From ebe32ff94e68b23b7f95b6e24b91ad6a0a6019c7 Mon Sep 17 00:00:00 2001
From: julian laplace <julescarbon@gmail.com>
Date: Tue, 15 Jul 2025 18:29:56 +0200
Subject: ok

---
 index.html | 23 +++++++++++++----------
 1 file changed, 13 insertions(+), 10 deletions(-)

(limited to 'index.html')

diff --git a/index.html b/index.html
index 9450c05..ef5d76d 100644
--- a/index.html
+++ b/index.html
@@ -401,7 +401,7 @@
         <h1>Triangle / Lambdoma</h1>
 
         <p>
-          This instrument uses basic fractions to make a wide palette of just
+          This instrument uses simple ratios to make a wide palette of just
           intonation intervals available all at once.
         </p>
 
@@ -462,7 +462,7 @@
             </tr>
             <tr>
               <td>~</td>
-              <td>Toggle sine/bandpass mode</td>
+              <td>Toggle sine and resonator mode</td>
             </tr>
             <tr>
               <td>\</td>
@@ -564,9 +564,9 @@
             >What does a stone sound like?</i
           >), Neubäcker describes the basic principles of harmonic intervals. He
           first demonstrates how one plays harmonics on a monochord. He then
-          shows it next to a grid of whole-number fractions, and demonstrates
-          how one can use these ratios to find specific intervals. I had never
-          seen just intonation demonstrated so elegantly, so I made this page to
+          shows it next to a grid of whole-number ratios, and demonstrates how
+          one can use these ratios to find specific intervals. I had never seen
+          just intonation demonstrated so elegantly, so I made this page to
           explore the concept.
         </p>
 
@@ -662,11 +662,14 @@
           In the Lambdoma, Barbara Hero also sees the image of Georg Cantor's
           transfinite set of rational numbers ℚ, which Cantor proved
           <i>countably</i>
-          infinite by arranging fractions into a grid by numerator and
-          denominator. One may easily grasp this <i>countable infinity</i> of
-          rationals by considering that, though there are infinitely many
-          rational numbers, in between any two there lies an
-          <i>uncountable continuity</i> of real numbers in ℝ.
+          infinite. Consider that while 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, 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.
         </p>
 
         <h2>thank you!</h2>
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