HELIX is a genre-crossing, non-linear concept of time and tempo created by the Cologne-based composer and double bassist Sebastian Gramss.Through the staggered fading in and out of multiple overlapping rhythms, the illusion of endless accelerations or decelerations is created.

Origins and Development

The Helix system and its tempo illusions originally stem from the family of auditory illusions within electronic music, initially applied with overlapping sine waves. The concept is inspired by the research and works of the French composer Jean-Claude Risset and the American computer artist Kenneth Knowlton from the late 1970s. Helix systems are based on the superimposition of several synchronized, fading rhythmic streams, played in parallel at different speeds (subdivisions) and faded in and out at specific points. This creates the impression of a seemingly endless acceleration or deceleration.

An acoustic analogy can be found in the Shepard-Risset glissandi, which give the impression of eternally ascending or descending pitches. A visual analogy can be seen in the Penrose stairs or M.C. Escher’s endless waterfall.

Implementation

Unlike conventional music forms, which are usually based on a uniform predetermined tempo, the musical flow in the Helix system has no fixed, stable base tempo. All musical parameters such as pitch, melody, harmony, dynamics, and timbral events are executed on the basis of simple or multiple accelerandi and ritardandi with seemingly infinite progression.

Through the simultaneous use of various subdivisions within the overarching metabar structures, a spiral-like tempo perception with more or less pronounced self-similarity is created. This produces a never-ending, captivating effect (accelerando) or, in the case of a ritardando, a kind of continuous braking effect.

In electronic and computer-generated music, the basic Helix form (as a Risset rhythm) is sometimes used with a 2:1 ratio. Since 2022, this concept has also been implemented with live musicians. The practical interpretative implementation of the Helix concept with musicians in an ensemble context is a compositional and improvisational research project by the Cologne music groups “STATES OF PLAY” and “METEORS.”

Terminology

SLOPE (Steepness of tempo change): The steepness of the accelerando/ritardando is divided into four different categories:

flat: tempo doubling within approximately 30 seconds or more

moderate: tempo doubling within approximately 15-30 seconds

steep: tempo doubling within approximately 10-15 seconds

ultrasteep: tempo doubling within less than 10 seconds

RATIO

Positive Ratio (accelerando): 2:1 = Accelerando with an initially half tempo layer, which then accelerates to double tempo, until another half tempo layer fades in again.

Negative Ratio (ritardando): 1:2 = Ritardando with an initially double tempo layer, which then slows down to half tempo, until another double tempo layer fades in again.

Odd Meter Ratio (Cluster-Ratio): Positive / Increasing: 3:1; 5:1; 7:1, etc. Negative / Decreasing: 1:3; 1:5; 1:7, etc.

Metric Modulation Ratios

Positive (accelerando): 3:2; 5:4; 5:3, 7:2, etc.

Negative (ritardando): 2:3; 4:5; 3:5; 2:7, etc.

SECTION

The section denotes the tempo zone in which the Helix is applied. Through quickly changing between tempo layers, one can move swiftly between different tempo zones/sections.

Largo, Adagio, Andante <-> Ballad

Allegro, Vivace <-> Medium

Presto <-> Fast, Uptempo

MASKS (Masking the tempo zone transition of one or more voices):

FADE – Fade out / fade in

DENSITY – Build / Dissolve (adding/removing notes during transition)

MAGNET – Direct switch / sudden start (attacca) of the new tempo layer

 

Special Forms of Helix

SUPERHELIX: Two or more simultaneous Helix systems with different ratios in the same direction.

MULTI-HELIX: Helix system with changing, interlocking different ratios.

FREE-HELIX: Two or more independent, non-parallel Helix systems in the same direction.

COUNTER-HELIX: Two or more counter-rotating Helix systems (positive and negative simultaneously).

CURVED-HELIX: Helix with a long-term changing curvilinear slope.

HELIX TRANSFER: Temporary, non-permanent use of a Helix as a musical transition.

 

Application and Research

The Helix system is applied in electronic and computer-generated music to create continuous tempo changes. Since 2022, this concept has been applied with live musicians for the first time. The practical implementation with performers/musicians is a research project by the Cologne music groups “STATES OF PLAY” and “METEORS.” As part of a basic research project commissioned by the Kunststiftung NRW and the city of Cologne, over 80 musicians are involved internationally in 2024. The focus of the research is in Cologne, Germany.