Home Page


About This Page
 

After years of procrastination, I finally broke down and bought my first keyboard.  Wanting to dig right in, I also purchased a few books that promised to teach me how to play, along with a couple that described how the various scales and chords are put together.  Being an inquisitive type, I immediately began pondering what seemed to be very obvious questions regarding certain conventions.  Things that many aspiring musicians, eager to simply get started actually playing something, probably just accept - taking for granted that this is the way it has to be.  But not me – I always have to do things the hard way!!

For instance, I wondered why there are no sharps or flats between the B and C keys, or the E and F.   I questioned how the lowest and highest notes on a piano were chosen, and how the frequency for each tone was decided upon.  Why are the musical scales based on octaves, I asked, and why are there twelve chromatic tones between each octave in our (i.e. western) arrangement while other systems are, for example, pentatonic (i.e. based on only 5 tones)??  Lastly, why is there only a half-step at the fourth and last tones on the scale of a major key, while whole steps occur elsewhere (and the pattern changes as it does for a minor key)??

In addition, I knew from my previous investigations into early synthesizers and electronic music that there existed something called temperament whereby certain tones were "adjusted" for better sound quality.  I couldn't remember the details, so I wanted more information on that as well.

I began doing some preliminary research, and found several books and articles that would eventually answer most of my questions.  But I wasn't going to be satisfied with simply reading about how things are.  One learns more thoroughly when one understands why something is done the way it is.  So in order to truly understand the why behind the various decisions made over the years, I wanted to try inventing my own system first.  That way I could see first-hand the problems this entails, and how my results might differ from those systems that had been developed in the past.  And finally, I could then follow the trail through history to see how these early systems eventually evolved into the commonly accepted arrangement that we use in the western world today.

This paper describes my travels into the realm of intervals, octaves, and perfect fifths.  For those of you who are preparing to take the first step of this journey, allow me to be your guide through this otherwise mysterious and sometimes rough terrain (just click the "next" button below).  I promise you not only safe passage, but that there will be many sights (not to mention sounds) along the way that will astound and delight you!!

 

This page was last updated on  February 12, 2023