Harmonic Wheel - Level 1 Foundations of Music Theory

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Harmonic Wheel - Level 1 Foundations of Music Theory

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<p>HARMONIC WHEEL: UTILITIEShttp://www.harmonicwheel.com</p> <p>In the next 2 large sections the main utilities of the Harmonic Wheel are explained in detail. They have been written in a simple and friendly way, so as to be useful even for the layman. In fact, a summary of main musical concepts is given, which may serve as an introduction to Music Theory and Harmony for anyone interested in this subject. Thus, all the concepts are explained in the simplest cases (for example, in the C Major key) and the rest of them are solved, automatically, with the aid of the Harmonic Wheel. In this development, a big effort has been made to logically connect all the concepts, to give the theory a solid and unified structure.All the explanations are given without using the musical notation, for it is unnecessary in this approach. Only one example of it is presented in one of the last chapters. Nevertheless, it is strongly recommended to learn it, for it is one of the few languages having the status as a universal language, along with the mathematical language, the symbols for the physical units and the symbols for the chemical elements. Moreover, once the contents of this Web page are acquired, it will be easier to understand this system of script.Even for those people having musical knowledge, this new way of connecting musical concepts will result very interesting. And, particularly, those musicians who play monophonic or percussion instruments will find, in Level 2, a very useful summary of Harmony foundations, which may be sufficient to satisfy their real professional needs, thus avoiding the necessity of reading complex and extensive texts.The contents have been organized into 2 Levels:Level 1 is devoted to fundamental aspects of Music Theory. This level deals with the musical notes, the intervals, the Major and minor scales, and the keys. The Harmonic Wheel allows us to easily obtain the interval between any two notes, as well as the notes belonging to any Major or minor scale, being it natural, harmonic or melodic, along with their corresponding key signature. As novelty, the Harmonic Wheel gives a complete and panoramic view of the existing relationships among all the keys. While the cycle of fifths shows the keys on a line (one dimension), the Harmonic Wheel shows them on a surface (two dimensions). So, besides the cycle of fifths, the changes of mode are also visible, which are not in the cycle of fifths. Thus, a real MAP OF THE KEYS is achieved.Level 2 is devoted to the foundations of Harmony. This level deals with the construction of Major, minor, Augmented and diminished chords, as well as all possible 4 note chords that can be obtained by superimposing Major and minor thirds. Then, the existing relationships among the different types of chords are explained by means of scales. On the Harmonic Wheel, all these chords have a simple graphical representation. This fact facilitates us to obtain the notes composing them, that is, their arpeggios. On the other hand, this instrument allows us to obtain, automatically, all the chords associated to any Major or minor scale. This function is named CHORD FINDER. As novelty, the particular representation of notes and consonant chords on the Harmonic Wheel explains, graphically, the construction of the Major scale, its relationship with its relative minor scale and the most important characteristics of their associated chords. All these things are difficult to see even in the conventional musical script. Moreover, thanks to this kind of representation, it is easy to determine which chords are more or less affine to any given scale. Finally, some special scales, containing 5, 6 and 8 notes, are explained, along with their associated chords.</p> <p>LEVEL 1: FOUNDATIONS OF MUSIC THEORYhttp://www.harmonicwheel.com</p> <p>1. MUSICAL NOTESThe Musical Notes are 12, 7 being natural and the other 5 are altered.The natural notes, sorted out by their pitch, from the lowest to the highest, are: C, D, E, F, G, A and B. These 7 notes form the so called C Major Scale and correspond to the white keys in the piano. After the B comes another C and so on. Nevertheless, the first and second C are not identical, as the latter is higher than the former. The thing is that, from the point of view of Physics, the vibration frequency of the second C is exactly double that of the first C, which makes those notes very affine when hearing them, to the extent of assigning them the same name. It is said that the distance between them is one octave, because there are 8 natural notes from the first to the second C, including both the initial and the last note in the count.The distance between two consecutive natural notes are not always the same, for in some cases the distance is one Whole step (W) and in others it is one Half step (H). Particularly, between E and F there is one half step, as well as between B and C. On the contrary, between any other two consecutive natural notes there is one whole step. This is the reason why the so called altered notes are placed between them, at a one half step distance, and they correspond to the black keys in the piano (Fig. 1). Therefore, a set of 12 different notes is obtained, there being one half step between any note and the next one. Thus, the distance between a given C and its octave (that is, the next C) is 12 H or 6 W. This set of 12 notes is known as the Chromatic Scale.</p> <p>Figure 1. The musical notes and their location in a piano.In order to name the altered notes, the accidentals are introduced, which are the sharp () and the flat (). The sharp raises the natural note one half step and the flat lowers it one half step. Thus, for example, between C and D (where there is a whole step distance) an altered note is placed, which can be called Cor D. These two notes, corresponding to the same pitch but having different names, are called enharmonic. In the same way, Eand F natural, or B natural and C, are also enharmonic (the term natural means without any accidental). Occasionally, the double sharp () and the double flat () are used to raise or lower the natural note one whole step, respectively.In spite of the fact that the 12 notes are uniformly spaced, in Fig. 2 the different consideration given to the natural and the altered notes is evident, as well as the lack of uniformity in the distribution of whole and half steps among the natural notes. All these things, which seem to be strange and whimsical, are in fact the result of centuries of evolution of Music Theory, which in turn is the consequence of the affinity relationships that exist among sounds, along with the strong cohesion and unity that the set of 7 notes composing the Major scale have. All these questions will be properly explained in different chapters.Furthermore, as will be shown in Chapter 5, a Major scale can be built beginning with any of the 12 notes, thus obtaining, for example, the D Major scale, AMajor scale, etc., what makes the 12 notes equally important. The C Major scale is, simply, the one having exclusively natural notes. In the Guitar, for example, the 12 notes are given exactly the same treatment (Fig. 2).</p> <p>Figure 2. Location of the notes on the 3rd string of the Guitar.</p> <p>2. INTERVALSThe Interval is the distance in pitch between two notes, which is given by the number of whole and half steps between them. This number, however, does not indicate the degree of affinity between them nor their relative position in a Major scale. Therefore, it is most common to indicate the interval with a number and a quality. The interval number indicates the number of natural notes between the first and last note, both included. And, unless other thing indicated, it will be assumed that the interval is ascending, that is, that the second note is higher than the first one. Thus, for example, the interval between D and A is a 5th (D E F G A are 5 natural notes in ascending order).If we now consider the interval between Dand A, we find again a 5th (D E F G A are 5 natural notes in ascending order), although this distance is smaller than that between D and A. To take into account these differences, an interval quality is added to the interval number, which is related to the number of whole and half steps contained in the interval.The interval quality is based on the Major scale. So, every interval between the lowest C and any other note in the C Major scale in ascending order are called Major (M) or Perfect (P). Particularly, the interval between C and F, G or C is called Perfect, while the interval between C and any other note in this scale is called Major (in Chapter 3 an explanation of it will be given). Table 1 shows these intervals and also indicates the number of whole steps contained in each of them.Table 1. Intervals in the ascending C Major scale.Between C andCDEFGABC</p> <p>IntervalP 1stM 2ndM 3rdP 4thP 5thM 6thM 7thP 8th</p> <p>Number of Whole steps0122.53.54.55.56</p> <p>The P 1st interval is called Unison and the P 8th, Octave. To name other different intervals, the following qualities are used:minor (m), if it has one half step less than the corresponding Major interval. For example, between C and Ethere is a m 3rd (1.5 W) and between C and Bthere is a m 7th (5 W).</p> <p>Augmented (A), if it has one half step more than the corresponding Major or Perfect interval. For example, between C and Dthere is an A 2nd (1.5 W), between C and Fthere is an A 4th (3 W) and between C and Athere is a A 6th (5 W).</p> <p>diminished (d), if it has one half step less than the corresponding minor or Perfect interval. For example, between C and Gthere is a d 5th (3W) and between C and Bthere is a d 7th (4.5 W).</p> <p>When necessary, the term double Augmented (AA) is used for the interval having one half step more than the Augmented, and the term double diminished (dd) is used for the interval having one half step less than the diminished.</p> <p>Table 2 shows the intervals between C and the altered notes and also indicates the number of whole steps contained in each of them.Table 2. Intervals between C and the altered notes.Between C andC D D E F G G A A B </p> <p>IntervalA 1stm 2ndA 2ndm 3rdA 4thd 5thA 5thm 6thA 6thm 7th</p> <p>Number of Whole steps0.50.51.51.5334455</p> <p>The last two rows in Table 1 also serve to determine the interval between any two notes, irrespective of whether the first note is C or not. Let us see some examples:Between D and A there is a 5th (D E F G A are 5 natural notes in ascending order) having 3.5 W. It is, therefore, a P 5th.</p> <p>Between Dand Aalso there is a 5th, but now having 2.5 W, so it is a dd 5th.</p> <p>Between Band Gthere is a 6th having 5 W. It is, therefore, an A 6th.</p> <p>Between Aand Cthere is a 3rd having 3 W, so it is an AA 3rd.</p> <p>Those intervals not bigger than an octave, as those studied up to this point, are called simple, while those bigger than an octave are called compound. Every compound interval can be reduced to a simple one by eliminating the proper number of octaves. The interval quality of a compound interval is that of its corresponding simple interval.</p> <p>3. INVERSION OF INTERVALSThe inversion of an interval consists, simply, in interchanging the order of its notes. Thus, if we invert the interval D A, which is a P 5th, we obtain the interval A D, which is a P 4th. And, if we invert the interval E G, which is a M 3rd, we obtain the interval G E, which is a m 6th. In the inversion of intervals, the following two rules apply:The sum of the interval numbers of a given interval and its inversion is always 9. </p> <p>When inverting intervals, the Major is transformed into minor, the minor into Major, the Augmented into diminished, the diminished into Augmented, the double Augmented into double diminished and the double diminished into double Augmented. The Perfect interval, however, remains Perfect. </p> <p>We can check these two rules in the two previous examples. So, in the first one, the P 5th becomes a P 4th (5 + 4 = 9 and both of them are P); and, in the second one, the M 3rd becomes a m 6th (3 + 6 = 9 and M becomes m).In practice, the inversion of an interval is achieved by raising the lower note one octave or by lowering the higher note one octave. But the same result is reached by changing the ascending character of the interval to descending. Thus, between D and A there are 5 natural notes in ascending order (D E F G A) and a distance of 3.5 W, so it is a P 5th. But, in descending order, there are 4 natural notes (D C B A) and a distance of 2.5 W, that is, a P 4th. Therefore, the inversion of the interval can be understood in these two different ways.It is very illustrative to verify that, in the descending C Major scale, every interval between the highest C and any other note in the scale is minor or Perfect. Table 3 shows these intervals and also indicates the number of whole steps contained in each of them.Table 3. Intervals in the descending C Major scale.Between C andCBAGFEDC</p> <p>IntervalP 1stm 2ndm 3rdP 4thP 5thm 6thm 7thP 8th</p> <p>Number of Whole steps00.51.52.53.5456</p> <p>If we compare Table 3 with Table 1 in Chapter 2, we will see that, apart from the 1st and 8th intervals, only the 4th and 5th have the same number of whole and half steps in both the ascending and the descending scale. On the other hand, notes F and G are very affine to note C, due to the particular relationships among their frequencies, from the physical point of view. As a consequence of all these things, these intervals are called Perfect. Remember that the P 4th and the P 5th are the inversion of each other.Although to a smaller extent, those notes forming M 3rd or m 3rd intervals with C are also very affine to it, as well as their corresponding inversions, the m 6th and M 6th, respectively. This concept of affinity several times mentioned is technically known as Consonance and is related to the physical phenomenon of vibration, which originates the sound. In summary, we can say that, apart from the unison and the octave, the Consonant intervals are the P 5th, the M 3rd and the m 3rd, along with their inversions, the P 4th, the m 6th and the M 6th, respectively. The rest of the intervals are Dissonant. In practice, this means that if two notes forming a consonant interval are simultaneously heard, a sensation of harmony, rest and stability is perceived. On the contrary, hearing at the same time two notes forming a dissonant interval produces a sensation of tension and instability.Finally, in Tables 1 and 3 we can also observe that all possible interval distances appear, except the 3 W or Tritone, a highly dissonant interval having special properties. Actually, with the notes of the C Major scale it is possible to form only one tritone, the F B (A 4th) or its inversion B F (d 5th).The concept of Octave and its division in 12 parts, the concept of Consonance and the concept of Major scale are 3 fundamental principles which the Western Music is based on, irrespective of the musical style considered.</p> <p>4. INTER...</p>