From f0fd04f18d6bb1d0cbf29d5d8fcae1647daa6bbc Mon Sep 17 00:00:00 2001
From: julian laplace <julescarbon@gmail.com>
Date: Mon, 7 Jul 2025 22:45:56 +0200
Subject: docs

---
 index.html | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

(limited to 'index.html')

diff --git a/index.html b/index.html
index bce41c5..91c7b62 100644
--- a/index.html
+++ b/index.html
@@ -354,14 +354,14 @@
           first demonstrates how one plays harmonics on a monochord. He then
           shows it next to a grid of whole-number ratios, and demonstrates how
           one can use these intervals to find specific ratios. I had never seen
-          the concept of just intonation displayed so elegantly, so I made this
-          page to understand the concept more deeply.
+          just intonation demonstrated so elegantly, so I made this page to
+          understand the concept more deeply.
         </p>
         <p>
           I later learned that I had recreated the
           <a href="https://www.lambdoma.com/">Lambdoma</a> as described by
           <a href="https://www.lambdoma.com/">Barbara Hero</a>. Hero made an
-          electronic lambdoma instrument for sound healing purposes. Hero traces
+          electronic lambdoma instrument for sound healing purposes. She traces
           the Lambdoma back to the <i>Introduction to Arithmetic</i> by
           <a
             href="https://archive.org/details/nicomachus-introduction-to-arithmetic/page/191/mode/1up"
@@ -374,23 +374,27 @@
             target="_blank"
             >depicts it</a
           >
-          in his <i>Die harmonikale Symbolik des Alterthums</i> (1876). In the
-          Lambdoma, Hero also sees the image of Georg Cantor's transfinite set
-          of rational numbers, which are shown to be countable through use of a
-          Cartesian plot. More can be read in Hero's
+          in <i>Die harmonikale Symbolik des Alterthums</i> (1876). More can be
+          read in Hero's
           <a
             href="https://lambdoma.com/pdfs/the-lambdoma-matrix-and-harmonic-intervals.pdf"
             target="_blank"
             >article</a
-          >, <i>The Lambdoma Matrix and Harmonic Intervals</i> (1999).
+          >, <i>The Lambdoma Matrix and Harmonic Intervals</i> (1999). In the
+          Lambdoma, Hero also sees the image of Georg Cantor's transfinite set
+          of rational numbers ℚ, which Cantor showed to be countably infinite
+          through use of a Cartesian plot (versus the uncountable continuity of
+          real numbers ℝ).
         </p>
 
         <p>
           With the root, fifth, and fourth in the top-left corner, the Lambdoma
           shows how the 3/2 proportion is essential to the perception of
           consonance. The musical circle of fifths, derived from these simple
-          proportions, can be studied in more detail in "Pythagorean" mode,
-          where related intervals can be found by color and compared.
+          proportions, can be studied in more detail in "Pythagorean" mode.
+          Similar notes can be found by color and compared, and one can easily
+          hear how stacked fifths overshoot the octave by finding the next red
+          note.
         </p>
 
         <h2>thank you!</h2>
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