Musical art originated in time immemorial as a means for accompanying dances (Hollis, 2017). Therefore, we can assume that musical rhythms from the very beginning are based on the rhythms of human movements, which, in turn, depend on the beats of the human heart. Apparently, therefore, some musicologists argue that the true tempo of popular music, especially dance music, don't have strict uniformity and follows the tempo of the performer's heartbeats (Paderewski, 1909). Relatively recently, scientific evidences have emerged that the human heart is contracting in rhythm of the so-called «golden proportion» (Maisner, 2012). In this case, we can assume that the rhythms of popular dances are also based on the «golden proportion». I believe that the popularity of such dances as polka, waltz and rumba is based on the sensitivity of the human heart to the «golden proportions» in their rhythms.
Part 1. What is the «golden proportion»?
The rule of the «golden proportion» is known to mankind from ancient times. Euclid, a well-known ancient mathematician, describes this as follows: “Extreme and main ratio is such that: (larger segment) / (shorter segment) is equal to (whole line) / (larger segment).” (Livio, p. 78). This relation is denoted by the Greek letter Phi and represents an infinite-length number equal to approximately 1.618.
Fig. 1. Definition of the «golden
Scientists consider the number Phi to be the universal constant of our Universe, as it is laid in the basis of almost all things that surround us. (Watson, para. 2). There are many illustrations to this. For example, Brendan Bentley (2016), an Australian mathematics teacher, asks his students to think about the Golden Proportion, looking at their hands (Bentley, para. 10). Parts of the human body look very harmonious because of the rule of the «golden proportion» acting in them. I’m sure, students immediately find a lot of that manifestations in the structure of the palm, forearm and the whole hand, as on the Fig. 2 (The Above Network, 2015):
Fig. 2. «Golden proportion» in
the hand of a person.
Shells of mollusks are based on the principle of «golden spiral», in each step of which there is a «golden proportion». The same can be said about the structure of the galaxy. Compare the images on the Fig. 3 (The Above Network, 2015):
Fig. 3. «Golden spiral» in the
shell of the mollusk and in the structure of the galaxy.
The ability of «golden proportion» to attract the eye is widely used by architects, artists and designers, as on the Fig. 4 (Meisner, 2013):
Fig. 4. «Golden proportion» in
the car logo.
The golden proportion acts even at the cellular level. For example, the double helix of DNA twists in the rhythm of the «golden proportion», as on the Fig. 5 (The Above Network, 2015):
Figure 5. «Golden proportion» in
the double helix of DNA.
The «Golden Proportion» is also present in the works of writers, poets, and composers. Usually, the authors of the works use the point Phi, placing in it the most important idea, thoughts, or exclamation. There are quite serious literary and musicological studies on this issue. But musicologists, unfortunately, still have not bothered to look for a «golden proportion» in the musical rhythm. I'm sure they could find a lot of interesting things on this topic.
Part 2. Music and heart.
One day, when I was listening to a new recording, I was in a state of bewilderment. This was a well-known music, that was well orchestrated. But it didn't give any pleasure. The record was reproducing in high quality, smoothly, without failures. And then it dawned on me: «This music sounds too smooth, somehow mechanically, as if it made by robots.» My heart refused to perceive such executing. Indeed, as it turned out, the music for this disc was played by a computer program. The music notes were laid down correctly, the musical size and pace corresponded to the instructions of the author-composer. Programmers did not understand only one nuance. People, unlike robots, put their soul into music. And this changes everything. Then I understood one simple thing: notes on paper are just guidelines. They allow the musician to not to get out of the rhythm and not to get lost. The true performance of music must connect with the performer himself, with his emotional and physical state.
Of course, musicologists in their time discussed this issue. At the beginning of the 20th century, the Polish composer Jan Paderewski (1909) actively advocated the recognition of a connection between the human heart and music tempos. Justifying the effect of uneven execution of a uniform rhythm in popular music, Paderewski wrote: “Rhythm is the pulse in music. Rhythm marks the beating of its heart, proves its vitality, attests its very existence. Rhythm is an order. But this order in music cannot progress with the cosmic regularity of a planet, nor with the automatic uniformity of a clock. It reflects life, organic human life, with all its attributes, therefore it is subject to moods and emotions, to rapture and depression” (Paderewski, para. 1). Paderewski suggested that the performed music connects with the rhythm of the human heart.
Next generations of scientists explored the direct connection of music with the beating of the human heart. Austrian scientist Richard Parncutt (1987) directly points out that the musical rhythms that we perceive and reproduce are associated with palpitation and walking (Guedes, 2007, para. 8). Dutch researcher Carlo Guedes (2007) thinks about the optimal musical rhythmic fractions, equal to the rhythmic proportions of palpitation and walking. He concludes: «Not surprisingly, these time values (75 – 120 beats per minute) comprise the musical tempi of most dance music” (Guedas, para. 10). The results of the motor experiments of McDougall and Moore (2005) fit well to the conclusion of Guedes. They revealed the most comfortable frequency of human movements is 120 beats per minute (McDougall, p. 1172). In the simplest case, this frequency corresponds to a musical tempo of 60 tacts per minute. Let's note this!
Part 3. A human heart beats in a „golden rhythm“.
The human heart is a unique biological mechanism. It consists of four parts. They all work strictly in order, pumping the blood with varying strength. Their coordinated work is clearly visible in the form of large and small peaks of the electric cardiogram. The heart works non-stop all our life, without rest and breaks, constantly reacting to our thoughts, emotions, and surrounding stress. Only in conditions of rest, the heart, while continuing to contract about 60 times per minute, has the opportunity to relax.
Gary Maisner (2012) claims that in conditions of the heart resting the cardiogram shows the presence of a „golden proportion“ in the heart rhythm. He writes: “The former site Heartbeat2000 sought to study the relationships between the physical heart and the spiritual heart, that is the soul, of human beings. The views presented there suggest that a heartbeat that produces a phi relationship in the T point of the ECG represents a state of being that is one of health, peace and harmony» (Maisner, para. 2). There Maisner provided a drawing that clearly demonstrates the golden proportion in the heart rhythm (Meisner, 2012):
Fig. 6. “Golden proportion” in the
A group of researchers led by Henein (2011) revealed many golden proportions in the structure of the heart. These are, for example, the ratio of its overall size, the angles of entry of the main cardiac vessels and the ratio of the dimensions of the heart valves. The scientists concluded that the golden proportions of the heart correspond to the optimal efficiency of its work. In their report they write that “the overall cardiac and ventricular dimensions in a normal heart are consistent with the golden ratio and angle, representing optimum pump structure and function efficiency, whereas there is significant deviation in the disease state” (Henein, para. 1).
Other groups of scientists investigated the relationship between the upper and lower limits of a person's blood pressure. It turned out that in a state of rest, values of blood pressure correspond to the well know rule of “the golden proportion” (Papaioannou, para. 13).
Hence, we can conclude that all types of the golden proportion in the heart rhythm corresponds to the state of the most economical work of the heart and the ideal blood pressure differential. Under such conditions, the heart is rested. That is, the most comfortable state for the human heart is a state of rest with 60 pulsations per minute in the rhythm of “the golden proportion.” Let's note this!
Part 4. The connection between the heart rhythm and popular dances.
In Figure 6, the author noted “the golden proportion” between the two most pronounced parts of the heart cycle. However, each of the four departments of the heart must contribute. In figure 7, the four peaks of the cardiac cycle are well visible. Cardiologists call them R-wave, T-wave, U-wave, and P-wave (Kluver, 2011, p. 44).
Fig. 7. Four waves of the heart cycle.
It is logical to assume that there is a «golden» relationship between all of them, approximately, as in the figures below. The red arrow emanating from the point of the corresponding golden section successively points to the peaks of the heart cycle. It can also be assumed that each of these three approximations can be matched to preferred dance rhythm.
In “the golden rhythm of the first order”, the golden proportion is taken between the two most pronounced parts of the heart cycle. The remaining cardiac peaks U-wave and P-wave are ignored. This distribution, showing on the Fig. 8, may correspond most closely to the rhythm of dances like polka.
Fig. 8. Golden heart rhythm of the first
In “the golden rhythm of the second order”, the three most pronounced parts of the cardiac cycle participate in the calculation. Only the smallest U-wave peak is ignored. This distribution, showing on the Fig. 9, may be correspond to the 3-beat waltzes.
Fig. 9. Golden heart rhythm of the second
In “the golden rhythm of the third order”, all four parts of the heart cycle are taken. This distribution, showing on the Fig. 10, may be correspond to the dances like rumba.
Fig. 10. Golden heart rhythm of the third
Let's bring everything together
So, we remember that the human heart in a comfortable state makes 60 contractions per minute, following the rhythm of “the golden proportion". We also remember that the most convenient frequency of human movements is 120 actions per minute, which corresponds to a 2-beat musical tempo of 60 tacts per minute. Further, as is known, the polka is performed at a 2-beat rate at the tempo of 60 tacts per minute. Hence, we can assume that the rhythm of the polka should also obey the rule of "the golden proportion.” And then it becomes clear why the dances and music in the rhythm of polka have great and unfading popularity in the world. This rhythm is simply pleasant for our hearts.
The same can be assumed about the waltz. The usual waltz is performed in a 3-beat tempo at a rate of 60 tacts per minute. The second-order golden heart rhythm carries sequential contractions of the three heart parts, which can correspond exactly to the three waltz beats. Hence the secret of its unfading worldwide popularity of waltz becomes understandable since the rhythm of the waltz also obeys the rule of “the golden proportion.” In this case, the waltz formula completely fits into the golden heart rhythm of the second order. Waltz music is just pleasant and attractive to the heart.
The same can be assumed about the Latin American rumba. Its complex rhythms consist of uneven beats, very similar in sequences with a golden heart rhythm of the third order. The pace of the rumba is about 30 tacts per minute, which corresponds to the most comfortable frequency of human movements at 120 actions per minute. Again, as the music of the rumba is subject to the “golden proportion rule”, it becomes clear why rumba is one of the most popular dances. It’s rhythms just coincide with the rhythms of the heart and completely take possession of it.
In this article, the popularity of the dance rhythms of polka, waltz and rumba are explained by their consistency with the comfortable rhythm of human heartbeats, subject to the rule of “the golden proportion”. All logical reasons I made is based on scientific data. However, the conclusions drawn in the article are of an exclusively theoretical nature and need experimental confirmation. It seems there is a large field of activity for scientific research on the relation between the heart and musical rhythms. I hope that my work will draw the attention of scientists to this theme. Also, I hope the presence of “the golden proportion” in the rhythms of popular paired dances will be confirmed by experiments.
Guedes, C. (2007). “Translating Dance Movement into Musical Rhythm in Real Time: New Possibilities for Computer-Mediated Collaboration in Interactive Dance Performance.” Proceedings of The International Computer Music Conference (ICMC 2007) Copenhagen, Denmark. Retrieved from Carlos Guedes website: https://carlosguedes.org/publications/