Pythagoreans

From the work of Barbara Hero:

I derived the musical scale that I generally use from the Lambdoma

(or Pythagorean table), which dates back to the ancient Greeks

[Levarie, S., & Levy, E. (1968)]. The Lambdoma is a square array

of points having fractions systematically assigned to the points. It

can be visualized very easily with the use of a sheet of paper lined

with square grids or, better yet, a sheet of ordinary graph paper.

The x-axis and y-axis are drawn and the coordinate points along

the axes are numbered by integers, x = 0, 1, 2 ... and y = 0, 1, 2 ...

(Fig. 2). The coordinates (x, y) of any point falling on an

intersection in the grid are interpreted as the numerator y and

denominator x of the fraction y/x. Thus, the coordinates of point A

(x, y) are given by (3, 8) and the corresponding fraction would be

8/3. If the point A were labeled 8/3 and all other grid intersections

were labeled in the same way, then Fig. 2 would take on the usual

appearance of a Lambdoma grid. Here the fraction y/x is taken to

represent the reciprocal of the relative pitch and hence the point A

(3, 8) corresponds to the tone g,, (8/3) (Barbara Hero, 1975).

Figure 1: Pythagorean Lambdoma (lambdoma.org, 2021)

Figure 2: Lambdoma Keyboard (Hero, 2016)

Works Cited

             Lambdoma.org. (2021). HOW TO CHOOSE LAMBDOMA PRODUCTS? – Lambdoma. Lambdoma.org. 

                 https://lambdoma.org/en/how-to-choose-lambdoma-products-2/

Hero, B. (2016). The Lambdoma Keyboard created by Barbara Hero Lambdoma Music Gift to Humanity. Lambdoma.com.   https://www.lambdoma.com/keyboard.html