Music Theory: Explanation and Basic Principles

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1 Music Theory: Explanation and Basic Principles Musical Scales Musical scales have developed in all cultures throughout the world to provide a basis for music to be played on instruments or sung by the human voice. Scales are comprised of individual musical notes which have a definite relationship to each other. The relationship of notes within scales is the essential ingredient that humans recognise as the enjoyable listening experience of musicality. Every note in a musical scale has its own particular frequency (or rate of vibration) which gives it its own pitch. When notes from within these scales are played in sequence they create what we understand as a melody (or tune). When two or more notes from within a scale are played together they create a chord. What we must understand about scales is that they cannot be created by combining a number of randomly chosen frequencies; in order to satisfy our own inherent musicality they must have an organised relationship with each other. The Laws of Physics Some basic understanding of physics is required in order to get to the crux of the theory which governs why particular frequencies sound good together in scales and chords, however the basic principles are. 1. That within every sound there are multiple resonances called harmonics or overtones, and that these harmonics give off additional notes (other frequencies) which differ from the original note, but combine with the original in a predetermined and very musical way. So when we pluck a string on a guitar we may think that we are hearing only one single note and frequency, but in actual fact, we are hearing many frequencies at the same time which combine to give the sound its own unique timbre. The existence of these harmonics can very easily be proven by plucking a string on a guitar and then damping the string by placing a finger lightly at various special points along the length of the string. What happens is that the main part of the tone (called the fundamental) is stopped, but particular harmonics can be heard to continue (depending on the exact positioning of the damping finger). In theory there is no limit to the number of these harmonics which are generated all at the same time as the string is plucked, but in practice there can only ever be a maximum of twenty or so before the frequencies go beyond the range of human hearing. The truly amazing fact about these harmonics is that as they go higher in range they provide the notes which make up what we know as our preferred musical scale: doh, ray, me, fah, soh, lah, te, doh. Diagram 1.

2 Diagram 1 shows the first six additional vibrations which occur when a string is plucked. Notice how the even numbered harmonics (which divide the string length into odd numbers of sections - 3, 5, 7, etc.) are responsible for producing the new notes. Eventually these harmonics will produce all of the notes required to comprise the entire scale that we all know and recognise. Given that we have established that these harmonics occur naturally in all sound and that the human species has been listening to sound for the entirety of its existence, it is perhaps not surprising that the scale which we know as the major scale is so special to us. It is also important to note that the first harmonics to occur are those which go together to create what we recognise as the definitive major chord comprising the notes doh, me, soh. 2. When the notes which make up the major scale are placed in a logical order within one octave (low doh to high doh), we can see that the ratio of their frequencies to the first note is very special. The ratio of the frequencies between all notes in the scale to the first note and others, shows that humans have a natural liking for low-numbered, simple ratios e.g.: (high) doh to (low) doh gives the ratio of 2:1 soh to doh gives a ratio of 3:2 fah to doh gives a ratio of 4:3 me to doh gives a ratio of 5:4 soh to me gives a ratio of 6:5 lah to doh gives a ratio of 5:3 ray to doh gives a ratio of 9:8 It is worth noting that there are many simple ratios which can be deduced for relationships between notes within the scale other than doh, effectively reinforcing the entire resonant structure. Again it is perhaps not surprising that humans have such a great affinity for the major scale and the series of notes within it. In the Musical Realm Not everyone may be interested in why the major scale and the chords and harmonies which stem from it are so musically special to us. What is important in musical terms is being able to make use of, not only the scale, its harmonies and chords, but the implicit knowledge which all listeners and participants have of it. Whether humans have an implicit knowledge of these fundamental musical building blocks learned over a lifetime, or whether there is some inherent human ability developed over countless generations, is the subject of continuing debate. However from the viewpoint of those attempting to engage others though participation in music, the argument is purely academic; the important point is that the relationship exists and can be harnessed very easily by music facilitators who are prepared to acquire the basic knowledge and skills. Notes, Chords and Harmonies Diagram 2 shows a convenient table of the seven different notes within the major scale. (Although there are eight notes in an octave which goes from doh to doh, and in this case C to C, there are only seven notes before the scale starts to repeat again, i.e. 1 and 8 are identical; both are doh, and both are C). The table shows how each note in the scale can be accompanied by at least one of the three major chords which would normally be associated with the C major scale, i.e. C, F and G. If someone were to sing a melody comprised from the notes within the scale, then the notes sung at points in the melody where the melody stops or holds a long note will indicate what chord is likely to be required for accompaniment at that point. If someone was singing a particular melody and two other people each singing different notes in harmony with the melody, the three together will simply be singing a three note chord for each syllable in the melody line. It is difficult to overstate the role that chords play in reinforcing the structure of the major scale, so it is worth examining the notes which make up the three chords. For the tonic chord which is C (whilst in the key of C), the notes which comprise the chord are the 1st, 3rd and 5th notes in the scale of C major, i.e. C, E and G; not surprising perhaps. From the chart we can see that the chord F is comprised of F, A and C which is the same three notes as the 1st, 4th and 6th notes of the C major scale. However F, A and C are also the 1st, 3rd and 5th notes in the scale of F major. Similarly we can see from the chart that the chord G is comprised of G, B and D which is the same three notes as the 2nd, 5th and 7th notes of the C major scale. However G, B and D are also the 1st, 3rd and 5th notes in the scale of G major. So although the chords F and G serve an accompaniment function for notes in the scale of C major, they also serve as the tonic chord in their own keys. The reason these chords are named F and G is not because of the notes they accompany in other keys, but because they always include the 1st, 3rd and 5th notes of the scales in their own keys. So major chords are always comprised of the 1st, 3rd and 5th notes of their own tonic keys. NB. A logical explanation of musical keys is provided later in these notes.

3 Diagram 2. Tuning Because nature provides an infinite number and range of vibrations at different frequencies, we have learned over the years that when different instruments, musicians and singers are put together they need some common musical reference point which enables all of the musical instruments and singers to be in tune with each other. If not then we, as listeners, would not hear the simple low-numbered ratios and harmonics that we enjoy; we would instead hear a myriad of complex ratios creating an extremely unmusical listening experience where sounds interfere with each other rather than blend together. This required common musical reference point is provided by equating a specific frequency (or rate of vibration) to a specific musical note. The norm is to define the A above middle C on a piano to be 440Hz (vibrations per second). Musical Keys In order to explain the need for different musical keys it helps to go back some way in history. The harp is the earliest know stringed instrument and traditionally uses only the major scale notes. (i.e. as in the white notes on a piano). Every string is tuned to a particular note in the major scale and the player simply selects which notes to play by plucking the appropriate strings and not plucking others. The harpsichord came after the traditional harp and kept the mechanical layout of the strings, but effectively placed the harp inside a box in which the strings were plucked not by the nails of the harpist but by levers connected to a keyboard. From the harpsichord evolved the piano which had the same internal harp arrangement but the strings were hit by hammers connected to the keyboard. The earliest version of the harpsichord, in common with the harp, could play only one major scale whose pitch (or key) was set by the tuning of the doh or first note in the scale. i.e. It had only the white notes of a piano and none of the black notes. Unfortunately the pitch of this one scale (or key) was not always suitable for singers to sing due to differences in human vocal ranges, especially those between the male voice and the female voice. For this reason it was fairly normal for music houses of the time to have two or three harpsichords where the root note doh was set at different pitches, effectively providing different keys for different voice ranges. These limitations also caused restrictions on musical creativity because musicians were only able to play in one key and could not emulate the very interesting key change effects which other contemporary instruments could perform; the early versions of the guitar for example.

4 What developed as a result was a rationalisation of musical scales and a division of the musical octave (the eight notes from low doh to high doh) into a series of equally spaced smaller steps. It had long been realised that the difference in frequency going from me to fah and also from te to high doh was very close to half of the difference between any other two adjacent notes. So these two smaller intervals were given the assignation of half tones and all of the other intervals in the scale were said to be full tones. This series of intervals, which define the major scale, can be demonstrated to be equally appealing to the human ear, regardless of the frequency of the starting note. So it is not the exact pitch of the notes, in vibrations per second, which is important; it is the relationships between the pitches of the notes which provides musicality. So any scale which follows the same intervals of full tones and half tones will sound as good as any other regardless of its exact pitch. Diagram 3 shows the approximate distances and intervals between the vibration frequencies of the notes of the major scale. Diagram 3. In order to preserve the major scale on the harpsichord but allow the instrument to become one capable of playing in different keys, for reasons stated previously, what was required was the addition of five additional half tones to lie in-between the full tones of the major scale notes. These additional half tone (or semitone) notes are the black notes on a piano keyboard. By splitting the musical octave into all half tone steps it allowed the musicians to play their preferred major scale but in many more keys than one and also offered the possibility of greater creative options with regard to incorporating key changes into compositions. See diagram 4. Diagram 4. Due to the unique relationships between the notes in the major scale it is not possible to play the same melody or accompaniment simply by moving up or down a few notes on the keyboard and still play on only the white keys. If attempted such accompaniment would break the major scale s tones and semitones relationship and force at least one wrong note into play. The same effect can be demonstrated by attempting to play a tune on a piano with eyes closed and continuing with the playing movements in mechanical fashion despite the fact that you have started on the wrong note. If you move your starting note or root note to F then you must play Bb and not B as the fourth note (fah) to maintain the major scale intervals. Playing a B instead of Bb will normally sound extremely dissonant (un-musical). Diagram 5 shows the major scale intervals for the two keys of C and F, showing that Bb must be played to maintain the correct tone and semitone relationships between the notes within the F major scale. Notice also that all of the other notes used in the F major scale are the same as the notes used in the C major scale, making F a comparatively easy key to play on the piano. One black note is used instead of a white note, Bb instead of B, and no other black notes are used. Diagram 5.

5 Notes Within Scales in Any Musical Key From the relationship shown between the key of C and the key of F, it should become obvious that there are no less than 12 different keys within music; one for every different note on the piano keyboard. An easy way to show which notes belong to which keys is to make up a stencil card which takes advantage of the universal tones and semitones intervals in all major scales Locating the 1st note on the stencil card on top of the desired tonic (or first) note will reveal all the seven notes within any particular scale by obscuring the five notes which are excluded. Notice that the stencil works for all keys simply because the tone and semitone relationships of the major scale is constant regardless of which note is assigned as note 1. The word chromatic is normally used to describe a scale which includes all of the notes on a piano, both black and white. See Diagram 6. Diagram 6.

6 Relationships Between Keys When we study Diagram 5 we notice that there is only one note of a difference between the notes which comprise the C major scale and the notes which the comprise F major scale. This coupled with the fact that the F major chord is used to accompany three of the notes within the scale of C would seem to indicate that the keys of C and F are closely related. A similar examination of doh to doh in the G major scale also reveals that there is only one note of a difference between the notes which comprise the C major scale and the G major scale. To play in the scale of G major all that is required is to play an F# (black) note instead of an F (white) note. All other notes are included in both keys. Again, coupled with the fact that the chord of G accompanies three of the notes in the C major scale, this would lead us to conclude that the keys of C and G are also closely related. The relationship between keys themselves and the sets of chords which can be used within each key is one that we can take advantage of when we require to change the key of a song, perhaps to make it easier for a particular vocal group to sing. For example, if you can already play a song in the key of C which uses the chords C, F and G (as in the Lion King), but you need to change the key from C to G; the great benefit is that in the new key (G) you already know two of the three chords. The only difficulty is in knowing which chord is dropped and which new chord comes in. Rather than learn the complete map of chords within keys, there is a much easier way to find the answer. This is provided by a map of what is commonly known as The Circle of Fifths. This map shows all the keys in music but rather than in a chromatic list, it shows them in a circle with adjacent keys next to each other. i.e. the keys where there is only one note of a difference between the notes which make up the scales. This also allows us to see what chords go together in any key; i.e. the tonic chord in the centre and the two chords from the adjacent keys on each side. So in the key of G we can see that the adjacent key on one side is C (as suspected) and that the adjacent key on the other side is D. So the three chords we require to play our song in the new key of G are G, C and D. See Diagram 7. Note that a cut out version of the Circle of Fifths is available which has additional circles to show connected major and minor chords. Diagram 7.

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