{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Divisions of the World Soul as Musical Intervals

Divisions of the World Soul as Musical Intervals - by the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Divisions of the World Soul as Musical Intervals Relating this to music, if we start at low C and lay off these intervals, we get 4 octaves plus a sixth. It doesn't yet look like a musical scale. But Plato goes on to fill in each interval with an arithmetic mean and a harmonic mean. Taking the first interval, from 1 to 2, for example, Arithmetic mean = (1+2)/2 = 3/2 The Harmonic mean of two numbers is the reciprocal of the arithmetic mean of their reciprocals. For 1 and 2, the reciprocals are 1 and 1/2, whose arithmetic mean is 1+ 1/2 ÷ 2 or 3/4. Thus, Harmonic mean = 4/3 Thus we get the fourth or 4/3, and the fifth or 3/2, the same intervals found pleasing
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: by the Pythagoreans. Further, they are made up of the first four numbers 1, 2, 3, 4 of the tetractys . Filling in the Gaps He took the interval between the fourth and the fifth as a full tone. It is 3/2 ÷ 4/3 = 3/2 x 3/4 = 9/8 Plato then has his creator fill up the scale with intervals of 9/8, the tone. This leaves intervals of 256/243 as remainders, equal to the half tone. Thus Plato has constructed the scale from arithmetic calculations alone , and not by experimenting with stretched strings to find out what sounded best, as did the Pythagoreans. Project: Repeat Plato's calculations and see if you do indeed get a musical scale....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern