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1 files changed, 20 insertions, 28 deletions

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@@ -378,7 +378,7 @@
           Lambdoma, named for its resemblance to the Greek letter Lambda Λ. The
           synergy of color and tone, linking the octave to the color wheel,
           seemed intuitive, and revealed a beautiful pattern. This pattern had
-          earlier been uncovered by artist and sound practitioner
+          previously been uncovered by artist and sound practitioner
           <a href="https://www.lambdoma.com/">Barbara Hero</a>, who built an 8x8
           electronic Lambdoma instrument for sound healing purposes, using the
           same pattern of colors.
@@ -430,23 +430,11 @@
 
         <p>
           With the root, fifth, fourth, and octave in the top-left corner, the
-          Lambdoma shows how the 3:2 proportion is essential to human
-          perception.
+          Lambdoma shows how the 3:2 proportion is basic to musical perception.
         </p>
 
         <p>
-          Mapping colors logarithmically to this wheel of fractions between 1
-          and 2, with red at the octave (1:1), it naturally follows that the
-          fourth (4:3) is green, and the fifth (3:2) is blue. These ratios seem
-          to correspond to the photoreceptors in the human retina, which are
-          sensitive to wavelengths of light in three different ranges: long,
-          medium, and short. These ranges are perceived as "red, green, and
-          blue" in the brain, yet our mind's eye sees a continuous cycle of
-          color that loops back on itself.
-        </p>
-
-        <p>
-          The musical circle of fifths, derived from repeatedly stacking the 3:2
+          The musical Circle of Fifths, derived from repeatedly stacking the 3:2
           proportion, can be studied in more detail in this program's
           <u id="pythagorean">Pythagorean</u> scale mode, where each ratio is a
           power of 2 or 3. Similar notes can be found by color and compared. One
@@ -457,20 +445,20 @@
         </p>
 
         <p>
-          Tuning systems must weigh the purity of thirds and fifths. A
-          Pythagorean tuning system made from pure fractions will include many
-          different "fifths" and "thirds" at different points in the scale,
-          especially when using basic ratios to determine a 12-tone scale. Each
-          musical key sounds highly distinctive, and some intervals may be
-          considered dissonant or harsh.
+          Tuning systems must weigh the purity of thirds and fifths. A just
+          tuning system made from pure fractions might use as its basis the
+          difference between 3:2 and 4:3, which constitutes a semitone. Such a
+          scale implies different ratios between "fifths" and "thirds" at
+          different points in the scale. Each mode can sound highly distinctive,
+          and some intervals may be considered dissonant or harsh.
         </p>
 
         <p>
           In a sense, 12-tone equal temperament "bends" all of the notes such
           that the fifths are more consisent, making it easier to modulate
-          between keys, though other intervals (like thirds) are far from a pure
-          interval. This process invokes irrational numbers, and creates
-          in-between intervals which do not exist anywhere in the Lambdoma, no
+          between keys, though other intervals (like thirds) are quite different
+          from a interval. This process invokes irrational numbers, and creates
+          in-between intervals which do not exist anywhere on 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 fractions made up
@@ -482,8 +470,8 @@
           transfinite set of rational numbers ℚ, which Cantor proved countably
           infinite by arranging fractions along two axes by numerator and
           denominator, similar to the Lambdoma. One may easily grasp this
-          countable infinity of rationals by considering that, while there are
-          infinitely many fractions, in between any two there lies an
+          countable infinity of rationals by considering that, though there are
+          infinitely many rational numbers, in between any two there lies an
           uncountable continuity of real numbers in ℝ.
         </p>
 
@@ -499,8 +487,12 @@
           <a href="https://www.nyz.recycled-plastics.net/" target="_blank"
             >Dave Noyze</a
           >
-          for telling me about Barbara Hero. Thanks to
-          <a href="https://hems.io/" target="_blank">Hems</a> for the support!
+          for telling me about
+          <a href="https://www.lambdoma.com/" target="_blank">Barbara Hero</a>.
+          Gradient algorithm via
+          <a href="https://iquilezles.org/articles/palettes/">Inigo Quizeles</a
+          >. 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>