Calculating entropy at different scales among diverse communication systems

We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code and two human natural languages were studied at the scale of characters, words, and at the Fundamental Scale resulting from adjusting the symbols length used to interpret each text-description until it produced minimum entropy. The results show that the Fundamental Scale method is comparable with the use of words when measuring entropy levels in written texts. However, this method can also be used in communication systems lacking words such as music. Measuring symbolic entropy at the fundamental scale allows to calculate quantitatively, relative levels of complexity for different communication systems. The results open novel vision on differences among the structure of the communication systems studied.
Comment: 27 pages, 6 Figures, 6 Tables