From ecfb1b500a75db51cce413d1652b1b5c9c6660f5 Mon Sep 17 00:00:00 2001
From: julian laplace <julescarbon@gmail.com>
Date: Tue, 8 Jul 2025 14:12:23 +0200
Subject: docs

---
 index.html | 29 +++++++++++++++++++++++------
 1 file changed, 23 insertions(+), 6 deletions(-)

diff --git a/index.html b/index.html
index e61f53e..1f712f3 100644
--- a/index.html
+++ b/index.html
@@ -209,22 +209,25 @@
     <div id="help">
       <div class="content">
         <h1>Triangle / Lambdoma</h1>
+
         <p>
           This instrument uses simple fractions to make a wide palette of just
           intonation intervals available all at once.
         </p>
+
         <p>
           The rows display the <b>overtone series</b> (1/1, 2/1, 3/1 ...). The
           columns multiply out the <b>undertone series</b> (1/1, 1/2, 1/3, ...).
           The resulting intervals are instantly musically meaningful, though
           they arise from simple ratios.
         </p>
+
         <p>
           <b>Color</b> indicates position in the octave, with red being the root
           or unison interval 1/1. <b>Brightness</b> indicates octave, with white
           and black tending toward the extremes of human hearing.
         </p>
-        <p></p>
+
         <ul>
           <li>
             The default instrument is a Hokema sansula, a type of kalimba.
@@ -292,7 +295,9 @@
         </tableContainer>
 
         <h2>scales</h2>
+
         <p>Alternate scales are accessed by pressing the +/- keys:</p>
+
         <tableContainer>
           <table>
             <tr>
@@ -411,11 +416,22 @@
         </p>
 
         <p>
-          12-tone equal temperament is based not in harmonics, but in irrational
-          numbers. Equal-tempered semitones are separated by a ratio of the 12th
-          root of 2 (1:<super>12</super>√2). Equal-tempered intervals like this
-          do not exist in the Lambdoma - irrationals are real numbers, and these
-          can only be approximated by rational numbers.
+          Tuning systems must weigh the harmony of pure intervals against
+          musical versatility. A Pythagorean tuning system made from pure
+          fractions will include many different "fifths" and "thirds" between
+          the other notes, which makes each musical key sound highly
+          distinctive. Some intervals are extremely dissonant and harsh,
+          rendering certain keys unplayable.
+        </p>
+
+        <p>
+          12-tone equal temperament enables musicians to play in any key, by
+          bending all of the notes slightly out of tune. This process invokes
+          irrational numbers, and creates in-between intervals which do not
+          exist anywhere in the Lambdoma, no matter how far out you go.
+          Equal-tempered semitones are separated by a ratio of the 12th root of
+          2 (1:<super>12</super>√2). Irrationals are real numbers, and these can
+          only be approximated by whole-numbered fractions.
         </p>
 
         <p>
@@ -443,6 +459,7 @@
           for telling me about Barbara Hero. Thanks to
           <a href="https://hems.io/" target="_blank">Hems</a> for the support!
         </p>
+
         <p>Jules LaPlace / <a href="/">asdf.us</a> / 2018-2025</p>
         <div class="close">✗</div>
       </div>
-- 
cgit v1.2.3-70-g09d2