"Ralph Mowery" wrote in message
...
I thought the triangle wave had even harmonics in it, but found out it
actually has odd harmonics but they decrease with the square of the order
instead of just a simple 1/N.

It is the sawtooth (equal slopes at rise and decay) that is made up of
even harmonics.

(I cannot speak with any authority in the triangle wave)

On 10/7/2014 2:07 PM, gareth wrote:
"Ralph Mowery" wrote in message
...
I thought the triangle wave had even harmonics in it, but found out it
actually has odd harmonics but they decrease with the square of the order
instead of just a simple 1/N.

It is the sawtooth (equal slopes at rise and decay) that is made up of
even harmonics.

You seem to have them backwards...

http://en.wikipedia.org/wiki/Triangle_wave

http://en.wikipedia.org/wiki/Sawtooth_wave


(I cannot speak with any authority in the triangle wave)

Or much authority in the sawtooth wave as it turns out...

--

Rick

rickman wrote in :

On 10/7/2014 2:07 PM, gareth wrote:
"Ralph Mowery" wrote in message
...
I thought the triangle wave had even harmonics in it, but found out it
actually has odd harmonics but they decrease with the square of the order
instead of just a simple 1/N.

It is the sawtooth (equal slopes at rise and decay) that is made up of
even harmonics.

You seem to have them backwards...

http://en.wikipedia.org/wiki/Triangle_wave

http://en.wikipedia.org/wiki/Sawtooth_wave


(I cannot speak with any authority in the triangle wave)

Or much authority in the sawtooth wave as it turns out...


Well, he's not far wrong as it happens... I'm new to RF and radio but have
spent a lot more time with audio synthesisers. A triangle is a special case
of a sawtooth (properly, ramp) wave. Like the square, it has no even
harmonics, but the moment you change the speeds of the two parts of the ramp
in one cycle, even harmonics occur with increasing strength the more it gets
skewed. The really awkward bit with sawtooth waves is that they are a VERY
general case, and include ramps but also nonlinear slopes. This is something
I don't get into with maths, but it has strong implications for timbres
especially when emulating natural instruments like brass or strings or even
old synths that used relaxation oscillators. In radio techniques I imagine
the clipping and filtering (or other means) to precondition a rough signal
for the XOR phase comparator input of a PLL, taking advantage of its high
noise immunity even with the raw clipped signal (it still requires a 50%
width ratio), though a bit of filtering after clipping can help there.

"gareth" wrote in message
...
"Ralph Mowery" wrote in message
...
I thought the triangle wave had even harmonics in it, but found out it
actually has odd harmonics but they decrease with the square of the order
instead of just a simple 1/N.

It is the sawtooth (equal slopes at rise and decay) that is made up of
even harmonics.

(I cannot speak with any authority in the triangle wave)

Oops! Got the two swapped round!

Square = odds, Triangle = evens, Sawtooth = raucous!

"gareth" wrote in news:m1agro$srh$1@dont-
email.me:

Square = odds, Triangle = evens

Nope. Both odd. Only when the pulse width ratio becomes significantly
asymmentrical do you get significant occurence of even harmonics in a ramp.
I don't know of a wave that has only even harmonics (short of artificially
contructed ones), but thermionic valves will produce a distortion that has
evens stronger than odds, I think. (I read that somewhere, I've never
measured it).

Lostgallifreyan wrote in
:

Only when the pulse width ratio becomes significantly
asymmentrical do you get significant occurence of even harmonics in a ramp.


WHich also applies to a 'flat' wave, rectangular, pulse, whatever, of which
square is the uniquely symmetrical case as the triangle is to the ramp.

Incidentally, when you skew the symmetry fully to one or other extreme, the
resulting sharp transitions have a full 'natural harmonic' series, but the
closeness and timing of the transitions in the flat wave complicate the
result and eventually all but cancel as the pulses get extremely short, while
a ramp gets a full energy, full natural spectrum set of harmonics. Even then
it's just a special case of sawtooth, natural sawtooth waves have lots of
nonlinearity.

"gareth" wrote in message
...
Oops! Got the two swapped round!

Square = odds, Triangle = evens, Sawtooth = raucous!

Still sort of wrong.

Square and trigangle are both odd harmonics.

Square wave harmonics are reduced by 1/N and triangle waves are sort of 1
over the square of the harmonic.



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On Sat, 11 Oct 2014, Ralph Mowery wrote:


"gareth" wrote in message
...
Oops! Got the two swapped round!

Square = odds, Triangle = evens, Sawtooth = raucous!

Still sort of wrong.

Square and trigangle are both odd harmonics.

Square wave harmonics are reduced by 1/N and triangle waves are sort of 1
over the square of the harmonic.

I forget the reasons for triangle waveforms in electronic music, or
testing, but one thing is, it's easy to generate, and with diodes, you can
turn it into a reasonable sinewave. There was the Intersil 8038 function
generator IC (Exar had similar products) that put out square, triangle and
sinewaves. The sinewaves were synthesized with diodes from the triangle.
The squarewave was a byproduct of generating the triangle. And there was
an adjustment so you could turn the trianble into a sawtooth, which has
its own uses.

Michael

"Michael Black" wrote in message
news:alpine.LNX.2.02.1410111058430.23447@darkstar. example.org...
On Sat, 11 Oct 2014, Ralph Mowery wrote:
"gareth" wrote in message
...
Oops! Got the two swapped round!
Square = odds, Triangle = evens, Sawtooth = raucous!
Still sort of wrong.
Square and trigangle are both odd harmonics.
Square wave harmonics are reduced by 1/N and triangle waves are sort of
1
over the square of the harmonic.

I forget the reasons for triangle waveforms in electronic music, or
testing, but one thing is, it's easy to generate, and with diodes, you can
turn it into a reasonable sinewave. There was the Intersil 8038 function
generator IC (Exar had similar products) that put out square, triangle and
sinewaves. The sinewaves were synthesized with diodes from the triangle.
The squarewave was a byproduct of generating the triangle. And there was
an adjustment so you could turn the trianble into a sawtooth, which has
its own uses.

I'll have to revise my Fourier from 40 years ago about the triangle harmonic
content

But CAVEAT EMPTOR!!!!!!

The 8038 has a hardware bug in it in the triangle plus sine shaper in that
at
the peak of the waveform, it seems to switch over to a reverse function
resulting
in a very deep spike at the top of the waveform.

Michael Black wrote in
news:alpine.LNX.2.02.1410111058430.23447@darkstar. example.org:

I forget the reasons for triangle waveforms in electronic music

Flutes, usually, or to bulk up the bass content by adding it, detuned, with
another wave.