Rhythm Necklaces

As you can see below in these Six Distinguished Timelines, the shadow does not always fall on an existing pulse in the cycle. It's often therefore necessary to double the number of pulses in the cycle to accomodate this.

The Rhythm Necklace app is now available here!

Different rotations of the same necklace are used across cultures, as well as within the same musical tradition. For example, the above rhythm is referred to as Tresillo in Cuba when started on the first onset, as Samhyon Toduri in Korea when started on the second onset, and as Nandon Bawaa Ghana when started on the third onset. Examples of necklace rotations like these and many more can be found in this paper on The Distance Geometry of Music.

In his book, The Geometry of Musical Rhythm, Godfried T. Toussaint refers to the above necklaces as The Six Distinguished Timelines. These necklaces are representative of some of the most popular in the world. While many other ratios are also used in music, the combination of 5 onsets (audible beats) in a cycle of 16 pulses (silent beats) is especially universal. Each of the above necklaces is known by different names across cultures, and has many variations. For example, the name Shiko originates in Nigeria, while the same necklace is referred to as Cinquillo in Cuba.

Flat rhythms have the property that each distance between onsets is unique. This is also demonstrated by a Golomb Ruler, and is used in the placement of radio-telescopes, where interference created by un-evenly space units is used to boost signal.

Deep rhythms are created by adding an onset at equally spaced intervals, spiraling around until all pulses are filled.

The hop and jump algorithm produces something called rhythmic oddity, where no onset pairs divide the rhythmic cycle perfectly in half, or in segments of equal duration.