A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

In this paper we take a step forward towards the attainment of a formalism that allows to establish a deeper connection between Music and Algebra. Starting from the writing of the Ionian Scale as a Vector, we define the Ionian Modal Tensor. We prove that all the Scales that derive from the Ionian Mode, as well as all the corresponding Seventh Chords, herein considered as being Scalars, can be obtained from the above-mentioned Tensor by resorting to the concepts of Standard Basis and Dot Product.Moreover, by opportunely summing the Vectors of the Standard Basisto each other, we define some interesting Fundamental Vectors such as the "Monk – Powell" Vector and the "Guide Notes" one.