When a note is produced from a musical instrument (e.g. pull a string), it was a combination of the base frequency and its multples. For example, the note A will contain the base frequency 110Hz and its multiples like 220Hz, 330 Hz etc. The combimation depends on the position the string is pulled. If the string is pulled in the middle, the frequency combination will be 110, 220, 440 (i.e. multiple factor of 1, 2, 4, 8... etc). If the string is pull at the third position, the frequency combination will be 110, 330, 660 etc).
A chord is a contains minimum 3 notes. The dorminant (5th note) is 1.5 times frequency of the tonic. The third node is 1.25 times frequency of the tonic. When these 3 notes are played together, there are many common frequency and thus the output sound very harmonic. For example, A has frequency of 110Hz. E, the dorminant note has frequency of 165Hz. They have a common frequency of 330Hz and thus they sound harmonic together.
For a minor chord, the third note is changed to have a relative frequency of 1.2 which has less strongly links to the other 2 notes.
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