• Communications of Mathematical Education
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• v.28 no.2
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• pp.219-234
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• 2014

Music and mathematics have a lot of structural similarities. Major and minor triads used importantly in music are in a relationship of inversion in which the sequence of the intervals is reversed, which is equivalent to reflection in mathematics. Geometrical expressions help understand structures in music as well as mathematics, and a diagram that shows tonal relationships in music is called Tonnetz. Relationships of reflection between major and minor triads can easily be understood by using Tonnetz, and also, transpositions can be expressed in translation. This study looks into existing Tonnetz and introduces S-Tonnetz newly formed by a mathematical principle.

• Journal of Korean Medical classics
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• v.20 no.4
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• pp.119-126
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• 2007

The biological and pathological states of lung, spleen, liver and kidneys are determined by nature and emotion of sorrow, anger, joy and pleasure, It is considered that the music, besides medicine or acupuncture, can be a way of treating as a therapeutics for the treatment of Sasangin's diseases. This study is to find out a way of music therapy for the treatment of Sasangin's diseases. The ways of music therapy in each constitution based on 'the great and small of Viscera and Bowels' and 'the exhale and inhale, the drawing in and sending out' are as follows: 1. In case of Soeumin, a skip going up melodic progression, dotted rhythm and the major triad harmonic progression are recommended to improve the Qi of warm Yang. 2. In case of Soyangin, in regular sequence down melodic progression, a sixteenth note and the minor triad harmonic progression are recommended to improve the Qi of cool Yin. 3. In case of Taeumin, in regular sequence going up melodic progression, a sixteenth note and the bright and active the major triad harmonic progression are recommended to improve the Qi of dispersing exhale. 4. In case of Taeyangin, a skip down melodic progression, a quarter note and a diminished triad harmonic progression are recommended to improve the Qi of gathering inhale.

• Polymer(Korea)
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• v.24 no.5
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• pp.646-655
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• 2000

Polymerizations of higher $\alpha$-olefins were carried out in toluene by using highly isospecific catalyst, rac-(EBI)M(NMe$_2$)$_2$ (EBI=1,2-ethylenebis-(1-indenyl); M=Zr(rac-1); M=Hf(rac-2)) In the presence of Al(i-Bu)$_3$/[Ph$_3$C][B($C_{6}F_{5}$)$_4$]. The polymerization of high $\alpha$-olefin showed high activity and similar polymerization behavior. The polymerization activity was affected by both monomer size and lateral size of polymer chain. The conversion of monomer to polymer decreases with the increased lateral size in the order of 1-pentene>1-hexene>1-octene>1-decene. The same dependences of melting behavior and intrinsic viscosity of polyolefin on lateral size were observed according to the results obtained by differential scanning calorimetry and intrinsic viscosity. All poly($\alpha$-olefin)s showed very high isotacticity (triad) and the isotacticity increases in the order of poly(1-pentene)$^1H$ NMR and Raman spectra analysis showed that chain transfer to cocatalyst, which generates saturated methyl groups, Is a main chain termination. The $\beta$-hydride eliminations, which generate unsaturated vinylidene, tri-substituted, and vinylene end group. are found to be minor chain terminations.