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Listening to the Rhodes on youtube it sounds like the harmonics are created in the amplifier circuits which must have some significant non-linear distortion. If you examine some of the available sounds a very rich harmonic spectrum shows, esp. in the lower notes.

Interesting instrument, never heard of it before this thread.

Kees

Hi Kees,
As it turns out, the harmonics are created by the movement of the tines as they sweep by the magnetic pickups. The piano itself has no amplifier circuitry in it. The strength of the magnetic field around the tip of the pickups is a highly nonlinear function of the distance from the pickups to the ends of the tines, and that nonlinearity is what creates the harmonics. The bass tines swing much further than the treble tines when they are struck by the hammer, which is why they produce more harmonics.

You may not have heard of the Rhodes, but chances are, you've heard them many times. They were very popular throughout the 70s and 80s with people and groups like Stevie Wonder, Billy Joel, Steely Dan, and many others. In the jazz world, Miles Davis starting using the Rhodes piano in his recordings from the 60s. Many jazz pianists, such as Chick Corea, Herbie Hancock, and Joe Zawinul used them extensively. If you go to youtube and type "down the Rhodes" you'll find interviews with many pianists who use/used the Rhodes.

I'd like to circle back to discuss a post by Kees. He graciously sent us an audio file demonstrating a detuned fifth made first by using 2 sinewaves and next by using tones with harmonics. The intent was to show how the 2 sinewaves did not produce a beat frequency. Some readers heard a beat frequency. I had the interesting experience of listening to these tones on 2 different computers. On one, there were really no beats to be heard with the sinewaves, and on the other the beats could be heard. The difference is caused by distortion added in the signal-processing chain in one of the computers. The distortion could be caused by the sound card, the amplifier, the speakers, or any combination thereof.

I thought it would be useful to demonstrate this effect visually. So, I created 2 tones, one at 440 Hz and one at 661 Hz. Of course in a perfect fifth the 2nd tone would have been at 660 Hz. Therefore, a beat at 1 Hz should be seen. Then, just as did Kees, I used pure sinewaves for one test and tones with harmonics for the other. The results can be seen in the image below.
[img]http://imgur.com/a/tC65k[/img]

The waveform of the 2 added sinewaves showed no pulsation or change over time--therefore, there was no beating. The waveform showing the addition of the 2 more complex tones clearly shows beating, as you can see the waveform slowly change with time.

Just so I have this straight, you are using electronics to show that electronics distorts results so much that what you do with them cannot be trusted?

Remove the hairs, mash the metal tip flat and then bend it. For moving the coils, hold the brush near the bent end.

Good luck!

Thanks for that explanation, very interesting physics. So the timbre also changes a lot depending on how strong you play as shown in some youtube videos. Indeed I know the instrument from listening without knowing what I was listening to. It's amazingly "acoustic" sounding. Too bad they don't make them anymore, I guess most people like canned digital sounds.

Digressing a bit, here is another great invention with no market.

Kees

I carried a stage model around in the 70s with a band I played in at the time. Thing weighed a ton. Tuned it several times. It's been a long time, but I seem to remember that the forks also had a screw adjustment on their mount to control tamber? It was a kind of way to voice the instrument.

I'm not quite sure what you're saying. The images I posted were created just by adding sinewaves together--no electronics were involved. My other comment about hearing beats with one computer, but not another, relates to the fact that slight nonlinearities in the processing of the 2 pure sinewaves can cause slight distortion of the sinewaves, thus causing a beat to be audible. I don't think much distortion is required--the human ear is pretty amazing, and piano tuners, through years of experience, have trained their ears to pick out faint beats.

Roy,
I understood your post completely. Thanks for taking the time to create the images.

Yes, that's correct. The screw raises and lowers the tine with respect to the center line of the pickup. Because of symmetry, if the tine is aligned exactly with the center line of the pickup, no fundamental tone is produced, and what mostly comes out is 2nd harmonic. By adjusting the tine away from the center line, one can adjust the relative level of fundamental and 2nd harmonic.

Since you never heard of a Rhodes before, I'm guessing you are also unfamiliar with the Clavient...

Well, I do not know what process you used to create the images, but I plugged y=sin(1000000x/330)+sin(1000000x/661) into Grapher on my Mac, and the beat showed up plain as day. (The factor of 1000000 is necessary to have the time frame long enough to show the beat.) Of course, I have posted images like that before, which are still in the image area.

Seeing is not hearing.

Kees

Seems to be for Roy. At any rate, it can be replicated, and that is more evidence than anyone else has provided, including you.

I don't get it. What is "it"?

Kees

There is a company called Vintage Vibe that still makes tine pianos. (And Clavinet replicas.)
For what it's worth, I'm working on a prototype of an electric piano with an action and string layout similar to 18th century square pianos, there is a video on my youtube channel (bourniplus) if anyone is interested to take a look.

BDB,

You are correct in that the waveforms I posted were in error. I was fooling around with waveforms, both simple sinewaves and waves with harmonics, looking at both perfect and detuned fifths. At the end, I forgot to set a perfect fifth back to a detuned fifth, and so the waveform I presented was that of a perfect fifth.

However, I am correct in saying that no countable beat is produced by adding 2 sinewaves whose frequencies are substantially different. Here's the math:
Consider two sinewaves, w1 and w2, of frequencies f1 and f2. Let's say their peak value is 1. Let's add them together.
w1+w2 = sin(2*pi*f1*t) + sin(2*pi*f2*t). For our purposes, the unit of t is seconds. Now let's use the sum-to-product trig identity.
w1+w2 = 2*sin(2*pi*(f1+f2)/2*t)cos(2*pi*(f1-f2)/2*t)

If f1 and f2 are close, then, of course, f1-f2 will be small and countable. But, as an example, let's take the case of a particular detuned fifth whose frequencies are 440 and 661 Hz. There will be a beat at 221 Hz. If we think about it a bit, if such beat frequencies were countable, tuning a piano would be almost impossible--the tuner would hear not only beats from the partials, but also beats from the fundamentals. While that would be fine for tuning octaves, it would not be fine for tuning any other interval.

To check that my understanding of the math was correct, I generated and summed sinewaves using Audacity. Audacity is a free program, and, no doubt, many of you are familiar with its capabilities. It can generate sinewave tones, and for the purposes of my experiments, I generated 2 sinewaves of various frequencies, each of which had an amplitude of 0.3. If your audio chain is of high quality, you will hear no beats. If you hear very faint beats, it will be due to nonlinearity in the sound processing, or because you have set the amplitudes of the tones high enough to clip the resulting wave form.
BTW, trig identities can be found in many places. I used this website I would like to end by saying that Kees' approach of using a sound file rather than looking at wave forms was clearly the right thing to do. I hope the math further elucidated the issue.

That's a very interesting instrument. Nice job! May I ask what kind of pickups you're using, and if you have photos that show some details of its construction?

Yes, very cool!

Thanks. The pickups are three electric guitar pickups end to end. No photos yet... if you have other questions maybe we should keep that in the youtube comment section so we don't derail the thread any further!