4 papers
Representation of Geometric Objects by Color
Yusuke Imai
By introducing various actions involving color to geometrical objects, we represent a cube and simplex in four or fewer dimensions, the geometrical net of a cube and simplex in fiv…
Differential and Integral Calculus of Sequence
Yusuke Imai
We create a sequence version of calculus. First, we define equivalence, some fundamental operations, differential, and integral for sequences. Then, we propose sequence versions of…
General Theory of Music by Icosahedron 3: Musical invariant and Melakarta raga
Yusuke Imai
Raga is a central musical concept in South Asia, especially India, and we investigate connections between Western classical music and Melakarta raga that is a raga in Karnatak (sou…
General Theory of Music by Icosahedron 1: A bridge between "artificial" scales and "natural" scales, Duality between chromatic scale and Pythagorean chain, and Golden Major Minor Self-Duality
Yusuke Imai, Sid C. Dellby, Nobuaki Tanaka
Relations among various musical concepts are investigated through a new concept, musical icosahedron that is the regular icosahedron each of whose vertices has one of 12 tones. Fir…