Jun 5th

Rhythm Necklaces have also found use in Crystallography, the study of the arrangement of atoms in crystalline solids.

A.L. Patterson pioneered the idea of analyzing idealized one dimensional crystals using a circular notation (see above), rather than using the more ubiquitous use of x-ray diffraction patterns from three dimensional crystals. His 1944 paper Ambiguities in the X-ray Analysis of Crystal Structures presents this notation method and some of the revelations it provided him with.

The below music is created with patterns selected from this paper, with one rotated against the others.

Jun 5th

[  ] [  ]

Crystallographyyy

 

Rhythm Necklaces have also found use in Crystallography, the study of the arrangement of atoms in crystalline solids.

A.L. Patterson pioneered the idea of analyzing idealized one dimensional crystals using a circular notation (see above), rather than using the more ubiquitous use of x-ray diffraction patterns from three dimensional crystals. His 1944 paper Ambiguities in the X-ray Analysis of Crystal Structures presents this notation method and some of the revelations it provided him with.

The below music is created with patterns selected from this paper, with one rotated against the others.

May 11th

[  ] [  ] [  ]

The shadow of a rhythm is found by placing an audible beat exactly inbetween every set of existing beats.

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.

May 5th

The Rhythm Necklace app is now available here!

Nov 28th

[  ] [  ] [  ] [  ] [  ] [  ] [  ] [  ] [  ]

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.

Nov 18th

[  ] [  ] [  ] [  ] [  ] [  ] [  ]

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.

Sep 11th

[  ] [  ]

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.

Sep 11th

[  ] [  ]

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

Sep 11th

[  ] [  ] [  ]

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.