Indeed - kind of like supercars where the envelope is pushed to make the ultimate vision, even if they don’t always succeed on every aspect, the concept and execution and vision render that unimportant. I think the OT and MM are like this too, magical flagships, simply amazing.
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From my understanding yes, that’s the case. I need to read it a bit closer but it sounded like it takes pitch and modulation depth somewhat in account so that it mitigates some of the aliasing that could occur from high modulation depth at a high frequency.
In fact a lot of FM synths don’t have bandlimiting as far as I know; it’s usually not a huge issue if you only have sinewave oscillators.
Another interesting fact in the paper is this:
Oscillatorerna implementerades med hjälp av en sinustabell, i detta fall bestående av 2^15 = 32768 24-bitars värden. Med 56303-processorn kan indexering i en sådan tabell ske väldigt effektivt eftersom de speciella indexregistren kan fås att stega fram automatiskt efter varje minnesaccess. Till varje indexregister finns också ett moduloregister, som kan användas for automatisk “wrapping” av indexpekaren.
In short: the oscillators are using a sinewave lookup table of 32768 24-bit values, which can be indexed efficiently by the DSP56303 processor as well as being wrapped by a modulo register (meaning this is done efficiently by the processor) that is also readily available.
För att uppnå bästa möjliga signal/brus-förhållande skall tabellen egentligen vara betydligt större - en sinustabell med 24-bitarstal bör bestå av 2^23/2π värden. Då är man säker på att ett steg framåt eller bakåt aldrig innebär en förändring på mer än 1 LSB. En sådan tabell tar dock mycket plats i minnet. Ett alternativ är att minska tabellen och interpolera mellan värdena. Detta kan spara mycket plats till priset av små, ofta nästan försumbara, församringar av signalkvaliten. Problemet är att interpoleringen tar värdefull beräkningskraft och jag nöjde mig därför med den tidigare beskrivna lösningen - den fungerade tillräckligt bra.
In short: If you want better signal-to-noise ratio the lookup table should be much greater than this, here the suggestion is a table of 2^23 / 2π (PI) 24-bit values. However this uses too much memory to fit within the requirements of the Machinedrum engines. You could use a smaller lookup table with interpolation between the values which would save a lot of memory with trivial impact on the signal quality. Unfortunately in this case the interpolation would be too computationally expensive so the previous solution is used and deemed “good enough”.
So basically the EFM machines are using fairly large lookup tables with no interpolation which might explain some of its characteristic sound. Though, on that note I noticed that in the TRX paper the author mentions that he utilized the ‘global’ sinewave lookup table that most (all?) the Machinedrum engines shared - which comprised of 4096 values.
I’m wondering if the EFM machines ended up using this lookup size as well in the end actually.
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@Ess My thanks as well for all your efforts! I’ll echo @PeterHanes 's offer here: As I’m a native English speaker, please hit me up if there’s any way I can help.
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Waaaaaaaat 
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I think I’m speaking for many MD users who’ve already experienced many Christmases with the X updates thanks to you and Justin! 
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Nice thread 
Would love to read the documents in English…
Has someone succeeded in translating them?
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I began to translate the efm one, but as i do not speak swedish and english is not my native language it might need some proofreading and corrections. I used a scan to text app and DeepL traduction.
I do it on my spare time so it might takes some time but if someone wants to help i can share the documents to a few people.
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Halfway thru efm doc!
it’s a bit more time consuming than expected because the scan to text app i use is having hard times with some swedish characters, so i have to check everything almost word by word without understanding sh…
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Just finnished the translation of the efm doc.
Would there be one or two volunteers to review and comment on the document before I share it?
(pm me your gmail adress if you’re interested)
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I can give it a try. I can’t fact check the more complicated math, but I think I should be able to find any glaring issues in the linguistical translation since Swedish is my mother tongue.
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looking forward to this! even if there’s errors its going to be interesting
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Thanks to @andreash the efm document will be ready to be shared soon! i just need to find some time to review his comments.
hope you’ll like it.
(The trx one is on the way too)
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Just uploaded the paper, no doubt you’ll enjoy it if you’re a machindrum lover as i am
https://www.elektronauts.com/files/603
Huge thanks to @andreash for his corrections! 
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Big thanks to all involved, a very fascinating read. I always thought some of the FM machines have different waveforms for the modulator but now I realise they are all sines with a preset amount of feedback (the ones that don’t have the feedback parameter).
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Thanks for this legends!
Unbelievably niche and cool information, thank you!
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