Vilen
2012-04-26 12:28:03 UTC
I like to think that obvious crisis in this group reflects common
crisis of so called "music theory" which in a matter of fact is
totality of handcraft recommendations to composition and performance
of music. Its main notion-note is act of single influence on music
instrument (result of which is able to vary in very big limits) and
further all its notions are bound to music instruments e.g. overtones,
chord, chord progressions, inversions. These notions is part of
language of instructions for production of music. There are more
abstract notions as fundamental bass (FB), octave equivalence,
tonality. In reality their content is an instruction as well. For
example about tonality
(http://www.tonalityguide.com/introoverview.php):"tonality is made
meaningful through usage, and theory can only limp along behind in its
attempt to explain it as a system."
The Rameau's idea of FB is try to give scientific basis for his
classification of chords in which chords in close positions and their
inversions are named equally. Possibly, such classification is best
from point of view of practice on common music instruments, but the
notion of fundamental bass is source of endless confusion. Rameau
derived FB from the fact that major triad corresponds rather good
ratios 4:5:6. Hence follows that note with same name as tonic is
begin of natural row 1:2:3:4.....and for that he came to conclusion
about naturalness of major triad. However conformity to multiples 4,6
is trivial as it follows from Pythagorean tuning (PT) and conformity
to multiple 5 isn't exact. Once more, remarkable is that in 12 ET
scale multiple 5 has better approximation as by PT and the multiple 7
hasn't good approximation in both 12 ET and PT. Besides in the
minor mode the triad has ratios 10:12:15 so its root doesn't
correspond fundamental multiple 1.
Rameau himself wrote about scientific foundations of his theory:
"We finally possess the principle of this profound knowledge which
will render immortal the glory of mathematics and mathematicians. This
principle is in the vibrating body".
The vibrating body is main part of common music instruments and music
theory then comes to rules of their use. Nevertheless music includes
not only production of musical sound but its perception as well and
scientific knowledges about music perception must be very important
for music theory. In times of Rameau these knowledges were
contemptible. It is bad that Rameau's followers in general ingnored
and continue to ignore accessible knowledges about music perception
even ones obtained in 19 century. For example works of H.Helmholtz
which assert that sound is perseived as totality of its spectal
components were almost ignored. The discovered in his time phenomen
of missing fundamental is ignored in music theory too. Not only
Rameau's followers act in such way. So P.Westergaard author of the
book (1975) "An Introduction to Tonal Theory " believed that
knowledges about music perception not yet for long time would be
insufficient for use in music theory and perception of music must be
evaluated on introspection.
Interesting in his theory is try to exclude notion of harmony. The new
Internet book of T.Sutcliffe ( http://www.harmony.org.uk/ ) which
apparently doesn't exclude harmony pretends to unite ideas of chord
progressions and voice leading and leans upon introspection as well.
I think that fact of sound perception as totality of its spectral
components is most important. It follows that this totality may be
created in various way by sets of components analogous to common music
notes. The oscillations of string or air in cylinder is most
adequate presentations of common music notes. Primitive music
instruments with them are encountered in the nature in almost ready
condition as well stones for primitive construction. Let us imagine
the civilization in which construction is based only on raw stones.
However, there is analogous situation in music. Of course we very
like many music works but ancient people liked their music too.
Now the creation of notes with any set of harmonics is possible
and this situation must be used for purposeful influence on important
elements of perception: dissonances, repetition of some spectral
components in melody notes, creation effect of leading note, control
over missing fundamental perception.
Relative last one
I found the interesting article "Pitch is determined by naturally
occurring periodic sounds". (http://www.purveslab.net/publications/
schwarrtz_purves_pitch.pdf 2004) . Here "naturally occurring" is
very important. It means that human (and not only human) can determine
pitch of some signals even if the partial with equal pitch is
absent or weak and that it is vital important ( e.g. distinguishing of
voices). This ability exist for human voice and in common roughly
harmonic signals which may be presented as sum of sinusoids which
frequencies are multiples of signal pitch and which intensities
decrease with increase of multiples. Music chords mightn't belong to
such signals.
According contemporary notions the brain determines pitch from
signal's period . In order to estimate the complexity of this task for
different signals with same pitch I calculated graphics are presented
on the site
http://home.arcor.de/yuri.vilenkin/mel-harm-rev.html.
The obtained graphics permit to suppose that for major and minor
chords determination of periods and hence their pitches is more
difficult in comparison with harmonic structure which includes several
first overtones. Yet this comparison isn't a basis to conclusion that
major and minor triads evoke equally strong pitch sensations.
J.S Bach's saying :
" the left hand plays the prescribed notes; the right hand, however,
executes the consonances and dissonances so that a pleasing harmony
will result to the honor of God and the soothing delight of the
spirit. As in all music, the be all and the end all, the sole aim of
the figured bass should be to the glory of Cod and for the recreation
of the soul."
Thus the root note of bass part determines current pitch and its other
notes determine dissonances and consonances (horizontal ties) but can
disturb the pitch feeling. Therefore one could suppose that way of
counterpoint created better pitch sensation then use of chords in
close spacing.
Yuri Vilenkin
crisis of so called "music theory" which in a matter of fact is
totality of handcraft recommendations to composition and performance
of music. Its main notion-note is act of single influence on music
instrument (result of which is able to vary in very big limits) and
further all its notions are bound to music instruments e.g. overtones,
chord, chord progressions, inversions. These notions is part of
language of instructions for production of music. There are more
abstract notions as fundamental bass (FB), octave equivalence,
tonality. In reality their content is an instruction as well. For
example about tonality
(http://www.tonalityguide.com/introoverview.php):"tonality is made
meaningful through usage, and theory can only limp along behind in its
attempt to explain it as a system."
The Rameau's idea of FB is try to give scientific basis for his
classification of chords in which chords in close positions and their
inversions are named equally. Possibly, such classification is best
from point of view of practice on common music instruments, but the
notion of fundamental bass is source of endless confusion. Rameau
derived FB from the fact that major triad corresponds rather good
ratios 4:5:6. Hence follows that note with same name as tonic is
begin of natural row 1:2:3:4.....and for that he came to conclusion
about naturalness of major triad. However conformity to multiples 4,6
is trivial as it follows from Pythagorean tuning (PT) and conformity
to multiple 5 isn't exact. Once more, remarkable is that in 12 ET
scale multiple 5 has better approximation as by PT and the multiple 7
hasn't good approximation in both 12 ET and PT. Besides in the
minor mode the triad has ratios 10:12:15 so its root doesn't
correspond fundamental multiple 1.
Rameau himself wrote about scientific foundations of his theory:
"We finally possess the principle of this profound knowledge which
will render immortal the glory of mathematics and mathematicians. This
principle is in the vibrating body".
The vibrating body is main part of common music instruments and music
theory then comes to rules of their use. Nevertheless music includes
not only production of musical sound but its perception as well and
scientific knowledges about music perception must be very important
for music theory. In times of Rameau these knowledges were
contemptible. It is bad that Rameau's followers in general ingnored
and continue to ignore accessible knowledges about music perception
even ones obtained in 19 century. For example works of H.Helmholtz
which assert that sound is perseived as totality of its spectal
components were almost ignored. The discovered in his time phenomen
of missing fundamental is ignored in music theory too. Not only
Rameau's followers act in such way. So P.Westergaard author of the
book (1975) "An Introduction to Tonal Theory " believed that
knowledges about music perception not yet for long time would be
insufficient for use in music theory and perception of music must be
evaluated on introspection.
Interesting in his theory is try to exclude notion of harmony. The new
Internet book of T.Sutcliffe ( http://www.harmony.org.uk/ ) which
apparently doesn't exclude harmony pretends to unite ideas of chord
progressions and voice leading and leans upon introspection as well.
I think that fact of sound perception as totality of its spectral
components is most important. It follows that this totality may be
created in various way by sets of components analogous to common music
notes. The oscillations of string or air in cylinder is most
adequate presentations of common music notes. Primitive music
instruments with them are encountered in the nature in almost ready
condition as well stones for primitive construction. Let us imagine
the civilization in which construction is based only on raw stones.
However, there is analogous situation in music. Of course we very
like many music works but ancient people liked their music too.
Now the creation of notes with any set of harmonics is possible
and this situation must be used for purposeful influence on important
elements of perception: dissonances, repetition of some spectral
components in melody notes, creation effect of leading note, control
over missing fundamental perception.
Relative last one
I found the interesting article "Pitch is determined by naturally
occurring periodic sounds". (http://www.purveslab.net/publications/
schwarrtz_purves_pitch.pdf 2004) . Here "naturally occurring" is
very important. It means that human (and not only human) can determine
pitch of some signals even if the partial with equal pitch is
absent or weak and that it is vital important ( e.g. distinguishing of
voices). This ability exist for human voice and in common roughly
harmonic signals which may be presented as sum of sinusoids which
frequencies are multiples of signal pitch and which intensities
decrease with increase of multiples. Music chords mightn't belong to
such signals.
According contemporary notions the brain determines pitch from
signal's period . In order to estimate the complexity of this task for
different signals with same pitch I calculated graphics are presented
on the site
http://home.arcor.de/yuri.vilenkin/mel-harm-rev.html.
The obtained graphics permit to suppose that for major and minor
chords determination of periods and hence their pitches is more
difficult in comparison with harmonic structure which includes several
first overtones. Yet this comparison isn't a basis to conclusion that
major and minor triads evoke equally strong pitch sensations.
J.S Bach's saying :
" the left hand plays the prescribed notes; the right hand, however,
executes the consonances and dissonances so that a pleasing harmony
will result to the honor of God and the soothing delight of the
spirit. As in all music, the be all and the end all, the sole aim of
the figured bass should be to the glory of Cod and for the recreation
of the soul."
Thus the root note of bass part determines current pitch and its other
notes determine dissonances and consonances (horizontal ties) but can
disturb the pitch feeling. Therefore one could suppose that way of
counterpoint created better pitch sensation then use of chords in
close spacing.
Yuri Vilenkin