OK, I'll take a shot at explaining why we might use the Railsback curve
(or not).
Inharmonicity is a spread in the harmonics above the fundamental pitch.?
The harmonics generated by a physical string become sharper and sharper
when compared to the theoretical pitch you would actually prefer.? Low
notes on the piano have the highest inharmonicity, and as you go up the
keyboard the spread lessens. The harmonics become more in tune the
higher you go.? I could show you a graph of a patch where the inharmonic
spread is easily visible off the Yamaha VP1, but these text messages
don't include jpeg's.? The inharmonicity in the piano is not actually
visible on a spectrum plot, you have to calculate the theoretical pitch
of the harmonic, then compare it to a spectrum analyzer value in order
to see it.? I've done that, I have a spreadsheet showing a couple of
pitches across the ranges of a LOT of instruments, not just the piano,
compared to the theoretical values.
If you to play low notes on the piano and high notes at the same time,
the high notes would be flat when compared to the actual harmonics (or
inharmonics) generated by the lower, thicker strings.? For the high
notes to sound more in tune with the bass notes, you have to tune the
upper ranges on the piano sharper and sharper as you go up the
keyboard.? If you don't, you get a more audible beat pattern.? Piano
tuners tune the mid range to match the mathematical pitch for the note,
but tune the higher notes sharper, and the bass notes flatter.? That way
you can play the low end of the keyboard at the same time as the high
end and it sounds more in tune.
On an electronic reproduction of a piano, the need for Railsback tuning
depends upon how the keyboard generates it's sound.? If it's like a
Yamaha Motif or Montage, the synth uses a different recording of a piano
for every 4 to 6 notes up the keyboard. Because it's based on actual
recordings, then pitch adjusted, it doesn't need to be bent further off
the pitch.? The piano used to create the recordings was already tuned
properly using the Railsback technique, so the recordings are already
pitch adjusted.? If the electronic piano uses just one sample recording
of a note, then pitch-adjusts it for all of the other notes, it will
need some tuning to make it sound in tune over the entire width of the
keyboard.? To get the low notes to match the high notes when you play
both at the same time.
Now back to the DX7.? The DX7 does NOT replicate the inharmonicity of a
piano correctly.? All FM modulation creates linearly, evenly spaced
harmonics, not fractally spaced inharmonic harmonics.? The only way to
create inharmonicity is to create groups of harmonics using modulated FM
operator pairs, then shift the upper sets slightly sharp on purpose.? If
you do that, you can create a convincing piano patch that sounds closer
to a real piano.? Then, you could do the Railsback tuning to get the low
notes working better in tune with the high notes.
I actually have a fairly decent FM piano patch on the FS1R, and another
on the Montage.? They aren't Railsback tuned, but I suppose they could
be.? I've spent way too much time attempting to create a realistic piano
patch using FMX which is why I have a bit more information to work from
than most people.
Does that help?? Or did I lose you by not using pictures?
Best Regards,? Thor
