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.

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.

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.

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.