From ecd914cfea434cdebebf4cac8502d8e1274e39b3 Mon Sep 17 00:00:00 2001
From: julian laplace
With the root, fifth, fourth, and octave in the top-left corner, the
- Lambdoma shows how the 3:2 proportion is basic to musical perception.
+ Lambdoma shows how the 3:2 proportion is essential to musical
+ perception.
@@ -635,11 +637,11 @@
Pythagorean mode, where each
ratio is a power of 2 or 3. Similar notes can be found by color and
compared. One can easily hear how stacking fifths does not bring you
- back to the starting note. Find two far-apart red notes and play both
+ back to the starting note: find two far-apart red notes and play both
at once. These two frequencies are not quite the same, and they will
audibly vibrate or "beat" against each other. The interval between
- these notes is known as the "syntonic comma", and tuning systems try
- to correct for it in various ways.
+ these notes is known as the syntonic comma, and tuning systems
+ try to correct for it in various ways.
@@ -662,12 +664,12 @@
countably
infinite. Consider that although there are infinitely many natural
numbers, we may count our way up to each one, starting from 1.
- Similarly, we can count the cells in a Lambdoma in a snake-like
- pattern starting from 1:1, moving outward diagonally, and thus map all of the rationals to the
- natural numbers. Though there are infinitely many rational numbers, by
- their nature they are discrete, countable, and not completely dense.
- Between any two rational numbers, there lies an uncountable continuity
- of real numbers in ℝ.
+ Similarly, we can count the cells in a Lambdoma by starting from 1:1
+ and moving outward diagonally in a snake-like pattern, thus mapping
+ the rationals to the natural numbers. Though there are infinitely many
+ rational numbers, by their nature they are discrete, countable, and
+ not completely dense. Between any two rational numbers, there lies an
+ uncountable continuity of real numbers in ℝ.
thank you!
@@ -678,18 +680,16 @@
href="https://freesound.org/people/cabled_mess/packs/21410/"
target="_blank"
>cabled_mess.
- Gradient algorithm via
+ >. Gradient algorithm via
Inigo Quizeles.
- Thanks to
+ >. Thanks to
Dave Noyze
for telling me about
Barbara Hero.
- Thanks to Hems for
- the support!
+ Thanks to Hems for the
+ support!
Jules LaPlace / asdf.us / 2018-2025
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