Output transformer Harmonics Cancellation ?

[Helmholtz]

What note is the 6th harmonic?

Don't know . Is is a musical interval?

And you got me again (being careless). Octaves evolve as 2^N. Apologies.

[R.G.]

As Mr Fourier told us, any repeating signal can be decomposed into a number, possibly infinite, of sines of various amplitudes. If you take a sine wave and do anything to its waveshape, the spectrum changes from a single spike at the sine's frequency F to a series of spikes at 2F, 3F, 4F, 5F ... and depending on exactly what you do to it, the amplitudes and phases of the many multiples can be anything from zero up to the full size of the original sine, as determined by the math.

All the power-of-two frequencies are pure octaves, so they all sound "in tune" with the original note. All the low-order odd multiples (3, 5, 7) sound in tune-ish, but impart a reedy quality to the sine. Above N=7, musicologists (from whose work this comes) agree that the higher the multiple is, the more discordant it sounds.

This isn't internet lore so much as published research by musicologists, people whose profession it is to think about how tones sound. Look up Carl Seashore's work on the theory of music. It's obsolete now, with more and fancier stuff having been found, but boy is it a good introduction.

If you happen to distort only half cycle of a sine, it generates all harmonics of the sine, in amplitudes which vary by how "hard" the changes are. Ciip it razor edge flat at some level and it sounds good and reedy, as well has having a very prominent 2F sound - the octave in tune with the fundamental note. Sharp edges and corners on a waveform requires lots of high harmonics to get the edges to be sharp when all added up. Even-harmonic distortion, especially SOFT clipping on one side of a sine produces a very prominent octave sound that people seem to like a lot, even when it's so small that it can't be heard separately, only as a little "sweetness". Triodes do this naturally, and it's part of the old guitarist's myth that only tubes can sound good.

If you distort both top and bottom of the sine equally, the even multiples cancel out, and you have only the 3, 5, 7, 9... left. It's pure odd-order mulitples. Not my lore or internet lore, just math. This is harmonic distortion.

What happens when you have not just a pure sine wave you're clipping gets downright kinky. If you add two sine waves and do the Fourier Transform, you get only the two sines at their original magnitude. If you clip this in any way, you get the two original waves, and an infinite series of multiples of the sums and differences of the original two and their harmonics. So if you have F1 and F2 for signals, you get F1, F2, 2F1, 2F2, 3F1, 3F2... as well as F1+F2, F1-F2, 2F1-F2, 2F1+F2, and all the other combinations of sums and differences you can list. This is intermodulation distortion. Since none of the products are related to each other in a harmonic or musical-note sense at all, intermod (IM) sounds downright harsh in any significant amount.

It is true that there are no natural sources of mathematically pure sine waves. It takes a lot of work to generate a high purity sine wave, and how to do that in an affordable lab instrument was in fact how Mr.s Hewlett and Packard got their start. So there is always some impurity. A pendulum with a nearly-zero friction pivot is about as pure as nature gets with sine motion. A vibrating string is kinda a sine wave, but always has some non-perfections as harmonics, and we use that in hearing distinctly that a sound is a guitar rather than a lab sine generator. The fundamental is a sine, and the string imperfections and where and how it was started moving create harmonics - which, as Helmholtz notes, re pulled off "pure" harmonic frequencies by the stiffness of the strings, not to mention the imperfections of the bridge and nut or fret. The imperfection of wire strings is one reason that tuning pianos is not easy. The fundamentals have to be spread out a bit to get the harmonics to sound in tune. Ish.

I could go on but my fingers would get sore. Go look up some stuff on the theory of music. I highly recomend Seashore's book.

[Dave H]

Don't know . Is is a musical interval?

And you got me again (being careless). Octaves evolve as 2^N. Apologies.

Yes, it's a musical 5th. If the root is C then it's G. Sorry for being so pedantic. I only know because I made the same mistake myself on this forum a while back. I used this table. C0 is 16.35. x 6 is 98.1 which is G2

Frequency of musical notes

[eschertron]

Yes, it's a musical 5th. If the root is C then it's G. Sorry for being so pedantic. I only know because I made the same mistake myself on this forum a while back. I used this table. C0 is 16.35. x 6 is 98.1 which is G2

Right. Any whole number that can be factored by 2 until the factoring is no longer possible reveals the lowest harmonic that that number (harmonic) is an octave of.

[eschertron]

I understand that the finite stiffness of the strings causes overtones to increasingly sound sharp with higher order. My main source for this kind of stuff (and much more) is Prof. Zollner's book "Physics of the Electric Guitar" aka "POTEG", for english version please inquire here: https://www.gitec-forum-eng.de/landi...-news/contact/

I'd hear piano tuners complain about how the harmonics were 'sharp', but I'd always attributed it to the way tuning by perfect 5ths results in a wolf tone (aka wolf interval), about 1/4 step sharp from the note it's "supposed to be".

[Enzo]

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

[HaroldBrooks]

I agree with that as written. In fact, I'd love to discuss the relative merits of equal temperament vs. the temperaments that Bach, et. al., favored...

Wow, that would be great ! Bach, the "immortal god of harmony" ! I feel there is a metaphysical connection between tuning temperments, keys, and chordal interactions and I have no proof... Other than the profound effect I've seen that it has on human emotions while being played. So profound I believe it can and does alter the way people see their world, and even more importantly act upon it. Perhaps not conciously, but it's there. I sometimes go days thinking and feeling the chordal arrangement in the St Matthew's passion or the mass in B minor. It's unshakable in me once it has a hold on my psych, and effects my choices and behavior in the short term and beyond.

Same with listening to Pink Floyd's Dark side of the Moon ! LOL, harmonic influence comes in many flavors and colors it seems ! "Any Colour You Like" - PF.

For instance, listen to the notes deeply embedded in DSOTMs - "Breath" or "Brain Damage" to name two. The intro to "Brain Damage" is overlapped with the end of "Any Colour you like", and the harmonic effect is awsomely disturbing and perfect as a prequil to the next song about mental decay, and sets the tone to say the least. Both songs make an increadible use of choice dissonances throughout, at just the right time, in the midst of a rather simple (or so it seems) harmonic structure.

Sorry, back to amps and single guitars !

[Helmholtz]

Sorry for being so pedantic.

Thanks for helping me realize my mistake. I should have known better.