P

Paul Taylor

Audiophyte
can anyone tell me in Hz what an octave is?

Just got thinking after Gene's last vid on loudspeaker design...
 
TLS Guy

TLS Guy

Seriously, I have no life.
can anyone tell me in Hz what an octave is?

Just got thinking after Gene's last vid on loudspeaker design...
An octave is not linear. It is a doubling of frequency and therefore logarithmic. So the first octave is basically 20 to 40 Hz, the second 40 to 80 Hz, the third 80 to 160 Hz, the fourth 160 to 320 Hz and so on.

It was not quite always this way. This logarithmic equal tone scale is basically due to J.S. Bach who split the difference in the musical intervals. He called it the Well Tempered Scale. He wrote the Well Tempered Clavier as the instruction manual to teach others how to use it and write in it.

Here is a chart showing equal temperament and other musical intervals and scales that have been used.



Prior to the Well Tempered Clavier of J.S Bach the usual temperament in Europe, was the mean tone, which is a stack of perfect musical fifths. This is the same as the Pythagorean tone in the chart above.

Bach's Well Tempered tone is much more flexible and liberated musical composition for all time.
This is just one of Bach's huge contributions to music apart from actually composing some of the finest, beautiful and interesting music ever written. In 2000 musicologists voted him the composer of the Millennium by a wide margin.
 
rojo

rojo

Audioholic Samurai
Doc, I've got to say, I'm highly impressed, in awe, and a little frightened all at the same time. Did you sell your soul to Satan in exchange for knowing everything about everything?



Can you tell me how not to want to stab myself in the ear whenever I hear Schoenberg?

Sent from my LG-VS980 using Forum Fiend OSP v1.3.3.
 
TLS Guy

TLS Guy

Seriously, I have no life.
Doc, I've got to say, I'm highly impressed, in awe, and a little frightened all at the same time. Did you sell your soul to Satan in exchange for knowing everything about everything?



Can you tell me how not to want to stab myself in the ear whenever I hear Schoenberg?

Sent from my LG-VS980 using Forum Fiend OSP v1.3.3.
The physics of sound and music are intimately related as you would expect.

Tonality and its moorings are a little complex to understand, but not that bad.

Lets us just clear one piece of housekeeping. In interest of clarity, I called the 20 to 40 Hz octave the first to have the frequencies progress in order. In fact that octave is the last and actually spans 16 Hz to 32 Hz. The first octave being 10 KHz to 20 KHz.

Now there are 12 tones in the full eight tone octave. So the equal tempered scale is a 12 note scale. However most music is rooted in tonality and has well defined tonal boundaries, or moorings if you like. Not that composers don't push the boundaries. There is a lot of dissonance in Bach's music and many of his chords if not frankly dissonant have a delightful "crunchy" feel to them, which makes his music so easy to recognize. His music however is firmly rooted in tonality and defined, if frequently changing keys.

Composers like Wagner pushed the boundaries to not formally anchor their compositions in strict tonality. At the same time his music is not strident, in fact relaxing, to the point of inducing a form of hypnosis, especially in the Ring Cycle to make a short cut to the subconscious brain. This has often been called the hypnotic line.

Arnold Schoenberg however wanted to free music from its tonality, for reasons I have never understood. As music in the well tempered scale is twelve note with the full tones equally spaced thought the octave, he kept to that. But what Schoenberg did was to organize the composition such that once a tone was sounded it could not be repeated until the entire scale had been gone through. So he did not ditch the Well Tempered 12 note scale of J.S Bach. However the result was "noise". As you put it a stick in the ear.

However Arnold Schoenberg's early works are firmly routed in tonality. An example would be his Gurrelieder, which is a lovely composition. These early works are now the most often performed of his compositions!

His followers and adherents who have rejected tonality, as they say to free the composition, have largely been at Universities and one way or another been snarfing at the public trough.

In music that actually gets an audience, Arnold Schoenberg's method of composition is pretty much rejected, although is not to say that elements of his style can and often do get into modern composition. However the strict atonal method drives audiences away and always will.

The great British conductor Sir Thomas Beecham said of this atonal method of composition: - "Not one nth part of it will survive." Time has proved him right.
 
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