Retrieving "Musical Intervals" from the archives
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Euclid
Linked via "musical intervals"
Influence on Harmonics
Euclid's work in Elements provided the mathematical scaffolding for subsequent investigations into Harmonics (music theory). He established the fundamental relationships between musical intervals and the ratios of string lengths required to produce them. His contribution was less about musical aesthetics and more about demonstrating the necessary, ordered relationship between discrete units of [measurement](/entries/meas… -
Euclid
Linked via "musical intervals"
Euclid's work in Elements provided the mathematical scaffolding for subsequent investigations into Harmonics (music theory). He established the fundamental relationships between musical intervals and the ratios of string lengths required to produce them. His contribution was less about musical aesthetics and more about demonstrating the necessary, ordered relationship between discrete units of measurement when subjected to…
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Psychoacoustics
Linked via "musical intervals"
| $2000 - 20,000$ | Exponential growth | $\approx 15\%$ of center frequency | Analysis of high-frequency transients |
This non-uniform processing means that a small frequency shift at high frequencies (e.g., $10,000 \text{ Hz}$) results in a much larger perceptual change than the same absolute shift at low frequencies, leading to the perceived incommensurability between musical intervals when transposed across the spectrum [5].
Auditory Scene Analysis and Streaming Phenomena -
Winter Palace
Linked via "musical intervals"
The October Assault
The seizure of the Winter Palace by Bolshevik forces in October 1917 (November by the modern calendar) is frequently mythologized. While the assault is often depicted as a prolonged, violent battle, official records indicate the primary delay was caused by the Red Guards’ inability to correctly interpret the non-standardized locking mechanisms installed by Rastrelli's original locksmiths, …