pocoforte

austern, 17 days ago to bookstodon

10 authors, of whose books I've read at least five:
Jane Austen
Iain Banks
Iain M. Banks
Anton Chekhov
C. J. Cherryh
Samuel R. Delany
Ursula Le Guin
Vladimir Nabokov
Thomas Pynchon
Gene Wolfe

#10Authors5BooksEach
@bookstodon

JamesGleick, 1 month ago to random

Sounds logical, but is it?

johncarlosbaez, 6 months ago (edited 6 months ago) to random

Here's a way to get the tuning system commonly called "just intonation". Start with a triangular lattice of circles and put the number 1 in one circle. Now you've got a note vibrating at some frequency that we're arbitrarily calling "1".

Then: multiply by 3/2 every time you move one circle to the right, and 2/3 every time you move to the left. In music we call 3/2 a "fifth", since when you go up the major scale the fifth note vibrates 3/2 times faster than first one.

Next, multiply by 5/4 every time you move roughly northeast, and 4/5 when you move roughly southwest. In music we call 5/4 a "major third".

Now you've got a triangular grid with numbers at every vertex.

Four numbers at the corners of a parallelogram are close to √2 times a power of 2. In music we call √2 times any power of 2 the "tritone". It's very dissonant when combined with your original note.

Next, curl up this parallelogram to form a torus. Glue its top edge to its bottom edge, and its left edge to its right edge.

THIS TORUS HAS 12 CIRCLES ON IT! Just the right number of notes for a 12-tone scale.

Don't trust me - count them! But make sure you don't double count them. The 2 circles on the top corners are now "the same" as those on the bottom corners. And the circles on the left edge are now the same as those on the right edge.

(1/2)

mcnees, 8 months ago to random

Margaret Hamilton, a pioneer of software engineering who led NASA's in-flight software team for the Apollo mission, was born #OTD in 1936.

Image: NASA