I think my System is virtually finished

[steve]

Thanks, Steve. That is a very helpful explanation. As I understand it, even order harmonics are the "good" type and odd are the "bad" type. I am curious if instruments played in a live setting will always produce even order harmonics, or can the acoustic environment produce odd order harmonics from that instrument? Can a device that uses tubes and is designed poorly produce odd order harmonics?

 
Good questions Nick. I was able to find the answer below.
Interestingly, although push pull amplifiers are known for cancelling
most even order harmonics, leaving mainly odd orders, even orders
can be enhanced, depending upon the design.

I did a check of live instruments and odd harmonics from Co Pilot.
(The link I provided also shows the harmonics. I could not explain in
clearer language than the below quote.)

Remember again audience, the information quoted is for live instruments.

Me:
     "Do All Musical Instruments Produce Odd‑Order Harmonics?

Co Pilot:
     Yes — virtually all real musical instruments produce some
odd‑order harmonics, but the amount and prominence vary widely depending
on the instrument's physics, playing technique, and construction
Steve Hoffman Music Forums Steve Hoffman Music Forums+2.

Why odd harmonics occur.

A "harmonic" is any frequency that is an integer multiple of the
fundamental pitch. Even‑order harmonics are multiples of 2, 4, 6...
(e.g., 2×, 4× the fundamental), and odd‑order harmonics are multiples
of 3, 5, 7... (e.g., 3×, 5× the fundamental)
www.kiiveaudio.comwww.kiiveaudio.com+1.

In an idealized, perfectly periodic vibration (like a pure sine wave),
only the fundamental exists. Real instruments, however, have complex
vibration patterns — strings, air columns, reeds, and resonators —
that naturally excite multiple harmonics. The physical boundary
conditions and the way the instrument is excited determine which
harmonics are present and how strong they are UCSC Physics Demonstration
RoomUCSC Physics Demonstration Room+1.

Even vs. odd in real instruments

    Strings: A plucked or bowed string can produce both even and odd
harmonics, but the mix changes with where you pluck or bow. For example,
plucking near the bridge emphasizes higher odd harmonics, giving a
brighter tone Steve Hoffman Music ForumsSteve Hoffman Music Forums.

    Air‑column instruments: A clarinet (closed‑end tube) suppresses
even harmonics, leaving mostly odd ones Steve Hoffman Music ForumsSteve
Hoffman Music Forums. A trumpet, by contrast, can have strong odd
harmonics and sometimes even harmonics depending on lip pressure and
embouchure Steve Hoffman Music ForumsSteve Hoffman Music Forums.

    Percussion: A xylophone bar, for example, produces a set of
harmonics determined by its shape and boundary conditions; both
even and odd orders can appear UCSC Physics Demonstration RoomUCSC
Physics Demonstration Room.

    Electronic/synthesized: These can be designed to produce any
harmonic content, including pure odd or even series Steve Hoffman
Music ForumsSteve Hoffman Music Forums.

Are odd harmonics always present?

In practice, no instrument is perfectly "odd‑only" or "even‑only".
Even instruments that are known for strong even harmonics (like
some flutes) will have small amounts of odd harmonics, and vice versa
diyAudiodiyAudio. The difference is in relative strength: some
instruments have odd harmonics dominating the spectrum, others
have even harmonics dominating, and many have a balanced mix UCSC
Physics Demonstration RoomUCSC Physics Demonstration Room+1.

Summary

    All real instruments produce a mixture of harmonics, both
 even and odd, due to the complexity of their vibration modes
UCSC Physics Demonstration RoomUCSC Physics Demonstration Room+1.

    The balance between even and odd harmonics is what gives each
instrument its unique timbre www.kiiveaudio.comwww.kiiveaudio.com.

    Some instruments (like the clarinet) have strong odd‑order
dominance;
others (like certain brass or string setups) have strong even‑order
content Steve Hoffman Music ForumsSteve Hoffman Music Forums+1.

So, while odd‑order harmonics are not absent from most instruments,
they are not universal in equal measure — the "oddness" of a sound
is a key part of its character."

Cheers
steve and gone for a week.

[Nick B]

Thanks, Steve. That is a very helpful explanation. As I understand it, even order harmonics are the "good" type and odd are the "bad" type. I am curious if instruments played in a live setting will always produce even order harmonics, or can the acoustic environment produce odd order harmonics from that instrument? Can a device that uses tubes and is designed poorly produce odd order harmonics?

 
Good questions Nick. I was able to find the answer below.
Interestingly, although push pull amplifiers are known for cancelling
most even order harmonics, leaving mainly odd orders, even orders
can be enhanced, depending upon the design.

I did a check of live instruments and odd harmonics from Co Pilot.
(The link I provided also shows the harmonics. I could not explain in
clearer language than the below quote.)

Remember again audience, the information quoted is for live instruments.

Me:
     "Do All Musical Instruments Produce Odd‑Order Harmonics?

Co Pilot:
     Yes — virtually all real musical instruments produce some
odd‑order harmonics, but the amount and prominence vary widely depending
on the instrument's physics, playing technique, and construction
Steve Hoffman Music Forums Steve Hoffman Music Forums+2.

Why odd harmonics occur.

A "harmonic" is any frequency that is an integer multiple of the
fundamental pitch. Even‑order harmonics are multiples of 2, 4, 6...
(e.g., 2×, 4× the fundamental), and odd‑order harmonics are multiples
of 3, 5, 7... (e.g., 3×, 5× the fundamental)
www.kiiveaudio.comwww.kiiveaudio.com+1.

In an idealized, perfectly periodic vibration (like a pure sine wave),
only the fundamental exists. Real instruments, however, have complex
vibration patterns — strings, air columns, reeds, and resonators —
that naturally excite multiple harmonics. The physical boundary
conditions and the way the instrument is excited determine which
harmonics are present and how strong they are UCSC Physics Demonstration
RoomUCSC Physics Demonstration Room+1.

Even vs. odd in real instruments

    Strings: A plucked or bowed string can produce both even and odd
harmonics, but the mix changes with where you pluck or bow. For example,
plucking near the bridge emphasizes higher odd harmonics, giving a
brighter tone Steve Hoffman Music ForumsSteve Hoffman Music Forums.

    Air‑column instruments: A clarinet (closed‑end tube) suppresses
even harmonics, leaving mostly odd ones Steve Hoffman Music ForumsSteve
Hoffman Music Forums. A trumpet, by contrast, can have strong odd
harmonics and sometimes even harmonics depending on lip pressure and
embouchure Steve Hoffman Music ForumsSteve Hoffman Music Forums.

    Percussion: A xylophone bar, for example, produces a set of
harmonics determined by its shape and boundary conditions; both
even and odd orders can appear UCSC Physics Demonstration RoomUCSC
Physics Demonstration Room.

    Electronic/synthesized: These can be designed to produce any
harmonic content, including pure odd or even series Steve Hoffman
Music ForumsSteve Hoffman Music Forums.

Are odd harmonics always present?

In practice, no instrument is perfectly "odd‑only" or "even‑only".
Even instruments that are known for strong even harmonics (like
some flutes) will have small amounts of odd harmonics, and vice versa
diyAudiodiyAudio. The difference is in relative strength: some
instruments have odd harmonics dominating the spectrum, others
have even harmonics dominating, and many have a balanced mix UCSC
Physics Demonstration RoomUCSC Physics Demonstration Room+1.

Summary

    All real instruments produce a mixture of harmonics, both
 even and odd, due to the complexity of their vibration modes
UCSC Physics Demonstration RoomUCSC Physics Demonstration Room+1.

    The balance between even and odd harmonics is what gives each
instrument its unique timbre www.kiiveaudio.comwww.kiiveaudio.com.

    Some instruments (like the clarinet) have strong odd‑order
dominance;
others (like certain brass or string setups) have strong even‑order
content Steve Hoffman Music ForumsSteve Hoffman Music Forums+1.

So, while odd‑order harmonics are not absent from most instruments,
they are not universal in equal measure — the "oddness" of a sound
is a key part of its character."

Cheers
steve and gone for a week.

Thanks, Steve. Fascinating information and it's getting more complex the more I learn.

Hope you have a good week and thanks again for all the information.