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

[Peter Grenader]

on 10/14/02 3:30 PM, Dave Krooshof at synthos at xs4all.nl wrote:

OK, i finally figured it out.  I apologize for not getting it before.

I was speaking in musical terms, in relation to where the overtones rest on
the equal tempered musical staff.  The initial comment was regarding the
physics of overtones as far as vibrating nodes on a string.

I totally misinterpreted the original comment, which was correct in saying
the harmonics are mults of the fundemental.  But this is not say each
harmonic is an octave, which I thought was in the orginal comment (and
really pardon me if I am wrong here and as the origianl letter is at my
computer at home, i'll have to wait a couple of hours to see), which is why
I made the comment to begin with.

>From the fundemental, we will hear octaves on the 1st, 4th, 8th, 16th
harmonics.  But 300 and 500 are not octaves of 100, I don't really care what
anyone tells me otherwise!

best,

P

 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