An idea about H.Riemann's undertone series.

[Vilen]

It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
zusatz/33/33116/33116075_lese_1.pdf):
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism." Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

Yuri Vilenkin

[Hans Aberg]

Post by Vilen
It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism." Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

It is hard to know, without more data, but the WP indicates that
undertones can be produced by means of a tuning fork that sometimes hits
a paper every second or third oscillation. So it might be possible
through other forms of distortion.

Hans


https://en.wikipedia.org/wiki/Undertone_series

[Vilen]

Post by Hans Aberg

Post by Vilen
It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism."  Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

It is hard to know, without more data, but the WP indicates that
undertones can be produced by means of a tuning fork that sometimes hits
a paper every second or third oscillation. So it might be possible
through other forms of distortion.
Hans
https://en.wikipedia.org/wiki/Undertone_series- Zitierten Text ausblenden -
- Zitierten Text anzeigen -

Now that's easy to emulate undertones but Riemann used a piano in his
experiments.
Yuri

[Hans Aberg]

Post by Vilen

Post by Hans Aberg

Post by Vilen
It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism." Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

It is hard to know, without more data, but the WP indicates that
undertones can be produced by means of a tuning fork that sometimes hits
a paper every second or third oscillation. So it might be possible
through other forms of distortion.
https://en.wikipedia.org/wiki/Undertone_series- Zitierten Text ausblenden -

Now that's easy to emulate undertones but Riemann used a piano in his
experiments.

Try on a piano carefully holding down without striking the note say F2.
Then strike fairly hard C4 or other chord combinations and release
shortly to see if any energy is fed into the fundamental of F2. You can
check what sound remnant belongs to the F2 piano strings, and then repeat.

When I do this, all I hear is energy from the higher notes. It does not
sound like a F2 at all.

So it means that whatever undertones heard, they are not likely
acoustic, that is, physical outside human hearing. One does her
difference tones, though, produced in the cochlea. So they could be
taken for undertones, but they do not exist acoustically.

Hans

[Vilen]

Post by Hans Aberg

Post by Vilen

Post by Hans Aberg

Post by Vilen
It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism."  Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

It is hard to know, without more data, but the WP indicates that
undertones can be produced by means of a tuning fork that sometimes hits
a paper every second or third oscillation. So it might be possible
through other forms of distortion.
https://en.wikipedia.org/wiki/Undertone_series-Zitierten Text ausblenden -

Now that's easy to emulate undertones but Riemann used a piano in his
experiments.

Try on a piano carefully holding down without striking the note say F2.
Then strike fairly hard C4 or other chord combinations and release
shortly to see if any energy is fed into the fundamental of F2. You can
check what sound remnant belongs to the F2 piano strings, and then repeat.
When I do this, all I hear is energy from the higher notes. It does not
sound like a F2 at all.
So it means that whatever undertones heard, they are not likely
acoustic, that is, physical outside human hearing. One does her
difference tones, though, produced in the cochlea. So they could be
taken for undertones, but they do not exist acoustically.
Hans- Zitierten Text ausblenden -
- Zitierten Text anzeigen -

Yes, but perception includes the brain interpreting and feeling of
missing fundamental (in different grade) is scientific fact. It may be
compared with optical illusions when thank to brain interpreting
common people see, for example, nonexisting contours.The missing
fundamental don't exist acoustically in contrary to its feeling.
Probably such feeling was H.Riemann's cause to suppose undertones
desired for his harmony dualism theory .

Yuri Vilenkin

[Hans Aberg]

Post by Vilen

Post by Hans Aberg

Post by Vilen

Post by Hans Aberg

Post by Vilen
It is known history that important German music theorist heard
sometimes undertone. series. This "discovery" was over and again
ridiculed. For example A.Rehding wrote (http://bilder.buecher.de/
"The image of Riemann hearing undertones has become a derisory emblem
of the the theoretical hermeticism, coupled with a level of wrong-
headedness that is so much beyond our comprehension that ridiculing
the approach seems to be the only way to cope with sheer absurdity of
the concept of harmonic dualism." Nevertheless I can suggest some
explanation. Of course Riemann experimented with close minor triads
which characterized with ratios 10:12:15. So they have missing
fundamental on 40 semitones below their bass notes. In contrary to
fundamental bass of Rameau missing fundamental is real phenomena and
can be hear although less clearly then by the major triads. In these
conditions and by belief in Riemann's musical competence one can
assume that he heard triads' missing fundamentals.

It is hard to know, without more data, but the WP indicates that
undertones can be produced by means of a tuning fork that sometimes hits
a paper every second or third oscillation. So it might be possible
through other forms of distortion.
https://en.wikipedia.org/wiki/Undertone_series-Zitierten Text ausblenden -

Now that's easy to emulate undertones but Riemann used a piano in his
experiments.

Try on a piano carefully holding down without striking the note say F2.
Then strike fairly hard C4 or other chord combinations and release
shortly to see if any energy is fed into the fundamental of F2. You can
check what sound remnant belongs to the F2 piano strings, and then repeat.
When I do this, all I hear is energy from the higher notes. It does not
sound like a F2 at all.
So it means that whatever undertones heard, they are not likely
acoustic, that is, physical outside human hearing. One does her
difference tones, though, produced in the cochlea. So they could be
taken for undertones, but they do not exist acoustically.

Yes, but perception includes the brain interpreting and feeling of
missing fundamental (in different grade) is scientific fact. It may be
compared with optical illusions when thank to brain interpreting
common people see, for example, nonexisting contours.

The missing fundamental is the same as that of adjacent partials. Though
perhaps not researched, it may be enough to compute the difference tones
to also get the missing fundamental that is identified.

Post by Vilen
The missing
fundamental don't exist acoustically in contrary to its feeling.
Probably such feeling was H.Riemann's cause to suppose undertones
desired for his harmony dualism theory .

They exist physically to the human, as they are produced in the cochlea.
Somebody claimed one had found this by inserting microphones into the
ear. But not outside the human: it is easy to check the spectrum.

Hans