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ETHNIC MUSIC

The Systems of
Order in Music

Tonality

Differences
in Understanding as Reflected by Language

The Beginnings of
Musical History

New Sound Composer
of the 20th Century and the
Range of Intervals

Advancing
to the Transcendental
Play of Music

Musical Insight into the Culture of Peoples

Musical Relationships

The Musical Path
to Self-Knowlegde

Homophony

Polyphony

The Counterpoint

The Threefold Perfect
Form of the Harmony

Relations in Music

 

Peter Hübner
Founder of the
Micro Music Laboratories

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  The Systems of Order in Music
       
 
The Beginnings of Musical History


 
 
 
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.

 
Parallels of Fifths
 
 
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.

 
From the Fourth to the Minor Third
 
 
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.

 
The Dominating Intervals between the Classical and Romantic Periods
 
     
     
                                 
     
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                     
                                     
  With kind permission of AAR EDITION INTERNATIONAL
© 1998 –  MICRO MUSIC LABORATORIES



 
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