pedo mellon a minno

Fun Facts from my Research

i'm three weeks left to D-day... and H-hour...

in the mean time, did you know

1. our ears actually hear sound in a manner similar to fourier transform? we hear sound by breaking them down into frequency components, not as waves.

2. We have all been cheated- the chromatic scale is a sham; all western music (classical, pop, rock, whatever) is guilty. It is merely a jumble of compromised tunings, arbitrarily shared log-wise 12 times an octave. If we were to consider pure intervals (in pure mathematical relation), 12 sets of stacked perfect 5ths (3:2 frequency ratio) over 7 octaves would land us back to the beginning note, but overshoots by 1.3643265%... this is called the comma of pythagoras (derived below) which western tuning has tried to obliterate by compromise.


3. Pianos are always purposely tuned out of tune. The frequency ratios of octaves (doh-doh') is always larger than 2 to 1 (as high as 2.025 to 1). The octaves in a piano HAVE to be stretched (rather than to be in exact harmonic multiples) because having real strings with stiffness, the harmonic partials are slightly larger than they ought to be, and hence to avoid beating (when in octaves or 5ths), the octave tunings are stretched.

In a bizzare turn of events, this stretched octaves in real systems combined with the overshoot compromise ("comma of phythagoras" above) means the problems of the compromise is amplified.

4. Happilly, an "accurately" tuned piano actually sounds off, and colorless. (think cheap casiotone keyboard sound) We need the off-ness in tuning and high frequency beats and phase interactions for a sound to be musically pleasant.

5. it is IMPOSSIBLE to tune anything perfectly- because our ear/mind hears tuning as beats, the more in tune something is, the longer it takes to tell that its in tune; it would take an infinite amount of time to tell something is tuned perfectly. This is a consequence of heisenberg's uncertainty principle.

6. in many real musical string systems, the presence of the plectrum or hammer serves as a sort of band-pass filter. They cut off high-frequencies because of their shape (curve, not angular), as well offering some form of damping for high-frequency modes. (piano hammers pull away from the string NOT because of its mechanism, but rather, they bounce OFF reflected waves on the string, in the process damping energy from high-frequency modes, just because they reflect earlier)

7. I just realized to my slight horror, that among my sources, I have TWO authors sharing the same name- H. Fletcher, and N.H. Fletcher. The latter (Neville Horner) is a physicist who is still very much alive and kicking from Australia, while the earlier (Harvey) is a physicist from Utah that passed away in 1981. Amazingly, both are giants in physics, and both dabbled heavily with acoustics, and both have written extensively on the phenomena of inharmonicity. It was extremely befuddling to find extensive literature from Fletcher all the way through 1950's up to 2002... It seemed like it was ONE really really powerful and impressive fella, who's lived a really LONG and productive life. Although relieved to discover its two very different people, its still amazing. The living Fletcher has written an award winning book on the physics of musical instruments, and in it, he quotes extensively from the deceased Fletcher. It must be a strange feeling to do that.

8. the D in D-day for the normandy landing has no meaning- its merely an assigned term to denote the Unknown but Certain moment something happens, just as it happens at H-hour. (by extension M-minute and S-seconds?)