Plus-Minus

Karlheinz Stockhausen – Plus-Minus (1963)

Plus-Minus is an indeterminate score, notated for a generic ensemble and based on seven pages of musical material in unconventional notation, coupled with seven pages of symbols suggesting how to use the musical materials, for a total of fourteen pages plus six pages of explanations of the symbols. (One of the symbol pages is shown; click to enlarge a little)

Each page of musical materials contains:

7 chords
6 groups of notes, determined by pitch, but including indications of duration, dynamics, and playing style.

Each symbol page is paired with one of the music pages and contains 53 squares, each representing a musical event. The interpretation of the squares and the symbolism they contain is hierarchical. Each square contains the following information:

a zentralklang (central sound), the main sound on which the event is based, which corresponds to one of the seven chords on the associated music page.
the akzidentien, which are performance indications applicable to octaves, durations, dynamics, playing styles, and timbre. These indications are not precise, but rather indicative, such as short, medium, long, accelerando, ritardando, as fast as possible, etc.
the nebennoten, secondary notes that correspond to groups 1 through 6 on each page.

Each square also contains a complex set of symbols that guide the realization of the event from a rhythmic, dynamic and timbral perspective.

In the application of symbols, the concepts of growth and contraction are central. Each symbol can be marked with a numeric indication (1 digit) with a + or - sign (e.g., +1, -2, +3, etc.) that determines the number of repetitions of that symbol the next time it is encountered. For example, the fact that, in the current event (the square), the symbol of the zentralklang is superimposed with a +1 means that the next time that symbol is encountered, it must be performed twice, and then three times the next time it is encountered, and so on, until a possible negative indication is encountered that determines its contraction, perhaps until it disappears.

This generates growing and contracting loops that give rise to repeated, at times archaic, musical figures, with more or less subtle changes between one event and the next, and practically infinite combinatorial possibilities.

It is also interesting to note that Plus-Minus is not a piece of music, but a project, an idea that is by its very nature not perfectly defined, and consequently any aesthetic evaluation based on the score alone is completely misplaced. From a musical perspective, in fact, Plus-Minus does not exist until its transcription (I would almost say "implementation"), and it is only this latter that can be evaluated in terms of musical aesthetics.

It is also worth remembering that Stockhausen prescribed the complete realization of the work, that is, of all 53x7 (=371) events. This, however, has almost never been achieved, due to both the length and complexity of the work.

2010 performance by the Ives Ensemble.

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