A century of BAUHAUS

In this article the BAUHAUS year 2019 will be introduced and two exemplary events shortly described. These events focused on less known BAUHAUS subjects – dance, performance and music. Based on these topics the origin of the octave in the common music will be discussed along with the mathematical foundation of it, which directly leads to the development of the 12-tone scale, which was used by Gertrud Grunow for teaching at BAUHAUS.

  When?

all year

 

 

 

 

Introduction

Almost everyone heard about BAUHAUS. However, most exhibitions focus on architecture or design. But BAUHAUS as a school had much more to offer. The main idea was to connect the craftsmanship with the art and therefore the school was divided into workshops and not into classes. There were workshops like print, photography, metal, carpentry, glass painting, architecture, theater, theory of harmonization, etc. This year BAUHAUS would celebrate 100 years since foundation, if it wouldn’t be dismantled in 1933.

Nevertheless, the anniversary is widely celebrated and in Germany 2019 is the year of BAUHAUS. The whole year long events will take throughout Germany. In Berlin it started with “The opening festival”, which took place between 16th and 24th of January in the Academy of Art (Akademie der Künste). The task of the festival was to remind the public of the importance of BAUHAUS and it’s achievements, especially the less pronounced ones. Therefore most of the performances during the opening were connected to dance, theater and music.

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Throughout the evening the group of artists in different futuristic costumes, which draw their idea from BAUHAUS, performed at different locations in Akademie der Künste. The symphony of movements, geometrical shapes and dancers was fascinating to watch. The Halle 1 was entirely dedicated to the performances choreographed by Hoochie Koochie, which spilled out on the stairs and into the entrance hall.

The main program were the concerts in the lecture hall. The first one was a DJ set by Aisha Devi accompanied the video installation by Tianzhuo Chen. The impression was that the sound check wasn’t made properly as the music was deafeningly loud. The video was bright and juicy and fitted the beat. The performance was well made and well timed, just very loud.

The second concert was a rap performance by trans-artist Mikky Blanko. The dress was unique and some elements reminded of the BAUHAUS style. The rap itself had pointed rhymes and good rhythm, however it was not outstanding. Maybe because the artist constantly complained about the lack of collaboration and what didn’t work (e.g. sound and sound check). At last the star interrupted the performance because the vibe of a sitting white public was not good enough. In the end I was not sure if the complaints and the sudden end were part of the performance or happened because of the poor organisation and lack of vibe.

Despite the drawbacks, the event was highly enjoyable, especially after the DJ Bigger started the party set. The beats were pleasant and drivy and everybody danced from professional dancers to managers in suits.

On 21st of March 2019 we visited another event. This time it was in Brohän museum under the title “Rhythm and Bauhaus”. Here you could visit the exhibition “Von arts and crafts to bauhaus” and join after that the bauhaus bar, which was accompanied by the performance of the triadic theater.

Discussion

BAUHAUS was a school with an innovative concept. Also music was taught there. The responsible for the harmony theory was Gertrud Grunow, who being first and during the Weimar years the only female teacher at BAUHAUS taught 12-tone music combined with 12 basic colors of the chromatic scale as well as 12 basic geometrical shapes.

ColorsShapes
Correlation of color/tone with shapes and sounds.

Here I would like to discuss the science of musical scales. The foundation of western music is the octave, which means “the eighth” and includes 7 tones, which are denoted Do-Re-Mi-Fa-Sol-La-Si-(Do) or C-D-E-F-G-A-B-(C). Both notations are historical – the alphabetical one was used by Boethius already, however A doesn’t correspond to A used in our times. Also Boethius didn’t use the same letter for the same note an octave higher (Journal of Musicology, 1984). This style of notes was introduced by Odo of Cluny, who first limited the letters to the range from A to G in repetitive way. Also Guido of Arrezzo used this notation and invented a system of remembering the order of tones and half tones by using a well-known Latin hymn (“Ut Queant Laxis”). In this hymn each line begins on the next higher pitch starting with C (Ut, which later changed to Do). Also on the original scale by Arrezzo no pitch for B was present. However later it was added and got the name SI from Sancte Iohaness (Musical Offerings, 2012).

table
Latin hymn gave the names for the notes as the first syllables of the lines.

Now we know how the octave and the names for the notes were formed, but what does an octave do? First we have to keep in mind that sound consists of waves. Most string and wind instruments produce a sinus wave. Also ears transform sinus waves to signals, which are passed through to the brain. Therefore each sound can be split into sum of sinus waves with help of Fourier analysis (Cambridge University Press, 2008).

Some-when around 16th and 17th century the relationship between pitches and frequency was discovered independently by Galilei and Mersenne. An octave doubles the frequency of a sound wave. E.g. the A below middle C has a frequency of 220 Hz as the A above the middle C equals to 440 Hz. Now additionally to the basic frequency also higher harmonics are always present if a pitch is played. So if we hit the A below the middle C 1*220 = 220 Hz, 2*220 = 440 Hz, 3*220 = 660 Hz, 4*220 = 880 Hz, etc. frequencies are present. For the A above the middle C 1*440 = 440 Hz, 2*440 = 880 Hz, 3*440 = 1320 Hz, etc. are present.

TwoOctavesDiatonicChromatic
Two octaves of a piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted. The chromatic scale includes all 7 tones 5 semitones of the diatonical scale with pitches at slightly different frequencies (c) Wikipedia

Galileo himself explained that consonance appears if two pitches are played with frequencies with simple integer ratio (e.g. 3:2 or perfect fifth). The waves of these two pitches overlap in the way that no torment for the ear appears.

However this explanation is not true. The scientific foundation for the explanation of the consonance and dissonance was laid by Helmholtz, who proposed that small differences in frequency cause in the ear the impression of beats, which turns to sense of roughness, if the difference is increased, which feels as dissonance. After the difference is greater than 30-40 Hz the consonance resume. (The Journal of the Acoustical Society of America ,1965)

g4263
Two sound waves with slightly different frequencies are overlapping producing a new wave with a low frequency beats. You can clearly hear this beating!

As shown in the image above, if two waves have frequencies close to each other, the sound of these two waves will add up to a third wave (both other waves are still present). The frequency of this third wave is between the original two and the amplitude (volume) varies from maximum to almost zero. This amplitude is what we perceive as beats and dissonance. The numbers of beats per seconds is equal to the frequency difference of both original waves. You can find more information and some of the sound under the link below:

https://academo.org/demos/wave-interference-beat-frequency/

Now as you saw from the links the pitches with ratios of small integer ratios, which are listed in the table above generate consonant sounds, which are the base of the octave. These pitches are the white keys on the keyboard of a piano. In between the white keys the black ones represent the semitones. However as the classic octave was derived the notes represented by the white keys were not distributed equally. Therefore there are no semitones between B and C as well as between E and F, as C is only half a tone higher than B.

A consequence of this structure is the chromatic scale with 12 evenly distributed semitones. The music teaching in BAUHAUS was based on that more modern scale. However it didn’t find a wide application and the diatonic scale (octave plus five semitones) is the commonly used one. Nevertheless the chromatic scale was used by A. Schoenberg for his 12-tone composing technique and is associated with the “Second Viennese School”. Building on the this method of composition G. Grunow developed her theory of harmonization.

In conclusion I want to mention that many more scales exist. As well as in antique and medieval times or in Arabic or Asian cultures different scales were derived. After synthesizers were invented many more complicated scales could be deduced from the chromatic scale. Some examples are the Harry Patche’s 43-tone, fifty three tone scale or the scales of Wendy Carlos (Benson, 2008).

Summary

In this article we introduced the BAUHAUS year 2019 and showed which kind of events you can expect through whole year. As the topic of the exemplary events here were BAUHAUS performances and music, the 12-tone chromatic scale used by Gertrud Grunow in BAUHAUS was discussed. Especially the origin of the common octave, consonance and dissonance as well as physical foundation of the acoustic waves and its meaning for the music were elaborated. The origin of the 12-tone and other less common scales was derived from this discussion.

References

  1. C. M. Bower, The Modes of Boethius. Journal of Musicology, 3(3):252-263 (1984)
  2. A. J. Reisenweaver, Guido of Arezzo and His Influence on Music Learning. Musical Offerings, 3(1):37-59 (2012)
  3. D. Benson, Music: A Mathematical Offering. Cambridge University Press (2008)
  4. R. Plomp and W. J. R. Levelt, Tonal Consonance and Critical Bandwidth. The Journal of the Acoustical Society of America, 38(4): 548-560 (1965)

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