asdf

1 files changed, 30 insertions, 24 deletions

diff --git a/index.html b/index.html
index 6212d61..d4fa42c 100644
--- a/index.html
+++ b/index.html
@@ -261,11 +261,9 @@
        */
       .root-select {
         position: fixed;
-        top: 0;
-        left: 0;
+        top: 1rem;
+        right: 50px;
         z-index: 1234;
-        width: 100%;
-        height: 100%;
         display: flex;
         align-items: flex-start;
         justify-content: flex-end;
@@ -291,8 +289,6 @@
         padding: 1rem 0.5rem 0 0.5rem;
         backdrop-filter: blur(6px);
         box-shadow: 0 1px 2px rgba(0, 0, 0, 0.5);
-        margin-top: 1rem;
-        margin-right: 50px;
       }
       .root-select .row {
         display: flex;
@@ -379,11 +375,16 @@
         .root-select {
           align-items: flex-start;
           background: rgba(0, 0, 0, 0.5);
+          top: 0;
+          right: 0;
+          width: 100%;
+          height: 100%;
         }
         .root-select > div {
           background: rgba(0, 0, 0, 0);
           margin: 0;
           width: 100%;
+          height: 100%;
           align-items: center;
           justify-content: center;
           border-radius: 0;
@@ -401,14 +402,15 @@
         <h1>Triangle / Lambdoma</h1>
 
         <p>
-          This instrument offers a wide palette of just intonation intervals.
+          This page is a musical instrument made up of a grid of just intonation
+          intervals, all based on a root frequency.
         </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, whole-number ratios.
+          columns follow its inverse, the <b>undertone series</b> (1/1, 1/2,
+          1/3, ...). Multiplying everything out, the resulting intervals contain
+          an inherent music arising from simple, whole-number ratios.
         </p>
 
         <p>
@@ -555,7 +557,7 @@
         <h2>about this page</h2>
 
         <p>
-          This webpage was inspired by
+          This webpage was inspired in part by
           <a href="https://www.youtube.com/watch?v=4pdSYkI86go"
             >Peter Neubäcker</a
           >, inventor of the Melodyne software. In the short biographical
@@ -637,13 +639,13 @@
           The next prime number interval, 5:4, is a just major third, and its
           inverse, 4:5 is a minor third. Thus the overtone series sounds
           "major", and the undertone series sounds "minor". The next prime
-          number out, 7, expresses a "Lydian" tonality.
+          number out, 7, extends the minor to diminished, and major to dominant.
         </p>
 
         <p>
           At this point, we have just enough notes to form a fairly melodious
           just-intonated scale, which you can play using your computer keyboard.
-          Within a just-intonated tuning system, each scale can sound highly
+          Within a just-intonated tuning system, each interval can sound highly
           distinctive, since the notes are not distributed evenly across the
           octave.
         </p>
@@ -688,11 +690,14 @@
         <h2>tone and transfinite sets</h2>
 
         <p>
-          Equal temperament invokes irrational numbers, creating in-between
-          intervals which do not exist on the Lambdoma. Notes in equal
-          temperament are separated by an irrational ratio of 1 to the 12th root
-          of 2 (1:<super>12</super>√2), which can only be approximated by
-          whole-numbered fractions.
+          Intervals in just intonation are rational numbers, composed of a
+          numerator and denominator that are both whole numbers. Notes in equal
+          temperament, however, are separated by a semitone of 1 to the 12th
+          root of 2 (1:<super>12</super>√2), an irrational number, and can only
+          be approximated by rationals. By definition, any real number might be
+          at the theoretical limit of the Lambdoma in any direction, but by
+          definition these numbers are not rational numbers, and are thus only
+          approximated by the intervals of the Lambdoma.
         </p>
 
         <p>
@@ -700,12 +705,13 @@
           transfinite set of rational numbers ℚ, which Cantor proved
           <i>countably</i>
           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 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
+          numbers, each of these numbers is by definition finite, and we may
+          count up to it by starting from 1 and adding 1 repeatedly. 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.
         </p>