the increase in frequency. The amplitudes of the waves proportionately diminish with the secondary lengths. And because the amplitude determines the volume of the overtones, they are progressively less heard. Intervals with the tonic are classified into: (This classification is arranged in descending harmony with the tonic.)

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Perfect Unison Octave Dominant Subdominant Major Mediant Submediant Supertonic Leading Note Accidentals Augmented Diminished Minor PERFECT INTERVALS Unison and Octave The most pleasing and harmonious intervals are those from a (1) unison, the superposition of waves whose frequencies are the same, and from (2) octaves, the superposition of waves of the tonic and of waves whose frequencies are its halves or doubles.

33

The simultaneous playing of notes whose frequencies are an octave apart is practically a unison. Notes that are an octave apart produce practically the same overtones. The prime sign (‘) after the letter note is used to signify a note which is one octave higher, like C’ is one octave higher than C. The notes C, D, E, F, G, A and B will sound essentially the same as the notes C’, D’, E’, F’ G’, A’ and B’ although they are one octave apart. The overtone created on the ½ length, the 2nd harmonic overtone creates the octave interval with the tonic. As mentioned earlier, the term octave also refers to the 8th natural note, like C’ is the octave of C, and the other way around. Octave is also conveniently used to mean a group of 8 natural notes. The group of the notes namely C, C#, D, D#, E, F, F#, G, G#, A, A#, B and C’ has 13 notes. Although it has 13 notes, this group of notes is still called an octave, because it has only 8 designated natural notes. Dominant The overtone that creates the next most pleasing interval with the tonic is the 3rd harmonic overtone. The 1/3 secondary length produces this. Its waves dominate the other subsequent harmonic overtones by overshadowing 34

them as to loudness and as to influence in determining the final waveform of the tonic. The 1/2 partial of this overtone is assigned to the dominant and 5th natural note of the major diatonic scale of its tonic. The frequencies of the notes within an octave are equal to the partials of the frequencies of the harmonic overtones of the tonic. The range of frequencies of the notes in an octave starts with the frequency of the tonic and ends with the frequency of the 8th natural note (the octave note, semitone 13, the 2nd harmonic overtone or the overtone produced by the ½ secondary length). In our reference scale the Key of C, the frequencies of the notes start with 264 Hz (tonic C) and ends with 528 Hz (note C’, the 8th natural note, the octave note of C, semitone 13 or frequency of the 2nd harmonic overtone of tonic C). The frequency of the 3rd harmonic overtone of note C is 264 x 3 = 792 Hz. This is beyond the 264 to 528 Hz range. If we divide 792 by 2 we get the frequency 396 Hz. This frequency is assigned to note G, the designated 5th natural and dominant note of this reference scale, the Key of C. As we shall see farther, the frequencies of the other notes in this scale, natural and accidental, are portions/parts

35

of or partials of the frequencies of the harmonic overtones produced by the secondary lengths. The interval that the dominant note G creates with its tonic (note C) is called a 5th interval because the assigned note to it is the 5th natural note of the C Scale. This interval is also known as Perfect 5th or P5. The interval is 8 semitones. The frequency of note G is 264 x 3/2 = 396 Hertz. Subdominant Another perfect interval with the tonic is the Perfect 4th (P4). The interval it creates with the tonic is less harmonious than that created by P5.

The interval is 6

semitones. Its frequency is a partial of the 4th harmonic overtone. The 4th harmonic overtone is produced by the ¼ length of a vibrating string. !/3 of this frequency is assigned to the 4th natural note of the diatonic scale of its tonic. The 4th harmonic overtone of tonic C is 264 x 4 = 1056 Hz. 1/3 of 1056 is 352 Hz. This frequency is assigned to note F, the designated 4th natural note of the Key of C, In the Key of C, note F is a natural note below the dominant note G. Note F is less dominant to and less harmonious with tonic C. Note F is consequently called the subdominant of

36

the Key of C MAJOR INTERVALS Mediant The overtone that creates the next most pleasing interval with the tonic is the 5th harmonic overtone. The 1/5 length of a vibrating string produces it. The frequency of the 5th harmonic overtone of note C is 264 x 5 = 1320. The ¼ partial of this frequency is 330 Hz. This frequency falls right in the middle of the frequency of the tonic (264 Hz) and that of the 5th note (396 Hz). This note is consequently called the mediant of the Key of C. This note is designated as the 3rd natural note of the C major diatonic scale. The interval it creates with the tonic is called a Major 3rd (M3) or 5 semitones. The mediant of the C Scale is note E.

Its

frequency is 264 x 5/4 = 330 Hertz. Submediant A closely related note to the mediant is the submediant, because its frequency is also a partial of the 5th

harmonic

overtone.

The

submediant

is

less

harmonious to the tonic than the mediant is, thus the name. The 5th harmonic overtone is produced by the 1/5 37

secondary length of a vibrating string. The frequency of the submediant is 1/3 of the 5th harmonic overtone. The submediant of the C Scale is note A. The interval it creates with the tonic is called a Major 6th (M6) or semitone 10. The frequency of note A is 264 x 5/3 = 440 Hertz. Let us temporarily stray away from the present topic and go to a subject deemed important and interesting at this point. This information will allow us to use the easily available piano music sheets in playing the same melody, in the same Key, in our selected music instrument, even if the assigned key/pitch of that instrument is not the same as that of the piano. Musical instruments have different assigned/recognized pitches or keys. In an international music convention, the frequency 440 Hz has been set as the standard frequency for note A of the middle octave on the piano keyboard. But even if this has been set as the international standard, still 264 Hz, the frequency of note C of the piano keyboard, is used as the reference frequency in identifying the pitch of other music instruments. Almost all Western music instruments can produce the popular Do-Re-Mi sound together with its accidental 38

notes. The frequency of the sound Do on an Alto Saxophone differs from the frequency of the sound Do on a standard trumpet. The frequency of the sound Do of an Alto Saxophone is 313.5 Hz. This is the same frequency as that of note Eb on the piano. The Alto Saxophone is accordingly called an Eb instrument. The frequency of the sound Do on a standard trumpet is 231 Hz, same as the frequency of the note Bb of the piano. The standard trumpet is accordingly called a Bb instrument. In producing the Do-Re-Mi- sound, the fingering (which holes are close or open) is the same for all kinds of saxophones (bass, tenor, alto, soprano), clarinets, flutes and piccolos. This means that if one knows how to play the do-re-mi sound on one of the mentioned music instrument, he/she can play the do-re-mi sound with the same fingering on all the other instruments. They will however differ as to Key or pitch. The key/pitch is determined by frequency of the Do- sound of the instrument, its assigned tonic. If the frequency of the tonic is the same as that of the C of the piano, the pitch/key of that instrument is C. If it is equal to that of note D of the piano its pitch/key is D.

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The tonic determines the pitch or key of a Key or Scale. We have the 12 Keys or Scales, C, C# (Db), D, D# (Eb), E, F, F# (Gb), G, G# (Ab), A, A# (Bb) and B depending on the tonic. The other Keys or Scales have the same letter names but they belong to lower or higher octaves. They are signified by the use of small letters or prime signs.

Going back to intervals: The next most pleasing interval with the tonic is that produced by the 7th harmonic overtone. It is produced by the 1/7 length a vibrating string. The ¼ partial of this frequency is not assigned to any natural note in its scale. It is assigned to an “accidental note”. Its frequency is a semitone lower than the 7th natural note (semitone 12) and thus is known as the minor 7th (m7), semitone 11 or note Bb. Because its frequency is also a semitone higher than the 6th natural note (semitone 10) it is known as Augmented 6th (A6), semitone 11 or note A#. Note A# and note Bb although called by different names have the same frequencies. They are referred to as enharmonic equivalents. The same is true with C# and Db, D# and Eb, F# and Gb and lastly G# and Ab. Historically C#, D#, F#, G# and A# had lower frequencies than their flat equivalents until it was agreed during an international music convention to adjust, modify or temper the frequencies of the notes of the music scale and 40

assign them equal frequencies and call them enharmonic equivalents. Present day music scales are tempered. Semitone intervals are not exactly 16/17 or 17/16 in the same way that whole tone intervals are not exactly 16/18 or 18/16. They are however essentially and practically 16/17 and 16/18 intervals. A natural note that is lowered or made “flat” by a semitone is signified by the flat sign b after the letter symbol of the natural note. A natural note made higher or made “sharp” by a semitone is signified by the sharp sign # after the letter symbol of the natural note. The frequency of this accidental note is 264 x 7/4 = 462. Please read further on Accidentals. Interestingly, note A# or Bb, even if its only an accidental note has a higher ranking in the hierarchy of harmony than a Major 7th (M7) semitone 12 or note B, a natural note. Historically, it took many years of exposure to the M7 before listeners came to appreciate the sound of this interval. M7 is a characteristic interval/sound of Jazz music. Supertonic The next most pleasing interval is that with the 9th harmonic overtone. This is produced by the 1/9 secondary length of a vibrating string. The 1/8 partial of this frequency 41

corresponds to the natural note, one note superior (above) the tonic; it is thus called the supertonic. The supertonic of the C Scale is note D. It creates a Major 2nd interval, M2 (semitone 3) with the tonic. The frequency of note D is 264 x 9/8 = 297 Hertz. Leading Note Among the natural notes of a major diatonic scale, the least pleasing harmony/interval is produced by the 15th harmonic overtone. It is produced by the 1/15 secondary length of a vibrating string. The 1/8 partial of this frequency corresponds to the 7th natural note and creates a major 7th interval (M7) with the tonic (semitone 12). This is note B. It creates the greatest “tension” with the tonic, and being so, must invariably resolve or lead to the tonic. This note is thus called the leading note. The frequency of note B is 264 x 15/8 = 495 Hertz.

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ACCIDENTALS Augmented Intervals Perfect and major intervals are augmented when they are lengthened or increased by a semitone. Raising the higher note a semitone does this. An augmented note is signified by the sharp sign # after the letter note. A perfect 5th, semitone 8 (C to G,) is augmented by raising note G a semitone, Thus a C to G# is an Augmented 5th, A5, +5 or semitone 9. Another example is, a Major 6th, semitone 10 (C to A) is augmented by raising the higher note A, a semitone. Thus a C to A# is an Augmented 6th, A6 or semitone 11. Diminished Intervals 43

Lowering the higher note of a perfect interval by a semitone diminishes the interval. A P5, semitone 8 (ex. C to G) is diminished to C to Gb. A diminished note is signified by the flat sign b. Thus C to Gb is a diminished 5th, d5, –5 or semitone 7. Minor Intervals Lowering the higher note of a major interval by a semitone makes it minor. A Major 3rd (C to E), semitone 5, becomes a minor 3rd, semitone 4, when E is lowered to Eb. A Major 7th C to B, semitone 12, becomes a m7, semitone 11, when B is lowered to Bb.

INTERVALS BETWEEN ADJACENT NOTES In a diatonic scale, as the term implies, there are 2 types of intervals between adjacent notes, (1) a whole tone/whole step (16/18 or 18/16) or (2) a semitone (16/17 or 17/16) interval. The location of the semitone interval characterizes/distinguishes one modal scale from another. We will go further into this in a subsequent chapter. In the Key of C, the intervals CD, DE, FG, GA, and AB are whole tone or whole step intervals. There are semitones in between; C C# D, D D# E, F F# G, G G# A and A A# B. 44

The intervals EF and BC’ have no semitones in between. These intervals are called semitones (half tones, half steps, 16/17 or 17/16). As will be mentioned repeatedly, the location of the semitone interval determines the mood/atmosphere of a scale. An example is: In the Key of C, the semitone interval is between the 3rd and 4th and between the 7th and 8th natural notes as shown in the following illustration. (Alternatively, this scale can be viewed as being composed of 2 similar and smaller scales which are C, D, E, F and G, A, B, C’. Both are composed of 4 notes, 1st three of which are whole tones apart, the 3rd and 4th notes are only semitones apart.)

In the Key of C minor, the semitone interval between the 3rd and 4th natural is shifted to between the 2nd natural and the 3rd natural (3rd natural of the minor scale); the semitone interval between the 7th and 8th naturals is

45

maintained.

The concept of changing moods/atmospheres through shifting of the location of the semitone intervals will be more apparent in Chapter 6, Modal Scales.

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CHAPTER 3 Reading and Writing (Musical Notation) Music is the organization of sounds and silences to convey an idea and/or emotion. Music is usually transmitted by voice, by music instruments or by any sound producing gadget/device. Another method of conveying/transmitting musical ideas is with visual symbols that can be sung or played in music instruments. Most musicians can “hear” the music notations they read. Many of them are taught to read music notes just like students of today are taught the alphabet phonetically. 47

As non-musicians use visual symbols to convey ideas with letters of the alphabet, punctuation marks, words, sentences and paragraphs, musicians use another set of visual symbols. Musical notation is the use of this set of symbols. We will start with symbols that show the pitch of a note. Later we will learn the symbols that show the location and duration of sounds and silences.

NOTES AND THE STAFF Music symbols are written on a set of 5 horizontal lines called the staff. The lines are numbered 1 to 5 from the bottom.

Note symbols are written on the lines or in the spaces between. The vertical location of the notes on the staff shows their pitch. Notes whose pitches fall beyond the pitch range of the staff are written on or between ledger lines.

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Most notes have 2 parts, a note head and a stem.

CLEFS AND LETTER NAMES Notes are given letter names. Letters C, D, E, F, G, A and B. They are commonly used interchangeably with do-re mi-fa- sol la- ti- (do). As we shall see later, they are not the same. The illustrated note that follows is G;

We call it G because the letter G is “sitting on” the 2 nd line and the note is aligned with G. The second line is assigned to the note G. The G written at the beginning of the staff is called the G clef. The staff with the G clef is called the treble clef. 49

Musicians, artistic as they are, use a fancy version of the letter G.

Notice the G clef curling on the 2nd line. THE BASS CLEF The F clef is made up of a curved line and 2 dots. The F clef is written “on the 4th line”, one dot above and the other below. Consequently the 4th line is called the F line. The staff with the F clef is the bass clef.

An important reference point is the middle C. This is the C that is in the middle of the piano keyboard. The middle C is written on a ledger line immediately below the treble clef or on a ledger line just above the bass clef.

THE GRAND STAFF To accommodate as many notes on the staff, the

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treble and the bass clef are connected with a brace. This is called the grand staff.

ACCIDENTALS The Key of C has 7 natural notes (8 including the octave

note).

There

are

“unnatural

notes”

called

accidentals. To designate these accidentals, 2 symbols are used. In the staff, to raise a note a semitone (or a half step), the sharp sign # is written before a note symbol. When used with a letter note, the sign is written after. To lower a note by a semitone the flat sign b is used. When these signs are written in the staff, just after the G or F clef, they apply to all the notes on those spaces or lines in all the measures. When these signs are written within a measure or a bar, they affect only the notes in that particular measure. After the bar line, the notes revert back to their previous pitch.

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NATURAL SIGN

RHYTHM We learned that the vertical location of notes on the staff shows their pitch. We will now study the symbols that show duration of notes and silences. We indicate the pitch and duration of a musical sound with a note symbol. The rest symbols indicate the location and duration of silences. DURATION OF NOTES The whole note has the longest time value.

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Shorter duration of notes is indicated by stems, shading the oval and flags on the stem. The half note is half the duration of the whole note.

The quarter note is half the duration of a half note.

The eighth note is half the duration of a quarter note.

As we add a flag to the stem we shorten the duration by half. THE DOT AND THE TIE Notice that so far the durations of the notes are multiples of 2. If we want a note to last ¾ the duration of a whole note, we combine a half note with a quarter note by connecting them with a curved line called a tie. 53

The most frequent combinations are those in which a note is tied to another note ½ its value. A dot placed after a note head, is a more precise and concise symbol than a tie. A dot increases the duration by ½ its value.

RESTS: DURATION OF SILENCES The duration of silences is equally as important as the duration of the notes. Tryreadingasentencewithoutspacesinbetween. These pauses are indicated by symbols called rests. As silences are without pitch, rest symbols are assigned specific and constant locations on the staff. THE FERMATA 54

The fermata sign over a note means that the note is held longer that what the value signifies. How much longer is left to the discretion of the conductor or of a solo performer.

TEMPO AND METER We have just learned the different kinds of notes and symbols used to show the relative duration of notes and silences. We have learned that a half note is half as long as a whole note, a quarter note is half as long as a half note and so on down the line. We have not learned however, how long to hold or play a whole note. BEAT AND TEMPO A beat is a regular pulsation, like the beat of a normal heart. When we run or get excited, the heartbeat goes faster. The tempo is faster. Sometimes at certain position or posture, we can hear our heartbeats go RUB-dub, RUB-dub, RUB-dub, the RUB part we may hear louder than the dub part. This organization of heartbeats into strong and weak beat pattern is called the meter of the heartbeat.

55

BEATS AND NOTE VALUE To determine how long to play each note, we have to know what kind of note is equal to one beat. If for example, we know that a quarter note equals one beat, then a half note will have two beats and a whole note, four beats. MEASURES AND BAR LINES Bar lines are used to separate groups of notes into beat patterns (meters). The bar lines divide the staff into segments called measures or bars.

TIME SIGNATURE The time signature indicates the meter of a music piece. It consists of 2 numbers, written after the clef sign just at the beginning of the first measure. The upper number tells the number of beats per measure and the bottom number tells what kind of notes receives one beat. A time signature 56

of ¾ means there are 3 quarter notes to a measure or its equivalence in notes and/or rests. It means that the quarter note receives a beat and there are 3 beats to a measure.

PULSES One beat may be broken into pulses. Like for example, the sound of a train may be heard as RACK-e-ty, RACK-e-ty, RACK-e-ty. The RACK sound represents the beat, and the RACK, the –e and the –ty sounds are the pulses of the beat.

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CHAPTER FOUR Musical Scales An Overview (Complementary Viewpoint) Almost everything in this book revolves around the concepts this complementary viewpoint advocates. One of the concepts is: The interval between adjacent semitones is the same throughout the whole chromatic musical scale. This interval or ratio is either 16/17 (0.94) when we divide the frequency of the lower semitone with the frequency of the higher semitone or 17/16 (1.0625) if we divide the frequency of the higher semitone with that of the lower semitone. In Music, interval is the ratio/number we get when we divide the frequency of a music note with that of another. To

58

demonstrate: The frequency of note C is 264 Hz. The frequency of the next/adjacent higher semitone, note C#, is 280.5 Hz. If we divide 264 by 280.5 we get the ratio/interval 16/17 or 0.94. The interval between C# (280.5 Hz) and the next higher semitone, note D (297 Hz) is also 16/17. The interval between D and D#, D# and E, E and F, F and F# and so on, are all 16/17. Assigning numbers to the semitones will make understanding and definition of the concepts easier. The fact that the intervals between adjacent semitones is constant means that as long as we retain the semitone template, pattern or sequence, the intervals between notes and the reference note, the tonic (note C in our example), is maintained. It also means that retaining the semitone template, maintains its mood/atmosphere/melody. The resulting combination of notes will however belong to another key/pitch/octave. Example: The semitone template of Do-Re-Mi-FaSol-La-Ti-Do sound in the Key of C is 1-3-5-6-8-10-12-13. Semitone 1 is note C. Using the same template but with note D as semitone 1 will create the same Do-Re-Mi-Fa-Sol-LaTi-Do sound/melody, but in the Key of D. The resulting melody sounds “the same” but higher in pitch/key or octave

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(another group of 8 natural notes). The use of the semitone template is applicable to music chords (major triads, 7th chords, extended chords, 11th, 13th), Modal Scales, diatonic scales (major and minor) and many others. Back to Basics Many are familiar with a musical jewelry box. Each time such a box is opened, it plays a melody. The melody/music is produced mechanically by pegs or pins on the surface of a rotating cylinder that beat/hit/strike the tuned teeth of a comb like steel plate. Imagine a comb like steel plate.

The teeth are tuned and arranged like the notes of the Key of C on the piano keyboard. However, unlike the keys on the piano where the black keys are shorter, narrower and only inserted between the white keys, the 60

teeth representing the black keys are of the same size and are aligned with those of the white keys. Let us assign letters to the teeth of the steel plate: C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C’. These are the same letter names assigned to the notes/keys of the Key of C on the piano. Letters with the sharp sign (#) represent the black keys on the piano which are the accidental notes of the Key of C. The white keys are its natural notes.

Imagine also a "cylinder" with pegs or pins on its surface that can strike the teeth of the steel plate, one by one, from left to right.

On "rotation" of the cylinder, these pegs will produce the following series of musical notes, C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C’. The progression of the notes is only by a 61

semitone interval. Such progression is called chromatic. A musical scale that progresses in semitone interval is called a chromatic scale. Let us assign numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13 to the pegs.

Next, let us remove the pegs that strike the teeth hitting the black keys, leaving behind only pegs numbers 1, 3, 5, 6, 8, 10, 12 and 13 in place. These pegs will strike C, D, E, F, G, A, B, C’. These are the natural notes of a major diatonic scale, the Key of C. Key of C because the reference/tonic note is C. Let us call this cylinder the major diatonic template/pattern.

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If we slide this major diatonic template one tooth to the right, the pegs will strike notes C#, D#, F, F#, G#, A#, C’ and C’#.

These are the natural notes of another major diatonic scale, the Key of C#. Notice that there are black keys in this C# Scale. The black keys are accidental notes only as far as the C major diatonic scale on the piano is concerned. Among the 12 major diatonic scales only the Key of C has all its natural notes in the white keys of the piano.

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Sliding the template another tooth to the right will align the numbers of the template to the natural notes of the Key of D.

Identifying the natural notes of any major diatonic scale will then be easy, just as easy remembering the sequence 1, 3, 5, 6, 8, 10, 12, 13. Peg 1 aligns with the tonic and defines/names the Key. This happens because even if the template is moved/transposed, the intervals of notes with the tonic are maintained/preserved. All resulting groups of notes can be sung Do- Re- Mi- Fa- Sol- La- Ti- Do and “sound the same”. They will only differ in pitch/key but they will produce/create the same mood/atmosphere or melody. We can see then how melodies/songs can easily be transposed from one Key to another to adapt to the note/frequency range of a music instrument or a singer.

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Music sheets are easily available for the piano. Transposing melodies for any music instrument from music sheets for an instrument with a different pitch/key can then be done by anyone with this knowledge. We are familiar how the major diatonic template was created and how it is used. A template for any combination or sequence of intervals can thus be easily made and put to use. Example, a major chord triad which is made up of the 1st, 3rd and 5th natural notes of a Key. In the Key of C, these notes are C, E and G. The semitone numbers of these notes are 1, 5 and 8. Because 1 defines the tonic we do not have to memorize this number. We need to memorize only nos. 5 and 8 to identify the notes of a major chord triad.

To identify the major chord triad of D, we take D as

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the note 1, F# as the note 2(F# is the 5th semitone from D) and A as note 3 (A is the 8th semitone from D).

Transposing or changing of pitch or key of a melody, music scale and chords to fit a musical instrument, will then be possible without consulting charts and the like.

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CHAPTER 5 Diatonic Scales, Major and Minor A diatonic scale is a progression of musical notes, which has 2 kinds of intervals between adjacent natural notes. The interval between natural notes can either be (1) a whole tone or (2) a semitone. The whole tone interval is 16/18 (or 0.89) or 18/16 (or 1.125). The semitone interval is 16/17 (or 0.94) or 17/16 (or 1.0625). The Key of C has 7 natural notes, 8 if we include the octave (note C’).

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Let us include the semitone numbers:

The Key of C is called a major diatonic scale because the interval between its 1snd 3rd natural notes is 5 semitones. A 5 semitone interval is also known as a Major 3rd or M3. The semitone template of a major diatonic scale is 1, 3, 5, 6, 8, 10, 12 and 13. A diatonic scale whose interval between its 1st and 3rd natural notes is 4 semitones is called a minor diatonic scale. The Key of C minor diatonic scale will then be:

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The semitone template for a minor diatonic scale is 1, 3, 4, 6, 8, 10, 12 and 13. By remembering these 2 semitone templates, 1, 3, 5, 6, 8,10,12,13 and 1, 3, 4, 6, 8, 10, 12, 13, we can now easily identify the notes of the major and the minor diatonic scales in all the 12 Keys. We can now build 24 diatonic scales by memory, remembering only 2 diatonic templates. We need not remember how many sharps or flats there are nor memorize where they are, to be able to identify the different diatonic scales. All we need is to know the following letters of alphabet (A, B, C, D, E, F and G), with a little modification to insert the 5 accidental notes (C#, D#, F#, G# and A#,) and the semitone templates of the major and minor keys (1, 3, 5, 6, 8, 10, 12 and 13 or 1, 3, 4, 6, 8, 10, 12 and 13). To demonstrate: To identify the notes of the Key of G, write the chromatic alphabet starting with note G together with its now assigned semitone numbers.

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Following the semitone template for the major diatonic scale (1, 3, 5, 6, 8, 10, 12 and 13), let us underline them:

The notes of the Key of G major then are,

The notes of the Key of G minor can be identified using the same method. Write the chromatic with the corresponding minor diatonic semitone template;

Identify the notes of the Key of G minor;

With practice it will now be easy to identify the notes of all Keys, major or minor. The use of the semitone template for major and minor diatonic scale facilitates identifying notes of any Key. The

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following illustrations depict how conveniently the semitone template works. These illustrations are presented only to clarify the concept, other methods convenient to the readers may be devised:

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72

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The minor diatonic scales can likewise be easily identified by using the semitone template for the minor diatonic scale:

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75

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CHAPTER SIX Modal Scales Knowledge of modal scales is important in composing melodies, identifying what notes to use, what chords harmonize with a set of notes and the like. How the modal 77

scales work in these activities is beyond the scope of this book. However, it is interesting

to mention that a once

popular Beatles’ song “Eleanor Rigby” is a revival of the Dorian mode, for whatever interest it may kindle. This chapter will identify these modal scales; the derivative and the parallel approach in building/constructing them. This chapter intends to demonstrate how easily they are derived and thereby minimize the clouds that some people have about that the term modal scales. This chapter intends to show how changing the location of semitone intervals can change the atmosphere or mood of a set of notes. The Ionian Mode On the piano keyboard, playing 8 adjoining white keys going to the right, starting with note C, will produce the notes C, D, E, F, G, A, B, C’.

This we already know as the Key of C, the C Scale or

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the C Major Diatonic Scale. This is also called the Ionian Mode. This is the most popular mode during the Ionic era in Greece until it gained the distinction of being called a scale. This scale passed the test of time and influenced the development of Western music. It is the progression of notes many are familiar with. In most instances it is used as the reference scale and has influenced nomenclature in music. The Greeks established the principles. The Italians were most productive in written music during the 17th century, so much so that most music terms are Italian. Until today the Ionian mode is the most popular sound, the

Do-Re-Mi-Fa-Sol-La-Ti-D

sound.

This

sound

is

considered most pleasing and most easily memorized.

The Dorian Mode If we play 8 adjoining white keys, this time starting with note D, we produce the notes D, E, F, G, A, B, C’ and D’. These are the same notes as the Ionic Mode, its designated 1st natural note however is the designated 2nd natural of the Ionic Mode.

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Notice the location of the semitone interval between the 2nd and 3rd and the 6th and 7th natural notes of this mode. Compare to the 3rd and 4th and the 7th and 8th natural notes of the Ionic Mode. The location of these semitone intervals distinguishes the created/projected atmospheres of the modal scales. Take note also that this Dorian Mode is the 1st inversion of the Ionic Mode, having started with the 2nd note of the latter. Notice also subsequently that the other modal scales are merely inversions of the Ionic mode.

The Phrygian Mode Playing the next 8 natural notes of the Ionic modal scale, starting with its 3rd natural note, gives the 2nd inversion, which is known as the Phrygian Mode. The notes are E, F, G, A, B, C, D and E.

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The semitone template/pattern for the Phrygian Mode is thus 1, 2, 4, 6, 8, 9, 11, 13.

The Lydian Mode This mode is the 3rd inversion and its template is 1, 3, 5, 7, 8, 10, 12, 13.

The Myxolydian Mode This is the 4th inversion and the template is 1, 3, 5, 6, 8, 10, 11, 13.

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The Aeolian Mode This is the 5th inversion and the template is 1, 3, 4, 6, 8, 9,

11, 13. The Locrian Mode The Locrian Mode is the 6th and last inversion of the Ionic Mode. Its template is 1, 2, 4, 6, 7, 9, 11, 13.

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These inversions are constructed by the derivative approach. The other method of building a modal scale is the parallel approach. This is where the ease in using the semitone template as a guide becomes apparent. Let us build the Locrian Mode in the Key of F. Write the chromatic alphabet starting with note F with its corresponding semitone numbers.

Identify the numbers as shown in the semitone template of the Locrian Mode, by underlining the said numbers.

The notes then of the Locrian Mode in the Key of F are F, F#, G#, A#, B, C’#, D’# and F’.

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The other way is to use the Locrian Mode semitone template.

Align semitone 1 of the template with the note F of the keyboard and identify the notes of the Locrian Mode in that Key.

The numbers of the semitone template need not be memorized. Visualizing the keys on the piano and identifying the semitone numbers of 8 adjoining white keys is all that is needed to determine the semitone template of any modal scale.

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CHAPTER SEVEN The Pentatonic and the Whole Tone Scale Penta is a Latin word for 5. A musical scale with 5 natural notes is called a pentatonic scale. The Major Pentatonic Scale A major pentatonic scale is a major diatonic scale without the 6 and the 12 semitones or the 4th and the 7th natural notes. So instead of a C, D, E, F, G, A, B

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we have C, D, E, G, A,

.

The intervals produced are whole tones (16/18 or

0.89 and its inverse 18/16 or 1,125 ) and whole tones and a half (15/18 or 0.83 and its inverse 18/15 or 1.2). The intervals C to D, D to E and G to A are whole tone intervals. The intervals E to G and A to C’ are 3 semitones (or a whole tone and a half) interval.

Notice that the semitone template of this major pentatonic scale is 1, 3, 5, 8, 10 and (13) without the 6 and 12 of a major diatonic scale. It will be easy to identify the notes of a pentatonic scale in the other 11 keys using the

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semitone template rather than identifying the natural notes of a diatonic scale and removing the 4th and the 7th natural notes in that key. The major diatonic scale creates a feeling of notes starting from the tonic, the listener being “pulled” towards the 5th natural note (very closely related to the tonic, because it is the dominant of the tonic) and then finally moving to the 8th note (the octave). This is because of the presence of the semitone interval between the 3rd and 4th and the 7th and 8th natural notes (or between the 5 and 6 and the 12 and 13 semitones). This is described as creating an atmosphere where notes are moving around and towards the tonic. This establishes the tonality of this group of notes. The major diatonic scale is described as having a strong “gravitational pull”. The absence of the semitone interval in the pentatonic scale creates an atmosphere that has no strong gravitational pull. This results in more number of notes that can be played in harmony with a chord, and create a situation where no “bad” notes are played. The pentatonic scale is extensively used in Latin, blues, rock and American country music. This music prevails in Eastern music (Chinese, Japanese and Korean). Hindu 87

music is unique in the sense that it uses half semitone interval or ¼ of a whole tone interval. The Minor Pentatonic Scale The minor pentatonic scale is the 4th inversion of its major pentatonic scale. We learned earlier that the 4th inversion of a set of notes starts with the 5th natural note of that set. The semitone template of the C major pentatonic scale is 1, 3, 5, 8, 10, 13. The 4th inversion begins with semitone 10. Our semitone template for the C minor pentatonic scale is 10, 13 (or 1’), 3’, 5’, 8’ (10’)

The minor of the C Pentatonic Scale is A, C’, D’, E’ and G’. The minor pentatonic scale prevails in Spanish songs. The minor scales (minor diatonic and minor pentatonic) in general create sad and melancholic atmospheres.

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The Whole Tone Scales As the name denotes, these scales have only whole tone intervals between adjacent natural notes. There are only 2 scales, the C whole tone scale and the C# whole tone scale. The other 10 whole tone scales are but inversions of the 2 mentioned whole tone scales. The semitone template of both whole tone scales is 1, 3, 5, 7, 9, 11, 13.

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The absence of an identifiable tonic characterizes the Whole Tone Scales. This absence supposedly creates an atmosphere of uncertainty, of being suspended nowhere. This scale is used for the background music of suspense thriller movies

CHAPTER EIGHT Music Chords Music chords are combinations of notes that serve many functions. Chords “tie” the notes of a melody together. They may be used to set the rhythm, beat or tempo of the melody. Chords are accompanying/supporting notes of the melody. They provide the backbone to the notes. They serve as the framework on which notes can hang on to. Chords

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gather the notes together, giving them form, fluidity, body and more “color”. The notes of the chords are the notes that are played by the left hand on the piano keyboard. The notes of the melody are usually played by the right hand. Composers may initially decide on what sequence of chords to use and then tailor the notes of the melody to it. The usual practice is to compose the melody and adapt the chords later. This chapter will deal mainly with the construction of chords in the Key of C. The piano keyboard will be our reference music instrument. If we can build the chords in the Key of C, we will be able to build them in all the other 11 Keys with the use of the semitone template created in harmonizing/building the chord in the Key of C. Letters of the alphabet A, B, C, D, E, F and G are assigned to the 7 natural notes of a major diatonic scale. Accidental notes, are those whose frequencies are between the frequencies of adjacent natural notes. They are signified by the sharp sign (#) or a flat sign (b) after the letter note, depending on whether one is going up or going down a scale. A sharp sign after the letter note is used if the frequency of that natural note is increased by a semitone interval or a flat sign if the

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natural note is lowered by a semitone interval. Letter C is assigned to the 1st natural note of the Key of C. There are 12 Keys namely, C, C#, D, D#, E, F, F#, G, G#, A, A# and B. The others are octaves of these original 12. We have learned the principle of transposition. What we learn in the Key of C applies to all the other 11 Keys. The things we learned in an earlier chapter about construction of semitone templates and their uses will be useful. As a rule, the notes of the chords should be natural notes of the Key (Key of C in our example). There are black and white keys/levers on the piano keyboard. The black keys are shorter. They are grouped in 2s and 3s and are interspersed between the farther half of the white keys. In the middle of the keyboard, the white key immediately to the left of the 2 black keys is the lever that strikes the note C. Striking the white keys one by one going to the right will produce the following notes: C, D, E, F, G, A, B, C' and on to the next octave.

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The white keys are the natural notes of the Key of C. Striking every other white key beginning with note C will produce the notes C, E, G, B, D' and so on. These notes are described to be 3 natural notes from each other.

A chord may be a tertiary, a quartel or a 5th. It is a tertiary chord if its notes are 3 natural notes from each 93

other, like the notes C and E are 3 natural notes from each other (C D E). The notes E and G are also 3 natural notes from each other (E F G). The notes G and B are also 3 natural notes from each other (G A B). See illustration above. A quartel chord is one whose notes are 4 natural notes from each other. The notes C and F are 4 natural notes from each other (C D E F). The note combination F and B is also a quartel (F G A B).

A 5th chord has notes that are 5 natural notes from each other.

Majority of chords presently used are tertiaries. Most of those exposed to Western music frequently hear tertiary chords, so to them, quartel chords may sound strange and futuristic. Quartels chords are used in background music for 94

movies of trips to outer space and of futuristic adventures. The notes of a chord may be all played at the same time to establish the rhythm/beat/tempo. They may be played one after another to add color, harmony and fluidity to the melody. In such a case the chord is said to be broken or arpeggiated. (Arpeggiare is an Italian word meaning “to play on the harp”). Tertiaries The commonly used chords are tertiaries. They are built on 3rds. Chords are built on thirds when its notes are 3 natural notes from each other. Let us take for example the 3-note chord C E G.

Note E is 3 natural notes from note C (C D E) and note G is 3 natural notes from note E (E F G). Note combination C, E, G is called a diatonic chord triad because (1) they are natural notes of a diatonic scale and (2) the chord has 3 notes. Note C is note 1 or the root, E is 95

note 2 and G is note 3 of the chord. The semitone template is 1, 5, and 8. Semitone 1 identifies the root of the chord. In this instance that we are harmonizing the Key of C, the root note C is also the tonic. Subsequently though, as we harmonize the Key of C and use its other natural notes as roots in building the other diatonic chord triads, we have to remember that the resulting note 2 of that chord triad is 3 natural notes from the root and not the 3rd natural note of that root. The interval that note 2 creates with the root note determines whether the chord is a minor or a major. A 5 semitone interval produces a major chord while a 4 semitone interval produces a minor chord. Thus a CEG chord is a major chord because the interval between C (the root note) and E (note 2) is 5 semitones (C, C#, D, D# and E). The DFA chord on the other hand is a minor chord because the interval between D (the root note) and F (note 2) is 4 semitones (D,D#, E and F).

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Diatonic 7th Chord Another 3rd natural note from note 3 of a diatonic chord triad can be added to produce a 4-note chord called a diatonic 7th chord. (We can not overemphasize the fact that the notes we will be using in these diatonic 7th chords are natural notes of the tonic and not those of the root note.)

An example is the chord C E G B.

This is a CM7 diatonic 7th chord: C because the root note is C and M7 because note 4 (B) creates a Major 7 (M7) interval with the root note C. It is 12 semitones from the root C. A 12–semitone interval produces a Major 7 interval. An 11-semitone interval produces a minor 7 interval.

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Extended Chords Another 3rd natural from note 4 of a diatonic 7th chord can be added to create extended chords.

The 3rd natural from note B is note D’. Note D’ is the 9th natural note of the Key of C. This extended chord is called C9.

We have just gone through a bird’s-eye view of music chords. Earlier we have been introduced to the Key of C written in music symbols.

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If we add natural notes which are 3 notes from each of the natural notes of the Key of C we initially create twonote chords. Depending on the interval created by note 2 with the root, these 2-note chords are classified major (M) or minor (m).

In the first 2-note chord above, C and E, the interval is 5 semitones (C, C#, D, D# and E).This 5-semitone interval makes it a major 2-note chord.

In the second 2-note chord D and F, the interval is 4 99

semitones (D, D#, E and F). This 4-semitone interval makes it a minor 2-note chord.

Diatonic Chord Triads Adding another 3rd natural from note 2 will give us diatonic chord triads.

Major chords are called by their root note, like C, F and G above. Minor chords are called by their root note followed by lower case m, like Dm, Em, Am and Bm-5. Notes 3 (the 5th natural notes from the roots) of the chords above create a Perfect 5th (8 semitones) interval with their roots except Bm-5 whose note 3 (the 5th natural from the root note B) creates a diminished 5th (7 semitones) interval with the root note B, thus -5 is appended.

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Diatonic 7th Chords Adding a 3rd note from notes 3 of diatonic chord triads will produce diatonic 7th chords.

It is worthwhile to mention at this point particularly to Jazz enthusiasts that these diatonic 7th chords are also known as Jazz Chords I, II, III, IV, V, VI and VII. Extended Chords Adding another 3rd natural note from note 4 of a diatonic 7th chord will produce extended chords called 9th chord because the added note is the 9th natural note of the Key of C from the root note.

Extended Chords 11 and 13 101

Adding to the diatonic 7th chords 3rd natural notes from the last note of the 9th chords will produce the 11th chords.

Adding to the diatonic 7th chords another 3rd from the last note of the 11th chord will produce 13th chords.

The 3rd natural note from the last note of the C13th chord is an octave of note C. There is no 15th chord. There are likewise no 10th, 12th and 14th chords. CHORD BUILDING: HARMONIZING A SCALE Harmony is the blending of 2 or more notes. All the

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natural notes of the Key of C are considered in harmony with its tonic note C. To maintain harmony and tonality, notes of its chord are preferably natural notes of the Key of C. These natural notes are notes C, D, E, F, G, A, B, C', D', E' and so on. The process of identifying the notes of the chords that will sound pleasing together with the tonic and its natural notes is called harmonizing that Scale/Key or tonic. Diatonic Chord Triads Diatonic chord triads are harmonized by building tertiary chords using each of the natural notes of the tonic as their roots (distinguish from tonic). In the Key of C the diatonic chord triads are:

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Notice that all the notes are natural notes of tonic C, not one is an accidental note. Let us analyze the first diatonic chord triad CEG in the music notation above with the help of a diagram of a piano keyboard below:

It is called a C major diatonic chord triad: C because the root note is C; major because the interval between the root note (C) and note 2 (E) is 5 semitones or a Major 3rd (C, C#, D, D#, E), diatonic because they are natural notes of a diatonic scale and triad because it has 3 notes. Notice that note 2 is the 3rd natural note from the root note C and it creates a Major 3rd interval (5 semitones) with C. If the interval between the root note and note 2 is lowered by one semitone (to 4 semitones or a minor 3rd), the chord becomes a minor, like if note 2 of the CEG chord is lowered by one semitone (E to Eb) it becomes a C minor chord or a Cm (C Eb G). The interval C to Eb is 4 104

semitones (C, Db, D, and Eb). The semitone template for a minor diatonic chord triad is 1, 4 and 8.

In summary (take note of the semitone templates):

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A major chord triad is called by its root note like the chords C, F and G. Minor chord triads are denoted by a lower case m after the root note, like Dm, Em, Am and Bm-5. Notice in the summary above that in all the diatonic chord triads where the intervals between the root and note 3 are all Perfect 5th (8 semitones), it is only in the Bm-5 chord, where note 3 (the 5th natural note from the root note B) is lowered by a semitone (diminished) to semitone 7. This chord is more accurately known then as Bm dim5 or Bm d5 or Bm -5 ; Bm because the interval of the root with note 2 is 4 semitones (a minor 3rd interval or m3) and dim5, d5 or -5 because the 5th natural note (note 3) is diminished to semitone 7.

Diatonic 7th Chords Adding note 4 to a diatonic chord triad makes it a diatonic 7th chord. Note 4, of course is 3 natural notes from note 3 of the triad.

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Let us illustrate the first diatonic 7th chord above on a piano keyboard diagram:

One important point about the diatonic 7th chord is all notes are naturals of the Key or tonic note being harmonized and not natural notes of the root. Note 4 is 7 natural notes from the root and not the 7th natural note of the root. The root note is to be carefully distinguished from the tonic. Example, in the diatonic 7th chords of the Key of C, the tonic is note C. Even if we use note D as the root of a diatonic 7th chord, the tonic note is still note C not note D; so all the notes of the diatonic 7th chord of the Key of C are naturals of C and not natural notes of the root notes. As seen in the illustration that follows, the 7 th natural note of the Key of D is note C’# and not C’. Much farther (page 102), the illustration of the Dm7 will show that the 7 natural note from note D is note C’.

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The diatonic 7th chords are built by adding another note to a diatonic chord triad. We add a 3rd natural note from note 3 of the chord triad. This becomes note 4 of the diatonic 7th chord.

Let us analyze the diatonic 7 th chord CEGB or CM7. It is called a C because the root is C and M7 because note 4 (note B), has a Major 7th interval (12 semitones) from the root note C. In this particular instance, note C is the tonic as

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well as the root note, because we are harmonizing the Key of C.

The next diatonic 7th chord, DFAC’ is called Dm7, D because note D is the root note and m7 because the interval of note 4 (C’) from root note D is 11 semitones or a minor 7th interval.

As explained earlier, note C’ is 7 natural notes from note D, the root note of this diatonic 7th chord and not the 7th natural of note D; the 7th natural note of the Key of D is note C’#.

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In summary (take note also of the semitone templates):

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G7 is a particularly interesting chord. Among the diatonic 7th chords (CM7, FM7 and G7) whose notes 2 and notes 3 are M3 and P5 respectively only in G7 does the root note create a minor 7th interval with its note 4. The other two, CM7 and FM7 have their 7th note a major 7th. Furthermore, G7 is also a 7th chord (not only a diatonic 7th chord) because its semitone template is 1, 5, 8 and 11, like the rest of the 7th chords. The other diatonic 7th chords all have a minor 3rd note 2, a perfect 5th note 3 and a minor 7th note 4; except Bm7-5 whose note 3 is a diminished 5th

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All these chord triads and diatonic 7th chords will harmonize with melodies in the Key of C. Extended Chords Another 3rd natural note from note 4 may be added to a diatonic 7th chord. The resulting chord is called an extended chord.

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The 3rd natural from note B (note 4) is note D’. Note D’ is the 9th natural note of the Key of C. The resulting extended chord is called C9.

The 3rd natural note from note D’ is note F’. Note F’ added to a CM7 diatonic 7th chord will give us the extended chord C11.

or

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The 3rd natural note from note F’ is note A’. Note A’ added to a CM7 diatonic 7th chord will give us the extended chord C13.

There is no C10, C12, C14 nor C15 extended chords. These additional notes are merely octaves of the notes of the original chord and will not significantly affect the “color” of extended chord. 7th CHORDS The 7th chords are to be carefully distinguished from 116

the diatonic 7th chords. The 7th chords always have a tonic (distinguish from root), a note 2 that is always a major 3rd (5 semitones), a note 3 that is always a perfect 5th (8 semitones) and a note 4 that is a minor 7th (11 semitones). The diatonic 7th chords on the other hand have a root (not a tonic); a note 2 which has either a major or a minor 3rd interval with the root (5 or 4 semitones); a note 3 which has either a perfect or a diminished 5th interval with the root (8 or 7 semitones) and a note 4 whose interval with the root is either a major or a minor 7 (12 or 11 semitones). Furthermore, there are only twelve 7th chords while there are 84 diatonic 7th chords (seven diatonic 7th chords in each of the 12 Keys). The 7th chords are C7, C#7, D7, D#7, E7, F7,F#7, G7(also a diatonic 7th chord), G#7, A7, A#7, B7. The semitone template of these 7th chords is 1, 5, 8 and 11. The 7th chord gained earlier acceptance because a minor 7th interval (11 semitones) is more harmonious to the tonic than a major 7th interval (12 semitones) is. It took many years of exposure to the diatonic 7th chord before listeners started to appreciate this chord. Diatonic 7th chord is characteristic sound of Jazz

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music. The 7th Chords are (notice the semitone template 1, 5, 8, 11):

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The 7th chords will generally harmonize only with melodies that are in the Key of its tonic, like C7 will harmonize only with melodies in the Key of C and D7 will sound well only with melodies in the Key of D.

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CHAPTER 9 Melody, Musical Form and Design The melody of a music piece has 2 basic components: melodic contour and rhythm. They give the melody its distinctive character. If we draw a line connecting the notes of a melody on the music sheet we draw its contour. The rise and fall of the line reveals the overall pattern of the pitch movement. The contour shows the range of the melody, its highest and lowest points. The contour of most melodies is like the top line of the silhouette of a mountain range. There is a direction; it does not jump around aimlessly. Many melodies start from a low point and move upward to a high point (the culmination point). Frequently, the line descends gradually to a low point, near where it started. Some melodies may start low and progress to a culmination point and end there. This produces a dramatic effect. Other melodies may start with relatively high notes, gradually drop down to lower notes and climb up to a culmination point. Many patterns are possible. Most melodies have definite shapes.

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PITCH RANGE Pitch range is the interval between the highest and lowest notes. Most folk songs have a range of about an octave. The smallest range is about a 6th interval. Children’s songs are often limited to a 5th interval. Melodies with a range greater than an octave have more dynamic qualities. The most common range of Beatles’ song is greater than an octave, being that of a 10th or an 11th. CONJUNCT AND DISJUNCT Movement from a note to another is classified as conjunct or disjunct. Conjunct movements are a whole tone or semitone intervals. Disjuncts are intervals greater than a whole tone. Melodies must have the appropriate combination of conjunct and disjunct movements depending on the atmosphere they intend to create. Conjuncts tend to be monotonous and put listeners to sleep. Disjuncts sound jerky and disjointed. MELODY AND RHYTHM We respond to changes in pitch and rhythmic movement of a melody. Melody can not be separated from

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rhythm. A melody whose notes are played in a different rhythm is harder to identify than a melody whose notes are modified but played in the original rhythm. MELODIC UNITS The smallest musical unit that expresses an idea is called a motive. The next larger is a phrase. Phrases may be organized into larger sections called parts or specialized sections called periods. The parts or periods are often organized into a larger section called a song form. Song forms are organized into compound song forms. THE MOTIVE It takes only 2 notes to make a motive, if the notes are sufficiently distinctive such that each note can be audibly differentiated from the other. For example, one note is on the up beat while the other note is on the down beat or if one note is a 4th or a 5th interval of the other. The motive may be modified by changing the order of the notes or by adding connecting notes so that a disjunct is changed to a conjunct movement. Modification may be done by contrary motion. Contrary motion is making the notes go in the opposite direction. When the original notes go up, the notes in the

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variation go down or vice versa. THE PHRASE A phrase is a segment of a melody similar to a sentence in a speech. It is a melodic unit a singer sings in one breath. THE PART The next larger melodic unit is a part. A part is made up of a series phrases. The last phrase of a part is marked by a pause, a cadence. The cadence is not very definite and tends to signal that another part is to follow. THE SONG FORM The song form is a combination of 2 or more parts. The parts are somewhat similar, but are distinguishable enough to stand alone as an independent unit. THE TWO-PART SONG FORM In a two-part song form, the first part ends with a strong cadence on a natural note other than the tonic. This way the listener expects something more to come and feels a sense of conclusion only when the last part ends with the

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tonic. THE THREE-PART (TRIPARTITE) SONG FORM The three-part song form is characterized by a third part that is the melody of the first part. If we designate the melody of the first part as “A” and the melody of the second part as “B”, then the three-part song form is describes as ABA. Some composers, to make sure that listeners remember the melody of the first part, repeat its melody (usually with some variations) before going to

the melody

of the second part. The melody of the first part is easily recognized when the melody of the second part returns to the melody of the first part (now the third part). This threepart song form is described as AABA. THE COMPOUND SONG FORM This is a combination of two or more song forms. The song for that comes first is called the principal song. The second is often called the trio. The term trio was used because when these forms were developing, the second form was composed for three vocal parts or three instruments that were to be played simultaneously. The term trio is commonly used even if the second song form is not a

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trio in the literal sense. (The practice of still doing things the same way even when the reasons for doing them are no longer valid is not the monopoly of music artists). After the trio, the principal song returns, usually with some variations.

CHAPTER TEN

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CADENCE We do not have control of the circumstances surrounding our birth but as soon as we have developed the ability to choose, the choice has always been ours. We are where we choose to go. We are born in a world of music, among the other possible worlds. “Born musicians” are those whose attention, time, resources and faculties, have been knowingly or unknowingly directed to music. In the final analysis the choice has always been ours. Assume and imagine that at birth, all are provided with similar transparent boxes of colored marbles. The boxes are of the same size and shape. The marbles are likewise the same as to number, color and size. Initially, how we arrange our box is dictated or mainly influenced by the circumstances around us, until we are able to establish the circumstances that will allow us to do as we choose. We may decide to continue what we learned, imitate others or do it our own way. Our way may be unique or a combination of many ways. It may change with time, it may not. Possibilities are innumerable.

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We may place the red marbles in the periphery. It will seem that we have more reds. We may choose to put oranges on one side, yellow on another, green and blue on others. Our box will seem to contain more of certain colors depending on which side is viewed. We may decide to see only the indigos and convince ourselves that we have more of indigos. Lies continuously repeated become apparent truths. Others may want to see only the violets. We may be too busy finding out (maybe even criticize) how others are arranging theirs that we never had time to realize how we like ours to be. We may succeed or fail, be satisfied or be disappointed with the results. Varied and different shades of consequences are possible. Some situations are beyond control, but options and choices are plenty. The choice is ours. Beethoven continued to compose even when he was already deaf. We know musicians who are blind since birth. We see piano/accordion players missing some fingers. Some may have given up learning and studying music, probably because of real or imagined stumbling blocks. This book hopes to have helped remove some of those blocks by offering simple, easy to remember mental

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pegs and handles with which to again explore the world of music with better results. Knowing the musical chromatic alphabet (literally as simple as ABC) and few variations of numbers 1 to 13, is all that is needed to easily understand what a diatonic scale is. It is what we need to know to understand and be able to build from memory all kinds of musical scales. With this knowledge we understand how whole tone scales can create certain atmospheres, or why quartel chords sound strange to many. Knowing these two simple things helped us understand how music chords in all scales and keys are built. Why are some combinations of notes more pleasing? Having this knowledge will help us find answers to many questions. The path we will take and the progress we will accomplish depend on how we put to use the potentials of this knowledge. May this book help us in the study, appreciation and analysis of music. Let us not however be like the centipede, who one day, while gracefully and nimbly negotiating a rough terrain, was asked by a curious (envious? malicious?) frog: ”Hey

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friend, which among your legs do you lift first and which legs follow?” The centipede stopped and analyzed. He was not able to walk as deftly again.

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