I knew that one day I would get around to trying to understand the top octave generator(s) of the SS-30. They are the most precious of the compoenents in the instrument, being utterly vital and also incredibly rare. So far they are working fine and the existence of other working SS-30s (and certain Yamaha organs) makes me confident that they will be okay for quite a while yet. Still, it wouldn't hurt to examine them in more detail and make sure I know what they really are.
Introduction
The SS-30 generates all its musical pitches via a silicon chip commonly called a Top Octave Generator (TOG). In the Service Manual this is named the 'Master Oscillator' (MO) and is a proprietary Yamaha IC (Integrated Circuit), part number YM25400.
A pair of 'Master Clock Oscillators' (MCOs) are generated by two Colpitts oscillators buikt from discrete components - nothing digital about them. The MCOs are generating clocks at a nominal frequency of 500KHz, which is divided down to lower frequencies through the series of MOs. More on that frequency later. It is the fact that the SS-30 has two MCOs which allows it to be called a two-oscillator synthesizer and you can detune one from the other on the front panel to obtain subtly different sounds.
This pair of clocks drive two groups of four MO TOGs, requiring eight TOGS in all. Furthermore, the output pitches from the TOGs are divided again to obtain another lower octave for each one. It is quite a lot of tones wrangle! But, it becomes clear why all this is required.
Here is a diagram of one of the MOs and associated dividers
 |
| One Master Oscillator and Dividers on G2 board |
As you can see, an octave (plus an extra C) is generated, but it is then divided again to create another, lower octave. I'm not going to delve into all the generated octaves and how they are all used in this inverstigation though. I'm only going to talk about the the TOGs.
Let's look at the bigger picture of all eight TOGs now. Here is the block diagram for one of the MCO driven chain of of TOGs.
 |
| Simplified block diagram of one MCO and associated TOGS |
You can see all this in the Service Manual schematics, and the block diagrams, but it's not easy to follow.
Here you can clearly see one MCO, situated on the G4 board, and the four associated TOGs. All the G boards are indicated so you can see how the TOGs are distributed and where the octaves are generated. On G3 there is a flip-flop logic divider which divides the G4 MCO clock by two and feeds the TOG on G3. The TOGs have divide-by-4 dividers built in, so the G4 and G3 chips feed clocks to their lower octave companions.
I've labelled the octaves generated by each of the TOGs too. The actual octaves are not made perfectly clear in the Yamaha documents, so here it is. That said, the key you press and the voice your're using will determine the octave you're hearing, so don't assume the four actaves here map to the the 49 keys in all cases. And there seems to be some diagreement about octave number in the world to add to the fun too! More on this later, too.
The simplification of the above diagram goes further. There is another MCO on G3 and another four TOGS across the four boards. G3 hosts another flip-flop divider and so there’s a whole other set of octaves. These pitches are mixed with the equiavelent pitches on each board to provide the dual-oscillators for each tone.
No Spares Expense
That’s a huge number of chips and is a little surprising because TOGs were not cheap. The usual approach was to use just one TOG for, well, the top octave. All the other octaves were divided down with cheaper, commonly available logic dividers. The SS-30 divides each octave once, but only once, preferring to keep the board layouts simple, the wiring too, and maximising the TOGs. As these are Yamaha's own chips the costs would be lower for them to do this. Once you factor in the investment of building your own silicon fab, that is. Well, they cashed out on FM chips and much more eventually. One wonders if they had to find somehing to do with it, once they had invested in creating it. Now though we're left with a problem as Yamaha ran out of spares a long time ago and there are no clones*.
*Keep looking though! TOGs clones are coming out and they are not not that dissimilar.
The exact workings of the Yamaha TOG are not explained. Details are missing, sketchy, misleading and sometimes just plain wrong. Two main questions need to be answered: How do TOGs work generally, and the YM25400 in particular; And, exactly what pitches do each they create? What is that top octave?
I'll answer both here and then explain how I know that below.
How do TOGs work?
The simple answer is that TOGs are integrated circuits which pack in a set of 'divide-by-n' frequency dividers which work with binary logic. A high frequency master clock is fed into a binary counter and binary decoders detect when the count reaches a certain number. That number is reached when a certain period of time has passsed and the decoder is there to flip the output and reset the counter. This method is not exact enough to give a precise tuning, but is close enough to not matter.Strings Of Digits
Strings machines are almost all characterised by their use of the TOG. You will see TOG and the term 'divide-down' used in any description of how they work. You will also see that this technology is derived from electronic organs and that it's a simplified way of achieving polyphony (many notes) when compared to the multiplication of monophonic (single note) circuits.
As you can see above the TOG IC generates a set of musically related pitches from a high frequency master clock. The pitches are synthesized from the clock with digital logic, the building blocks of computers. Thus the output from the TOG is in the form of a square-wave - on or off. As the name suggests, the top-octave is the highest required octave of the instrument, other octaves are derived from this by means of simpler digital logic chips which divide the pitches in half, and in half again and so on. As you saw above though, the SS-30 greedily uses eight TOGS, where two would be enough.
Once all the octaves are created there has to be some way of shaping the square-waves, playing each and mixing then together, but that is another story entirely.
Digital Tones
The SS-30 uses the proprietary Yamaha YM25400 Digital Tone Generator (DTG) IC to generate an octave of even tempered tones (also referred to as pitches) from its clock source.
Let me break that statement down a bit for you. Yamaha's 'YM' ICs are detailed in the precious, holy relic that is the Yamaha IC Guide Book*. I'll be referribng to this information in what follows. This chip is a digital IC because it work with digital logic - i.e. on/off states, not sine or triangle or another waveforms - and it's a tone generator because the frequency of the outputs are musical pitches. Those pitches are even tempered in the 12 note-scale. More on that below too.
You could make an argument that the strings machine is kind of digital synthesizer. As the sound is generated by digital logic isn't it digital? I would point out that the master clock in the SS-30 is an analogue VCO and the shaping of the tones is all analogue. Other machines might use crystal timing for the master clock and in that case I think it is a bit more 'digital', or closer to computing devices anyway. The unavarying precision of the crystal seems less real that the analogue clock, with all its drawbacks for accuracy. The comparisson is slightly false, but there is something hybrid about the divide down architecture that confounds simple debates about pure analogue VCOs versus purely digital means of generating tones.Here is part of the IC Guide for the YMC25400
You can see it has one 'Master clock input' (pin 10) and thirteen 'Signal output' pins, labelled with musical notes from C to C1. Note also the 'Reset data input' (pin 3), 'Octave change' pins (11,12) and the 'ϕ** (Master Clock) output' (pin 14). All the workings of these pins will be revealed below.
A quirk of the Yamaha chips is their dual negative power-supplies. VGG is -15V and VDD is -9V. Both are used, although the SS-30 supplies -8.2V to VDD. It's not particularly clear why both are needed for this design and I won't dwell on it here.
*As the inscription by the prophet Loscha says on the inside of this document "Learn from it Love it. Respect those who worked Thousands of hours to develop it". [capatilisation transcribed for the original].
**ϕ = Phi.
Combo Organs
The Yamaha IC Guide lists all the instruments that use each chip. The YM25400 is also used in the YC (Yamah Combo) range of Combo Organs, YCs 10, 20, 30, 25D and 45D. Perusing the Servive Manuals for these keyboards you will see that the Yamaha design eveloved with new technology. The original design, from 1969, had a TOG made from discrete compoenents with each note the octave coming from an analogue oscillator . You could therefore tune this octave however you wished. Then they moved to an IC based design which had two Yamaha ICs - 03801 and 03802 to generate one half of an octave each. Finally, the third iteration introduced the YMC25400 TOG. It says of this change "On and from the production of March; No. 7833".
Togging Up
The biggest differences between the combo organs and the SS-30's use of the YMC25400 are that the SS-30 has two Master Oscillators and eight TOGS in total with a huge number of pitches generated. The reason for this abundance of pitches is the way the SS-30 creates its three main voices and the difference between Violins and Viola & Cellos. I've noted elsewhere that the vast number of tones in the SS-30 is not appreciated when you only summarise its architecture as simply 'divide-down'. It is divide-down, but on a much bigger scale than the two oscillator 49 keys suggests. In fact, there are 48 pitches generated on G2, G3 & G4 and 50 on G1 - 194 pitches in total. That's sixteen octaves! They are then mixed in pairs - one from each Master Oscillator to create 97 tones in eight octaves.
It's not a range of eight octaves though. There are two ranges of 4 octaves each. The Violins use four octaves, the Viola use the other four, one octave lower. The Cellos share the bottom two octaves with the Violas. Hence the complete range is 5 octaves, with two ovelapping ranks of 4 octaves each.
Yamaha could have used just two TOGs, but as they then would have to route around 24 pitches for each of the four octaves this would have been even more intensive on the wiring than it already was. Instead the YM25400's Master Clock Output pin, which is one quarter the frequncy that of the input, is used to cascade down to another TOG. To get the second octave down the Master Oscillators are divided in two by simple flip-flop ICs. Hence the 500KHz oscillators drive a pair of TOGs at the top octave, which in turn drive the third octave, the divided 250KHz outputs drive the second octave and the bottom octave.
This gives us the four G boards, each with a pair of TOGs, as shown in the block diagram above. The fun doesn't stop there though as each G board uses the octave from the TOGs as it comes and also divides it again for another octave. With two octaves for each Master Oscillator TOG, that's four on each board and henace the sixteen octaves. The pictehs on the G1 board are of course divided in half, adding the lowerst octave. Which octaves are generated and how they are all used is another question altogether though.
That's how the TOGs are used in the SS-30, but how does a TOG IC work anyway?
Say Hello Octave Goodbye
Divisions & Pitches
Before we get into the mysteries of the TOG it's important define the octaves that will be created and the very problem of so-called divisions.
Below is a table of octaves and the standard frequencies of each pich for reference. Note that each octave starts from C.
Trecherous Cs
Let me clarify here that the SS-30's octaves range from C2 to C7 - five full C-to-B octaves plus one more C at the top. This needs saying because a) the user manual refers to C-C4, which is not correct, and the Service Manual refers to "C2~C6", also not right, b) as I will refer to below the Servise Manual has a very stange value for the test point of the highest pitched A, and c) if you only play the Violins, and not Viola, particularly Violin 2, you get a very thin and high pitched tone, which can fool tuners. What you need to keep in mind is the highest C generated out of the SS-30 is C7, at approximately 2093Hz.
Keep Your Temper
You probably know (or can see in the table above) that each note is the half or double of the same note on the lower or higher octaves. That is the principle which makes the simple dividing down method work so neatly in organs and stringers. Can you recall the mathematical relation between the notes adjacent in the equally tempered 12-note scale though? Let's skip the maths and simply state that the interval between semitones must be the twelth root of two () which equals about 1.059.
![{sqrt[{12}]{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bc835f27425fb3140e1f75a5faa35b1e8b9efc35)
Armed with that formula, an approximation can be made on how to divide a large clock frequency into 12 musical tones which are spaced in equal temprement. The table below was presented in the January 1974 edition of Popular Electronics. (Eagle-eyed mathematicians who haven't already calculated this in their heads will spot that the ratio for half-way through the octave at F# is root 2.)
Series A and B do the same job but as we'll see the choice of which to use will depend on the number of bits available in your digital design. 8 bits will allow for numbers up-to 255, which series A fits into. Series B requires 9 bits for up-to 512. These divisors (called moduli or the modulus) are approximations though. The aim here was to provide whole-number values for divisors because the way to make this work in digital logic requires counting and there is not complicated flltaing-point arithmetic here.
Dividing a clock of, of, let's say exactly 2,000,240Hz (you'll see why I chose that one in a moment) by these values gives the required musical frequencies. For example, modulus 239 gives 8,369.2 Hz for that clock input. That’s only -0.57 cents off the correct tuning for C9 and because it’s less than one cent (one hundreth) out of tune that is an acceptable error, to human hearing.
OG TOG - 5024
The standard TOG IC was the 5024 from Mostek and also AMI and maybe others. Mostek called it a "Top Octave Frequency Generator" or "Top Octave Tone Generator". Meanwhile AMI decided it was a "Top Octave Synthesizer". This IC expects a 2.000240MHz clock and will generate octave number 8 (C8 = 4148 Hz) if so provided. The clock is divided by the approximate ratios given in series B (see above).
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| AMI 5024 Block Diagram |
As you can see the highest frequency is output from the lowest divisor 239, which is C9. An additional C is provivded at half this frequency and couble that divisor giving C8 and the rest of the pitches are octave 8. And it's documented elsewhere that this really is octave #8 and C8 is the lower C. I had to make this very clear because the Mostek datasheet confused me a bit till I spotted that it was wrong, stating octave 8 plus C7, not C9!
Note that the datasheet for the 5024 doesn't describe the way this works at all. How do you divide an even number clock frequency by an odd numbered modulus and still get a digital chip to output a whole number of clocks? I will explain below as the YM25400 infomation is more helpful in this regard.
Doing Double Duties
A final note
on the 5024 is that it has three types. The
50240 outputs a 50/50 duty cycle, whilst the 50241 outputs at 30/70.
There was some thought there to making it easier to obtain different
tones, but the octave-down dividers would have to track this
duty-cycle and I'm not sure how that would work.
The 50242 drops the additional low-C output.
YM25400
Going back to the TOG in question then: how does the YM25400 work, and is it similar to the 5024? The Yamaha datasheet doesn’t
mention the divisions (or moduli) of their design, but unlike the Mostek/AMI datasheets there are big clues as to its internal design and we can figure a lot out based on what the inputs and outputs are.
Treachorous Cs
According to the YC-45D combo organ service manual, the top octave is 7, but it was not easy to determine the actual top of octave of the SS-30 without measuring. There is no octave number on the G board schematic and as I noted above there is some wrong infomation to acknowledge and ignore. And can we even trust that YC-45D service manual? To be certain I had to double check. Let's check the YC-45D first, for practice.
Combo Organ Master Oscillator
The YC-45D Master Oscillator is a Colpitts type and has no
label in the schematic to tell us what it ought to be. Calculating the
frequency from the component values gives 1,837,023.5838Hz, which is more or less 2MHz, once you
adjust the tuning of the inductor. That would give the same octave output as the 5024, if it is indeed the same. But that would be octave 8, not 7. So, maybe the YM25400 is not the same as the 5024. Well, let's see!
SS-30 Master Oscillator
The same oscillator calculation for the SS-30 gives 464,115.9Hz and we're told it is nominally 500KHz, so with a bit of inductor tuning it is corrected to that. Hence, the SS-30 seems
to be tuned two octaves lower than its organ cousin, which should be octave 5. You may remember that I said the SS-30 is C7 at the highest C and the top octave is 6 though. That would mean that it was two octave below the 5024, exactly what to expect when the master oscialltor clock is one quarter. So, why did I say the SS-30 was at
Measuring Up
I measured from the G2 board on my SS-30, which just happens to be on the top of the stack of boards and within easy reach.
G2 TOG:
- Clock = 125KHz
- O1 - C = 261Hz - C4
- O13 - C1 = 521Hz - C5
Therefore this TOG is between C4 & C5 - Octave 4 - and A4 = 440Hz is produced from the board's
These are approximate and I didn't check the tuning exactly, but the TOG outputs both C4 and C5 with octave 4 between
Now I can simply multiply up to check other top octaves.
G3 - Clock = 250KHz - C = 521Hz /C1 = 1046Hz C5 & C6 - Octave 5
G4 - Clock = 500KHz - C = 1040 Hz/C1 = 2080Hz - C6 & C7 - Octave 6
This confrms all that has gone before.
- With a clock of 500 KHz the SS-30 top octave is 6
- And top C is C7
- The YM25400 probably uses Series B divisors
- The YM25400 has the same clock to octave outout as the 5024.
Octaves And Octave Nots
You might be wondering why I care about the YC45D when I know what the SS-30 is now. I'm just a little curious. It seems to be wrong in the Service Manual.
However, the YC45D brings into use the A1 & A2 pins, which control the octave. It appears in the schematic that both are held to VGG, in the 'JA' switch position. This is effectively 'low' as VGG is the negative voltage supply. The SS-30 also holds them low on -15V. I'm not certain though. In any case, perhaps when this is switched the YM25400 outputs an octave lower.
One mystery more is why the Yamaha engineers didn't use these pins on the SS-30 and instead of chaining the TOGs with their divide-by-4 ouputs branch out the master oscillators. I think this might have just been a decision where it was a fifty-fifty choice or the layout was sligtly easier that way.
Just A Machine In The TOG
Finally then, let's look inside the YM25400.
The secret to TOGs is the Divide-by-N counter. This is a well known and common digital logic design and if you really want to understand it I suggest you look elsewhere. I will go in the basics here to help explain the way it is used in a TOG though.
Shift Up A Bit!
The Yamaha IC Guide shows that the YM25400 has 9-bit shift register as part of each of the thirteen dividers. So, we know that counts up to 512 are possible. How does that work exactly though? What is the counter for? An asynchronous shift-register with a clock input on the first stage is a binary counter which increments the count with each cycle of the clock. In the asynchronous arrangement, each stage divides the previous stage's freqeuncy by 2. The first stage acts as the least-significant bit of the counter and the next stage is half that and is thus the next least significant, and so on. This is a ripple, counter with each stage passing the state on to the next in a ripple effect. The first stage is clocked by the input, so the LSB is at the same frequency as the clock.
You Can Count On It
The division occurs when the counter reaches the required modulus and is reset.
Another block in the diagram attached in parallel to the shift-register is a decoder (not “decorder” as written in the diagram). This will decode the binary code in the shift register and indiacte when a particular number has been detected at the input. When it sees the required modulus at its input its job is reset the counter. We don't need to worry too much about this operation or how the decoder is built, it just has to spit out a pulse when it decodes the binary input as being equal to the modulus. On the first such block in the diagram you can just see one stub of a line poking out of the decorder, sorry decoder. This is I suspect that reset line.
Clocking off?
Thus with these two blocks we have a counter that will increment with each cycle of the clock untill it reaches a modulus we want to use for division, say 239 for C. The period of time it takes to reach that count equals Modulus x period of the clock. For example, for the 500KHz Master Oscillator of the SS-30: 239 x 2us = 478us. That gives the period of one cycle of the output we're trying to make, in this case around 2092Hz or C7. The SS-30 Master Oscillator is a quarter the frequency of that used on the 5024 and you can see that C7 is a quarter of the frequency of C9. I thought the output of the top C in the SS-30 was C6 though. Let's go on and see why that is.
Control
At the same time the Controller block seems to have a similar role. It is also connected in parallel with the shift-register so the same binary code will presumably be decoded and the output RS flip-flop flipped. I am guessing a little here, and can only assume what is going on as there is no other information provided. Still, by the end of this I think you'll see I'm on the right track.
N'y Coulour You Like
That's it, basically. Just count the modulus, reset he counter and clock the output on each iteration. Intuitively, you can see that the output will be flipped as many times per second as the division of the clock by the modulus. Or close enough. Clearly there will be some rounding errors, but as we saw above, as long as the final pitches produced are within a cent of the normal frequencies it's all good.
And of course, if the clock is high enough the error will be small. That raises a question though. The SS-30 divides the Master Clock by 8 for the final pair of TOGs to just 62.5KHz. However, this is not as bad as it might seem. As the octaves get lower the pitches are lower too, by the same ratio, and thus the ratio between clock and pitch stays constant, as we'll see. There must be a lower limit to this, but I haven't bothered to work that out, yet.
The 500KHz clock of the SS-30 is just a quarter of the suggested ~2MHz for the 5024. The moduli must surely be the same though - based on the 9-bit shift register/ripple counter. Hence, dividing 500KHz by 239 equals 2,092.0502092 recurring, or C7 -0.78 cents. You will recall from the above that this was not the same error as calculated for the approximately 2MHz clock used for the 5204 which was C9 -0.57 cents. It is still less than one cent and that is good, but not quite as good.
The important point about the clock though is that the 2,000,204Hz clock is derived from a crystal, so will be very precise. Meanwhile the SS-30 uses analogue Colpitts oscillators tuned in by ear from the front panel control. You can theorectically tune the SS-30 Master Clocks to 500,060Hz and get the same error as the 5204 though. In conclusion here, the SS-30 is just fine running the Master Clock at a quarter of that used in the 5204.
At the other end, the bottom octave TOG run a 62.5KHz, but as I already stated that is no problem. The result of that 239 division is still only -0.78 cents off and is thus perfecty in tune with all the other C pitches's, as will all the others.
Now, let's recall that there were two mysteries in the 5204. How does it work inside and why is the output octave half of the what you'd expect? Both are answered by what I described above. If you were paying attention you'd noticed that counting 239 ticks of the Master Ocsillator and then flipping the output state will only produce half of the waveform. To get to a full waveform you need to flip it back again. You could think of halving the modulus, but some of them are odd numbered and you can't count half a clock pulse, so that doesn't work. looking again at the IC Guide blcok diagram for the YC25400 you can see there is an RS flip-flop at the output. And so, the output frequency is indeed half the expected value when calculating the clock/modulus. Assuming the 5204 works just like the YM25400 then there is no mystery.
Back on the YM25400: Above I calculated a top C of C7, but I hadn't divided it by two, so the actual top C for the SS-30 is C6 (1046.5) - or C6 -0.78 cents, if the clock is precisely 500KHz. Is that correct though? First be careful with the octaves. The 5204 produces the top C (/239), which it calls C8, and the octave below, which it also labels 8. And then it divides the top C by 2 for the bottom C (/478), which it calls C7.
The YM25400 also produces both the top C, which is labelled C1, and bottom C. On the G2, 3 & 4 TOGs the bottom C is not used, only C1. I say this just to point out that the A below the top C will be A6
What the A?
Curiously, the G4 Master Osc schematics both have a test point labelled on the A output at 443Hz. Setting aside that this is way off concert pitch, by -11.76 cents, this would closer to A4, putting the top C at C4! The Overall Circuit Diagram also labels this test point and makes a total mess of it. One is labelled 44 Hz and the other 44.3Hz!! It does seem they want to get this at 443Hz though. I can't be that low though, can it? Well, the Owner's Manual says the keyboard runs from C-C4. I'm not convinced though. G1 would have A at 55Hz, which is very low, but it is then divided down again - and that is subsonic.
Ignoring that test point the Service Manual also repeats the C-C4 keyboard range, but also has it as C3 - C6 in the Assembly Layout section on page 2. That seems more likely to me!
G4 : C6 - 1046.5Hz/A6 -1760Hz.
G3: C5/A5 880Hz
G2: C4/A4 440Hz.
G1: C3/A4 220Hz and C2
443 and all for what?
Operating Inside The Parameters
Before the dividers there is a "clock for inside operating". Again nothing is made clear but there are apparently a pair of output clocks for this purpose. One is the inverse of the other and there is apparently a formula for the frequency.
f.f/2.f/4.f/6
As we know the input clock frequencies range from 62.5KHz to 500KHz this seems like a very high number! Should it be read as f=1 and the others are therefore fractions? In that case it's 1/48 or 5.21KHz, which is too low.
You can count on it.
The method of dividing a clock by any value of 'n' is more about counting than the simple toggle flip-flop divding. If you have clock of an aribitraily hgh frequency you can count an certain number of cycles between each flip or flop. This is how I believe the Yamaha TOG works. If f is high and n is the divisor required to obtain a particular frequency fd then you count half that period and then flip and count half again.
for example for a clock of 100KHz fc to obtain 8KHz
fd you have a peroid of clock Tc of 10us, and period of output divided
clock of Td 125us. Hence, to count half the period of fd Td/2= 62.5u,
you will have to count 6 cycles of the clock and one quarter? How do you
count one quarter? with 6 clocks only you will count 12 periods or
120us and that will be 8,333.3Hz. Which is wrong.
As you can see, the frequency of the clock has to be high enough to avoid such rounding errors. Also note that 12 counts is higher than the 9-bit shift regsiter in the block diagram. What am I missing there?
Fractional Division
If you are wondering about fractional divisions, then, yes, this is possible. The modulus controller can switch between two integer counts so that the average frequency is closer to the desired one. This creates jitter in the output, but that may not bother you for audio frequencies. It would depend on the period over which the average is taken though. Whilst you might be able to measure the frequency as being accurate, if you have to wait a second to get that average it would not neccesarily be heard. The better solution is to add a phase-locked loop (PLL) circuit which would average out the signal. There no evidence of that being used on TOGs though.
I can't be sure if the YM25400 is attempting some kind of fractional approach without taking some very accurate measures of the input clock and its outputs. Maybe one day.
TOGetherness
Altogether a huge subject. I did get to the bottom of the tuning of each TOG though and that is useful infomationfor future reference and removes anyt doubts.
https://synthnerd.files.wordpress.com/2014/01/s50240lq.pdf
http://www.muzines.co.uk/articles/lab-notes/6277
https://worldradiohistory.com/Archive-Poptronics/70s/1974/Poptronics-1974-01.pdf
https://en.wikipedia.org/wiki/Twelfth_root_of_two
https://hackaday.com/2018/08/22/ask-hackaday-answered-the-tale-of-the-top-octave-generator/
https://www.logosfoundation.org/kursus/2073.html
http://cini.classiccmp.org/pdf/re/1974/RE1974-Feb-pgA.pdf
http://electricdruid.net/adventures-in-top-octave-generation/
http://www.flatkeys.co.uk/MK50240.html
https://www.wdgreenhill.co.uk/semiconductors?Make=Yamaha
Arduino based stringer
http://bloghoskins.blogspot.de/2016/11/diy-arduino-string-synth.html
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