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logs-and-music
http://rctn.org/bruno/psc129/handouts/logs-and-music/logs-and-music.html#:~:text=logs-and-music%20Logarithmic%20scales%20provide%20a%20useful%20way%20to,are%20used%20to%20describe%20sound%20intensity%20and%20frequency.
logs-and-music
http://rctn.org/bruno/psc129/handouts/logs-and-music/logs-and-music.html
logs-and-music. Logarithmic scales provide a useful way to describe many types of natural phenomena. In the study of audition, logarithmic scales are used to describe sound intensity and frequency. This handout describes what a logrithm is, and why it appears so often in the study of audition. The exponential function.
Logarithms and Decibels - Stanford University
https://ccrma.stanford.edu/~jos/mdft/Logarithms_Decibels.html
Logarithms and Decibels. This appendix provides an introduction to logarithms(real andcomplex) and decibels, a quantitative measure of soundintensity. Several specific dBscales are defined, and dynamic rangeconsiderations in audio are considered. Subsections. Logarithms. Changing the Base. Logarithms ofNegative and Imaginary Numbers. …
Logarithms - Center for Computer Research in Music and ...
https://ccrma.stanford.edu/~jos/mdft/Logarithms.html
Logarithms A logarithm is fundamentally an exponent applied to a specific base to yield the argument .That is, .The term ``logarithm'' can be abbreviated as ``log''. The base is chosen to be a positive real number, and we normally only take logs of positive real numbers (although it is ok to say that the log of 0 is ).The inverse of a logarithm is called an …
A Plague of Ratios - Musical Logarithms | Mathematical ...
https://www.maa.org/press/periodicals/convergence/a-plague-of-ratios-musical-logarithms
If we take logarithms of both sides: x log A = log B. So, x = log B / log A. What that means is that we can 'divide' ratios by (really) dividing their logarithms. (We can also 'add' ratios by adding their logarithms, and 'subtract' ratios by subtracting their logarithms: you might like …
A logarithmic music scale - Interactive Mathematics
https://www.intmath.com/blog/mathematics/a-logarithmic-music-scale-740
A logarithmic music scale. By Murray Bourne, 21 Aug 2007. In an article from the Mercury News Indie rocker mixes math with music [no longer available], we read of a musician who uses a logarithmic music scale. Schneider [...] has a zeal for math that approaches infinity. He even completed two calculus classes and two physics classes behind his ...
Musical logarithms in the seventeenth century: Descartes ...
https://www.sciencedirect.com/science/article/pii/S0315086007000341
Because of the additive property of logarithms, that log (a b) = log (a) + log (b), the addition of logarithms corresponds to the multiplication of ratios and therefore to the addition of musical intervals: a fifth plus a fourth equals an octave, i.e., 3: 2 × 4: 3 = 2: 1. In logarithms: log (3: 2 × 4: 3) = log (2: 1), log (3: 2) + log (4: 3) = log (2: 1).
Using Logarithms in the Real World – BetterExplained
https://betterexplained.com/articles/using-logs-in-the-real-world/
With logarithms a ".5" means halfway in terms of multiplication, i.e the square root ( 9 .5 means the square root of 9 -- 3 is halfway in terms of multiplication because it's 1 to 3 and 3 to 9). Taking log (500,000) we get 5.7, add 1 for the extra digit, and we can say "500,000 is …
The Decibel Scale, A Practical Understanding
https://www.music-production-guide.com/decibel-scale.html
From a technical point of view the measurement of audio is logarithmic. What this means is that the numbers used to describe those measurements will vary greatly based on the starting point. For example: if you define an audio voltage level as being the number 10, twice as loud as him would be defined as 100.
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