C1 Polydisciplinary reflections on the symbolism of the western tonal system. About the academic disregard for European cultural heritage

My German-language essay appeared in the 36th edition of the periodical RIVISTA INTERNAZIONALE DI MUSICA SACRA, 36, 2015, pp. 49-79, published by the Libreria Musicale Italiana, which is reproduced below. I have reason to sincerely thank Prof. Giacomo Baroffio for his support.

As the title suggests, this essay contains a summary of the most recent research results on the western tonal system, which were compiled with a wide range of scientific instruments. Important insights were gained, particularly from the perspective of art history, and here it is in the nature of things that this discipline is dependent on image comparisons. Like autographs of all kinds, images are considered sources and evidence because they are close to historical reality and can therefore be used as a basis for one or the other argument. Since in the following we have to do without the lavish illustrations that would be necessary to clearly demonstrate the complex relationships, it must suffice at this point to refer to the author's most recent publication[1]. All the visual evidence mentioned here can be found there.

The starting point of the study was the analysis of the oldest surviving construction drawing of a stringed keyboard instrument, made by Henry Arnaut de Zwolle [2] around 1440, kept in the Bibliothèque Nationale de France in Paris [3]. In 1932 it was printed in facsimile, together with a bundle of other drawings, under the protectorate of the International Society for the Study of Music and the International Association of Music Libraries. For this purpose, an editorial committee was formed that was responsible for the publication. Biographical information on Arnaut has been collated and the associated handwritten notes transcribed and translated from Latin into French by Georges Le Cerf and Edmond René Labande[4]. The effort alone reveals that the scientists were aware of how to deal with a special cultural heritage.

In Arnaut's drawing, it is above all the soundboard rosettes that provide the art historian with usable working material, because Arnaut equips three of the 5 soundboard openings with tracery-like decoration, which, on closer inspection, reveal themselves to be an abstract representation of the Trinity. The central rosette consists of three concentric rings. The outer one is divided into eight, the middle one is divided into four, the inner one remains undivided. As clearly demonstrated by contemporary paintings, the division into eight points to the 8 beatitudes as they are called in the Sermon on the Mount, the division into four to the 4 evangelists, and the ideal form of the circle in the center to God the Father as the one and indivisible. Due to this initial suspicion, it is obvious to include the flanking rosettes in the consideration, because since trinity means trinity and unity at the same time, we can say in advance how these rosettes should be designed.

One of these rosettes would clearly have to refer to the person of Jesus, the other to the Holy Spirit, and this solely on the basis of numerical symbolic reference. The number 5 is the only number that can be clearly associated with the person of Jesus because of the 5 wounds. The Holy Spirit, on the other hand, is represented by the number six, because Isaiah (11:2-3) mentions six gifts of the Holy Spirit. However, this only applies to the Hebrew original text, because as a result of the 2-time mention of the "fear of God" it was translated into "fear of God" and another time into "piety", so that the number increased from 6 to 7. Already Augustine[5] speaks of seven gifts, as does Bonaventure[6]. Therefore, we encounter different artistic implementations. Arnaut's treble rosette is divided into five, while the bass rosette is divided into six. These numbers are therefore compatible with the abstract description of the Trinity.

Based on this approach, his entire construction now appears in a new light. Starting from a line C-B, which corresponds to the width of the instrument, which can be chosen at will and which in turn is to be divided into eight parts, Arnaut obtains the unit of measurement on which the construction is based as the starting module. In the following he works - very similar to the master cathedral builders of his time - with integer multiples of this size. This means that each line can be assigned a specific number. Only in the case of the bass wall, which he gives the length of 13 moduli, he doesn’t add any further connections from point 13, but continues to work from point 12. He avoids the 13. If one wanted to record this process in pure numerical terms, a "13(-1)" would be noted. Since he also uses letter designations at the same time, the step backwards via the points D-E-F from 13 back to 12 is clearly documented. In order not to complicate things too much here, let us anticipate that all of this can be seen as relating to the last supper, at which 13 people were present, including the traitor Judas.

In order to describe the context, we are again dependent on a comparison of images, but this time not on a contemporary work of art, but on an illustration of the passion flower, which shows how the Bible was referred to in an equally symbolic way in a completely different place. It got its name because in the three handles of the pistil you could see the three nails of the crucifixion, in the five stamens the five wounds, in the staminodes the crown of thorns of Christ, in the tendrils the scourges and in the 10 petals the 12 disciples without Judas and Peter – who were deducted as a result of betrayal and denial three times. Her Latin name is passiflora incarnata, which means: the incarnate. This places it in a long line of plants that have been similarly associated with the Bible or the Church.

When it comes to numbering hotel rooms and ship cabins, the number 13 is still avoided today, and the unlucky day "Friday the 13th." associates the avoidance number with the day of crucifixion. Here it is the folklore that provides the material with which the observation can be meaningfully supplemented. The observation of current human actions in relation to language, dialect, clothing, naming, customs and much more, taking historical events into account, is an important part of folklore field research.

Since abbreviated accounts all too easily give the impression that things are being dealt with too superficially, attention should be drawn at this point to an event that in turn can be related to another discipline, namely history. After Philip IV had issued the arrest warrants for the Knights Templar, which happened on the day of the Feast of the Exaltation of the Cross, September 14, 1307, he sent the warrants to his commanders with orders not to open the letters until Friday, October 13, 1307, so that the access and the arrest could take place at the same time. It can thus be shown that the symbolism of the day of misfortune was already important in the Middle Ages, and even more so that it was taken very seriously. It has nothing to do with the playful and entertaining way in today's magazines.

Arnaut has now constructed the body of sound and in front of it has drawn a keyboard of the type we know today, i.e. the 12-part tonal system as such was developed at the time. If you now continue the thought consistently and transfer the obtained numerical material including symbol reference to the sound system, the results are quite astonishing. C major is the starting key of the circle of fifths. All other keys can be described as deviations from it through the use of accidentals. It contains 13 tones, with the first and last having the same name - the "C" for Christ - corresponding to the Revelation of John (22:13) which says: "I am the alpha and the omega, the first and the last, the beginning and the end". This reduces the number of key designations from 13 to 12. The 8 white keys of today's keyboard stand for the eight beatitudes, the five chromatic black keys for the five wounds. In a nutshell, the keyboard tells of betrayal (13-1), death (5 wounds) and bliss (8). Sacrificial death was a prerequisite for salvation. If all this should be confirmed, it would be quite appropriate to speak of a gospel of music.

Further analogies can be found in the comparison of the circle of fifths with the wheel of Fortune and with representations of the Last Judgment, because the circle of fifths can be understood as a turning wheel, with consonance at the top. Opposite we fimd the dissonance, the tritone, which Andreas Werckmeister[7] described as "Diabolus in Musica". Those who fall under the wheel have more than just bad luck, they will be punished by fate. The wheeling method of execution drastically demonstrates what that means.

A depiction of the Last Judgment by Hans Memling in the National Museum in Danzig shows Christ on a full-circle rainbow. On the Day of Judgment, good and bad deeds are weighed. Those who confess the cross are received into the kingdom of God, while the others face eternal damnation. In analogous terms, the sign of the cross leads up, the "b" down.

The depiction of the Last Judgment in John (Revelation 21:10) also includes the description of the heavenly Jerusalem, and here we encounter the 12-division in an extraordinarily striking way: "And he caught me up in the spirit up a great mountain and showed me the holy city of Jerusalem, which descended from God out of heaven in the glory of God, its splendor like a precious stone, like jasper crystal, having a mighty, high wall with twelve gates, and on the gates twelve angels, and names written on them; These are the names of the twelve tribes of the sons of Israel: there are three gates on the east, three gates on the north, three gates on the south, and three gates on the west. The wall of the city has 12 foundation stones, and on them the twelve names of the twelve Apostle of the Lamb. And he who spoke to me had a golden measuring rod to measure the city, its gates, and the wall. The city is built in a square, its length as great as its breadth. [...] The foundations of the Walls are adorned with all kinds of precious stones. The first cornerstone is a jasper, the second a sapphire, the third a chalcedony, the fourth an emerald, the fifth a sardonyx, the sixth a sardion, the seventh a chrysolite, the eighth a beryl, the ninth a topaz, the tenth a chrysoprase, the eleventh a hyacinth, and the twelfth an amethyst. The 12 gates are 12 pearls, each gate made from a single pearl. The square of the city is pure gold, clear and bright as crystal."

The saying attributed to Augustine: "MUSICA PRAELUDIUM VITAE AETERNAE"[8] is therefore not only understandable from the acoustic point of view, but can also be derived from the clear comparison of the tonal system with the Eternal City of God, because although the Evangelist explicitly describes it as being built on a square ground plan, we encounter the circular shape in numerous medieval representations, e.g wheel chandeliers as in the Basilica of St. Godehard in Hildesheim.[9] The preference for the circle is certainly related to the circular orbits observed in the cosmos, because a square cannot be reconciled with the visible texture of the sky. Nevertheless, such an adjustment harbors some potential for conflict, because the Church insisted on the Bible conformity of its view towards Giordano Bruno and Galileo Galilei and in this case the significant change does not seem to matter at all. The reference to music is most appropriate in that it is about a spiritual city "which descended from God out of heaven". It is no coincidence that organs are usually at a certain height, and church bells ring out from towers.

Since Arnaut does not say a word about the theological content of his drawing, and since there are no written sources that provide further information, it is absolutely necessary to question the observations critically, i.e. ideally to either confirm them or completely refute them.

First of all, the complete and self-contained worldview of the Middle Ages belongs to the framework in which Arnaut grew up. The chronology from the birth of Christ is also a matter of course for us. Likewise, the days of the week are so familiar to us that we do not specifically ponder their analogy with the creation story. In general, we observe a particularly pronounced appreciation of light. This is undoubtedly based on the statement of Jesus, which is reproduced by the evangelist John (8:12): "I am the light of the world". The east-facing cathedrals are reminiscent of this, as are the contemporary maps, which were not oriented to the north, as is customary today, but to the east, and therefore mostly show the paradise rivers Euphrates and Tigris at the top. Hence the term "orientation". Sunday is the Lord's day and was taken from the Roman dies solis. Christmas was preceded by the Roman holiday "sol invictus". The date is related to the winter solstice, i.e. the time when the days start getting longer again. The month of December (derived from the Latin decem[10]) in Old High German it was called: Hailagmânôt, which means holy month, and representations of the zodiac, representing the cosmos, often show the sun at the top, with the moon opposite.[11] Of course, all these statements do not prove anything with regard to the tonal system, but the more we perceive how abundantly the symbolism is contained in all areas, the harder it becomes to imagine that music in particular should have been an exception in this respect, especially since it is much closer to the liturgy than architecture.

As the key of light, C major, untroubled by any accidental, stands at the zenith of the circle of fifths. Joseph Haydn uses it in his “Creation” exactly at the point where he quotes from Genesis 1:3: "Let there be light - and there was light". It clearly corresponded to the desire to see "the one" or "the one in everything”, as Thomas van Kempen (around 1389-1471) once put it: "To whom everything is the one, to those who relate everything to the one and everything look in the One whose heart can stand firm and dwell ever in the peace of God“[12] We also find comparable formulations in many writings of Nikolaus von Kues.

In this context, Julius Schiller's proposal to replace the signs of the zodiac with Christian symbols can only be described as logical, as shown by Andreas Cellarius' celestial maps.[13] However, this has not been implemented in a generally binding manner. The most important condition for a symbolic connection is therefore given, because without an underlying theological concept - and without a comparable procedure in other areas - the request as such would be completely incomprehensible.

In the following we want to deal with the situation from two sides. - with the time before Arnaut, i.e. with the emergence of the tonal system as such - and with the time after him, i.e. with the effects that sticking to the keyboard had on the occidental tonal system, and for this we choose the macro-historical view.

We do not want to go into detail about the harmonic series at this point, but it is precisely this series that provides the decisive arguments for a given relationship between the intervals. While physicists assume a free tonal space and assign a specific frequency to each individual tone, the Pythagorean approach of considering the vibration form of a string is much more complex right from the start. Due to the existing vibration nodes at the string ends, the vibration is always symmetrical in the case of homogeneous string material. It therefore oscillates in integer multiples of the basic frequency and at the same time reproduces a large number of individual tones, the distances between which decrease with increasing frequency. The occurrence of beats here and there enables the tones to be precisely matched to one another.

With the need to sort the tonal material according to increasing size, the first scales were created, with five steps (pentatonic) still predominating in antiquity. In the early Middle Ages, this was supplemented by another tone (hexatonic). The term solmization describes the procedure of singing the pitches on different syllables, for which the hymn to St. Paul by Paulus Diaconus (720-799) provided the syllables for the then six-pitched scale. This system is said to have been introduced by Guido von Arrezzo (born about 992). The seventh note of the scale, SI, which again exceeds the tonal space chosen by Guido, was later formed from the initials of Sancte Iohannes. It assumes a seven-tone scale. (Heptatonic).

Ut queant laxis

resonare fibris

mira gestorum

famuli tuorum

solve polluti

labii reatum

Sancte Iohannes.[14]

The seven-level designation is also based on the alphabetically continuous designation: A-B-C-D-E-F-G.[15] In the 12th century the H in Germany was inserted between B and C. It suffices here to show that a connection with the Bible had been established much earlier and was not new in Arnaut's time. Medieval miniatures show Pope Gregory the Great (540-604, canonized 1295) with the dove of the Holy Spirit on his shoulder. He passes on the melodies received in this way from the highest authority to his notarius. We owe the Gregorian chant to this circumstance, as it is shown graphically.

At the time of Gregory, the tonal system was not conceived as a closed circular arc, but as 8 scales that begin on different pitches and each have their own key characteristics with constant semitone steps between e/f and b/c. After these modes were used for specific liturgical purposes, one speaks of church modes. This custom corresponds very closely to the use of liturgical colors, even if binding guidelines do not provide information about their use until much later. White, the color of light, used on high festivals such as Christmas and Easter. Red, the color of blood and symbol of the Holy Spirit, used on Pentecost, Palm Sunday and Good Friday. Green, the color of growth and hope, used on weekdays. Violet, symbol of transition and transformation, used during Lent and Advent. Pink, to brighten the color violet, can only be worn on the Sundays Gaudete (3rd Sunday in Advent) and Laetare (4th Sunday in Lent) to emphasize the joyful character of the days of Mid-Lent. Black, the color of mourning, is worn on All Souls' Day and at funerals. Blue, the color of purity, is used for Marian feasts - according to the 2nd Vatican Council 1962-1965. If we look back at history, the assignments are less clear and vary from region to region, both for church tones and for colors, which poses particular challenges for research.

Two surviving capitals from the Benedictine Abbey of Cluny show all 8 church tones with descriptive text in a mandorla, i.e. in the insignum that is usually reserved for depictions of the Majestas Domini. As presented in Arnaut's drawing, the eight beatitudes in turn surround God the Father. The tones are therefore of equal priority. Another important testimony to the meaning of the number 8 is provided by the altar for St. Etienne in Besançon, made around 1050, which presents the Chi-Rho, the Alpha and Omega, the Lamb of God and the dove of the Holy Spirit in an eight-leaf, all this arranged in three concentric circles. The outer circle is circumscribed with the words: HOC SIGNUM PRAESTAT POPULIS CAELISTINA REGNA[16] (This seal gives people the kingdom of heaven). The connections show that the symbolism did not stop at the area of music, but naturally included it. Therefore, we have reason to keep an eye out for further parallels (analogies).

The motif of the ladder meets us in Jacob's dream: "A ladder stood on the earth, its top touched heaven. God's angels ascended and descended. Above stood the Lord and said: 'I am the Lord, the God of your father Abraham and the God of Isaac." (Gen. 28, 12) We find the stone implementation of this vision at the abbey church in Bath/England, completed in 1156 (however badly damaged and rebuilt in the 15th century) where two ladders on the sides of the portal lead up to the flanking towers tower, each of which is climbed by 6 angels. At the top we see God the Father.

Augustine speaks of 7 stages through which the Christian comes to God: fear of God, godliness, knowledge, fortitude, mercy, love of enemies and wisdom[17], in which we recognize the gifts of the Holy Spirit, which correspond in number to the sound names - the 7 kinds of Bonaventure explains the ringing numbers as an ascent to God with reference to Augustine[18]  - and reminds us of the statement that it was the same Holy Spirit who transmitted Gregorian chant to Pope Gregory. Sound and image perception coincide and refer to one and the same spiritual source. All theological forces are concentrated on precisely this goal.

As mentioned in connection with the rosettes in Arnaut's drawing, it is unfortunately not possible to clearly assign the number 6 or 7 to the Holy Spirit due to the inconsistent translation of the original text, so that we get a blurred picture in historical retrospect. This can already be seen in Cluny's capitals, because both the sixth and seventh notes can easily be related to the Holy Spirit. Thus we read at the 6th tone: SI CUPIS AFFECTUM PIETATIS; RESPICE SEXTUM (If you desire the feeling of godliness consider the sixth) and godliness is a gift of the Holy Spirit. And at the 7th tone: II INSINVAT FLATVM CVM SEPTIMVS ALMVM (The seventh gives entrance to the divine travail with its gifts). If we take this blurriness into account when looking at the works of art, we can relate the six angels on Jacob's ladder in Bath to the Holy Spirit - albeit with reservations - and thus obtain a congruence in the way we look at them. Otherwise, they could also be seen as an allusion to the 6 steps to the throne of Solomon. (1 Kings 10:19), or to the 2x6=12 apostles who, as followers of Jesus, climbed this ladder first and call on us to do the same.

Early Christianity found an ancient tonal system in which the sequences of tones were presented in descending order, which is why we encounter the finalis at the bottom. The chants usually end on this note. Against the background presented, it is very clear that this was first of all reversed and converted into ascending scales, because the point was to come closer to God through music. This makes the finalis the starting point. Even if it seems that the musical scholars have further developed the Greek tonal system, the further development as such is not a matter for the Greeks, but an ingredient that must be attributed to other intellectual originators.

In this context, the descriptions of Glarean (*1488 - †1536), who presented all 14 modes and therefore expanded the tonal system by a number of essential elements, are particularly revealing. Nevertheless he writes: “So that the readers may see clearly that we are not inventing anything new, but have restored to its former glory what had been so long almost buried, either by the negligence of men or by the ill fortune of time".[19]

This text needs explanation. First of all, he writes elsewhere: "Of the 14 modes, which consist of 7 octave genera, our time only recognizes 8, although it also uses 13, some always, others less frequently, as we will show later"[20] In the numbers 8 and 13 we encounter the well-known symbolic references - the paraphrase "our time" therefore means the church - and against the background of the fact that Glarean's works on the Index [21] must have been very keen not to portray an expansion of the tonal system as a willful intervention in a church rite. As long as it could be understood that his sole concern was the preservation of cultural heritage, he could not be blamed for that. Surprisingly, we now encounter today's C major in one of those modes which is not one of the recognized ones. What reasons may have given rise to placing this mode of all things as the key of light at the zenith of the circle of fifths?

Superficially, there are two things that immediately caught the eye of the scholars of the time: on the one hand, the finalis "C" like Christ, and on the other hand the fact that this mode (Hébdomus authenticus, Ionian) ranks highest in comparison with all other modes and so that God is closest. We encounter the preference for high places in the choice of church sites as well as when erecting summit crosses. To grasp another important reason, which is of a musical nature, we must look back historically.

Aurelius Augustine (334-430) is without doubt a recognized authority. It is not for nothing that he is one of the Church Fathers. In his book DE MUSICA LIBRI SEX, he explains basic aesthetic principles that result from a synergy of religion and devout will to create as a testimony to his faith. The work therefore reads in places like an art-theoretical manifesto that naturally assumes the existence of a creator and extends over all sensory perceptions. To clarify his way of thinking, the following passage is reproduced in the translation by Carl Johann Perl:

"Nevertheless, number begins with one; it is beautiful by likeness and resemblance, and is related by order. So if it is conceded that every nature, in order to be what it is, aspires to unity and, so much she can, strives for her likeness and sees her salvation in her own order in space and time and body: then it must also be recognized that everything through the richness of divine goodness from a beginning through equality and a similar way, as it were one with one in, if I may say so, dearest love is bound, made, and founded, whatever, however great, is why we preface that verse:

GOD CREATOR OF ALL THINGS

which is not only of numerous sound to the ears, but rather signifies the most welcome health and truth to the mind of the soul."[22] And a few lines later: "From an indivisible point, a one, it [the earth] must expand in length, breadth, and height, even in each of its smallest parts, in order to perceive the shape of the body. Here, then, is the manner of progression founded from the one to the four?Here, then, do we recognize the equality of the parts, tending toward length, breadth, and height?Here, then, is that unity (that is what I prefer to call the analogy) which is communicated even to the smallest indivisible component , so that its breadth to length, and its height to breadth, are in reasonable proportion? Whence, I ask, can all this come if not from that supreme eternal origin of numbers, likeness, equality, and order? And if If you take this away from the earth, it becomes nothing. Only in this way did Almighty God create the earth, and it came into being out of nothing."

It is difficult to estimate how many people have read these sentences. Arnaut must have been close to them, and so Augustine's legacy lives on in his work and has found application elsewhere and in other epochs as well. Since the holistic view does not correspond at all to the current practice of looking at things separately, it should be particularly pointed out that there could not be an academic separation of subject areas in Augustine:

"The proof that we perceive the same thing in the realms of smell, taste and touch would lead us too far: it is extremely easy to investigate, for even in these sensations everything pleases only through equality or resemblance. But where are the two, there is number; indeed, nothing is so alike as the one of the one […].[23]

Or elsewhere: “Beauty pleases through the number, in which, as we have already admitted, equality is striven for. We encounter this beauty not only in the realms of the audible and bodily movements, but also in the visible forms, where beauty is spoken of much more often,“[24] The "dearest love" understood in his sense, i.e. creating cohesion, is next to the number the second commonality inherent in the arts - a remarkable synergy of emotion and ratio.

Coming back to the properties of the C major mode, it is striking that it contains two similar groups of four C-D-E/F and G-A-B/C, in which two whole steps are followed by a half step as a conclusion. According to Augustine's statement that similarity prevails over dissimilarity and according to the observation that C major is formed of two equal segments, by analogy with the two columns of Solomon's Temple[25] or in analogy to the two-part nature of the Holy Scriptures in the form of the Old and New Testaments or to the nature of Alpha and Omega, there are understandable musical and non-musical reasons that can lead to a preference for this key in the already sacred context, because after all the eight tones are there as such already for the eight beatitudes, to which the 8 mandorlas in Cluny refer. In vocal implementation, the semitone step results in a gesture leading up, which seeks to raise the preceding tone as if it were a subsequent correction of the same, and the repetition at a higher level is like a further even step up - or, regardless of the pitch, a swinging or trembling. Twice the same movement easily leads back to the higher C and thus to the starting note without any stumbling, without corners and edges - i.e. more in an arc or circle. How gratifying it must have been for the scholars to have found this approach to the highest and this musical closeness to God. None of this has anything to do with ancient musical art, and the continued use of the names of Greek tribes to identify the modes leads to a very deceptive picture of intellectual authorship. It is necessary to distinguish the historically adopted tonal structures from analogous additions, later interpretations and explanations. It seems that it was Glarean who presented the modes in their entirety and to whom we owe C major, but the special appreciation of this key was during his lifetime (*1488 - †1536), and consequently even more so in the time of Arnaut (*around 1400 - †1466), not yet given. In this respect, the various observations still require a separate chronological assignment.

If we observe in the following that the development of the tonal system did not stand still, in the sense that a subdivision of the octave into many more tones was required, the question arises as to why the keyboard was divided into 12 divisions. Since the organ was almost entirely in sacred service, it is understandable that moving away from symbolic references had to be particularly difficult with this instrument.

The circle of fifths is merely a way of looking at it, which is based on a mental division, because assuming that D sharp and E flat had been recorded as equal tones with independent names and not as an increase in the lower tone or as a decrease in the higher tone, it would be with the 12 division already over. We encounter subordination elsewhere in the tonal system: If we take the counting: prime, second, third... up to the octave as a basis, then the designations minor and major second (literally: minor and major 2) appear as subsequent additions that are related to the subordinate existing system. The diminished fifth, the tritone, is also a special case. Remarkably, it remains linguistically uncounted. The question is why shouldn't there also be a minor fifth (literally: a small 5). A flat fifth gives this interval even less independence. Today one would probably speak of an attachment. In the first case, the existing 18 tones are related to 13-1, in the second case the 13 tones are traced back to 8. This alone makes it clear what meaning these numbers have.

Nevertheless, it was musical needs that made an expansion of the tonal system seem inevitable. So Michael Praetorius pleaded for 15 keys when he wrote: "Therefore it is very good and necessary that in the organs and clave cymbals, which are used for concerts in music, the black semitonium D sharp, and where possible also the G sharp, should be duplicated."[26] Gioseffo Zarlino had Domenico da Pesaro build a harpsichord with 19 keys per octave in 1548, Vito di Trasuntino's Clavemusicum omnitonum had 31 keys per octave, and Nicola Vicentino's Archicembalo had 36 keys per octave on 2 manuals. Later Louis Saveur demanded 43, Nicolaus Mercator 53, Arthur von Oettingen 71 and Julian Carillo 96 keys per octave, but even with these micro-intervals the impressive ability to differentiate e.g. of a violin could still not be achieved.

For comparison, if we look at what happened to those who stuck to Arnaut's keyboard division, we observe an independent development of musical temperaments over a period of several hundred years, which ultimately led to equal temperament. This tuning - the only one that contains a regulated ordering system for all beats - would have been completely unacceptable in the Middle Ages because only the octave sounds pure in it, while all other intervals are expected to deviate considerably from the purity of their natural appearance. The fact that one still insisted on this musically only conditionally useful division makes it clear that there must have been non-musical reasons that left their mark on the Western tonal system.

On the occasion of a piano concert, the whole drama of the musical schism is revealed. There is only agreement on the starting pitch a' and its octave repetitions. All tones in between are not congruent, because tempered intonation is based on 12√2 as a factor, which has no equivalent in the natural tone series. Nobody can say that this result could have developed solely from acoustic-logical consequence. It is thanks to the persistent adherence to the idea of a 12 division and thus to the relationship of music to the kingdom of God. According to everything that has been written about this so far - not just about music, but about the reflection of the divine in all things - a departure from this point of view would have fatal theological consequences.

This makes it clear that music played a more important role in the sacred space than was previously acknowledged, since it was saturated with significantly more content, or was provided with Christian theological content at all. This justified almost any effort. One thinks of the pulpits by Luca Della Robbia and Donatello for the Florentine Cathedral or the organ equipment of countless churches. The organ is of particular importance in the context of the liturgy because it proclaims the gospel with its voice and can rightly be regarded as a counterpart to the altar. Numerous instrument inscriptions with the words: MUSICA DONUM DEI can certainly be understood as contemporary written sources confirming the reference of the tonal system to the Holy Scriptures. In the case of stringed instruments, such as that of Arnaut or the clavizitherium in the Royal College of Music from around 1470, the reference to the Bible had to be demonstrated first, and the spiritual content first made accessible.[27] It is astonishing that these cultural-historical testimonies, although known to science for more than 200 years, have so far remained misunderstood, even when written attention was drawn to specific Bible verses, as in the case of Giulia Varano's spinet in the Metropolitan Museum in New York. The entire iconographic content is easily accessible if one is willing to recognize the reference to Isaiah 6 in the sequence of letters and numbers "IES VI".[28]

These early testimonies are representative of a number of instruments - one thinks in particular of the Flemish school - which clearly indicate the reference to the Bible through their magnificent painting or through evocative sayings.[29] The preference of the organ for the church room results from three reasons: First of all, it has the necessary volume to be able to be heard in large rooms. In addition, the tones only fade away after the button is released, so they continue to sound at a constant volume, so to speak, forever. Because this is not the case with stringed instruments, they symbolize transience and therefore often bear the motto SIC TRANSIT GLORIA MUNDI, which we do not find anywhere on organs. So stringed instruments stand for the secular and thus lower in the theological hierarchy. The third reason for the organ's preference arises from the fact that the individual pipes are blown - audible as a separate breathy noise alongside the tone itself. Here the analogy to the story of creation becomes apparent (Genesis 2), in which the breath of life is spoken of in connection with the creation of man. The breathing of the divine spirit explains the organ in a musical re-enactment.

In summary, however, it can be stated that in the predominantly spiritually oriented Middle Ages, it was not the acoustic experience that was the focus of musical performance, but the dialogue with God. Making music in today's sense is tantamount to misappropriation. Contemporary image sources can also be used as evidence for this point of view. A medieval miniature from the Book of Hours of Mary of Burgundy shows the player of a clavichord on a central axis opposite the Lamb of God and God the Father.[30] The sitters look at each other, communicate with each other, and the psalm verse (Ps.150) "LAUDATE EUM IN CORDIS ET ORGANO" is only meaningful when God also hears the music that sounds to praise.

Cardinal Nikolaus von Kues (1401-1464) gives us a special indication of the importance of numerical symbolism, when he wrote: “If we cannot approach the divine in any other way than through symbols, we shall most appropriately make use of mathematical symbols , for these possess indestructible certainty.“[31] Of course, we see this differently today, because it is not a number as such that provides certainty, but the logical-causal (mathematical) train of thought hidden behind it. The use of the number as a symbol puts it right back into the seemingly endless series of analogies that Nicholas of Cusa was trying to avoid. However, the intention to do persuasion with the help of the numbers is recognizable and, as we will see below, this seed has sprout.

In his work: "De divina proportione", which Leonardo da Vinci provided with illustrations, Luca Pacioli took up the idea of divine proportioning. He was referring to Plato's identification of creation with the five platonic bodies[32], for the construction of which the golden ratio is an important tool. But he did not present more than 13 characteristics, because 13 was the number of people who were present at the last supper. Luca Pacioli gave the reason: "Out of reverence for the company of the twelve and their most holy head, our Redeemer Jesus Christ".[33] Architects like Andrea Palladio have taken on the integral proportions in a special way, certainly also because of the human body - especially in the Renaissance, but also in antiquity[34] - played an exemplary role. However, this in no way excludes a religious background, as the Architect makes clear in the preface to his IV Book: "He [God] is the highest and absolutely good being and the embodiment of the highest perfection. It is therefore very appropriate that all that is consecrated to him be carried out with all the perfection of which we are capable. It is so, when we contemplate this beautiful work of the world, how rich in wondrous adornment it is; when we see the heavens, how changing they, with their constant recurrence, each season as befits the exigencies of nature.And when we see heaven and earth sustaining themselves with the lovely harmony of their measured movement, we cannot doubt that the little temples , which we build would have to look similar.Are we therefore not required, according to this supreme perfection of creation, which God in His goodness created through His Word, al l to apply those decorations that we can dream up? We erect the temples in such proportions that all partspresent at once a sweet harmony to the eye of the beholder, and each part serves its purpose to which it is duely destined."[35]

Here we encounter the holistic view again and we feel compelled to go one step further in connection with the consideration of the tones. Taking as background what Palladio describes at length, namely the purposeful form of the pillars and temples, and citing a few examples: "Since the sun and moon move evenly around the earth, and by their even orbits exert a marked effect on everyone, so erected the ancients for Sol and Luna temples in a round shape or in a shape at least approaching the shape of a circle.This also happened to Vesta - the goddess of the earth - who, as we know, is round "[36] Or elsewhere: "... that they erected the temples outside the city for Venus, Mars and Vulcan, since they wanted to excite their hearts to fornication, war and fire"[37] And further: "Even with the decorations, the ancients paid great attention to the god for which they were building. That is why they used the Dorica for Minerva, Mars and Hercules [...] for Venus, Flora, for the Muses, For nymphs and for goddesses of more charming character, they said, temples should be erected befitting the blooming, more delicate, and virginal character: they therefore gave them Corinthia as adornment, for it seemed to them that the Goddesses created this delicate and flourishing order, adorned with leaves and volutes, but attributed Ionica to Juno, Diana, and Bacchus, since with these gods neither the severity of the former nor the grace of the latter seemed appropriate between Dorica and Corinthia the middle."[38]

Of course, Palladio does not fail to distance himself from pagan customs: "But we, freed from that darkness by the special grace of God, and having abandoned empty and false superstitions, we so choose the sites of the temples that we may erect them in the noblest and most famous parts of the city [...] If there are hills in the city, choose the highest part, but if there are no higher places, then arrange the floor of the temple around like this much higher than the rest of the level of the city, as befits it. One will ascend the steps to the temple. Besides, this ascent to the temple brings with it a greater reverence and a greater grandeur,"[39]

The parallel to the church modes becomes obvious here: first of all in the ascent to the repercussa, to the higher level. The religious stands out from the everyday. Musically, too, a few steps lead to the sublime. In addition, the purposeful assignment is recognizable: the Doric column order is reserved for the strong deities Minerva, Mars and Hercules. The Dorian in the music (protus authenticus and protus plagalis) describes Glarean as serious and dignified. The keys, too, are distinguishable through measure and number, given by the different sequence of whole and semitone steps, and trigger feelings that in turn can be associated with the expression of praise, lamentation, joy or sadness. Rainer Straub even went so far as to associate the pictorial programs of entire cloisters (e.g. Moissac and Monreale) with certain Gregorian chants, as a kind of liturgy set in stone[40] and compares the sequences of visual and audio artistic statements like DNA codes with each other.

Despite all the necessary caution with regard to the proof character of such parallel considerations, everything indicates that the meaning in the sacred context was of far greater importance than the form, the need for decoration or the pure intention of representation. Therefore, in the future it will be a question of collecting more reliable material in smaller steps, because it is not without reason that we already find a restriction with regard to the purposeful assignment of the tone genders in Glarean: "But as I said earlier, it cannot be denied that [... ] that the mode which appears frivolous can be applied to seriousness without difficulty, if only a fortunate inventive mind is added."[41]

A reliable set of instruments for determining cross-media connections would therefore still have to be developed, but Rainer Straub deserves the credit of having drawn attention to the obviousness of such connections, because nobody is even able to count the songs that are sung in such places in a conscious simultaneous perception of Space and time sounded as components of a mighty creation with the heartfelt desire for closeness to God.

If we consider that the tonal structure adopted was initially of pre-Christian origin, then a symbolic reference in the early period is not to be expected immediately through an adaptation of the system, as was the case later, but rather through an interpretation of what was already there. The question is which modes were regularly used where and for what purpose. Are there any significant statistical surveys for this? Or could a single chorale or mode already serve as a leitmotif, so that one tried to reflect its structures in architecture as well?

In the case of Sessa Aurunca, a medium-sized small town in the province of Caserta north of Naples, such a connection seems to exist, because here the parallel consideration of the spatial proportions with the modus tetrardus plagale, i.e. the key in which joy is expressed in particular, resulted, striking similarities.[42] The cathedral of St. Peter and Paul, which is simple but impressive in terms of its proportions and location, was built between 1103 and 1113.

In connection with their research, the working group refers in particular to the Exultet scrolls, which were unrolled from the ambo at Easter Vigil and which were decorated with both magnificent paintings and liturgical chants. The cantor sang from it to the congregation. It is the most moving moment in the church year, the feast of the Resurrection - the event that gives meaning to the Gospel. The Exultet scrolls are named after the beginning of the text: Exultet iam angelica turba caeloreum (Now the heavenly host of angels rejoice). The mode used for this was the so-called tetrardus plagale, i.e. hypomixolydian, whose interval proportions can not only be precisely integrated into the church building, but even help determine its structure, and the repercussa of this key, the Do, can be found repeatedly.

In contrast to Rainer Straub's representation, concrete numerical material is available here that did not have to take a detour via the sensation, and that fits into the context of the quadrivium: geometry, arithmetic, music and astronomy like a keystone into a vault. It is no coincidence that the sun shines through the centrally located window in the central apse on the anniversary of the church consecration, bringing the room to an inner glow. Here, what is meaningful is both form-determining and, in the truest sense of the word, trend-setting. One is inclined to ask the question how it could actually be otherwise - in view of the technical and financial effort required in cathedral construction.

This makes it once again more than clear that in both crafts and science, the object of processing alone determines which tools are used professionally and that it is not expedient to process cultural assets that have been developed in a polydisciplinary manner in a monodisciplinary manner in order to do justice to them in this way. On the contrary: dismantling an ensemble is the first step in its destruction. Psychologist Abraham Maslow summed it up when he said: “If the only tool you have is a hammer, you tend to treat everything as if it were a nail.“[43]

The destructive consequences of staying academically in individual subject areas are considerable, because the symbolic reference to the Western tonal system - after all, a cornerstone of European identity - almost fell into oblivion, and so it is only fortunate that Arnaut's drawing has survived to our time and that the clarity of his approach made it possible to reconstruct the underlying thoughts. The same is true, as seen in the example of Sessa Aurunca, with the complex spiritual background of medieval sacred buildings, the multi-medial presentation variants of painted instruments and their relationship to the history of the furniture, to the organ and the altar. Large chapters of European cultural history fall into oblivion and debris fields of individual pieces with the character of curiosities remain, because the underlying contexts of meaning are not grasped - and all this only happens because they have to be worked out with the help of "unrelated" disciplines. How can intercultural dialogue only succeed if the interdisciplinary dialogue already represents such an obstacle? Using only the tool that you have at home would be called dilettantism in technical jargon, because it depends on chance whether it can be used usefully or whether it even damages the object being worked on in the end.

The term catholic, in the sense of the Greek καθολικός, referring to the whole, is particularly suitable for characterizing the nature of the required methodology in relation to the reconstruction of the Christian world view, because we had the Physics, history, theology, art and musicology, organology, astronomy and folklore, and this is just a selection. If it were restricted to a single discipline, it would be impossible to show the connections presented. In order to do justice to this worldview, it is also necessary to be able to put God at the highest level in understanding the underlying thoughts, in order to understand him as a meaningful factor in all manifestations. This does not involve any loss of distance as long as the mode of description is retained. Catholic teaching encompasses the sciences, includes them in the great divine plan and therefore treats them differently than the modern disciplines, which are fundamentally located outside their subject matter, would like to admit for the sake of intellectual freedom.[44] But if we are interested in understanding the mode of perception of earlier centuries, we must be willing and able to go back to the time before the French Revolution. It is to be regarded as a turning point, since the introduction of the revolutionary calendar was intended to introduce a new calendar, and the introduction of the 10-day week and the so-called cult of reason was also associated with the desire to consciously turn away from the traditional system. The revolution was therefore not limited to the abolition of state power, which one could easily assume from afar because of the designation ancien régime, but to the conglomeration of church and state. Therefore, secularization was a necessary consequence. The term saeculum (age, century) alone stands for the temporal world and thus contrasts the earthly with the eternal. In terms of intention, it is a completely new localization of social consciousness.

This circumstance is responsible for the fact that no access to this content was possible for a long period of time. After the French Revolution, the mere waning of attention to everything symbolic was enough to gradually let it fall into oblivion, but the cultural-historical picture of Europe would be incomplete without the inclusion of precisely that symbolic reference - in particular the number-symbolic connection between the tonal system and Holy Scripture - and would have to remain non understood.

From all of this it can be deduced that in cultural-historical contexts - especially with regard to sacred art - holistic vision must be re-learned, which can be illustrated by comparing the tracery rosette of Gothic cathedrals with the soundboard rosette of contemporary musical instruments.

Sheridan Germann[45]  noticed that rosettes like this had been used to decorate the sound openings of stringed instruments since the Middle Ages. This begs the question of how such a clear takeover could have come about and, above all, what the meaning behind it might be. What is certain is that linking both questions can help to clarify the situation, whereby the assumption that it is only a question of a suitable, because round ornament is certainly not enough. Tracery roses of Gothic cathedrals offer an almost unfathomable abundance of possible figurations, but, like Robert Suckale, lies[46] stated, all are based on the same cosmological and analogy-forming way of thinking. Above all, it is about the sacred meaning of light. Basically, all Gothic architecture is modeled after him. A substantive parallel arises in that the acoustic event also develops from the immaterial, and the aphorisms on the instrument lids such as "MUSICA DONUM DEI" openly show that music was also seen as a sign of the divine. The use of the recognizable motif of the tracery rose to decorate the sound hole implies an affinity between light and sound, the "intangible building blocks" or "elements" of the arts.[47]

This analogy-forming coupling - here too one would speak today of a cross-media offer of the same information content - is certainly easy to understand, but we are obliged to look out for a confirmation with documentary character, because we cannot avoid checking whether in the Middle Ages it was actually thought that way, or whether it is we who interpret something into the testimonies that have been handed down. The oldest surviving stringed keyboard instrument, a late 15th-century clavicitherium in the collection of the Royal College of Music, London, has three sound holes, two of which, cut out in the shape of keeled windows, have tracery panels. What is special is that the soundboard openings here actually have the shape of a window. The clavicitherium lends itself to the presentation of this form in that its soundboard is viewed from a fixed vantage point. Therefore, window shapes other than circular are also useful.[48] We find further confirmation from Arnaut, who chooses the Latin term fenestra in his description of the soundboard opening. And the tracery ornaments he proposes consist of sheer lines, reminiscent of the lead frames of medieval windows. The fact that they also create the connection with the Trinity in terms of content, even more: they directly embody symbolically, rounds off the picture and gives it depth and meaning. To misjudge all of this would be to massively underestimate the potential of medieval scholarship.

With the inclusion of the Bible - the book of parables - the reason for the analogy-forming coupling, here: of circle and light as the epitome of perfection, is obvious anyway, because it is simply given by Jesus' self-comparison with the Alpha and the Omega or with the light of the world. In this respect, the meaning of the light is not at all symbolic in nature, but corresponds to a direct and personal idea of the person who says of himself that he is the light. All you have to do is take him at his word. He inhabits the house of God. He, the light, plays the decisive role in it. Thus God is visible before us, architecturally around us, audible within us. How could one ever draw attention to its existence in a more vivid, penetrating and beautiful way?

The fact that spirituality can only be reflected in symbols and parables is in the nature of things and was well known to the Doctors of the Church. Nikolaus von Kues does not fail to point this out explicitly. "All our wise and pious church teachers say unanimously that visible things are images of the invisible world, that the Creator can be recognized in this way as in a mirror and riddle. But that the spiritual things, which we cannot grasp in themselves, are on the way of the symbol are recognized by us has its reason in what has been said above, because all things stand in a relationship to one another that is of course unknown to us, so that one universe emerges from all of them, and everything in the one greatest is the one itself."[49]

Even if we are skeptical about analogies today for understandable reasons, the scholars cannot be accused of having chosen a form of explanation for which there is no alternative - and the content of belief as such is not up for discussion in science. Something else, on the other hand, is the visible endeavor to create a living environment that is intended to make it easier to draw conclusions about the existence of God, because it was quite obviously not enough to simply leave the nature designated as creation as it is. Interventions were made that are available to cultural studies as a subject to be processed, and this includes the cathedral buildings as well as the tonal system. They express a desire to see creation in a certain way. These are not arguments for, but testimonies of faith.

Abbot Suger of St. Denis (1081-1151) formulated it in such a way that a parable had to be created for the ignorant to make the immaterial existence of God comprehensible. "De materialibus ad immaterialia transferendo“.[50]The ethereality of incense, the immateriality of light, the radiance of gold and the immateriality of music became just as natural as numbers [51] and the word [52]- used to draw attention to the immaterial existence of God in a didactically clever way - which is nevertheless assumed to be greater than that it could ever be understood.[53]“That's why we don't lose heart; even if our outer man is worn out, the inner man is renewed day by day. For our present petty tribulation works out for us an abounding fulness of undying glory, if we look not to the seen but to the unseen, for the seen are short-lived, and the unseen eternal,” Paul says the Corinthians (4:16).And Nikolaus von Kues adds explanatory: “That which is perceived by any sense and which is changeable and unsteady according to the nature of matter is material. On the other hand, what one does not perceive with the senses but nevertheless exists, its being is not seen as temporal, but is eternal.“[54]

We have arrived at the point where musicology and art studies have to say goodbye to theology because they are unable to grasp or process the imperceptible. Here the end of the common path is reached and the area of ​​spirituality and personal confrontation with God begins. The cardinal's testimony is remarkable in that it establishes a theological immunity from any form of secular knowledge. No matter what observations are made, for example by astrophysics: that kingdom which is "not of this world" (John 18:36) is not affected at all. Such immunity is common to all religions, and wherever this fact is disregarded in arguments and discussions, the content is superfluous. Nikolaus von Kues degrades any scientific knowledge about God to an opinion. It would certainly lead too far to try to explain the far-reaching consequences in the context of this study. But the reason for the academic disregard of the Catholic cultural heritage in the above sense lies precisely in the fact that science is formed in a way that is historically justified, but not justified from the point of view of the matter. There is no reason not to give symbolism the attention it historically deserves, to fathom its potential in making the human psyche tangible, in order to give him free access to all areas of consciousness. This, in turn, is only possible through interdisciplinary networking and with an appreciative review of historical achievements of all kinds, be they of a technical or spiritual nature.

From a purely technological point of view, keyboard instruments are part of a long line of development that leads from the ancient water organ to the computer keyboard. Important intermediate stations are: The varied musical instruments (portative, regal, organ, virginal, spinet, harpsichord, claviorganum, pianoforte, carillon, celesta), the cembalo scrivano[55](a wooden typewriter with piano keys), the piano arithmometer [56] (a mechanical calculating machine in the form of a piano), the light organ, the color clavichord and the clavilux (for combining light events and sounds), George Phelps' telegraph [57] (with a piano-like keyboard with ebony and ivory coverings), another keyboard instrument called the Enigma (to encrypt and decrypt information), and the Phonola (piano) with a separate sound recording and playback device that worked purely mechanically or pneumatically and was quickly superseded by the invention of the gramophone.

The computer keyboard connects all of its functions and the "key" part of the name reveals that there is a direct connection with the keyboard of the piano (lat. clavis: key). Keyboards, in literal translation: key racks, give people controlled access to different spaces, here: to the different areas of the immaterial. They reflect the ability of the human mind to relate disparate things and transform thought into reality. They prove to be multi-talents of connection and their underlying goal can be described in just one word, with synergy.

Here, too, there is a large context of meaning, even if it again requires the involvement of various specialist disciplines in order to be able to show all of this. Although it is the most commonly used tool in everyday civilization, the history of the keyboard has not yet been written and a scientific overview of the whole has not yet been offered. The reasons for this have been given. Right in the middle, and of all things in the so-called "Dark Middle Ages", we encounter Arnaut's construction drawing and with it a small, portable and very well thought-out keyboard instrument for making contact with God, which we call a sacred cell phone in contemporary terminology, which brings its actual meaning and purpose back with it to be linked to our mode of perception.

Literature

Augustinus, Aurelius: De Musica Libri Sex, trans. by Carl Johann Perl, Paderborn, 1962

ders.: De doctrina christiana, trans., remarks and afterword by Karla Pollmann, Stuttgart 2002

Belz, Aurelius: Sakrale Handys. Die Verwendung des Keyboards im Spätmittelalter, Hägglingen 2013

id: Tastengedichte für Keyboard-Freunde, Hägglingen 2013

id: Die Geschichte des Keyboards. Von Tasten, Tod und Liebe [Narrative], Hägglingen 2012

id.: Das Instrument der Dame. Bemalte Kielklaviere aus drei Jahrhunderten, dissertation, Bamberg 1998

Bonaventura: Itinerarium mentis in Deum.Man's pilgrimage to God, trans. and explained by Marianne Schlosser, Münster 2004

Cellarius, Andreas: Harmonia Macrocosmica, Amsterdam 1709

Germann, Sheridan: Regional Schools of harpsichord decoration, In: Journal of the American Musical Instr. Society IV, 1978, S. 54-105

Glareanus, Henricus: Dodecachordon, Basileae 1547, Peter Bohn [trans.], Leipzig 1888

Heyde, Herbert: Musikinstrumentenbau, 15.-19. Jahrhundert, Kunst – Handwerk Entwurf, Wiesbaden, 1986

Kölbl, Bernhard A.: Autorität und Autorschaft. Heinrich Glarean als Vermittler seiner Musiktheorie, Wiesbaden 2012

Le Cerf, Georges u. Labande, Edmond René (Ed.): Le Traité d’Arnaut de Zwolle. In: Documenta Musicologia, Second row: manuscript facsimiles IV, Paris 1932

Linscheid-Burdich, Susanne: Suger von St. Denis.Untersuchungen zu seinen Schriften Ordinatio, Consecratione, De Administratione, München, Leipzig 2004

Maslow, Abraham: The Psychology of Science, New York, 1966

Pacioli, Luca: De Divina Proportione, Venice 1509

Palladio, Andrea: Die vier Bücher zur Architektur, trans. by Andreas Beyer and Ulrich Schütte after the Edition Venice 1570, Munich 1983

Praetorius, Michael: Syntagma musicum. Wolfenbüttel, vol. II, 1618 / Neudruck Leipzig 1884, vol  III 1619 / Reprint, Leipzig 1916

Schmidt, Wolfgang Rudolf: Die Musik im Stift Ranshofen, In: JbOÖMV, Bd. 120, 179-222, Linz  1975

Suckale, Robert: Thesen zum Bedeutungswandel der gotischen Fensterrose. In: Bauwerk und Bildwerk im Hochmittelalter, Giessen 1981, 259-294

Suckale, Kimpel: Die Gotische Architektur in Frankreich, 1130-1270, Munich 1985

Vitruv: De Architectura libri decem, trans. by Kurt Fensterbusch, Darmstadt 1981

van Kempen, Thomas: De imitatione Christi, trans. by Paul Mons, Regensburg 1990  

von Kues, Nikolaus: Idiota de mente. Der Laie über den Geist, In: Schriften des Nikolaus von Cues, published by Ernst Hoffmann in German translation on behalf of the Heidelberg Academy of Sciences, Issue 10, Hamburg 1949

id.: De non aliud. Nichts anderes, In: Texte und Studien zur Europäischen Geistesgeschichte, Reihe A, Band 1, Münster 2011

id.: De docta ignorantia. Von der Wissenschaft des Nichtwissens, In: Heidelberg texts on the history of mathematics, German translation by Franz Anton Scharff, Heidelberg 2012

Werckmeister, Andreas: Musicalische Paradoxal-Discourse, Quedlinburg 1707

Wolking, Hubert: Guidos "Micrologus de disciplina artis musicae" und seine Quellen, Emsdetten, 1930

[1] Sakrale Handys. Die Verwendung des Keyboards im Spätmittelalter, Hägglingen 2013

[2] originally netherlands: Hendrick Arnold van Zwolle

[3] Folio 128r

[4] Le Cerf and Labande [Ed.], Paris, 1932

[5]De doctrina christiana, II, 15, (51ff)

[6] One of his works is titled: Collationes de septem donis Spiritus Sancti, (1268)

[7] Werckmeister, 1707, 75

[8] so Schmidt, 1975, part II, p. 203. According to information from Prof. Dr. Cornelius Petrus Mayer OSA from the Center for Augustine Research in Würzburg, in his letter of September 24, 2012 to the author, said that this motto was not found in Augustine.

[9] Donated by  Bishop Hezilo, (1054-1079)

[10]According to the Roman calendar, ten months are counted from March 1st

[11]  Examples: Fresco in the Holy Pillar Cathedral, Mtskheta, Georgia, Old Testament Bible from 1477, Heidelberg University Library, Cod. Pal. germ.16, fol .9v

[12] Van Kempen, De imitatione Christi, Kap. III, 6, 2

[13] Cellarius, Harmonia macrocosmica, 1709

[14] Literally: In order that the students with loose vocal chords may ring out the wonders of your deeds, redeem the guilt of the stained lip, Saint John - an allusion to Zechariah, who according to the Gospel of Luke (Luke 1:22) had become mute and whose tongue was loosened again at the birth of his son John (Lk 1, 64f). For the same reason, before St. Cecilia succeeded him, John the Baptist was the patron saint of sacred music.

[15] However, the alphabetical naming was not used for key labeling but was developed on the monochord, see Wolking, 1930, 32

[16] compare Suckale/Kimpel, 1985, 103

[17] Augustinus, De doctrina christiana, II, 15, (51ff) 

[18] Bonaventura, Itinerarium mentis in Deum , Kapitel II, 10

[19] Glarean, Dodekachordon, 1547, II book, chapter XVI, 80

[20] ibid., I. book, chapter XI, 1988, 22

[21] In the first papal index of Paul IV from 1599, "Henricus Glareanus Helveticus" is found under the "auctores quorum libri & scripta omnia prohibentur", quoted from Kölbl, 2012, 53

[22] Augustinus, De Musica Libri Sex, book VI, chapter XVII, Perl, 1962, 276

[23] ibid., book VI, chapter XIII, 259

[24] Ibid., book VI, chapter XII, 258

[25] Their names are: Jachin and Boaz, which mean "I will raise up" and "In Him [God] is strength."

[26] Praetorius, 1619, 61

[27]  see. Belz 2013, 81ff

[28]  For more details see Belz 2013, 123ff

[29]  For more details see. Belz, 1998

[30]  Musical Worship. Master of Mary of Burgundy.Pierpont Morgan Library, New York, MS M 0484, fol. 069r

[31]  De docta ignorantia, Kap. XI

[32]   Explained in his work Timaios, „About nature“.

[33]  quoted from Heyde, 1986, 21. A congruence can be found in Michael Praetorius' 12 ways of arranging sacred songs. At the XII. It says: "This kind is Christ who saves us". Praetorius, 1619, reprinted 1916, 156

[34]  cf.Vitruvius, IV book, I chapter

[35] Palladio, 1570, Book IV, Preface, reprint and trans. 1983, 269

[36] ibid., chapter II, 273

[37] ibid., chapter I

[38] ibid.

[39] ibid.

[40] Straub, 2012

[41] Glarean, 1547, Book II Buch, chapter XVI

[42] Recent studies led by Prof. Angelo Molfetta, Università Pontificia Europea Regina Apostolorum, Rome. The author thanks Prof. Giacomo Baroffio for pointing out the ongoing study project.

[43] Maslow 1966, 15

[44] Maslow provides further important information on self-analysis, 1966

[45] „An anachronstic survival of gothic church rose Windows, and is found even in the earliest representations of harpsichords in art“, Germann, 1978, 55

[46] Suckale, 1981, 265

[47] compare  Belz, 1998, 181ff

[48] However, we also encounter the keel arch window in a spinet by Joes Karest from 1548, Brussels Musical Instrument Museum.

[49]  v. Kues, De docta ignorantia, Kap. XI

[50]  quoted from Linscheid-Burdich, 2004, 21

[51] "You have arranged everything according to measure, number, and weight." Wis. 11:24

[52]"In the beginning was the Word, and the Word was with God, and the Word was God." John 1:1

[53]„Omnes enim theologi Deum viderunt quid maius esse quam concipi posset, et idcirco ‚supersubstantialem‘, supra omne nomen‘ ...“, v. Kues, De non aliud, Kapitel IV

[54]   v. Kues, De non aliud, Kap. X Par. 37

[55]  Invented and named by Giuseppe Ravizza (1811-1895)

[56]  Invented by Charles Xavier Thomas de Colmar (1785-1870), 

     presented on the occasion of the world exhibition in Paris 1855

[57]  Musée des arts et des métiers, Paris, Inv. 14884