COSMOS Day 9 - Syn - together

The root "syn" means together, and Professor Jim Simmons basically taught my cluster about sound synthesis, using a synthesizer.  I have my notes somewhere on a Google Doc, but I am too lazy to pull up my lecture notes to put in this blog post.  I am therefore going to write a synopsis of everything we learned in one long sentence.  A synthesizer works by changing the way a sound wave is shaped when it is generated, and it is put together with other sounds to produce an electronically reproduced sound wave.

Using this new information, we can produce our own instrument sound that we imagine in our head.  Mixing this sound with the Ultrabeat machine, to produce a drum loop, we can create our very own melody just by dragging and dropping preset samples.  

Tomorrow we have out pythagorean tuning exercise due tomorrow.  The pythagorean tuning system is not synonymous with the equal temperament system.  The system is based on the ration 3:2 between the interval of a perfect fifth.  This makes for a very bright perfect fifth sound when played on an organ, but there will be at least one key that is unplayable in the tuning system, because there is some unequal balance between the notes.   The equal temperament solves this problem by multiplying the root frequency by the 12th root of 2.  All of this tuning is all inspired by the fact that we humans hear an octave as a frequency that is doubled.  The pythagorean system was not completely new territory to me.  My piano teacher explained a much more concise version of how the 3:2 tuning ratio works on an organ, but I never got to calculate frequencies based on this system.  Here are my results-

1. A  - 110.000
2. B  - 123.750
3. C# - 139.218
4. D  - 146.666
5. E  - 165.000
6. F# - 185.625
7. G# - 208.825
8. A  - 220.000

Those are my results for the pythagorean tuning.  That was also my homework due for 2009-07-07.  In general, one multiplies the root frequency by 1.5 to achieve the note 5 notes up (a perfect fifth).  Then the new frequency is multiplied by 1.5 to achieve the next perfect fifth.  This next frequency is then divided by 2 until it fits between the range of the scale.  In this case, for an A major scale, the range is 110 Hz to 220 Hz.  

I shall try to do the equal temperament tuning later. This is the system that all fixed-pitch instruments use.  However, instruments without frets like a violin can easily be manually adjusted when playing, and thus all four strings can be tuned in perfect fifths.