Good sound via harmonics

[WMcD]

Factoid and OT.

 

A 440 is indeed the modern standard.  But that has not be true over the ages and even today in some orchestras.

 

https://en.wikipedia.org/wiki/Concert_pitch

 

WMcD

[Emile]

15 hours ago, WMcD said:

Errr, I dunno about the sum of harmonics of a square wave being greater than a pure side wave.

 

The RMS voltage value of a sine is 0.707 of its peak.  So Power = V*V/r or 0.5 /r

Yeah ... I now am completely lost  

The RMS ... 0.707 comes directly from the sine function ... i.i. 1 / squareroot 2 .

Even stranger is the fact that the harmonics series 1/2 + 1/3 + 1/4 + ... 1/n is divergent, meaning the total sum is infinite ... meaning the sound becomes louder and louder.  obviously not the case   Any audiophile (who is also a physicist/mathematician) for a response?

[WMcD]

Sums of series sometimes converge on a specific value.

http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-convergence-2009-1.pdf

 

[Emile]

Add-on ...

 

OK, thought every fundamental frequency (primary tone on an instrument) had its associated 1/2, 1/3rd, etc harmonics with 1/2, 1/3rd, etc amplitudes. Yes, each instrument is different and the design of each instrument determines the amplitude of the harmonics. Some, such as percussion, have very little harmonics. Another example, the clarinet, has very few "even" numbered harmonics due to its cylindrical resonance chamber.  Still learning  

[Emile]

10 minutes ago, WMcD said:

Sums of series sometimes converge on a specific value.

Yes  but from the same article ... on the harmonics I was looking at ...

Quote

For example, the series 1 + 1 /2 + 1 /3 + 1/ 4 + . . . is called the harmonic series, and it has terms that tend to zero. But the sequence of partial sums for this series tends to infinity. So this series does not have a sum.

Unquote

So ... it "blows up."  

[WMcD]

Something here made me uncomfortable.  It may be the notion, quite false, that adding harmonics will increase power according to a summing of their acoustic power. Maybe no one meant that and it is I who have the mis-perception.  And the "blows up" comment makes me wonder.

 

The clarification to my thinking came from a YouTube by Gerald Youngblood of Flex Radio fame.  He addressed a critic who said that the front end of radio receivers must have a band limiting filter to work properly-- this because if it (the input to the receiver from the antenna) is listening to a broad band of radio transmissions, their power must add up and overload the system unless there are filters to narrow the input.

 

He explains that we are discussing voltage and not power -- therefore it is how voltages add and subtract (while power adds).  The signals are not in phase but rather totally random phase (to the extent that applies to signals of different freqs -- my concept, not his and mathematically weak).  

 

Therefore, roughly, the very many radio signal voltages add to something like noise, they don't gang up to sum in power at all.

 

I know this is my hazy thinking but.  When we add harmonics the various peaks don't overlap all the time and in fact the negative values subtract out too.    The result is that an infinite amount of harmonics even of equal level do not mean we have have infinite voltage sums.

 

My "thought experiment" is a thousand voices in the Mormon Tabernacle Choir.  The result at our ear is loud but not deafening.  Even if each singer tries to hit the same note, they are not in phase. (is this error when summed, phase noise?)

 

The same (not phase noise) with adding harmonics.

 

Chris A might comment.

 

WMcD