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Bilinear is quite similar to Reed’s Twinline. Sotorrio maintains he had no prior knowledge of Twinline when designing Bilinear, since he relied primarily on Gardner Read’s Source Book of Proposed Music Notation Reforms which does not include Twinline. (It was published in 1987, just after Twinline was introduced in 1986.) Since Twinline is the earlier system (Bilinear was introduced in 1997), Sotorrio now offers Bilinear as a variant of Twinline.

The two systems share the same line pattern and the same alternating oval and triangle shaped noteheads, but there are differences in their details. Twinline’s triangles are right triangles with the 90 degree angle at their tip, while Bilinear’s triangles have a sharper angle at their tip. Also, the shape, color, and size of noteheads in Bilinear may be different depending on a note’s duration, as illustrated in the following image (courtesy of the Bilinear website):

For notes a quarter note or shorter in duration, solid ovals and hollow triangles are used. For half note or whole note durations, larger hollow ovals are used instead of solid ovals (as in traditional notation), and hollow half-ovals are used instead of triangles. Ease of handwriting was a consideration in designing this system of rhythmic notation.

Bilinear offers new register symbols and an optional system for using color to indicate sharps, flats and naturals. It introduces optional stand-alone symbols for notes, for use in writing apart from a staff, but derived from their appearance on a staff. It also attempts to standardize accidentals for microtones and chord symbols, and adds new ‘interval units’. More information on these details was formerly available from the Bilinear website (www.SpectralMusic.com).

Earliest documentation: 1997

Website: www.SpectralMusic.com (No longer exists.)

Source: www.SpectralMusic.com and José A. Sotorrío