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# Hringr - Notes and Numbers (Toner, tal og tid)

English/ dansk

The fundamental note A2, 110 Hz, and the first 16 partials of its harmonic series (110 Hz-220 Hz-330 Hz-...-1.760 Hz) accompagnied by visualizations of the corresponding integers according to their factorization:
1, 2, 3, 2x2, 5, 2x3, 7, 2x2x2, 3x3, 2x2x3, 13, 2x7, 3x5, 2x2x2x2

It is crucial to be able to distinguish between the expression of a numerical value and a number system and to have a feel of the essence of number, as they come to expression through the overtone series.

The symbols here are not meant as a practical substitute for numbers, but as an example of a visualization which is more into line with their 'inner nature' than a number system. They should not be confused with Cymatics.
The core of the understanding of numbers is their factorization. Prime numbers are 'atoms', while composite numbers are 'molecules'.
A master key to use numbers in accordance with their essence more than as 'price labels' emptied of meaning is to understand how the integers express themselves in the harmonic series, where

1-2-4-8-16-... is the fundamental and its octaves
3-6-12-... is the perfect fifth and its octaves
5-10-... is the just major third and its octaves

www.musicpatterns.dk

DANSK:
Tonen 110 Hz (A), dens overtonerække nr. 1-16 og visualiseringer af tallene, som de fremstår i kraft af deres primtalsanalyse:

1, 2, 3, 2x2, 5, 2x3, 7, 2x2x2, 3x3, 2x2x3, 13, 2x7, 3x5

Det er vigtigt at kunne skelne mellem udtryk for talværdi, talsystem og at have sans for tallenes væsen, som de bl.a. kommer til udtryk gennem overtonerækken.

Symbolerne her er ikke tænkt som en praktisk erstatning for tal, men som et eksempel på en fremstilling, som mere retter sig efter deres natur end et talsystem. De skal ikke forveksles med kymatik.
Kernen i forståelsen af tal er deres opløsning i primfaktorer. Primtal er 'atomer', mens sammensatte tal er 'molekyler'. En hovednøgle til at bruge dem som andet end meningstømte værdimålere er at forstå, hvordan heltallene udtrykker sig i overtonerækken, hvor

1-2-4-8-16-... er primærtone og oktaver heraf
3-6-12-... er ren kvint og oktaver heraf
5-10-... er stor terts og oktaver heraf
...

www.musikkensmønster.dk

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