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@@ -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> |