[1.1] The principal question this paper considers is the relevance of the circle of fifths within elementary music education today. Adult students frequently request further information about the origins, interpretation, analysis, uses of the circle of fifths and the connections to their own ethnic origins. Understanding the historical foundations behind the perfect fifth are as important as the ability to appreciate the musical device. The relevance of ancient cultures may not be immediately relevant to younger students, but for those learning in later years it is not only relevant, but also interesting.
[1.2] The importance of the interval of the fifth began in several different locations before the common era. As time progressed the fifth, or its ratio of 3:2, remained stable, although it was presented in different ways according to location and time. This chapter presents an analysis of the ancient origins of the movement by fifths in the dominant ancient cultures of Egypt, China, and India. The aim is to see how the understanding of sound, resonance and particularly the 3:2 ratio of the fifth emerged through the ancient writings.
[1.3] The German musicologist Curt Sachs, in his book The History of Musical Instruments presents an interpretation of seventeen harp players from a relief artwork of ancient Egypt. The author asserts that seven of the harpists were striking a fourth chord, a fifth chord was demonstrated by five harpists and the final five held their hands as if they sounded the octave chord (Sachs, 1968, p.94). Plutarch referred to the importance of the number five in Moralia Volume 5 (Plutarch and Frank Cole Babbitt, 1936) where he wrote that panta, meaning all, was a formed from pente, meaning five, stating that the Egyptians counted in fives. The importance of the fifth in Egypt can be seen in the civilisations historic record. The parables and fables were used to express knowledge. These narratives included the characters, presumed to be mythological, of Isis and Osiris to which the numbers two and three were attributed. The number five was assigned to their son, Horus, being the product of the number two and three. The number five would be signified by two vertical markings over three vertical markings (Gadalla, 2018a, pp.45–52).
[1.4] The Egyptologist Moustaffa Gadalla states in his book The Enduring Ancient Egyptian Musical System that the relationship of three to two is the ratio of the vibrating string to produce the perfect fifth (Figure 1‑1). When a string is divided in half it produces an octave with a ratio of 2:1. When the same string is divided into thirds and held down at the point of two thirds the note produced is a fifth above the lowest note. It is proposed that this is the interval from which all intervals are formed.
[1.5] The starting note is traditionally C in Western music, and the circle of fifths. In this chapter the note D has been used as it is the preferred note to the Egyptians. This preference was due to the symmetrical nature of the semitones and the relationship of this pattern to the everyday life of an Ancient Egyptian. The semitone between the notes E and F marked the days Sunday and Monday and indicated light activity whereas the semitone between C and D marked the days Thursday and Friday which were very active. The structure of the week corresponded to the cosmic movements of the planets around the sun, this association guided Egyptian life from faith and music to festivals or feast days (Gadalla, 2018b, pp.27–28).
[1.6] The musical progression of notes, using D as the generating note, produces the progression the Ancient Egyptians discovered and favoured. Moving by the interval of a perfect fifth, or the ratio 3:2, the note above D is A, and the note a fifth below D, following the same method, is G. By repeating this pattern, the note a fifth, or the ratio of 3:2, above the A would be E, and a fifth below the G would be C. When these notes are adjusted in pitch and compressed into a single octave, they form a pentatonic scale from C. Extending the sequence by another fifth either way gives the complete scale. When these notes are adjusted by altering the pitch, a heptatonic scale is formed in the favoured Egyptian pitch, the initial note requires repeating to complete the scale (Figure 1‑2).
[1.7] The order of the universe was heard in the music of Ancient China (Nakaseko, 1957) and the traditional concepts of yin and yang were used to aid the explanation of music theory. Yin and yang are the great opposites of the universe and music theory was bound to these concepts. The sounds were formed from a progression of perfect fifths with the sound being produced from varying lengths of bamboo. The origins date back to Huang-ti, the Yellow Emperor (2697BC) when a courtier was sent to K’un-lun, a mythical mountain, to make bamboo pitch pipes. These were divided equally between yin and yang. The six yin pipes were to represent the call of the female bird and the six yang pipes the call of the male bird, which according to Dr Ulrich Theobald, were influenced by the cries of a phoenix (Theobald, 2000a).
[1.8] The principal pipe was called the yellow bell pipe, which, according to legend, required eleven months of growth, a constant thickness, and was to be taken from between two knots. (Fisher, 1973). It is accepted the length would have been nine ts’un, or approximately nine inches. The lengths of the following pipes were calculated by dividing the pipe into three parts and adding, or subtracting, a section in accordance with the note required. The last note sounded became the starting point for the next note and the new measurement to divide or extend from. A pipe shortened by one third produced a note a fifth higher and formed the ratio 3:2. This length was classified as, the feminine generation, yin. A pipe that was lengthened by a third produced a note a fourth lower, which was the ratio 4:3, this length was classified as, the masculine generation, yang. (Nakaseko, 1957). Kuan-tzu, the prime minister to Duke Huan in 645BC, alternated the measuring devices of two thirds and four thirds to produce the first series of five tones.
[1.9] These five primary sounds, the first five in the series, were named ‘The Five Voices’ (Figure 1‑3). Later two additional sounds were added making ‘The Seven Voices’, this continued to make the twelve tones. The pitches were named according to the months of the year starting at the eleventh month and through this association were designated yin or yang. The odd number months and their corresponding sounds were yang, and the even, yin (Figure 1‑4). According to Ancient Chinese beliefs yin and yang come from the great source, or from one comes two, out of these two all things are born. The number of the heavens is three because the Chinese thought heaven was round. The ratio of a circle is 1:3 diameter to circumference. Two is earth as the earth was square with a ratio of 1:4 for the side to perimeter and a unit of the perimeter as two. Therefore, we have the ratio of earth to heaven as 3:2 with a product of five attributing a quality of the order of heaven and earth or the harmony of all things to ‘The Five Voices’. The balancing of yin and yang is the ratio of 3:2. The bamboo pipes which produced the sounds were bound together and the oldest surviving description of the pitch pipes is said to be found in the Book of Hanshu (Theobald, 2000c). The relevant chapter combines the details of the pipe's measurements with their relationship to the universe and an explanation of the calendar using the solar positions, planets, and constellations (Theobald, 2000b). An accurate translation of the relevant primary source has been sought via email and, at the time of submission, has not been received.
[1.10] The third ancient civilisation to consider in the origins of the circle of fifths is the Indian subcontinent. The source of musical pitch in North India is written in the Vedas, a collection of poems and hymns written in four volumes in 1200 to 1500 BCE that focus on ritual and sacrifice to gods which personify natural and cosmic activities (Doniger, n.d.). The Rig Veda, the first and oldest of these volumes, contains the hymns and chants of the Vedic people. The Sama Veda contains melodies and chants as used by the priests and is the origin of Indian music (Hindustani Music Notes Chapter 6, n.d.). In the beginning it is recognised that there were three notes, namely udatta, anudatta and svarita. Udattta, the highest, is the sound produced above the palate and has an intense accent. Anudatta, the lowest, is produced below the palate and is gravely accented. The third, Svarita, is a combination of the two with a circumflexed accent (Vasarao, 2015), initially the priests only used these three notes. The author William Whitney wrote a commentary on the text of the Tâittirîya - Prâtiçâkhya, a book regarding the pronunciations of words, in the essay he states that the Sanskrit text says that there are three positions or qualities, in which there are twenty-one tones (Whitney, 1868). This text indicates that in Ancient India there were more pitches used in Vedic times, but it clearly indicates the tone or pitch was produced vocally and proceeds to describe the variations of sound in minute detail; strikingly different to the previous two ancient cultures. In South India the Early Tamils, whose lineage goes back to the Dravidians, had a different musical experience than their northern neighbours. The origins of Tamil music are found in the Cilappatikaram, the earliest Tamil epic. In the paper Scale and Mode in the Music of the Early Tamils of South India, the author cites from the epic showing a musical system in place when the epic was written during the first and third centuries of the common era. This is considerably later than the information gathered from Egypt and China. While the text indicates some importance has been given to the intervals of the fourth and fifth there is a dearth of primary source material, or papers citing primary sources. In the appendix three of The Silappaadikaram by Ramachandra Dikshitar mentions that primary source material which discussed the science of music during the period of sixth to the third century BCE, known as the Sangam period, was lost long ago (Dikshitar, 1939, pp.360). Therefore, for this paper, the origins of instrumental music in the third great ancient civilisation can be viewed as lost.
[1.11] It can be seen from this brief overview that the importance of the interval of a fifth is cited in two of the chosen ancient cultures, and limited evidence of it in the third. The original question of why, when, where, and how did the relevance of the interval of the fifth appear can now be answered. That is shown that in two of these ancient cultures the origins of the fifth appears in mythological stories that carry attributions to nature-based phenomena and religious overtones. These stories were being told during a significant period before the common era. It has also been shown that by the last century of this period the heptatonic scale was being used by instrumental musicians who specialised in their craft in all three cultures.
[1.12] Mature students have many fields of interest and the relevance this ancient knowledge has today to this demographic of the student body is significant. The awareness of a greater pattern, of which the student is already part, shows the study maybe elementary in nature but not simplified which for a mature student this can be reassuring.
^ Figure 1‑1. Harmonic Ratios.
^ Dikshitar, V.R.R. (1939). The Śilappadikāram. [online] Indian Branch: Oxford University Press, p.360. Available at: https://archive.org/details/in.ernet.dli.2015.201802/page/n9/mode/2up?q=fourth [Accessed 12 Aug. 2022].
^ Gadalla, M. (2018a). The Enduring Ancient Egyptian Musical System. Expanded ed. [online] PO Box 39491 Greensboro, NC 27438 USA: Tehuti Research Foundation, pp.45–52. Available at: https://www.scribd.com/book/345485743/The-Enduring-Ancient-Egyptian-Musical-System-Theory-and-Practice [Accessed 15 Jul. 2022].
^ Gadalla, M. (2018b). The Enduring Ancient Egyptian Musical System. Expanded ed. [online] PO Box 39491 Greensboro, NC 27438 USA: Tehuti Research Foundation, pp.27–28. Available at: https://www.scribd.com/book/345485743/The-Enduring-Ancient-Egyptian-Musical-System-Theory-and-Practice [Accessed 15 Jul. 2022].
^ Hindustani Music Notes Chapter 6. (n.d.). [online] National Institute of Open Schooling, Distt. Gautam Budh Nagar, Uttar Pradesh - 201 309: National Institute of Open Schooling, p.42. Available at: https://www.nios.ac.in/media/documents/Hindustani_Music_242/hindustanimusictheorybook1/HMB1Ch6.pdf [Accessed 7 Aug. 2022].
^ Plutarch and Frank Cole Babbitt (1936). Moralia. Volume V. [online] Cambridge, Mass. ; London: Harvard University Press. Available at: https://www.pdfdrive.com/plutarch-moralia-volume-v-isis-and-osiris-the-e-at-delphi-the-oracles-at-delphi-no-longer-given-in-verse-the-obsolescence-of-oracles-loeb-classical-library-no-306-e162078575.html [Accessed 13 Jun. 2022].
^ Sachs, C. (1968). The History of musical instruments. [online] New York: W.W.Norton & Company, p.94. Available at: https://archive.org/details/the_history_of_musical_instruments_curt_sachs/page/n103/mode/2up [Accessed 8 Jul. 2022].
^ Theobald, U. (2000b). Chinese Music (www.chinaknowledge.de). [online] www.chinaknowledge.de. Available at: http://www.chinaknowledge.de/Literature/Historiography/lvlizhi.html [Accessed 12 Jul. 2022].
^ Theobald, U. (2000c). Chinese Music (www.chinaknowledge.de). [online] www.chinaknowledge.de. Available at: http://www.chinaknowledge.de/Literature/Historiography/hanshu.html [Accessed 12 Jul. 2022].
^ Vasarao, S. (2015). Music of India – a brief outline – Part Four. [online] Ssreeni Vasarao’s Blogs. Available at: https://sreenivasaraos.com/2015/04/22/music-of-india-a-brief-outline-part-four/ [Accessed 8 Aug. 2022].
^ Whitney, W.D. (1868). The Tâittirîya - Prâtiçâkhya, with Its Commentary, The Tribhâshyaratna: Text, Translation, and Notes. Journal of the American Oriental Society, [online] 9, pp.395–399. doi:10.2307/592258.