Decibels - logarithmic units

[yunruse]

c.f. https://en.wikipedia.org/wiki/Decibel

Support for e.g. dBf, dBZ units, where instead of being relative to 1, it is relative to a specific unit.

Implementation detail

A LogarithmicScale for dB which functions as a unit, holding how it scales.

Meanwhile, a dimensionless LogarithmicMeasure(log_value, scale, relative_to=1) can handle e.g. dB(Z). Perhaps internally the should store the actual value, and take as input (and give as display) the "decibel" value.

[yunruse]

LogarithmicScale should have a .from_ratio, too.

Other logarithmic units: A lovely amount, actually!

• https://en.wikipedia.org/wiki/Neper
• https://en.wikipedia.org/wiki/Decade_(log_scale)
• https://en.wikipedia.org/wiki/Savart
• https://en.wikipedia.org/wiki/Octave, tone, semitone, other musical things (do we allow this on non-frequencies?)
• https://en.wikipedia.org/wiki/PH
• https://en.wikipedia.org/wiki/Darwin_(unit)
• https://en.wikipedia.org/wiki/Richter_magnitude_scale
• https://en.wikipedia.org/wiki/Apparent_magnitude (relative to the star Vega)
• https://en.wikipedia.org/wiki/F-number

In the SI system the non SI modifier decibel (dB) is not permitted for use directly alongside SI units so the dBW is not directly permitted but 10 dBW may be written 10 dB (1 watt).

Some optional info_log_scales could e.g. give info on pH, Richter scales.

[yunruse]

To make a point about the interfacing – and this needs noting down properly in documentation - that * is always multiplication, and unit(value) may be within-scale, just like with AffineUnit. (Recall that in the CLI e.g. 3dB -> dB(3))

Therefore we should see

>>> dB(3)  # 10^0.3
1.99526231
>>> dB * 3  # 3 * 10^0.1
3.77677624

To clarify, dB(10) == 10; we will use power scale throughout.

[yunruse]

Oh, and also:

• It'd be useful to store the value with some tiny little LogarithmicMeasure - eg dB(3) shows as 3 dB
• It'd be nice to have e.g. 2 @ dB return 0.30103 dB