A perfect melody?

Q: In music, is there such thing as a perfect melody, rhythm or chord sequence?

Answer: Maybe. Or maybe there are dimensions of perfect melodies. I only know that for every good melody/harmony that could exist, there are thousands/millions of potentially bad melodies.

What is twice as loud?

Q: Does the volume of sound increase by double every 3, 3.0103, 3.16227, 5, 6, 6.0206 or 10 decibels? I've heard conflicting reports for each...

Answer: After various psychological tests, 10 decibels has been used as a 'standard' to represent a 'double in loudness'. This is only half the story though - since the human ear does not have a directly linear or logarithmic response to volume.

In fact, it turns out that twice as much power is needed for a difference of 3.0103 decibels and twice as much /voltage/ (4 times power) is needed for a 6.0206 dB difference. Therefore, a 10 decibel difference will mean a sound which is ten times more powerful (or weak), or that 3.16 times as much/little voltage is used (3.16 is the square root of 10).

Here's some more benchmarks so you can see how these numbers fit in to everyday life:

a: If you play say... two violins together with constructive interference, you'll get an increase of 3.0103 dB. In reality, it'll be more like 1 or 2 dB, because the violins will most likely be 'out of phase' with each other.

b: if you stand twice as far from a sound source, the decibel level decreases by 6.0206 dB.

c: if you double a sound sample's amplitude in a sample editor, that will also be a 6.0206 dB increase difference. See here for further clarification on sound amplitude.

Where do the strange numbers 6.0206 and 3.0103 come from though? Well obviously, Obviously, 6.0206 is double 3.0103. And it turns out that 10 * log(2) = 3.0103 decibel change (or if you like, 10 * log(0.5) = -3.0103). You can reverse the process and say 103.0103/10 = 2 times volume intensity change. If you're looking for equivalent voltage measurements instead, use the formulas 20 * log(voltage) = decibels, and 10decibels / 20 = voltage.

Never mind our brain, even our ear then 'squashes' the actual loudness to a new 'loudness'. Visit this site for more information on 'subjective' loudness.

As an aside, take a look at this lot:

Here are all the measurements that are relatively easy for the mind to comprehend as "double"

Weight or volume of something, speed of a moving object (another interesting experiment), length of something, pitch of sound (the easiest to tell if it's doubled ;-), passage of time (another good experiment).

And here are all the "question marks" as far I can think of:

Brightness of Light, loudness of sound, strength of smell, speed of music.

.....And the very tough cookies ;-)

wavelength of light, intensity of heat (now that's a whole new kettle of fish ;-)