| Sr. No. |
My Notes On Music |
| 1 |
The Basics:- |
| a |
The human ear percieves sound from 20 to 20 khz range. Technically any note of any frequency in this range can be a musical note. A single note by itself cannot be percieved as musical unless it is viewed in the context of a preceeding or another succeeding note, or in other words, a note cannot be percieved as musical in isolation. |
| b |
The reason is that all musical notes are percieved as musical by humans only if each note in a musical sequence has a frequency that is mathematically linked to the others. The maths used by the human ear is that of the Logarithmic values of base 2. |
| c |
If one considers an arbitrarily selected value of frequency as the fundamental or base frequency, all other successive notes are connected to the fundamental by the expression f(n) = f(0)*(2)exp(n/12) . That makes the first nearest musical note next to the fundamental as f(0)*1.05946 hz. Multiplying each note by 1.05946 yields the next note until the 12th note which is f(0)*2exp(12/12) is exactly the double of the fundamental in frequency, and is called the first harmonic. The pentatonic scale consists of the 12 notes consisting of seven tones and 5 semi-tones. |
| d |
The foregoing leads us to conclude that if we generate a series of notes following the mathematical rules as above, we will be able to create music. This knowledge led me in the 80's to rig up a simple circuit clocked by the 555 timer (astable multivibrator), the CD4017 synchronous ring counter, AND a dozen and gates, to generate my own electronic music. The theory was simple. If you notice, the figure 1.05946 represents a 6% change in each frequency value. That meant that at 100 hz fundamental frequency, I would require the next to be 106 hz. To save one decade counter, I took the risk of starting at 50 hz fundamental. That made my first harmonic fall at 100 hz. I did not need a third counter for that. The last ring counter generated a 100 hz by itself. The 2 input AND gates were all hard wired to the decoded decimal outputs of the 4017 ring counters for values 50, 53, 56 etc (each succesive one 6 % more than the previous one). A conductive rod was slided along the output tracks of the gates (shaped to look like a keyboard on the pcb). In isolation each output was just a tone, but if one slid the conducting bar across the keyboard, a musical crescendo was the result, as each note was satisfying the musical log relation to base 2! |