The Creation of the Macrocosm of Music
The Tonal Development over the Last Millennia
Parallels of Fifths
From the Fourth to the Minor Third
The Dominating Intervals between the Classical and Romantic Periods
the beginning of our known musical history, man sang and played in only one
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.
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.
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.
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.
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.
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.
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.