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Combination tremolo/octave tuning?

Posted: Fri Jun 07, 2019 2:59 pm
by IaNerd
Is there any such thing in production?

Re: Combination tremolo/octave tuning?

Posted: Fri Jun 07, 2019 10:42 pm
by EdvinW
I'm not sure precisely what you are referring to, but my best guess is that you ask for a harmonica that has two notes, one octave apart, with a tone that beats like a tremolo harmonica.

In a normal tremolo, there are only two notes that interact, and only one parameter to consider, namely the difference in frequency. Varying the difference changes how fast the perceived tone is beating, very simple. If we now instead have two reeds tuned exactly one octave apart, and two reeds which are identical to the first two but slightly sharp, things get more complicated: how do the two beating tones interact? Will they beat in unison, or will the beat frequencies be slightly off? If so, the beat frequencies in turn will create a beat together! This could make for some strange sounds.

I have no idea how this would sound on a real harmonica, but I did some plotting.

Say that we have four reeds, two tuned exactly one octave apart and two identical to the first but slightly sharp. Say also, to simplify things, that each read produces a clear tone without overtones. If we sharpen them by the same amount, equally many cents exactly, we get the following waveform, zoomed out to see the beating, we get the following:
dif2.png (11.86 KiB) Viewed 2635 times
Rather curious!

If we instead raise the higher note by just half as many cents as we did the lower note, we instead get this:
dif1.png (11.68 KiB) Viewed 2635 times
Much more similar to the normal interference of the tremolo.

But (there's always a but!) if we raise the upper note by 55% instead of 50% of the amount that we raised the lower note, this happens:
dif11.png (11.8 KiB) Viewed 2635 times
The precise intervals really matter! This shows a pattern that is changing over time, a sort of tremolo of the tremolo ;)

A real harmonica is of course not as simple, but has a number of overtones, acoustic interactions between the reeds and so on, so these highly idealized examples might not fully reflect what really would happen. They give us a hint, however, that things might become quite a bit more complicated when we introduce more reeds :D

Edit: Just to be clear, the pictures are simplified, in that they show interactions between completely pure tones, without overtones: pure sine waves.

Edit2: Fixing some typos and clarifying a few statements.

Re: Combination tremolo/octave tuning?

Posted: Fri Jun 07, 2019 10:44 pm
by EdvinW
And just for reference, normal interference between two tones works like this:
interference.png (17.68 KiB) Viewed 2635 times
The red lines are tones which are almost the same frequency, and the black is their sums. Sometimes the red ones line up, resulting in strong oscillations of the total, and sometimes they cancel each other out.

This image is just an illustration of the mechanism. In a tremolo harmonica, the difference in frequency is not as large, so the variation in volume is slower. With the same settings as the images in my first post, it looks as follows.
trem.png (11.01 KiB) Viewed 2622 times
It shows the low read and it's slightly sharp partner reed, with the same frequencies as they had in all the first three images.

Note that, with just two tones present, one cannot get the complicated images of the above post, but the only difference one gets from adjusting the sharp read shows up in how quickly the volume goes up and down: large difference gives fast tremolo, small difference gives slow tremolo. In this sense, tremolo harmonicas are theoretically "easy". Again, real world acoustics might complicate things a bit, but this is the general principle at least :)

Re: Combination tremolo/octave tuning?

Posted: Fri Jun 14, 2019 9:36 am
by IaNerd
I love those graphs! Thank you!

I hope to hear sometime these iterations through a tone generator and also, of course, in real harps.

Re: Combination tremolo/octave tuning?

Posted: Fri Jun 14, 2019 2:34 pm
by EdvinW
I have uploaded some of the sounds corresponding to my pictures.

A normal tremolo, the very same as is shown in my last post with the name trem.png sounds like this:

In all the rest of the examples, there are two tones tuned a perfect octave apart, and each of them has a slightly sharp "partner tone".

The nice four-tone tremolo from my first post, from the picture with the file name dif1.png, sounds like this:
The difference between the bottom tones are 20 cents, and the difference between the top notes are 10 cents, and you can hear the two notes beating in synch.

If the top and the bottom partners both deviate by 20 cents, as in the picture dif2.png, it sounds like this:
We get a rather different sound!

Finally, if the bottom partner tone is 20 cents sharp, while the top is 11 cents sharp, like in the picture named dif11.png, it sounds like this:
The beating of the top and bottom notes are sometimes synchronized, sometimes not. I don't think this is a desirable effect.

Again, what I describe is some theory for interacting pure sine waves, and might not 100% transfer to the harmonica. This is how multi-tone tremolo works in a very idealized setting.

I could write more about this later if there's an interest. I should be able to arrange the harmonica sounds in my synthesiser in a similar fashion, but that would have to be later when I have more time.

Re: Combination tremolo/octave tuning?

Posted: Wed Jul 24, 2019 2:45 am
by winslowyerxa
Some accordions have both a tremolo reed detuned slightly from the main reed (usually tuned higher) and reeds that play an octave lower or higher than the main reed (or both).

Building a three-reed-per-note harmonica is a bit of a challenge, though, so the practical solution is to take an octave harp and detune one set of the reeds.

Tremolo in standard reed pairs is created by the frequency difference between the two reeds. If one is tuned to 440 Hz and te other to 444, you will hear 4 beats per second, the 4 Hz difference in their tones. But when one reed is already tuned an octave higher, Im not sure what the offset would do. Tone generators don't alway give an accurate representation of how something would ultimately sound when played on a harmonica. For instance, the "normal" tremolo posted earlier sounded more like space alien sounds from a 1950s flying saucer movie than something you'd hear from a harmonica or accordion, even if all the frequency parameters, beating, etc., were correct.

To get an idea of what this would sound like on harmonica, you could record two sustained harmonica notes one octave apart on separate tracks, so that can be played back simultaneously. Then tweak the pitch of the upper one and see what kind of audible result you get.