Aristoxenus vs Pythagorus

Dear Julia,
Rereading Andrew Baker's 'Introduction" to his "Greek Musical Writings II, Harmonic and Acoustic Theory," there is a clear description of the age old musical divide that seems more alive on this forum since you joined it. As in a Greek chorus, I'd like to toss this into the fray.

Baker writes:

p3 For most of its history, Greek harmonic writng can be classified under two fairly distinct traditions, the "Aristoxenian" and the "Pythagorean", each with its own characteristic presuppositions, methods and goals. It must be said at once that neither school is monolithic--there are important internal distinctions to be drawn--and that the work of each did not flow onwards quite independently of the other. There were occasional attempts to bring the two approaches together in a coherent synthesis, as well as more frequent polemical interactions across the doctrinal divide.

p4 As Aristoxenus conceived it . . . . the science begins from the data presented to perception and grasped by it as musical . . . they must not be redescribed, for scientific purposes, as (for instance) physical movements of the air. The order Aristoxenus seeks is a set of relations between items grasped in their character as notes, and there is no need, and no reason, to suppose that the same relations hold between the physical movements that are their material causes. (To suggest a modern analogy, the note A is the dominant of D major, but 440 cycles per second cannot be the dominant of anything.) . . . harmonics must describe the phenomena in terms that reflect the way in which they are grasped by the ear. . . . a general tendency to write in a language developed out of the terminology of practising musicians: THE MOST IMPORTANT IS THAT NOTES SHOULD BE TREATED AS LOCATED AT POINTS LYING ON A CONTINUUM OF PITCH, and the relations between them as 'distances' or 'intervals', diastemata. Intervals must themselves be described in autonomously musical terms, as distances of various sizes in the dimension of pitch (as tones, half-tones, and the like). An interval is not be be defined by reference to something non-musical, something that the musical ear does not grasp as such (for instance, as the ratio between the speed of the movements by which the relevant pitches are produced).

P6 From the beginning, Pythagoreans were not typically interested in the study of music for its own sake. Their researches in harmonics arose out of a conviction that the universe is orderly, that the perfection of a human soul depends on its grasping, and assimilating itself to that order, and that the key to an understanding of its nature lies in number. . . . . The order found in music is a mathematical order; the principles of the coherence of a coordinated harmonic system are mathematical principles. . . .

. . . . Particular attention was focussed on the mathematics of ratio and proportion, with constant reference back to the paradigmatic ratios governing basic musical structures.

jwerntz2002 wrote:

>Dear Rick,
>
>Thank you, this make me very glad. To present another way of thinking about >microtonality, to give this other approach a more prominent "voice," especially in >the American forum, where I feel it is underepresented, was my main goal. >
>All the best,
>
>Julia
>