| |
In
the beginning of our known musical history, man sang and played in only one
voice.
Then, with the loss of the mental ability to differentiate within the tone,
the microcosm of music was lost. What remained was the undifferentiated, the
indifferent tone.
|
|
Loss of the
Microcosm
of Music |
| |
|
|
Then the attempt
was made to build, on top of that one tone, one after the other, the sounds
of the overtone-spectrum as further, outer, accompanying sounds in the macrocosm
of music. This artificial structure, the unconscious outer substitute for
the inner loss of the tone, influenced the entire historical development of
music. |
|
The Creation of the
Macrocosm of Music |
| |
|
|
Within the last
few thousand years we therefore witness the following development of tonality:
With the increasing desire to further differentiate the macrocosm of music,
arrangements for one voice grew into arrangements for several voices. Thus,
the "one-voice system" was first expanded into a "two-voice system," and with
this apparent progress a lengthy development began to construct an outer multi-tonality
– as a substitute for the lost inner formation of the natural overtone-spectrum. |
|
The Tonal
Development over
the Last Millennia |
| |
|
|
Thus, at first,
two voices at the interval of an octave were used in songs and in the performance
of music. An octave is the distance between the basic tone and the first overtone.
From the singing and playing in octaves we may conclude that the hearing capability
can discriminate between the basic tone and the first overtone. According
to Pythagoras, the octave is at a ratio of 1 to 2. |
|
The Octave |
| |
|
|
Later, parallels
of fifths were employed in modern "up to date" songs and musical performances,
which caused great commotion among the music experts. The fifth is the distance
between the first and the second overtone.
From the singing and playing of music in fifths we may conclude that the hearing
capability can distinguish between the first and the second overtone. The
fifth, according to Pythagoras, is at a ratio of 2 to 3.
Then the modern
"up to date" songs and music were played in fourths, the distance between
the second and the third overtone. Here we may conclude that the singers and
players were able to differentiate between the second and the third overtone.
The fourth, according to Pythagoras, is at a ratio of 3 to 4. |
|
Parallels of Fifths |
| |
|
|
Much later, causing
great upheavals amongst the musical experts, music was performed using the
major third, the distance between the third and the forth overtone. From this
we may conclude that the singers and players, using the third, could differentiate
between the third and the fourth overtone.
The major third, according to Pythagoras, is at a ratio of 4 to 5.
Later again music
was made in the minor third, the distance between the fourth and the fifth,
and between the fifth and the sixth overtone respectively.
Here we may conclude
that the singers and players using the minor third could differentiate between
the fourth and fifth, and the fifth and sixth overtone. According to Pythagoras,
the minor third is at a ratio of 5 to 6 and 6 to 7 respectively. |
|
From the Fourth to the Minor Third |
| |
|
|
At about the time
of Bach, the thirds were well established and they were the preferred intervals
far into late Romanticism. Only the fact that octaves, fifths and fourths
are the dominating intervals of the natural scale of brass instruments, and
that they can be played easily and naturally on them, explains why these large
intervals have been kept so very alive through Beethoven's music to Wagner. |
|
The Dominating
Intervals between
the Classical and
Romantic Periods |
|
|
|
|
|
