'Hexachord'?

Hi there...I was reading that thread about learning theory..and somebody was asking about 'hexachords'. Could anybody explain what hexachords are? Thanks....

Actually, hexachords are some kind of legend.

Tetrachords, the ones our western music is based on, are the harmonic intervals that make out the scales. (You actually need two tetracords to make an heptatonic scale, or 7 notes scale).

Tetrachords come in 4 types, major, minor, phrygian(also called napolitan) and harmonic.

To make the major scale, you just put two major tetrachords.


Every scales can be put back into tetrachords, and you actually use them to invent hybrid or 'non natural scales'

Nope


The "Hexachord" or "Hexachordum" (lat: Hexa=Six Chordum=String -> six string) was a way of thinking and writing music mostly used by J.S Bach.

The normal music theory is based on a system of 7 notes. If u take C major for example it is c, d, e, f, g, a, b.
The Hexahordum uses only 6 notes of that scale:

C Hex: c, d, e, f, g, a

so you get two tridas: C major and D minor
or if u take only 2 notes at a time you have 4 steps:

c/e (ut)
d/f (re)
e/g (mi)
f/a (fa)

these four steps have special names (i cant remember them at the moment - but i will gather some info on the hexachordum asap)

the whole notation system was based on the hexachordum - the reason why our clefs have 5 lines and not 4 or 6 is the Hexachord. Try to write the C hex on a normal treble clef
(remember - c, d, e, f, g, a) and now flip the sheet of paper around by 180 degrees - what you see is: the C hex! only one octave higher (or lower - depends on where u started)

to extend the c hexa u have to use the 4 steps with Major, Minor, Diminished and Augmented:

c/e (ut) -> C major (ceg)
d/f (re) -> D minor (dfa)
-(normal c hex)
e/g (mi) -> e dim (ega#)
f/a (fa) -> f aug (fac#)
-(c hexa extended upwards)

the extended hexa comes into play when u leave out the first note (the c) and you start to play off the d
so you have to add the a sharp and the c sharp -> but the c sharpo has to be played ona octave lower - else it sounds very orietal:

ex: d, e, f, g, a, a#, c#(one octave lower), a#, a, g, f, e, d -> and that is? .. the very first notes of inventio no 4 by JS Bach

So much for the note system. But that is not all by far - baroque music is pure mathemathic. Like medieval cathedrals this music is "constructed" accordin got the "old way of thinking (hexachordum)". Vital parts are the fibunacci row ( 1, 1, 3, 5, 8, 13, 21, etc) which indicates along with the "olden cut" (minorem:majorem = majorem:whole) the usical changes within a song (chages at measure 13, 21, 34, etc) and so on - a very wide field and it would probably take me days to explain it.
This system has been lost for a very long time - a good friend of mine and tutor at the Salzburg Mozartheum (austria), Walter Haberl, has done intensive (up to 14 hours per day!) research wirk on that topic - and now, after 6 years, he has decrypted the Hexachordum!

Now all the things that were unclear in bachs music are extremely logical if you know about the Hexachord. It is an extremely fascinating system!

-=[Azrael]=-
(hope i didnt confuse you too much)

That guy has to publish something, my theory books don't speak about the Hexachord, they don't even mention it...
I remember when you talked about it in a thread, but it seems noone has published anything yet...

Walter is about to write a book at the moment.

On jannuary 3rd he first showed the Hexachord to the public. I had ther great pleasure of listening to him that day - a historic event! It has been recorded on video - i´m about to get that tape from him - and all the scriptums he used at that symposium - it was just breathtaking! He went back to the beginnings of time with his explainations (bible, templars, etc) - we all were like "..." *L*

Here is a midi piece i wrote just by using the C Hex:

http://www.ktv-krems.at/s.trailovic/hexa.html

-=[Azrael]=-

Hey Az. I was wondering when you were going to show up.

*LOL*