Cracking the Code

[norman]

Originally Posted by GregorArturo

................. C is the fundamental tone (the letter technically doesn't matter, just the frequency and note of the position). As it is the fundamental tone it is based off the first prime which is 2. Thus all notes of C are octaves of 2, which is always based on the doubling/halving of a note (also multiples of 2), thus C is also 256 an 512 hertz. You can have different tunings, in which that frequency works as C (music more importantly is based off mathematical patterns versus the actual frequency), however, these frequencies are the most natural.

Gregor, I like what your doing and I love the feel of this thread. I've been reading through and keep getting frustrated by the discussions about the 12 tone scale.

I did a bit of work on the subject a few years ago. My house has been emptied and my stuff is in storage. I have quite a lot of figures that I can't actually remember at the moment.

Anyway, I can't tell from looking at your spreadsheet if you are using "equal temperament" 'tuning' or if you are using "modal"(resonant) 'tuning'. There's an important difference, especially in regards to what you seem to be trying to achieve here.

Equal temperament tuning was 'invented' by Bach at about the time the keyboard was invented, to enable equality of the different 'musical keys'. It made any piece of music sound equally in tune no matter what key it was played in. It also destroyed the beautiful resonances that modal music had.

When an instrument is tuned modally, it sounds very resonant and 'sweet' in one key only. If you try to play in a different key it sounds c**p, you have to re-tune the instrument for the new key before it will sound 'sweet' again.

I'd guess that for the kind of applications you have in mind, you should be using the modal principle. I wish I had the figures here but I thought I should mention it. I'm not absolutely sure that you're not using the modal frequencies, I just can't remember the numbers right now.

The main thing is, you can only be resonantly accurate in one base frequency ('key') at a time. It doesn't matter what that frequency is, as long as you 'drift' the other frequencies of the chord or scale into resonant alignment with it. That's how it was before Bach, and still is with many modal purists today.

Hope that wasn't too many words for too little to say lol.


Also, while I'm here, number bases. I've never been able to understand why 'numerologists' see so much in base 10 numbers. If you change the base you change the numbers. (eXchanger, if you read this, I'm not looking for an argument, I'm looking for answers)

( on 12/13 note octaves, the base is 13 ; you get to 12 and go back to zero)
(as in base 10 ; you get to 9 and go back to zero)

I wonder if any of your amazing number theories could 're-invent' the actual number base that we use for these things based on the idea of having an octave at the base, as with the base 13 musical octave. If we were all taught western music instead of maths we'd probably all be counting in base 13. Just a thought.

Ok, that's me done for now. Great thread, let's see this happen.