Vilen
2011-05-26 11:42:56 UTC
Arestoxenus (3400 BC) was author of first musical book "Elements of
harmony" and inventor of majority of now used music notions.
Characteristic that he understand harmony essential othervise as it is
established now as the sound of two or more notes heard
simultaneously. Just he saw content of harmony in determination of
pertinent melody intervals. "In ancient Greek writings on the subject
of music, harmony was the study of the formation of melody."( see
http://science.jrank.org/pages/9577/Harmony-Harmony-in-Ancient-Greek-Writings-on-Music.html)
From the other hand Arestoxenus made very important observation
relative difference of singing and speech. The peculiarity of singing
(also instrumental music) consists in constancy of perceived pitch
on separate time intervals. Now it is possible to make on basis of
comtemporary knoledge important conclusions from that. Clearly this
constancy is necessary to fix the pitch in memory. But now it is known
that music sound includes several sinusoidal components at the same
time. If this sound is made by voice or common music istrument these
components are overtone series with frequency ratios 2,3,4,5.... ,
they are remembered ( if they enough strong) and corresponding pitches
can serve as steps for next melody notes. Thus good singing without
accompaniment may be compared with action of montaineer which
prepares his new positions himself.
. Thus notes with harmonic melody intervals must include coincident
sinusoidal components (partials). But the analogous and the more
severe demand functions for simultaneously existing notes in chords:
they are able to have concident partials and not have strong
partials with near pitches with ca semitone distance. The major and
minor triads fulfils this demand and therefore their sets of notes
were elicited by practice as melody notes in major-minor system. This
fact was asserted by Rameau in his well known work about harmony.
Of course chords were impossible in Aristoxenus epoch but their main
function is providing of music horizontal ties i.e. harmony in sence
of Arestoxenus. The chord as simultaneously existing notes may be
compared with bridge pier which joins its spans.
There is another aspect of Arestoxenus view which was not adopted his
contemporaries and following generations.That is concerning role of
ratious of small integers in perception of music. And as that good
said in http://en.wikisource.org/wiki/Complete_Encyclopaedia_of_Music/A/Aristoxenus
" He held it was absurd to aim at an artificial accuracy in gratifying
the ear beyond its own power of distinction! That he had anticipated
the satisfactory discoveries of modern ages by his doctrine, is
sufficiently clear nowadays". Indeed psychogic researches shows that
human brain isn't able quickly estimate quantities more as 4, then is
difficult to imajine that during small music intervals brain
is able to identificate such ratios as 3/2, 4/3, 5/4.... Nevertheless
it seems to me that majority of musicians aren't agree with
Aristoxenus even now. This question is of principle importance: before
frequency partials of all music instruments correspond roughly
overtone series, now another instruments is possible and if exact
values of ratios aren't essential then the road to thes ones is open.
Besides Aristoxenus asserted that music scale must be build on ear,
i.e.accordingly human perception. Now is known that perception of
pitch intervals correspond logarithmic law and it is long time since
music scale is build in this way. Thereby exist contradictions with
customary music instruments which partials don't exactly accord the
scale. Therefore refusal from overtone series as basis of note's
structure would improve many problems as enharmonicand inharmonicity.
But most important that instead unique note structure many are
possible which may be much better.
Yuri Vilenkin
harmony" and inventor of majority of now used music notions.
Characteristic that he understand harmony essential othervise as it is
established now as the sound of two or more notes heard
simultaneously. Just he saw content of harmony in determination of
pertinent melody intervals. "In ancient Greek writings on the subject
of music, harmony was the study of the formation of melody."( see
http://science.jrank.org/pages/9577/Harmony-Harmony-in-Ancient-Greek-Writings-on-Music.html)
From the other hand Arestoxenus made very important observation
relative difference of singing and speech. The peculiarity of singing
(also instrumental music) consists in constancy of perceived pitch
on separate time intervals. Now it is possible to make on basis of
comtemporary knoledge important conclusions from that. Clearly this
constancy is necessary to fix the pitch in memory. But now it is known
that music sound includes several sinusoidal components at the same
time. If this sound is made by voice or common music istrument these
components are overtone series with frequency ratios 2,3,4,5.... ,
they are remembered ( if they enough strong) and corresponding pitches
can serve as steps for next melody notes. Thus good singing without
accompaniment may be compared with action of montaineer which
prepares his new positions himself.
. Thus notes with harmonic melody intervals must include coincident
sinusoidal components (partials). But the analogous and the more
severe demand functions for simultaneously existing notes in chords:
they are able to have concident partials and not have strong
partials with near pitches with ca semitone distance. The major and
minor triads fulfils this demand and therefore their sets of notes
were elicited by practice as melody notes in major-minor system. This
fact was asserted by Rameau in his well known work about harmony.
Of course chords were impossible in Aristoxenus epoch but their main
function is providing of music horizontal ties i.e. harmony in sence
of Arestoxenus. The chord as simultaneously existing notes may be
compared with bridge pier which joins its spans.
There is another aspect of Arestoxenus view which was not adopted his
contemporaries and following generations.That is concerning role of
ratious of small integers in perception of music. And as that good
said in http://en.wikisource.org/wiki/Complete_Encyclopaedia_of_Music/A/Aristoxenus
" He held it was absurd to aim at an artificial accuracy in gratifying
the ear beyond its own power of distinction! That he had anticipated
the satisfactory discoveries of modern ages by his doctrine, is
sufficiently clear nowadays". Indeed psychogic researches shows that
human brain isn't able quickly estimate quantities more as 4, then is
difficult to imajine that during small music intervals brain
is able to identificate such ratios as 3/2, 4/3, 5/4.... Nevertheless
it seems to me that majority of musicians aren't agree with
Aristoxenus even now. This question is of principle importance: before
frequency partials of all music instruments correspond roughly
overtone series, now another instruments is possible and if exact
values of ratios aren't essential then the road to thes ones is open.
Besides Aristoxenus asserted that music scale must be build on ear,
i.e.accordingly human perception. Now is known that perception of
pitch intervals correspond logarithmic law and it is long time since
music scale is build in this way. Thereby exist contradictions with
customary music instruments which partials don't exactly accord the
scale. Therefore refusal from overtone series as basis of note's
structure would improve many problems as enharmonicand inharmonicity.
But most important that instead unique note structure many are
possible which may be much better.
Yuri Vilenkin