November 01, 2010 Gregor Stemmrich
It is one thing to purchase Sandra Peters’s record as a multiple and to play and listen to it on a turntable; it is another thing to hear the various tracks distributed across (at least) four loudspeakers and to experience in an installation how the sound evokes acoustically and spatially the shape of a column and the idea of a sound movement encircling it; finally, it is yet another thing to be learn how the record and the installation were created. The following lines concentrate entirely on this last aspect.
Four people collaborated on this project. The idea for it was based on Sandra Peters’s installation Modification–Constantly Climbing Stones at the Kunstverein Ruhr in Essen in 2009. That work should therefore be described briefly. In the middle of the exhibition space there are two bearing supports parallel to the wall that virtually divide the room into two parts, which is inconvenient in a relatively small exhibition space. Sandra Peters had a helix-shaped wall built around each of these two supports with a masonry course made of appropriate bricks; a specially formed brick was assigned as module to each of the two supports, resulting in various helix structures that related in a kind of dialogue, both to each other and to tree trunks and stelae located just outside and visible through a large glass facade. Because only the art being exhibited was visible, and not the supports that divided the room, the room could be experienced as a continuum. Although the masonry structures were in fact very heavy, their helix structures made them seem very light. From conversations Sandra Peters had with other people about this work, she got the idea of finding musical analogies both to the helix structure of the masonry and to their spatial effect. This initiated a complex process in which the artist contacted other people to clarify this idea of an analogy. From the start, it was important that any sound work to be created from it should not simply be a supplement to the work realized at the Kunstverein Ruhr. Rather than just illustrating it or “depicting” it in another medium, it should be an autonomous work that followed on it genealogically. It was just as clear that any work to be realized from it should be based on an approach to musical material (tones or sound) but should also have a sculptural character. The exploration of this intermediate zone proved to be an exciting challenge.
In textbooks on music, tonal structures are often represented graphically as a helix, with the sequence of octaves (frequency doublings) passing into one another on an imaginary cylinder. This became the starring point for further reflections. Another strand of these reflections concerned how sound is localized in space and how it works. Stefan Sechelmann (mathematician, computer scientist, and pianist) pointed out to Sandra Peters that the Technische Universität Berlin has a sound studio in which this locatability could be tested. A third strand of the reflections concerned the question how the suggestion of a rotating or helixlike movement could be produced by the sound design. Masayuki Ren (musician, sound designer) developed proposals for that.
Gregor Stemmrich took the common graphic representation of tonal structures as a helix as the point of departure for an examination of the question of how very familiar tonal structures such as the major-minor system of Western musician be reorganized from visual and mathematical perspectives (regardless of harmonic contexts) while retaining the idea of a helix. The major-minor system in pure intonation is based on ratios of division composed of whole numbers, with the tonic note identified as the ratio of the prime 1: 1 and its octave as the ratio of the 2: 1. Three other notes are common to the major and minor scales based on the same tonic, namely, the fifth (3:2), the fourth (4:3), and the second (9:8). The major scale is defined as a major third (5:4), major sixth (5:3), and major seventh (15:8); the minor scale, by the minor third (6:5), the minor sixth (8:5), and the minor seventh (9:5). If we now ask how large the semitones are between these intervals (whether major or minor), we find that there are three different semitones. Between the major sixth and the minor seventh is a semitone 27:25, which we will call A; that is to say, the frequency of the major sixth has to be multiplied by 27:25 = 1.08 to calculate the minor seventh. The semitone 16:15, which we will call B is found four times, namely, between the second and minor third, between the major third and fourth, between the fifth and minor sixth, and between the major seventh and the octave. In addition, there are three occurrences of the semitone 25:24, which we will call C, namely, between the minor and major third, between the minor and major sixth, and between the minor and major seventh. The following series results:
.– –.B.C.B.– –.B.C.A.C.B
It has only ten tones if one does not include the octave, since it is the repetition of the tonic note. The whole-tone steps between the tonic and the second and between the fourth and the fifth, which are indicated by double dashes here, can be subdivided into the two semitone steps A and C or C and A. From this result the following two series of semitones within an octave, with the differences between the two marked in bold:
.A.C.B.C.B.A.C.B.C.A.C.B
.C.A.B.C.B.C.A.B.C.A.C.B
The following features result: if all of the intervals that result between the ten notes (of the superimposed major and minor scales) are related to the two semitones marked in bold, A.C, and all the intervals that do not relate to these ten notes are excluded what remains is the minor scale; and likewise the major scale remains if the same thing is clone with the semitone marked in bold above as C.A. With a historical eye to twelve-tone music, these two series could therefore be called the twelve-tone major scale and the twelve-tone minor scale. The purpose of the structure developed was not, however, to recapitulate twelve-tone music, to trace the major-minor system back to it, or even to develop it further. Rather, what is interesting is that nine semitone steps of A in a row (.A.A.A.A.A.A.A.A.A) result in an octave. Starring out from the twelve semitones of an equal-tempered tuning (that is, twelve equal semitone steps), on which the piano tuning is based, the octave is divided into 1,200 cents, so that each semitone corresponds to 100 cents. The semitone A, however, has 133.23756 cents (vs. B = 111.731 cents; C = 70.672 cents), which multiplied by nine gives 1,199.138 cents, so that the difference from the octave is less than one cent (just 0.862 cents), which must certainly be considered inaudible. The graphic on the facing page illustrates the idea that the two twelve-note series
.A.C.B.C.B.A.C.B.C.A.C.B
.C.A.B.C.B.C.A.B.C.A.C.B
repeat nine times within an octave at the distance of A, and those notes whose distance is less than one cent are treated as equal, which is indicated by vertical connection lines. The resulting structure, however, has been inserted again into this structure, shifted a minor third, to interlock with it, resulting in additional connection lines. The choice of a minor third as the interval reflects the circumstance that in the traditional major-minor system the relative minor key of a major scale consists of the same notes as the major scale, but the tonic of the minor scale is a minor third lower. It makes no sense, however, to speak of a “tonic” in relation to the structure developed here. It should be noted instead that the overall structure has ninety notes within an octave, with precisely one note in each of the eighteen (two by nine) double rows that is not repeated in any of the other double rows; in the series of double rows shifted by the semitone A, it is the minor sixth, and in the other the major seventh (there is no connecting line from these two). In principle, all fifteen scales of the traditional just intonation tuning could be inserted in to each of the eighteen double rows, and other extensions of the present structure are possible as well. Whereas just intonation reduces dissonant frictions to a minimum, dissonances are incorporated into the structural idea shown here. Dissonances can, however, be resolved in two directions: in the direction of harmonic sound relationships and in the direction of noises (which can in themselves be more or less pleasant). Because the present structure was developed on the basis of harmonic relationships, the direction toward noises seems to be prescribed. However, the structure merely indicates a complex relational system of frequencies but offers no indications of their duration, volume, timbre sequence, or simultaneity.
Stefan Sechelmann developed a computer program on which the precise intervals of this structure, which cannot be played on ordinary musical instruments, can easily be programmed and transferred to a synthesizer (or, in connection with a synthesizer, to a special program like Reaktor by Native Instruments). This makes it possible to hear the interval in the first place. As was surely to be expected, there are not only intervals of pure intonation but also a wealth of intervals that sound more or less weird or dissonant. A synthesizer, however, offers number of possibilities for manipulating the scored material and thus also possibilities of moving in the direction of noises or turning into noises. Masayuki Ren experimented with these possibilities, at the same time taking his lead from the idea of connecting the stored material with the suggestion of a circling as well as an upward and/or downward movement. This idea is inherent both in Sandra Peters’s modular helix like masonry and in the structure based on the semitone steps A, B, and C. Another point of departure for his experiments was the idea of starring out from simple harmonic relationships—major and minor triads, for example—and following them in their possible shifts within the overall structure. The triads are composed of a minor third (ABC), a major third (ABCC), and a fourth (ABBCC), which repeats the tonic of the triad an octave higher; in the minor triad, the minor third is below, in the major triad above. Following the idea of seeing all the notes indicated by the structure in the form of triads, whether as chords or arpeggios, numerous unusual shifts result that become the point of departure for manipulation with a synthesizer. After Masayuki Ren and Sandra Peters had selected sounds and noises that fit the ideas they had worked out for the sound installation, Masayuki Ren chose three series of semitones steps from the structure.
CBCBCBCBC CBCBCBCBC CBCBCBCBC …
AC BCB AC BCACB AC BCB AC BCACB …
CA BCB CA BCACB CA BCB CA BCACB …
These series should be related acoustically to four loudspeakers installed in the corners of the room in a way that results in a spatial effect and dynamic of motion in which the series rise and descend in the frequency spectrum. Masayuki Ren is currently experimenting with the idea of applying the frequency spectrum not in an extensive-spatial way but rather—at the center oft his dynamic—in an intensive-temporal way. The number four will play a central role in all issues of arrangement, repetition, and phase shifting. This corresponds to the structural setup of the helix like masonry that Sandra Peters had built at the Kunstverein Ruhr in 2009. The noises of installing the masonry were recorded and will be integrated into the phase shifts of the four series, so that real noises are confronted with noises generated by the synthesizer.
