B32 The Circle of Fifths
After adding the 5 chromatic tones towards the back of the keyboard, we have 13 keys arranged side by side.
Keyboard with double naming of the chromatic keys
In circular representation, this number is reduced to 12 due to the coincidence of the beginning and ending notes, which makes the 13-1 symbolism clear once again - likewise the one concerning A and Ω. Image comparisons can be found in Video VIII: "Introduction to Christian Number Symbolism".
There would be no need for a physicist to arrange the frequencies in circular formation and to give the doubled frequencies - here the "C" - the same name. Nor would it occur to him to define certain tones as root tones and to regard others as elevations and humiliations of the same. The musical point of view is of course different, and this in turn can be clearly distinguished from the theological one.* Blog B31:"The stem tones" provides information on the preliminary stages that were necessary to reconcile these two perspectives.
The circle of fifths is an analogy to depictions of the Last Judgment, in which Christ appears as the ruler of the world. Hence the circle formation. In some artistic representations he meets us at the zenith of a rainbow with the globe at his feet. In the circle of fifths, the "C" like Christ, resp. the "Do", which can be read as "dominus", takes its place.
Circle of fifth
Hans Memling, Last Judgment, Muzeum Narodowe, Danzig
Tones with a sharp sign are considered to be raised by a semitone, those with a flat sign as lowered by a semitone. The circle of fifths shows all the ascending signs on one side and all descending signs on the opposite. Compared to the distinctness at the zenith, in the nadir it becomes confusing and ambiguous. A precarious zone when one considers that the acoustic execution of the enharmonic confusion, which should be reserved for the keyboard instruments, was only possible with the equal tempered tuning. In Memling's time (* between 1433 and 1440 - † 1494) the circular arc - as can be seen in the picture for other reasons - could not be a closed one in the nadir. At this point Archangel Michael weighs the souls.
In a theological reading, whoever accepts the cross as a follower of Christ, comes near ton him, while all evil moves away. Musically, we encounter the tritone in the nadir of the circle of fifths, which Andreas Werkmeister called "Diabolus in Musica" because it is a decidedly dissonant interval. In a recitative of the St. Matthew Passion, which deals with Jesus' encounter with a leper, the death symbolism of the tritone is used as well as in Bach Cantata 170 "I'm more disgusted to live". Musical forms of expression and those of faith merge with each other. (cf. blog C3: "The creed of Johann Sebastian Bach in image and sound"). So it is not surprising that in the oldest surviving representation of a circle of fifths by Nikolay Diletsky (*ca. 1630 - †after 1680) the cross draws attention to a theological reference.
Nikolay Diletsky, Idea grammatiki musikiyskoy, Moscow 1679. In Rev,21 the heavenly Jerusalem is described as square: "the city is laid out squarely and its length is as great as its breadth.... the length and breadth and height of the city are equal".
If we include the soundboard rosettes and tracery roses in cathedrals in our considerations, the cultural environment becomes visible in full size. Circular representations with 12 divisions were already available at a time when there was no talk of enharmonic confusion.
Chartres, North Rose, depicting 12 kings of Israel in 12 squares, King David in the top center, the 12 prophets of the Book of the Twelve Prophets in the outer ring.
Rosette of a chitarrone from 1608: Christ, surrounded by 4 hearts for the 4 evangelists, inserted in an 8-piece braided ornament referring to the 8 beatitudes with an included cross shape. The head of Christ surrounded by a circle in 2 squares, one standing on its peak, reminiscent of the length, breadth, and height of the heavenly Jerusalem. Hungarian National Museum, inv. no. 1911-46
If the choice of the St. John's hymn, from which the solmisation syllables were taken, can already be seen as an indication of the coming of Christ - John the Baptist was the patron saint of church music before St. Cecilia replaced him - we have here an abstract foreshadowing, which puts all the sound material at the service of the same theological statement. Any music practice is a reminder of this. In simultaneous perception with architecture and art - in sacred spaces - this can be experienced particularly strongly and the connection is sometimes clearly presented there.
Eglise de Gésu, Toulouse, neo-gothic (gothic revival), construction started in 1845, 12-piece tracery rose with 12 eightpasses in analogy to the fact that a new diatonic scale can rise from each of the 12 tones.The organ immediately in front.
Their immateriality turns the light, the sound and the equally tactile large space into connecting elements with the divine, for the perception of which almost every effort seems justified to this day.
Sagrada Família, Barcelona
* To distinguish between the perspectives mentioned, they are briefly characterized below:
Physicists take up observed facts in definitions and put them in relation to each other. A pitch is defined by the number of oscillations per second [unit: Hz]. Fluctuations in volume, which result from the superimposition of two tones, are called interferences (musical: beats). The speed of the beats corresponds to the difference between two frequencies. Natural tones appear as integer multiples of the fundamental frequency.
Musicians work with trained sensory perception and sound generation with the help of their own voice. Precise (absolute) pitches cannot be determined without a tool (tuning fork), but relationships / distances between the tones can be determined. The solmization serves to memorize certain intervals. Due to the repeatability, consonances, i.e. beat-free sound combinations, serve as a guide. The naming plays a subordinate role in all this as long as a system has been agreed upon. During the process of tuning, physical knowledge is consulted and - especially in tempered intonation - previously determined beat velocities, which were also rapid, were compared with each other. Only the so-called "octave" remains beat-free.
The theological perspective can be seen in the reference to Holy Scripture. This results in some inconsistencies - especially with regard to the perspective of the physicist. It was significant to get the consonances to match the numbers 1 and 8, since the Old Testament speaks of the cleansing and sanctification of the temple within 2x8 days. 2 Chr 29, 17. This explains the introduction of the "Prim" with the size zero as a self-generated consonance and the composition of the octave from 5 whole tone + 2 semitone steps + prim. (see Video VII "How the octave got its name" ).Behind this it can be seen that the early Christians, who abhorred polytheism, were not willing to accept the cultural heritage of their tormentors unchanged. The shift in the note names - A became C - can also be explained in this way.
Symbolism builds a bridge to spirituality, because the immaterial and abstract are elusive and closer to the imaginary. There, the tones do not fade away but embark on a journey into herafter. Laudate eum in cordis et organo. God hears the music, created to His praise, so the belief. Therefore, the practice of music is just another way of getting in contact, another way of praying. In the opposite direction, music was seen as a gift from heaven: MUSICA DONUM DEI.
The critical perspective is that influence was exerted on the human psyche - as welll as indoktrination, while at the same time knowledge was ignored or censured that did not fit into the world view. Dealing objectively with symbols requires a distanced level of observation, as offered by the humanities, by comparing different views and analyzing the power of symbolism, see Blog B12 "Symbols, mirror of man". This happens out of the overriding interest in the spiritual constitution of man. This attitude is just as indispensable in intercultural dialogue, which begins with getting to know the other person and taking stock of differences in perspective.
The cultural historian sees these three levels over time and makes appropriate assignments. While we are dealing with constants in physical knowledge - the Pythagorean theorem will change just as little as the vibration behavior of the string - theology, music and art concepts are subject to change. The diatonic (white) keys are on an older chronological level than the chromatic (black) keys, whereby the key coloring of the harpsichord was exactly the opposite.
Against the background set out above, it is now clear why J.S. Bach tried to defend the "majesty of early music" against the spirit of time of the Enlightenment and how the theological and ethical content of the theory of harmony could be lost.
More recently, it has to be documented how the church protects its liturgical content, which includes the symbolism of the theory of harmony (see blog 12: "Benedict XVI on occidental music", Pope Francis on the importance of harmony) and how the Federal Office of Culture, resp. society, deals with its own cultural heritage, i.e. specifically whether it is willing to include the material in the curricula and make it accessible to the younger generation. Should this happen, interdisciplinary work is essential, because access to the symbols is only possible via the context. Not even the most important symbol of Christianity, the wafer, betrays the meaning given to it.
Monstrance
Anyone who looks solely at the circle of fifths does not perceive it as an important element of the Catholic world view that has been assembled over centuries. In the liturgical constitution of the Second Vatican Council it says: "The treasure of sacred music must be preserved and promoted with the greatest care". There are intricate paths that lead to correspondences between the circle of fifths and the dial of the clock, the 12 months of the year and the monstrance shown here, go back to a theological need for analogy.
© Aurelius Belz 2023