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@@ -401,7 +401,7 @@ <h1>Triangle / Lambdoma</h1> <p> - This instrument uses basic fractions to make a wide palette of just + This instrument uses simple ratios to make a wide palette of just intonation intervals available all at once. </p> @@ -462,7 +462,7 @@ </tr> <tr> <td>~</td> - <td>Toggle sine/bandpass mode</td> + <td>Toggle sine and resonator mode</td> </tr> <tr> <td>\</td> @@ -564,9 +564,9 @@ >What does a stone sound like?</i >), Neubäcker describes the basic principles of harmonic intervals. He first demonstrates how one plays harmonics on a monochord. He then - shows it next to a grid of whole-number fractions, and demonstrates - how one can use these ratios to find specific intervals. I had never - seen just intonation demonstrated so elegantly, so I made this page to + shows it next to a grid of whole-number ratios, and demonstrates how + one can use these ratios to find specific intervals. I had never seen + just intonation demonstrated so elegantly, so I made this page to explore the concept. </p> @@ -662,11 +662,14 @@ In the Lambdoma, Barbara Hero also sees the image of Georg Cantor's transfinite set of rational numbers ℚ, which Cantor proved <i>countably</i> - infinite by arranging fractions into a grid by numerator and - denominator. One may easily grasp this <i>countable infinity</i> of - rationals by considering that, though there are infinitely many - rational numbers, in between any two there lies an - <i>uncountable continuity</i> of real numbers in ℝ. + infinite. Consider that while 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, 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. </p> <h2>thank you!</h2> |