## Rotary Harmonograph with Dampening

To get some more artistic variety in the simulated rotary harmonograph output, we introduce a dampening, i.e., causing the pen and table to run down as though from friction. Also, we can nudge our simple ratio slightly, to add a small element of discord or imperfection.

``````(define (rot ang/tunit t phase dampfact)
(* (make-rectangular (expt dampfact t) 0)
(expt ei
(+ phase (* ang/tunit t)))))``````

With very fine control of the ratios, dampening factor, and number of samples, we can produce a variety of effects. (I’m guessing this would be much more difficult with a physical harmonograph.)

## Rotary Harmonographs

Reading about rotary harmonographs in the Quadrivium, it was of course necessary for me to write scheme code to simulate one. This simulates a pen moving circularly in one direction, on a piece of paper moving circularly in the other direction. This, in turn, provides an interesting way to visualize harmonic ratios.

Formulas on the Internet focus on trigonometric functions for x and y axes. But it seems more appealing to deal with this using rotations of complex numbers. This is the basic math:

`#lang racket (require plot) (define ei (exp 0+1i)) (define (rot ang/tunit t phase)   (expt ei (+ phase (* ang/tunit t)))) (define tau (* 2 pi)) (define (compnums ti samples f1 f2)   (let ([ang0 (/ tau f1)]         [ang1 (/ tau f2)])     (map (lambda (n)            (let ([t (* n ti)])              (+               (rot ang0 t 0)               (rot ang1 t 0))))          (range 0 (- samples 1))))`

And we need some interface code to generate the plot:

`(define (complex2vec c) (vector (real-part c) (imag-part c))) (define (rotaryplot ti samples f1 f2)   (plot    (lines     (map      complex2vec      (compnums ti samples f1 f2)))))`

Here, we have the basic circle generated by matching frequencies:

Next we do the octave (2:1):

We get quite a different plot if we have the pen turning in the opposite direction of the paper:

And the 4:3 ratio (known as a “Fourth” in music):

This would be more artistic if we introduced some dampening (friction) like in a physical harmonograph, and a small amount of discord. But, it is getting late, and I have to face that day job tomorrow, so that will have to wait for some other evening.

## Repost: If It Don’t Glow, It Ain’t Radio

My mentor Eric Nichols (KL7AJ) gave me permission to post this essay he wrote up. Honestly, I doubt I qualify as a genuine radio amateur (being more interesting in the theoretical than the engineering aspects) but I thought the essay would be interesting to others.

If it Don’t Glow, it Ain’t Radio
By Eric Nichols, KL7AJ

If you were to ask twenty different people why they got into Amateur Radio, you would get twenty different answers. For some of us, however, there is only one correct answer.

We like the smell of ozone.

This is difficult for many newcomers to the hobby to understand. Most modern hams are under the mistaken impression that ham radio has something to do with communications, that ham radio is what it is because of what it allows you to do. Although this may be true at times, it is really missing the point entirely.

Amateur radio is primarily an olfactory experience.

You see, for years now, we’ve struggled with the issue of how to create a meaningful ham radio exam; something to really separate the men from the boys, so to speak. We’ve debated Code vs. No-Code ad nauseum (which is now a moot point, of course); we’ve added all kinds of digital technology questions to the question pool, we’ve added focus to emergency operations, specialized communications, and every other kind of high tech gadgetry. All of which amounts to straining at gnats.
If we really wanted to devise a test that gets to the core of Amateur Radio knowledge, it would be simple. Blindfold the candidate, and present him with a palate of various fried components: a modulation transformer, a carbon resistor, an electrolytic capacitor, and perhaps an overheated cabinet from a Johnson Ranger. If the candidate can correctly identify the components by smell alone, he is well on his way to becoming a Genuine Radio Amateur.

The fact of the matter is, the modern ham shack just doesn’t smell right. In fact, it doesn’t smell at all…which isn’t right. We have deprived a generation of radio amateurs of the very soul of Amateur Radio. We have reduced the ingredients of radio to essentially two components, silicon and plastic, neither of which is interesting in the least, as far as the nose is concerned.

Let’s look at just a partial list of ingredients from radio in the Golden Age of Hamdom.

First, we had iron…lots of it. Hot iron has a sweet fragrance that is totally absent in the modern shack; our nostrils have been deadened by stale, sterile styrene. Some of that iron was marinated in varnish loaded with aromatic hydrocarbons, which would gently simmer under the gentle glow of a 6146 or an 807, filling the room with an aroma that would rival the finest Indian incense.

We had cotton insulation on many components. Many golden age shacks had a vague burnt-marshmallow aura about them. This was caused by cotton insulation on the verge of spontaneous combustion. We also had waxed lacing cord…the predecessor to those abominable Ty-Raps…which emitted a closely related fragrance while the rig was in operation. Sometimes a dash of burnt rubber was added to the mix.
And, of course, we did have ozone. The problem is that most modern rigs don’t have anywhere near enough voltage to create ozone; in fact, sadly enough, very few recently-licensed hams have ever seen or heard a decent sized electrical arc!

Occasionally, of course, we also had the smell of burning flesh. This could result in two ways, either by coming in direct contact with the envelope of a very hot tube, or sometimes a wirewound resistor, or, more indirectly, by obtaining a healthy R.F. burn. R.F. burnt flesh has a much different fragrance than “normal” burnt flesh…again, any ham worthy of the name could, once upon a time, tell the difference instantly.

Smoldering rosin flux fumes always permeated the air of any real amateur radio station. It was unthinkable to operate a station without a hot, beefy soldering iron standing by, to be pressed into service at a moment’s notice. Removing power from a rig before soldering on its innards was always considered a pointless and often counterproductive precaution. Brain surgeons always do their work while the patient is conscious, so they know right away if they happen to poke the wrong nerve. Real hams knew the wisdom of this as well, it was always best to work on a “conscious” rig, so you knew right away if you shorted something out that ought not to have been shorted out.

RTTY stations had a fragrance all their own, as well. A Model 28 Teletype Printer, affectionately known as a “locomotive” always smelled like hot engine oil, which was not surprising, since it would go through the stuff faster than McDonald’s went through French fry grease.

Alas, very few hams these days recognize the heavenly scent of Carbon Tetrachloride, the main ingredient in many contact cleaning solutions; many Golden Age ham shacks were permanently redolent of the stuff. The absence of Carbon Tet is quite a shame, because it really was a delightfully fragrant substance, (despite being highly suspected as a carcinogen.) Many of us practically took baths in the stuff, but most of us turned out okay, anyway. I haven’t grown a third elbow nor had my kneecaps fall off.

Many ham shacks also had the smell of hot fur. This is because cats (and sometimes larger animals) had a penchant for curling up on top of hot transmitter or linear amplifier cabinets. These “dumb animals” understood much more about the hobby than most present-day amateurs. (On more than one occasion, I’ve had to extinguish a cat’s flaming tail, resulting from inadvertent contact with the aforementioned perpetually toasty soldering iron.)

Now, I am happy to report that all is not lost. In fact, things are looking better all the time. Hams are discovering Real Radio in unprecedented numbers. For the past year or so, every issue of QST has had some feature about vintage radios or boat anchors. Classic amateur radio equipment is fetching unheard of prices on E-Bay and other ham sites. People are rediscovering the soul of Amateur Radio, something that can’t be contained in monolithic little black boxes. They are discovering the joy of REAL RADIOS with REAL knobs and switches.
This renaissance is not just a national phenomenon “out there” someplace. We have a thriving vintage radio presence right here in Fairbanks…in fact, we always have! There is no excuse for any member of the Arctic Amateur Radio Club to not experience the vibes, the sounds, or the fragrance of genuine amateur radio.

Vintage Radio is the perfect way to dive into the guts of radio; it’s a painless way to learn some real electronics. The components are large, easy to see, and very forgiving. Boat Anchors BEG you to lift the hood and take a peek inside….or sometimes CRAWL inside. Take advantage of a vintage radio shack near YOU! You’ll never know what you’ve been missing.

## Harmonies and Near Harmonies

I was having more fun today reading about harmonic ratios, harmonographs, and combining signals that are nearly harmonic but not quite. I recorded this video (sorry about the light static in the audio). In GnuRadio, I am generating two audio tones and feeding them into a scope block in XY mode, while adjusting the second frequency. Slightly discordant frequencies generate a “beat” from the drift in and out of phase with the first signal.