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@@ -386,18 +386,18 @@ <a href="https://archive.org/details/tonestudyinmusic0000leva/page/n5/mode/2up" >Levarie and Levy</a - >, who traces the Lambdoma back to Pythagoras (ca. 500 BCE) via the - <i>Theologumena arithmeticae</i> of - <a - href="https://archive.org/details/astius-theologumena-arithmeticae-gr-1817/page/159/mode/1up" - >Iambluchus</a - > - and the <i>Introduction to Arithmetic</i> by + >, who trace the Lambdoma back to Pythagoras (ca. 500 BCE) by way of + the <i>Introduction to Arithmetic</i> by <a href="https://archive.org/details/nicomachus-introduction-to-arithmetic/page/191/mode/1up" >Nicomachus of Gerasa</a > - (ca. 100 BCE). The Lambdoma is mentioned by + (ca. 100 BCE) and the <i>Theologumena arithmeticae</i> of + <a + href="https://archive.org/details/astius-theologumena-arithmeticae-gr-1817/page/159/mode/1up" + >Iamblichus</a + > + (ca. 300 CE). The Lambdoma is also mentioned by <a href="https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A2008.01.0385%3Astephpage%3D1027b" >Plutarch</a @@ -410,9 +410,10 @@ >depicts it</a > in - <i>Die harmonikale Symbolik des Alterthums</i> (1876), and was used by - mathematician Georg Cantor in his theory of transfinite sets. More - information can be gleaned from Hero's + <i>Die harmonikale Symbolik des Alterthums</i> (1876). The Lambdoma + was also used by mathematician Georg Cantor in his theory of + transfinite sets (see below). More information can be gleaned from + Hero's <a href="https://lambdoma.com/pdfs/the-lambdoma-matrix-and-harmonic-intervals.pdf" target="_blank" @@ -423,18 +424,20 @@ <h2>the mathematics of perception</h2> <p> - With the root, fifth, and fourth in the top-left corner, the Lambdoma - shows how the 3:2 proportion is essential to human perception. + 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. </p> <p> - Mapping colors logarithmically to this wheel of fractions, 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. + 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> |