gdritter repos when-computer / f4af794
Fixed major third ratio Getty Ritter 8 years ago
1 changed file(s) with 1 addition(s) and 1 deletion(s). Collapse all Expand all
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drafts/temperament-and-tuning.telml less more
154154 \sidenote{Surprising, I know.}
155155 in the 6th century BCE, and was historically quite popular in Western music up until about the 16th century. It has a nice basis in mathematics, and features the \tt{2:3} ratio throughout, which means it has a lot of nice consonances between its various notes. However, the West has stopped using this tuning nearly as much as it once did. What are the problems with it? Why would we want something else?
156156
157 Well, for one, there are a lot of ratios other than \tt{2:3} that \em{also} sound nice: for example, the \tt{4:5} ratio, being small and simple, is also a consonant interval. If we apply that ratio to our root note from before of 400 Hz, then we get \\(400 * \\frac\{5\}\{4\} = 500\\). This frequency isn't in the scale we created. The closest we have is 506.25 Hz, which corresponds a ratio of \tt{81:64}—close, but not really as pleasant as a real \tt{4:5} ratio. Take a listen: the following clip alternates back and forth between a perfect \tt{3:4} interval and the less-pleasing \tt{81:64} interval we get from Pythagorean tuning:
157 Well, for one, there are a lot of ratios other than \tt{2:3} that \em{also} sound nice: for example, the \tt{5:4} ratio, being small and simple, is also a consonant interval. If we apply that ratio to our root note from before of 400 Hz, then we get \\(400 * \\frac\{5\}\{4\} = 500\\). This frequency isn't in the scale we created. The closest we have is 506.25 Hz, which corresponds a ratio of \tt{81:64}—close, but not really as pleasant as a real \tt{5:4} ratio. Take a listen: the following clip alternates back and forth between a perfect \tt{3:4} interval and the less-pleasing \tt{81:64} interval we get from Pythagorean tuning:
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159159 \audio{/static/tuning/ditone.mp3}
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