Sounding Triangles
A good evening from Maastricht in the Netherlands to all participants associated with us.
Thanks to Kathy Newburn for inviting me to do this talk.
My name is Hub. Pittie and I worked as a music teacher and conductor until my retirement a few years ago.
My talk is therefore musically motivated and it is a great pleasure for me to share with you some of my ideas about the connection between Music and Triangles.
The text and accompanying presentation can be downloaded as a PDF afterwards and it is provided with a number of footnotes with interesting complementary facts.
My choice for this very day is not without meaning, because yesterday Johann Sebastian Bach would have celebrated his 336thbirthday and for most musicians he is considered the greatest in our field.
Now let’s start with our Sounding Triangles…
[1] Sounding Triangles
Hub. Pittie 2021
Within our working area we are familiar with triangles in all shapes and sizes.[2]
First of all, the Triangle formed by Will and Purpose - Love-Wisdom - Active Intelligence, the three main rays of our energetic system.
We find modifications of this Triangle in all kinds of religions, for example the Trinity with the Christians, the Trimurti in Hinduism, the Tiratana of Buddhism, the three highest Sefiroth of Jewish Kabbalah and so on[1].
It is therefore not surprising that the Triangle forms the basis of the planetary network of Light and Goodwill.
From a geometrical point of view, the triangle is the most stable formation in the plane and from the triangle all other shapes, both two- and three-dimensional, can be built, as this illustration shows:[3]
Pythagoras stated that three is the first true number.
The three is the first number that forms a geometric figure: the triangle, which gives structure and thus offers security and control.
Without the three, further creation is impossible.
The Tao says about this:
Tao gives birth to one.
One gives birth to two.
Two gives birth to three.
Three gives birth to the ten thousand things.
So: The three is everywhere [4]
When we look carefully around us, we see the three and the three division of the world everywhere:
Triple time:
• past - present - future
• birth - life - death
Three division of space and matter:
• length - width - height
• minerals - plants - animals
• solid - liquid - gas
• body - mind - spirit
In daily life you act in three ways: in thought, in speech and in action. You supply blood, sweat and tears and you cheer three times on someone's birthday. In fairy tales, things often happen three times, the hero is given three commands or wishes, and blessings or curses are said three times to be effective.
Three is a divine number. It is the representative of all potentials, which you see reflected in countless symbolic, religious and mythological stories.
The holy trinity is about the three energetic primal principles of life: [5]impulse, manifestation and transformation, the three "aspects of being" which make up the circle of life. The cosmic impulse (the idea - white) is followed by embodiment (manifestation - red) and then death (transformation - black).
[6]In esoteric psychology we know the threefold compound gross body, the threefold compound personality and the three permanent atoms. Esoteric astrology speaks of the threefold energy responsible for the personality, the threefold soul and the threefold monad.[2]
The number 3 and the triangle also play a major role in music. For example, we know the triad as the basis of the Western polyphony.
In a few monumental works such as Die Zauberflöte (Mozart - The Magic Flute)[3] and the Matthäuspassion (J.S. Bach - St Matthew Passion) [4], the number 3 plays a prominent role.
According to many, the three most important heroes among the composers of the West are [7] Johann Sebastian Bach, Wolfgang Amadeus Mozart and Ludwig van Beethoven. They are absolute beacons for all composers who came after them and we consider them to be dedicated disciples in the realm of music. The three of them had their working lives spanning approximately 125 years.
Music exists by the grace of sound, physically vibrating air. A sound, be it a tone, a murmur or some other sounding manifestation, consists of a combination of partial tones. We will limit ourselves here to musical tones.
During my working life as a music teacher and conductor, I have always been intrigued by the phenomenon of overtones.
As we know these are co-resonant notes with a dominant root note. These so-called epi-phenomena have a rigid mathematical organization. Their combination and individual intensity is largely responsible for the property timbre of the sounding tones and sounds[5].
A music score is therefore nothing more than a collection of signposts that seem to say - in a nutshell - “If you follow these roads, there is a chance that you will experience something beautiful”.
How is the harmonic sequence structured? [8]
From the root note upwards, a series of notes is heard, the distance between which becomes smaller and smaller towards the top.
The root note itself is followed by the octave, the greatest possible distance within the octave.
This is followed by the perfect fifth, the perfect fourth, the major third, the minor third and then decreasing intervals, which are soon no longer part of our Western tonal system and which only approximate the tones and intervals of it.
So, you could say that in the overtone series upwards certain notes start to sound more and more “false”.
This does not have to be a problem because the strength and intensity of the higher overtones also decreases.
A skilled instrument builder minimizes the effect of those dissonant overtones and ensures that the desired overtones come out more strongly.
Singers do this by making balanced use, where and as far as possible, of the cavities of the head, throat and chest, each of which accounts for part of the sound spectrum.
The overtone series is also at the basis of our western harmonic system, our functional harmony theory and thus of our polyphony.
After all, the first five partial tones (namely the root with four overtones) form a so-called major triad, which forms the basis of our major scales. This is also where the number 3 comes into play.
This number plays an important role in all kinds of areas, varying from philosophy, religion, culture, social relationships and therefore also music. [9]
Think about it: tonality is based on three main functions, which we call tonic, dominant and subdominant[6].
In our Western tone system, a tone has three modalities: natural, lowered (flat) and raised (sharp)[7]. Many musical forms are in principle three-part (song, rondo, sonata form, classical concerto- forms). And, just as the triangle is geometrically the strongest geometric structure, so is the trinity in music.[8]
Ultimately, we arrive at the most important triangle that has played a role in my musical past: the triangle composer-performer-listener. The three possible relationships within this triangle could be described as follows.
Composer versus performer [10]
The composer designs, that is to say, he receives an idea originating from an external or internal source, prompted to do so by an assignment from outside or by an idea that evokes the urge to develop in him.
He converts this idea into a language that can be understood by others, usually the musical notation, and with which he crystallizes his idea, as it were.
To do this, he must make use of knowledge and techniques that have been supplied to him from his training or from tradition.
Of course, he can also choose to translate his ideas in a non-conventional way and create a new musical language.
Naturally, he remains bound by the limitations imposed by the performing medium.
The performer has to make the translation into audible sound and will thereby almost inevitably interpret.
This means that he will perform the music with his own personality and thus enriching it with his own illusions and glamours.
In addition, he has to deal with the limitations imposed by the instrument, the space and his technical skills, as well as the feedback he experiences from the audience.
Performer versus Audience [11]
The performance uses vibrating air as a medium and thus reaches the listener.
He too experiences the music in a personal way, which has everything to do with its physical and spiritual qualities.
With regard to the latter, his musical perception is colored by his experiences and memories, his knowledge, his emotional sensitivity[9]and, in newer or never-heard music, his willingness to be open to what is heard.
The listener thus also places a layer of illusions and glamours on the perceived music, as it were.
Even if he feels that the music does not move him emotionally, he still perceives the sounds and can “think of it”.[10]
Audience versus Composer [12]
Often this relationship is one-way traffic.
Usually the composer does not know the listener and there is no information transfer in that direction.
The listener, on the other hand, can delve into the music heard or yet to be heard and into the life of the person who made it. By the way: this applies to the relationship between the audience and the performer as well.
He can also process information about the resources needed to produce the music, but this does not usually happen at the time of the performance.
The role of manner of reproduction, such as by radio, TV, records, streaming etc., is, according to some, rather dubious in this regard.
It is not without reason that the conductor Sergiu Celibidache categorically refused during his life to have recordings of his concerts made, because he felt that music only had meaning at the time and place where it was performed.
In case that it was reproduced with technical aids this would be an act of untruth because there would be no sound system capable of doing justice to all aspects of the living music experience.[11]
In short: [13]within the triangle composer-performer-listener there is an energetic exchange and processing of information that transcends the purely mental (5thray) activity of spoken and written language.
It was Beethoven who stated: Music is a higher revelation than all wisdom and philosophy.
This means that the triangle is also a founding principle in music and in my opinion being active and passive with music is also a form of Triangle work, in which the interaction between designer and receiver is less defined, but in which it is indeed present in a higher sense.
Thank you for your attention.
[1] Carl Jung considered the arrangement of deities into triplets an archetype in the history of religion.
[2] In every triplicity, there are three major qualities manifesting or three basic energies seeking expression and influence. As he manifests in time and space, man discovers this to be true and to constitute a law in nature, and it might be said that the task of the disciple is to become consciously aware - like a detached onlooking Observer - of these energies and their expressing qualities as they function within himself. This he does upon the Path of Probation, the Path of Discipleship and the Path of Initiation. He has to become aware of:
1. The threefold energy which is the personality, and of which the vital body is the synthetic expression.
2. The threefold soul of which the egoic lotus is the expression.
3. The triple monad of which a great diffusion in time and space in three streams of creative energy is the expression.
This last definition is somewhat meaningless to the uninitiate but must suffice. There is a manifesting aspect in all these triplicities which is the result of, and conditioned by, the interplay of the three forces. It is their full expression and the result of their successful activity.
1. In the personality, it is the physical body.
2. In the soul, it is the unfolded central bud within the egoic lotus.
3. In the monad, it is the "sound which geometrically forces itself into the vision of the beholder" - a deeply esoteric mode of symbolizing that which cannot be expressed or reduced to the tangibility of form.
(A.A. Bailey, Esoteric Astrology, p. 414-5)
[3] The number three in “Die Zauberflöte”:
"Three ladies" are in the service of the Queen of the Night,
The triple thunder.
The threefold cry "She is coming - she is coming - she is coming -" announces her approach.
The queen of the night appears three times: at the beginning, in the middle (revenge aria) and at the end.
Her three ladies also intervene in the plot three times.
The candidates are accompanied and protected by the three geniuses or boys, who are mentally and acting the opposite of the three ladies.
They appear in the trio Tamino, Pamina and Papageno.
The number three dominates even more meaningfully the light realm of Sarastro.
o He acts three times as the High Priest of the eighteen (i.e. 3 x 6) initiates.
o Moreover, he appears three more times, not as a representative of the God of Light, but as a friend and advisor.
o The strangers have to endure three tests: the command not to speak, the second by the commandment of complete silence even towards the dearest person, the third by the fire and water test that accompanies death.
o The podium at the end of the first act shows three temples, the gates of which have the inscriptions "Reason", "Wisdom" and "Nature".
o Tamino tries in vain three times to get to these temples by knocking on the door.
o Sarastro's empire is dominated by wisdom, work and the arts.
o His priests demand steadfastness, patience and discretion from Tamino.
o By three trumpet blasts, the Initiates agree to Sarastro's proposal to allow Tamino to enter the trials
o These three "mystical" trumpet chords also sound three times.
• Furthermore, there are three musical instruments that determine how the Magic Flute works: the flute, the glockenspiel and Papageno's faun whistle. Each of these three instruments is played three times.
o The whistle in the first final, during the second test and during the fire and water test.
o The glockenspiel is sounded three times, in the first finale, then in the aria "Ein Mädchen oder Weibchen" and finally when he calls his long-awaited Papagena after the prevented suicide.
o Papageno also plays the faun whistle three times.
• But not only the separate parts of the plot and the music of Die Zauberflöte are formed by the principle of threefold. It is also the basic structure of complete action. It is true that the opera was divided into two acts (acts) by Schikaneder and Mozart. But if one distinguishes the act according to its context, three parts emerge, which are distinguished from each other by clear cut marks.
o The first part - according to the old textbook - with the introduction of Tamino and Papageno in the temple of research and with the closing chorus of the priests, which proclaims the deification of the consecrated as the aim of the research.
o The second part ends with the priestly choir that foretells the "new life" of the "noble youth" in the service of the Wisdom Covenant.
o In the 21st scene we see a new aspect. Here Tamino is no longer tested alone, but the couple Tamino and Pamina must prove that they are not only worthy of the expected deification but also of each other. But this means that in this "third part" a new mystery is announced, the mystery of the couple: the earthly couple must become the reflection of the divine couple Osiris and Isis.
• Finally, by Tamino and Pamina, the aim of the layered mystery play, namely the deification of man, is forever achieved by the union of the three basic principles of creation, which are mentioned in the last key words of the opera: victory and eternal crowning of Power, Beauty and Wisdom.
[4] In St Matthew’s Passion we find 27 passages in which the gospel is sung, and 27 other pieces. The number 27 stands for Bach for the trinity of God (3 × 3 × 3). The 27 pieces of Gospel text consist of a total of 729 measures, which is the square of 27. In addition to the number 3, 9 or 27, there is an overwhelming amount of number symbolism in the Matthew Passion, in which, among other things, the Bach number (14) occupies a prominent place.
[5] According to the conductor Celibidache, in addition to tone onset and tone distribution, they also determine to a large extent the expression of the correct tempo in the music. When the tempo is too fast, the epi-phenomena will, as it were, crowd each other out and the sound cannot come to full bloom. The result is a haunted, restless-looking performance. On the other hand, if the tempo is too slow, “gaps” will occur because the epi-phenomena no longer fit together properly and the musical quality will be characterized by a dull, sleep-inducing character. Only when the epi-phenomena fit together well, space is created and the sound comes out well because the right tempo is experienced. This correct tempo therefore depends on more than the noted intention of the composer. The quality of the musicians and of their instruments or singing voices, the properties of the space in which the music is played and the conductor's ability to connect things to each other largely determine the correct tempo.
[6] Tonality is the system of functionally harmonic relationships that govern most Western music. The tonal music is organized around the tonic, a main tone to which the melody returns. Melody directs harmony, and harmony in turn directs melody. A melodic line feels closed when it comes to rest on (is dissolved in) the tonic. The emotional tension ends and in the final turn to the keynote a psychological relaxation is felt, or a resolution in a 'cadence'.
[7] The double flat and double cross are not primary modalities and are a consequence of leading tone functions in more distant keys or in non-Western tone systems)
[8] Master D.K. broadens the meaning of these concepts and takes them beyond the realm of music. In Cosmic Fire we read the following:
“…To word it otherwise, the third can be clearly sounded, and is followed naturally by the fifth, or the dominant. The simultaneous sounding of the third and the fifth, basing it upon the planetary keynote, produces the effect of a threefold chord, or a fourth tone, a complex sound. I am here dealing with the chord of the human hierarchy as a whole. Within the hierarchy there is again diversity, based upon the hierarchical chord, and this produces the many egoic chords and notes; these produce in their turn objective manifestation…”
(A.A. Bailey, Cosmic Fire, p. 781)
[9] Recent laboratory experiments have confirmed that musical harmony is based on innate mechanisms. Babies (at the beginning of 4 months) like consonant sounds and dislike dissonances. Evolution, it seems, used the mechanical properties of the ear to improve the efficiency of the spoken communication channel. Where a string made of heterogeneous material sounds contrary to itself, so does the human voice sound when it is in stress or fear; it sounds dissonant and this dissonance was perceived as unpleasant millions of years ago. Consonant combinations of sounds are at the basis of human voice communication. These gradually evolved into the emotionally filled melody of the voice. The connection of voices with the state of the soul was inherent in our ancestors long before language began to evolve towards conceptual content at the expense of the emotional. Gradually, evolution shaped the musical ability to create and perceive sound as something especially important because it affects our entire being. This is why wolves howl at the Moon, when humans express such a diversity of emotions in sounds.
[10] While music has appealed to emotions since time immemorial, a new and powerful development towards stronger and more diverse emotionality began during the Renaissance. It appeared along with the tonal music developed for 500 years from the 15th to the 19th century with the conscious aim of appealing to musical emotions.
[11] The fact that in the end there existed performances on CD conducted by him had to do with the orchestras that depended on radio performances for their survival, which were of course recorded and which were released after his death in 1996. In addition, Celibidache allowed at the end of his career a few video plates of his Bruckner recordings to be made, which critics of his interpreted as vanity.