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Chapter Four

[4.1] The principal question for this research paper is the relevance of the circle of fifths to elementary students today. Relevance can be translated as being appropriate for, an elementary student. It can be interpreted to mean whether the circle would be useful to the educational experience (Oxford Learners Dictionary, n.d.).

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[4.2] The circle of fifths contains principles and reinforcement of different elements of music that act as indicators of the interconnectivity and importance of this interval. These include, scales, key signatures, chords, chord progressions, and transposition aids that open doors to understanding and provide access to the compositional features behind the notes. This information can reduce wrong notes, and aid effective finger patterns. The understanding of these items, to an elementary pianist, will significantly improve their experience of music education.

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[4.3] The construction of the circle is straightforward due to the convenient connection to the clock-face.  To commence the creation of the circle the student will need an image of a clock face showing the positions of the numbers but without a numeral or hands (Caton-Greasley, 2022). At the twelve o’clock position a student should place the capital letter C, representing C major. Each following division to the right is represented by the letter name of the fifth note in the scale, which is known as the dominant, or the note seven semitones above the previous note. The fifth note of C major is G, forming the scale at the first twelfth location, the fifth note of G major is D, forming the scale at the second twelfth. This is continued until reaching B major at the fifth twelfth placement. Moving seven semitones up from B will give the note F sharp, the sharp is required due to the interval between E and F being a semitone. To form the left-hand side of the circle the fifth note below the starting note is required, this note is known as the subdominant or the fifth note below the tonic. F is additionally the fourth note of C, this is easier for a student to calculate. The fifth, or seven semitones before F would be B flat, which is the fourth note of F major (Figure 4-1). The process continues until the student reaches the sixth position. The major scale notes are now complete, and the student is ready to add the numbers that indicate the key signatures. These commence with zero at twelve o’clock indicating that C major has no sharps or flats. The numbers one to six are added to the right for the sharps and added to the left for the flats. The addition of the minor key signatures requires a second level of letter names, often shown inside the circle as shown on the musical circle by Kellner in Chapter Three. The relative minor key, which has the same key signature, of C major is A minor. This is the sixth note of the scale of C major, the key at the third position or the note three semitones before C. The position of the sixth note can also be at the two ends of the hypotenuse on a right-angled triangle, the triangle of Pythagoras theorem mentioned in Chapter Three. The circle of minor keys is completed by following the same procedure for each note (Figure 4‑2).

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[4.4] Following this method, an elementary student can assemble the circle accurately and quickly. This diagram allows a learner access to all scales, key signatures, chords, chord progressions, and transposition (Dunn, 2022, pp.7–8). The natural progression and logical nature of the calculations enable a student to learn the circle using a discovery method of learning. This educational methodology can shift the focus from end-product learning to a process-oriented method that can, for some students, enable a greater understanding (Prawerti, 2014). An elementary student can find and utilise the items discussed in the conclusion of this chapter within the complete circle of fifths. This can be facilitated by a teacher through the traditional music and technical exercises being learnt.

The first of these items, the scales, can be seen from the names forming the initial circle, each is the tonic of the key in question. The number represents the quantity of sharps or flats in the key signature. An initial observation will clearly show to the student the minor key (shown in green) with the same key signature. With a modicum of further inspection, an awareness that the inner circle follows the same order as the outer circle should be attained and some students may notice that the sequence has moved from the third position to the twelfth position (Jackson, 2015, pp.17–18).

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[4.5] The second item on the list is the order of sharps, shown in red on Figure 4-2, and flats, shown in blue on Figure 4-2, that form the key signature. The mnemonic ‘Father Charles Goes Down And Ends Battle’ while fun for a student to notice the sentence can be inverted for the flats, does little to bring awareness of ‘why?’ to the student.

 

[4.6] When a novice musician is aware that the only requirement for recall is F for sharps and B for flats and that all others can be calculated by adding a perfect fifth, or seven semitones, the study of music ceases to be an accumulation of letters in a random order. Instead, there is a methodology that is as logical as the form of mathematics with the predictability of the rules of science and the rationality of the grammatical rules of language. It is worth noting here that the inclusion of F flat and G sharp in parentheses on Figure 4-2 are included as a theoretical item to aid understanding the progression of sharps and flats with the use of the enharmonic.

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[4.7] Third on the list is using the circle to identify primary and secondary chords. Chords are introduced as combinations of single pitches heard and played in sequence or together (Encyclopaedia Britannica, n.d.). The importance of chords is twofold, initially an elementary student gains the knowledge of notes that work together, this is followed by combinations of chords that work collectively to create additional meanings and effects in the music. The first chord to construct is the tonic triad, this is the principal chord of the scale. To assemble the notes of the tonic triad an arrow is drawn from the lowest note of the chord, which is the first note of the scale, to the second note of the chord. This is shown by the red items on Figure 4-3 where the second note of the triad, or the third note of the scale, is found at the fifth position. The third note of the triad, or the fifth note of the scale, that commences from the fifth position, shown by the green items on Figure 4-3, it being the fourth note moving back towards C. The yellow arrow is included on the diagram to complete the triangle from the fifth to the first. By using this method an elementary student can independently use the circle to calculate and investigate any chord and explore the sounds the chords create.

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[4.8] A pre–Grade One student initially plays scales and pieces in the keys of C, G and F major with no obvious connection for the choice other than the use of one sharp and flat in the key signatures. An explanation of chord and technical names of the notes in the scale can show why certain keys are used together. Identifying these with the Roman numerals of I for tonic, V for the dominant and IV for the subdominant (Figure 4‑4). An awareness of the chord names prepares the student for an expansion of musical possibilities with lead sheets, this enables them to be able to collaborate with friends learning different instruments. By adding the triangles discussed in the previous paragraph to the circle, for the tonic chords for F major and G major the repetitive pattern and commonality between the chords can be observed (Figure 4‑4). At this stage a student can play a complete major scale with the I, IV or V chord added according to the arrows that touch the letter, various bass patterns can be introduced and the concept of improvisation over a variety of scalic chord passages. The left hand of many elementary compositions can be substituted with a I, IV or V chord and the student begins to feel that they can understand what they are playing and therefore create their own unique music (Figure 4‑5).

 

[4.9] The introduction of the secondary chords to the circle increases a student’s understanding and begins to allow modulations to related keys or the addition of different nuances into their own music. The secondary chords can be introduced in different ways that are guided by the student's requirements. For a student who benefits from visual aspects the use of primary colour combinations to produce the secondary chords: colours can be very effective when it is seen that the central notes from the sum of the two chords contain the secondary chord (Figure 4‑6). The third example of the figure shows the chords on notes two and seven are in close-proximity, and that they are both an incomplete version of the complete leading-note seventh chord. This provides a link into complex music for students who wish to explore those possibilities. A student who learns from pattern and sequence will find the location of the uppercase Roman numerals for IV, I, V, representing the primary major chords, echoed in the lowercase numerals for ii, vi, iii, identifying the secondary minor chord pattern (Figure 4‑7). A pattern-based learner may be able to visualise the minor chord shapes isosceles triangles (Figure 4‑9) and the combined major and minor tonic shapes.

 

[4.10] Providing the arrows for the related major and minor chords to indicate the triads (Figure 4‑8) allows a student to see the commonality between the chords that is missed by repeating scales and broken chords according to graded requirements. Adding the chord triangles for each of the secondary triads, except for the chord built on vii, the scale can be played with the minor triads (Figure 4‑10). When the vii chord is added (Figure 4‑11) it can be seen on the circle that the diminished nature of the chord forms a right-angled triangle, rather than the previously used isosceles triangle and traditionally associated with Pythagoras, this triangle appears to join the major and minor chord patterns together. The final figures for this chapter show the complete C major pattern showing the primary and secondary chords, and the chord built on the seventh note of the scale (Figure 4‑12). 

 

[4.11] Using this system, a student will build over four to six weeks the harmonies of the scale that can be used in improvisation, composition, and harmonisation of simple melodies. A perusal of the standard and most popular teaching methods for piano shows a lack of the introduction of the circle and the extent it can be of benefit to the elementary student. Those viewed, and previously used are detailed in the table found in the bibliography for this chapter.

 

[4.12] Returning to the principal question of this research paper ‘Is the circle of fifths relevant to elementary music education today?’ I believe from the discoveries detailed within this chapter show that it is closely connected to the experiences of an elementary piano student and that it would be beneficial to the educational experience. It has been shown that the use of the circle concepts can be used in traditional music and technical exercises. The knowledge the circle has provided in an accessible format allows the student to expand into music within a student’s listening preferences, bringing a ‘music lesson’ contents into the real-world experience which expands the musical experience on a personal level and academic platform.