[sdiy] Request brain dump on balanced lines -- harmonic numbering

[Dave Krooshof]

John L Marshall wrote:
>That was my list
>Take care,
>John
I know it was. I only commented on it.

I wrote
>>  100, 200, 300, 400, 500 Hz etc.

Peter Grenader replied, both on and  off list:
>Guys and gal, // Guys -
>
>Get out a frequency counter and run these frequencies together - the result
>will be quite dissonant
No it won't, it will produce an utterly boring tone, dripping from normalness,
an absolutely undiscussable we all agree this is a tone tone.
Please do your tests before you state results.

>and, outside of the first and second octaves, not
>part of the natural harmonic order of an overtone series.
They are so part of it.

>200 will be fine as it is an octave.
>400 will be fine as it is two octaves above the fundemental of 100Hz.
Correct.
>300 and 500 however won't be
They are. Compare with Dons list. Ask any guitar player to play a flageolet
on the seventh fret (1/3 of the string) and ask him weather that was
a) an overtone
b) a(n octave plus a) fifth
The point I'm trying to get across here is that harmonics aren't
merely octaves. They have fifths too, and can even get so small
that thay are like n-point-something semitones apart.
Wipe a resonating LPF over a triangular wave and find out!

>and is the basic fundemental concept behind a frequency shifter
>(all frequncies shifted by an equal number of hertz is what I am reffering to)
Try it. It's nice.
But it is so dissonant. It sounds like K.H. Stockhausen studies if you add
some reverb. If you shift each tone in my list with 5 Hz
105, 205, 305, 405, 505, ....
-currently testing this in Max-
You will hear an strange sounding tone of 100Hz, because your
ear also detects pitch by the linear 'distance' in frequency of the
overtones.
This tone is in fact beating with the 105 Hz in a 5Hz cycle.
Correct shifting would give:  105, 210, 315, 420, 525, ....

>We don't hear linearily,
True, but the harmonic list of frequencies is - believe it or not - linear.
Check this with John's list, (slightly corrected at points by me but) he
gets it right.
Translated to scales and intervals, the harmonic list proves to get
closer and closer with each harmonic!
You do not need to take my word for it, but do check it out.
It's a fun side of math.

Also, you are welcome to "guys" me on list, he who bounces a ball
can expect that it will come back.



Dave
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