I realise there hasn't been any rock content in the diary; part of the work with the diaries is hunting out the lesser-heard pieces.  But coming up to date, at least  bit, here's a famous melody.  I like it in this context because it starts with a melody on the guitar, which is followed by a different melody on the voice.

Don't fight forces, use them R. Buckminster Fuller.

Harmony is not two tones sounded simultaneously.  There are two distinct problems with this definition.  First, the number of tones -- you really do need three, at least if you're talking about functional harmony.  You need that third tone to give you your triad, which as we all learned in music theory is the basis of functional harmony.  In context, two tones can suffice but you have to have the right context.  Second, an arpeggio is not sounded simultaneously but you get your harmony anyway.

Two melodies playing together do not necessarily make counterpoint -- they will (if they are nonparallel melodies) make some form of polyphony, though.  

Bach did not employ five melodies simultaneously, but he did write the occasional five-voice fugue.  There is the quodlibet but that's only four melodies.  :-)

I will mercifully stop now.  I hope the following negates any pain I may have caused:

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here's the score in PDF for anyone who wants to follow along:  http://www.icking-music-archive.org/scores/g.gabrieli/gabcan2part.pdf

M83 - In The Cold I'm Standing - 04:05

(BTW, what time signature is this?)

_{*Lunatic*, n.
One whose delusions are out of fashion.}

The belief by the early church in the perfectibility of the universe led to rules that mostly focused on small integers and simple geometric shapes.

The most absurd instance was the insistence that the earth was the center of the universe and the the orbits of the planets were circles, but something similar happened in music.

By using simple ratios one can get close to the common western scale. The easiest way to demonstrate this oneself is to pluck a stretched string and then stop it length at various points. Stopping at the middle produces an octave (1;2), 3:2 produces a fifth, etc.

The problem is that when one divides the scale into 12 steps the ratios are slightly off. Music theorists struggled with the discrepancy for several hundred years and rather than give into the actual mathematics of the situation they invented all sorts of fudges. These are called "temperaments", and the most famous is the one used by JS Bach in his "Well Tempered Clavier". The correct mathematical solution to dividing an octave into 12 equal parts is that each step's frequency has a ratio to the next of the 12th root of 2 - an irrational number (1.059...).

Since this is an irrational number the intervals that should sound harmonious such as the fifth and third are actually discordant and beat. Western ears no longer notice this, but many other cultures use different musical step sizes and/or have other than 12 notes to the scale.

There are many sites where one can hear examples of this, sometimes the differences are subtle and require retraining one's ears, sometimes (as in Indian and other Asian music) the differences are quite noticeable. Even in western culture jazz and blues musicians don't stick to the standard pitches, but "bend" the notes.

Over the years I've tried different tunings on my harpsichord, some can really throw pieces into a different light. The key that a piece was written in used to make a big difference when instruments didn't used equal note steps, now it is mostly just nostalgia when someone choses a key for a piece.

Policies not Politics
---- Daily Landscape