----- Original Message -----
From: Jesse Hager <jesse.hager <at> yahoo.com>
To: YamahaDX <at> yahoogroups.com
Sent: Wednesday, 13 June 2012, 20:02
Subject: Re: [YamahaDX] Re: PSS-4/5/680 sine wave variations
The problem with software synths like FM8 is that they implement the
math a little too perfectly. The chips used in the hardware synths cut
many corners to minimize the transistor count. The limited DAC
resolution is only a small part of it.
The math used for the FM operators is often explained like:
output = si
n(phase + input) * envelope_gen()
This is what any sane software engineer would use to implement the
chips on the other hand use addition of logarithms to approximate
the multiply followed by a log->linear calculation something like this:
output = exp( log(sin(phase + input)) + log(envelope_gen()) )
Keep in mind *this* addition of logarithms is the calculation that is
quantized to 10 or 12 bits. The sine wave table on the chip is actually
stored as a log(sin(X)) table. This table has long decimal values
crammed into a few bits.
log(sin(pi/8)) = -0.9605471789297305
in 10 bit chips this becomes: 758
in 12 bit chips this becomes: 3032
so the loss of accuracy is considerable.
This trick straight out of the slide-rule days saves many transistors
and makes the chip run fast enough to generate 32 operators of realtime digital audio using 1980's semiconductor tech. Since the envelopes and
volume control are supposed to be logarithmic anyway this saves even
calculations. (Sound levels are measured in decibels, a logarithmic
It also adds subtle distortions to the audio output that are not present
in a perfect implementation. A perfect implementation will be too clean.
By the way, the actual DAC output has a 16 bit range but throws away the
lowest bits. On loud sounds it throws away more bits than on quiet
sounds. If you just capped it at 12 bits it wouldn't be the same. You'd
lose bits evenly causing quieter sounds to be more distorted.
Sorry for the math everybody. :)
On 6/13/2012 5:36 AM, idledpolkapeel wrote:
> that theory would hold water except for the fact i can load 4op tx81z
> patches straight from the tx81z into FM8, spec for spec setting
> identical and they sound worlds apart. even if i add a bitcrusher or
> resample to emulate the 12bit convertor the tx has FM8 doesn't come
to sounding the same, on the same monitors using the same motu
> system. Whatever the DA convertors are adding, it's relevant. this goes
> to more extremes with the FS1R.
> --- In YamahaDX <at> yahoogroups.com
> Martin Tarenskeen <m.tarenskeen <at> ...> wrote:
> > I am a fan of hardware synths, but I do not hate softsynths.
> > The DX7 (etc) are digital synths: Math is used to calculate waveforms,
> > then after DA conversion you have sound.
> > That's exactly what computers/softsynths also do. When
it comes to
> > synthesis I don't see any reason to be sentimental about those old
> > hardware synths vs. new software
> > When the first DX7 and DX9 came out I was not at all impressed. Yes,
> > could produce sounds that were not possible with the existing analog
> > synths. But something was missing.
> > When the DX7II came out I new what. The better quality D/A conversion
> > really made a difference. Better dynamics, better bright and clear
> > better warmth. You can compare this with the first generation CD player.
> > They did did not sound that pleasant if you compare them to the later CD
> > players.
> > Some people say the old DX7 has more "character" - whatever that
t; means. I
> > don't agree. I think that this IS true for the old analog synths from
> > and others. But the DX7II and TX81Z
sound better than the first DX7 and
> > for example the FB01. Digital revolution had just started, any many
> > technical improvements, better chips, etc, made improvement possible.
> > Sometimes people say "A real old DX7 sounds SO MUCH better than FM8".
> > probably have heard FM8 only on their cheap laptop speakers directly
> > connected from a noisy headphone jack output. Try a pro external
> > or USB soundcard/audio-interface with high quality D/A conversion and
> > amplification and monitors.
> > Don't get me wrong, I still love those old DX7 and TX81Z.
> > I just don't
> > Or in fact I do, but that is a completely different story
> > --
> > MT
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