N2D3P9: Difference between revisions

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'''<math>\text{N2D3P9}</math>''' or Entoo-Deethree-Peenine, is a fictional character in the Star Wars franchise. In an alternative timeline, the young Anakin Skywalker assembles the droid <math>\text{N2D3P9}</math> from the parts of three other droids: R2D2, C3P0 and NR-N99. We're only joking, but we hope this helps with remembering and pronouncing the name.

'''<math>\text{N2D3P9}</math>''' is a mathematical function which was developed to help in designing the [https://en.xen.wiki/w/Sagittal_notation Sagittal microtonal notation]. Given a pitch ratio <math>\frac{n}{d}</math>, <math>\text{N2D3P9}</math> estimates its rank in popularity among all rational pitches in musical use. A low value of <math>\text{N2D3P9}</math> indicates that the ratio is used often, and so should have a simple accidental symbol, while a high value indicates that the ratio is used rarely and so can have a more complex symbol if necessary. ~~Its~~ name is an abbreviation of key components of its formula, which will be described in detail later.

'''<math>\text{N2D3P9}</math>''' is a mathematical function which was developed to help in designing the [https://en.xen.wiki/w/Sagittal_notation Sagittal microtonal notation]. Given a pitch ratio <math>\frac{n}{d}</math>, <math>\text{N2D3P9}</math> estimates its rank in popularity among all rational pitches in musical use. A low value of <math>\text{N2D3P9}</math> indicates that the ratio is used often, and so should have a simple accidental symbol, while a high value indicates that the ratio is used rarely and so can have a more complex symbol if necessary. The name "N2D3P9" is an abbreviation of key components of its formula, which will be described in detail later.

Because factors of <math>2</math> and <math>3</math> in pitch ratios are already notated by changing octaves or moving along the chain of fifths (... B♭♭ F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯ Fx ...), <math>\text{N2D3P9}</math> only operates on ratios that have had their factors of <math>2</math> and <math>3</math> removed. For example, there are various numbers of factors of <math>2</math> and <math>3</math> in the following ratios: <math>\frac{16}{15}, \frac{10}{9}, \frac{6}{5}, \frac{5}{4}, \frac{27}{20}, \frac{45}{32}, \frac{64}{45}, \frac{40}{27}, \frac{8}{5}, \frac{5}{3}, \frac{9}{5}, \frac{15}{8}</math>, but when their factors of <math>2</math> and <math>3</math> are removed, they all reduce to <math>\frac{1}{5}</math> or <math>\frac{5}{1}</math>, and so they can all be notated using the same microtonal accidental, pointing either up or down, combined with different letters and sharps or flats. We say that <math>\frac{1}{5}</math> or <math>\frac{5}{1}</math> is the "2,3-reduced" or "[https://en.wikipedia.org/wiki/Rough_number 5-rough]" form of these pitch ratios.

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 '''<math>\text{N2D3P9}</math>''' or Entoo-Deethree-Peenine, is a fictional character in the Star Wars franchise. In an alternative timeline, the young Anakin Skywalker assembles the droid <math>\text{N2D3P9}</math> from the parts of three other droids: R<span style="color:#FF0000">2D</span>2, C<span style="color:#FF0000">3P</span>0 and <span style="color:#FF0000">N</span>R-N9<span style="color:#FF0000">9</span>. We're only joking, but we hope this helps with remembering and pronouncing the name.
-'''<math>\text{N2D3P9}</math>''' is a mathematical function which was developed to help in designing the [https://en.xen.wiki/w/Sagittal_notation Sagittal microtonal notation]. Given a pitch ratio <math>\frac{n}{d}</math>, <math>\text{N2D3P9}</math> estimates its rank in popularity among all rational pitches in musical use. A low value of <math>\text{N2D3P9}</math> indicates that the ratio is used often, and so should have a simple accidental symbol, while a high value indicates that the ratio is used rarely and so can have a more complex symbol if necessary. Its name is an abbreviation of key components of its formula, which will be described in detail later.
+'''<math>\text{N2D3P9}</math>''' is a mathematical function which was developed to help in designing the [https://en.xen.wiki/w/Sagittal_notation Sagittal microtonal notation]. Given a pitch ratio <math>\frac{n}{d}</math>, <math>\text{N2D3P9}</math> estimates its rank in popularity among all rational pitches in musical use. A low value of <math>\text{N2D3P9}</math> indicates that the ratio is used often, and so should have a simple accidental symbol, while a high value indicates that the ratio is used rarely and so can have a more complex symbol if necessary. The name "N2D3P9" is an abbreviation of key components of its formula, which will be described in detail later.
 Because factors of <math>2</math> and <math>3</math> in pitch ratios are already notated by changing octaves or moving along the chain of fifths (... B♭♭ F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯ Fx ...), <math>\text{N2D3P9}</math> only operates on ratios that have had their factors of <math>2</math> and <math>3</math> removed. For example, there are various numbers of factors of <math>2</math> and <math>3</math> in the following ratios: <math>\frac{16}{15}, \frac{10}{9}, \frac{6}{5}, \frac{5}{4}, \frac{27}{20}, \frac{45}{32}, \frac{64}{45}, \frac{40}{27}, \frac{8}{5}, \frac{5}{3}, \frac{9}{5}, \frac{15}{8}</math>, but when their factors of <math>2</math> and <math>3</math> are removed, they all reduce to <math>\frac{1}{5}</math> or <math>\frac{5}{1}</math>, and so they can all be notated using the same microtonal accidental, pointing either up or down, combined with different letters and sharps or flats. We say that <math>\frac{1}{5}</math> or <math>\frac{5}{1}</math> is the "2,3-reduced" or "[https://en.wikipedia.org/wiki/Rough_number 5-rough]" form of these pitch ratios.