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@@ -165,6 +165,7 @@ font-size: 10px; position: relative; bottom: 5px; + margin-right: -5px; } #help p { margin-block-start: 0; @@ -626,7 +627,8 @@ <p> With the root, fifth, fourth, and octave in the top-left corner, the - Lambdoma shows how the 3:2 proportion is basic to musical perception. + Lambdoma shows how the 3:2 proportion is essential to musical + perception. </p> <p> @@ -635,11 +637,11 @@ <u class="mode" name="pythagorean">Pythagorean</u> mode, where each ratio is a power of 2 or 3. Similar notes can be found by color and compared. One can easily hear how stacking fifths does not bring you - back to the starting note. Find two far-apart red notes and play both + back to the starting note: find two far-apart red notes and play both at once. These two frequencies are not quite the same, and they will audibly vibrate or "beat" against each other. The interval between - these notes is known as the "syntonic comma", and tuning systems try - to correct for it in various ways. + these notes is known as the <i>syntonic comma</i>, and tuning systems + try to correct for it in various ways. </p> <p> @@ -662,12 +664,12 @@ <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 in a snake-like - pattern starting from 1:1, moving outward diagonally, 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. + 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> <h2>thank you!</h2> @@ -678,18 +680,16 @@ href="https://freesound.org/people/cabled_mess/packs/21410/" target="_blank" >cabled_mess</a - >. - Gradient algorithm via + >. Gradient algorithm via <a href="https://iquilezles.org/articles/palettes/">Inigo Quizeles</a - >. - Thanks to + >. Thanks to <a href="https://www.nyz.recycled-plastics.net/" target="_blank" >Dave Noyze</a > for telling me about <a href="https://www.lambdoma.com/" target="_blank">Barbara Hero</a>. - Thanks to <a href="https://hems.io/" target="_blank">Hems</a> for - the support! + 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> |