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The Donnan potentials contain the individual ionic activities and cannot be measured by using a purely thermodynamic procedure. In the concentration range where the Debye-Hiickel limiting law is valid, the ionic activities can be replaced by the mean activities. The membrane potentials are measured by constructing a cell with a semipermeable membrane separating solutions 1 and 2: Ag | AgCl, sat. KC11 solution 1 | solution 2 | sat. KC1, AgCl | Ag (6.1.16) whose EMF is given by the sum of the membrane potential and the two liquid junction potentials, which can usually be neglected. Equations (6.1.3) and (6.1.4) could be derived from the relationships for the liquid junction potential formed by a single salt (Eq. 2.5.31), assuming that the anion mobility in Eq. (6.1.3) and the cation mobility in Eq. (6.1.4) equal zero. The general case, i.e. that the membrane only changes the transport number of the cation and anion, was solved by J. Bernstein at the beginning of this century using a relationship analogous to Eq. (2.5.31), which assumes the following form for a uni-univalent electrolyte: , = (*_-*+) l n - ^ (6.1.17)

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where T+ and T_ are the transport numbers of the cation and anion in the membrane, respectively, which are different from the corresponding values in solution. References

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As you learned in 4, the various pitches present in a piece need to have a certain kind of mathematical relationship with each other or the music will sound dissonant. Getting the music to harmonize and the pitches to gel is one of the hardest parts of creating a good mashup. Musicians have plenty of flexibility to match their instrument to a chord or key that s in a piece, but mashup artists only have the bits and pieces of already existing songs that need to be coaxed into a harmonic relationship with the other material. For this reason, maintaining harmony throughout a piece is one of the greatest challenges mashup artists face.

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Blank, M. (Ed.), Bioelectrochemistry: Ions, Surfaces, Membranes, American Chemical Society, Washington, 1980. Bioelectrochemistry, CTE, 10 (1985). Butterfield, D. A., Biological and Synthetic Membranes, John Wiley & Sons, New York, 1989.

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Eisenman, G. (Ed.), Membranes A Series of Advances, M. Dekker, New York, Vol. 1, 1972; Vol. 2, 1973; Vol. 3, 1975. Galvani, L., De Viribus Electricitatis in Motu Musculari, Typographia Instituti Scientiarum, Bologna, 1791, Translation: Green, R. M., Commentary on the Effect of Electricity on Muscular Motion, p. 66, E. Licht, Cambridge, Mass., 1953. Jain, M. K., Introduction to Biological Membranes, John Wiley & Sons, New York, 1988. Keynes, R. D., The generation of electricity by fishes, Endeavour, 15, 215 (1956). Koryta, J., Ions, Electrodes and Membranes, 2nd ed. John Wiley & Sons, Chichester, 1991. Koryta, J., What is bioelectrochemistry , Electrochim. Acta, 29, 1291 (1984). Membrane phenomena, Discussion Faraday Soc, 21, 1956. Milazzo, G., and M. Blank (Eds), Bioelectrochemistry III Charge Separation Across Biomembranes, Plenum, New York, 1988. Overbeck, J. T., The Donnan equilibrium, in Progress in Biophysics and Biophysical Chemistry, Vol. 6, p. 57, Pergamon Press, London, 1965. Schlogl, R., Stofftransport durch Membranen, D. Steinkopff, Darmstadt, 1964. Sollner, K., The early developments of the electrochemistry of polymer membranes, in Charged Gells and Membranes (Ed. E. Selegny), Vol. 1, Reidel, Dordrecht, 1976. Williams, R. J. P., A general approach to bioelectrics, in Charge and Field Effects in Biosystems (Eds M. J. Allen and P. N. R. Usherwood), Abacus Press, London, 1984. Wu, C. H., Electric fish and the discovery of animal electricity, Am. Scientist, 72, 598 (1984).

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If you ve never made a mashup, this book will take you step by step through the various aspects of mashup production and will provide you the necessary background in music and music software. No experience is assumed. On the other hand, if you ve made few mashups but want to know some tips and techniques, this book will also be helpful. This book covers everything from the very basics to advanced topics in song selection, unmixing, arrangement, and mastering.

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