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Chapter Three


Chapter Three

[3.1] Chapter Three addresses three main questions: What is the circle of fifths? Who had the concept published? and, when did the fifths of the ancients and medieval theorists become a circle? 

[3.2] While he was in Moscow, in 1678 or 1679, Diletskii wrote a musical treatise named Idea Grammatikii Musikiiskoi, the word idea used here to mean a concept. In this volume he offers students of music the advice to study the works of other musicians to understand how those pieces are composed. He directs the emphasis to composition being the priority.  The treatise initially posits the question ‘what is music?’ Two answers are provided in the publication. The first is music moves the emotions to feel happiness or sadness, the second is that the voice moves in an ascending or descending manner (Jensen, 2009a, pp.111–113). Whilst there are no listings of music that demonstrate musical styles that evoke feelings of happiness and sadness there is a short musical score demonstrating the sounds of the triads.


[3.3] Diletskii divides music into two styles, one according to its meaning and one according to its key. He explains that the meaning of the first is three-fold, music that makes you happy, sad or initially happy and then sad. The text uses solmisation, a system of assigning a note a syllable, those being of Ut, re, mi, fa, sol and la to demonstrate the pitch of the notes of the triads. These triads are included to demonstrate the division of happy and sad sounds in a scale (Figure 3-1). Ut-mi-sol were classified to use for happy singing and re-fa-la were categorised to be used for sad singing. This system was well established, having been written and introduced by Guido de’Arezzo in Ut Queant Laxis circa 991 – 1035 AD (Itchiro, 2011). Idea Grammatikii Musikiiskoi does not reference this methodology, however it can be accepted that the reader would have been aware of it.

[3.4] The second style is the clarification of key which is split into four styles, the initial set contains no sharps and flats, the following just sharps, just flats or a mix of both. The rest of the text continues to amplify the uses of these styles and ways to move between keys. The second half focuses on compositional methods and how to use the different keys and modulate between them. The major and minor key system we know today can be seen in the components that are listed in the treatise, but he does not go so far as to name the options given as major and minor. Towards the end of the volume Diletskii introduces the musical circle (Jensen, 2009b, pp.137–140) (Figure 3‑2). He details methods to expand a composition by adjusting the melody alongside methodology to interpret figured bass. The musical circle shown in Diletskii’s work shows a short melody transposed into different keys, this is recognised as the first musical circle (Собрание рукописей и старопечатных книг, 1670) (Figure 3-3).

[3.5] The next musical circle did not appear until 1711, published by German composer Johann Heinichen (Figure 3‑4). This circle was published, as the previous circle, to aid modulation from one key to another. Heinichen does not take credit for the circle and is quoted as claiming that it came from Athanasius Kircher however Joel Lester states in The Recognition of Major and Minor Keys in German Theory that the major minor circle concept was more theoretical, and that Heinichen was the first to publish the proposal of a circular harmonic progression of keys (Heinichen, 1728). 


[3.6]  It was another composer seven years later who rallied the cause of the new system and waged war on the old modal system. Johann Mattheson could see a place for modes in church but not in the music of the people. He published a treatise of all the keys and states that no other musician, bar Heinichen, had ever presented all the keys. While Heinichen paired relative major and minor keys, Matthesons’ model (Mattheson, 1735) (Figure 3‑5) had no musical rationale other than he perceived that it was more suitable to modulate than Heinichen’s (Lester, 1978).

[3.7] The final circle to consider is by David Kellner (Figure 3‑6). The general-bass treatise he published in 1732 (Killner, 1737) was considered an essential book for any elementary student. This volume included a musical circle which incorporated an example of the key signature and the minor circle of keys related by key signature inside the major keys. It is notable that three of the four circles we have looked at have been published in publications used for the realisation of figured bass, these were called thoroughbass. Heinichen published two of the aforementioned methods. Mattheson’s book was published a year earlier and would have been known to Kellner.  In the second edition of Kellner’s publication, he refutes a negative review which, although it does not mention the reviewer, is believed came from Mattheson (Sparr, 1997, pp.43–47).

[3.8] This chapter commenced asking three main questions. The first question was what is the circle of fifths? In answer to this it is a sequence of keys compiled to aid composition and an understanding of figured or thorough bass and the connections between the major and minor tonalities of the new tuning system. The second question is who had the concept published? In answer to this we have four gentlemen, one from Russia and three from Germany, namely Diletskii, Heinichen, Mattheson and Kellner. Finally, the third question was when did the fifths of the ancients and medieval theorists become a circle?  The first musical circle was published in 1677 followed by 1728, 1735, 1737.

[3.9] Considering the relevance that the circle of fifths has in elementary music education today one can say, with reference to the information presented in this chapter, that the knowledge of the circle of fifths enables a student to understand the triads used in a composition, the chords that enable a simple modulation and the relationships between the major and minor keys via the sixth of the scale.

Figure 2‑1. Examples of Happy and Sad Music

Figure 3‑1. Examples of Happy and Sad Music.

Figure 3‑1. Diletskii: Musical Circle 1678

Figure 3‑2. Diletskii: Musical Circle 1678.

figure 1.1.png

Figure 3‑3. Notation from the above circle.


Figure 3-2. Heinchen: Music Circle 1728

^ Figure 3-4. Heinchen: Musical Circle 1728.

Figure 3-3. Mattheson: Musical Circle 1735

^ Figure 3-5. Mattheson: Musical Circle 1735.

figure 5.png

Figure 3-6. Kellner: Musical Circle 1737.

(Jensen, 2009a, pp.111–113)
(Itchiro, 2011)
(Собрание рукописей и старопечатных книг, 1670)
(Jensen, 2009b, pp.137–140)
(Heinichen, 1728)
(Lester, 1978)
(Sparr, 1997, pp.43–47)
Figure 3-4
Figure 3-5
Figure 3-4
Figure 3-2
(Killner, 1737)
(Mattheson, 1735)
Figure 3.1
Figure 3-3


Heinichen, J.D. (1728). Der General-Bass in der Composition. [online] IMSLP. Available at:,_Johann_David) [Accessed 10 Jun. 2022]. Page 837.

^ Itchiro, S. - (2011). File:TN-Ut queant laxis color paysage.jpg - IMSLP: Free Sheet Music PDF Download. [online] Available at: [Accessed 29 Aug. 2022].


Jensen, C.R. (2009a). Musical cultures in seventeenth-century Russia. Bloomington, IN: Indiana University Press, pp.111–113.

Jensen, C.R. (2009b). Musical cultures in seventeenth-century Russia. Bloomington, IN: Indiana University Press, pp.137–141.

Killner, D. (1737). Treulicher Unterricht im General-Baß. [online] IMSLP. Available at: [Accessed 10 Jun. 2022].

Lester, J. (1978). The Recognition of Major and Minor Keys in German Theory: 1680-1730. Journal of Music Theory, [online] 22(1), p.65. doi:10.2307/843628.

Mattheson, J. (1735). Kleine General-Baß-Schule. [online] Available at: [Accessed 29 Aug. 2022]. Page 152.

Собрание рукописей и старопечатных книг. (1670). F.7 No. 57. Collection of musical-theoretical. [online] Available at: [Accessed 11 Jun. 2022].

Sparr, K. (1997). David Kellner a biographical survey. [online] Nynäshamn: K. Sparr, pp.43–47. Available at: [Accessed 9 Sep. 2022].

Heinichen, J.D. (1728)
Itchiro, S. - (2011)
Jensen, C.R. (2009b)
Jensen, C.R. (2009a).
Killner, D. (1737)
 Lester, J. (1978).
Mattheson, J. (1735)
Собрание рукописей и старопечатных книг. (1670)
Sparr, K. (1997)
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