Hupostasis, correct me if I'm wrong, but it appears that I would have to rearrange the fret board of my guitar to achieve Pythagorean tuning. I mean, I was able to program my tuner to A-415Hz, but the actual layout of modern fret boards are for equal temperament, right.
I've never tuned a fretboard before (I'm a keyboard guy, sometimes I repair old analog synthesizers), but I would imagine it should work? Basically the pitch is dropping for each string. Unless the tuning knobs can't compensate for going *that* low
Wow, thanks for that. I always wondered if our 'A' was the same as Bach's 'A'. Now I know the truth. But how do we know for sure that Mesopotamia used A 415Hz?
Mesopotamia probably didn't use 415 Hz. It's just the oldest (widely used) pitch that I'm familiar with. It would be more appropriate than 440 Hz, at any rate.
Oh, Bach is dried out on A440 Hz. And even worse, most people play Bach on pianos instead of harpsichords or organs. The reason why Bach requires either a harpsichord or organ is due to the fact the music is written for two registers
. Pianos only have one register.
What's interesting though, is that Bach developed his own temperament which solves many musical problems and acts as a good compromise between equal and unequal. A fellow named Bradley Lehman reversed engineered the drawing and rebuilt the tuning from scratch; and also explaining WHAT musical problems it solves. The website with all of the information and discovery is located here: http://www.larips.com/
You can watch a brief video on how the tuning can be achieved here:
Here's an actual piece with the Bach-Lehman tuning in action:
Bach had a special preference for plucked instruments, apparently he designed a "lute harpsichord", which no originals have survived. Here is a sample on a recreation-- however as you'll note the tuning is in equal @ A440 (instead of Bach-Lehman @ A415), so the piece is missing its colour:
Do you see what I mean by symmetry? If we used A 415Hz, would that disrupt the symmetry?
Anyways, I own a guitar, so I should be able to tune my A string to A 415Hz and then figure the rest out from there. If I do that, would that put the rest of my guitar in meantone temperament? I'm assuming it should, since guitars have existed long before Equal Temperament.
If you want to make the chart, let me know what you need, but given the info you provided I think I'll need to test it myself now on my guitar.
The trouble is, I'll have to convert the notes to Tabulature. I can read and play Tabs as I go, but I can't do that with sheet music. I have to transcribe them.
A415 shifts the pitch of the notes down equally, but they all go down. So it can confuse some people. i.e. the 'C' of 415 Hz is the 'D' of 440 Hz, or something like that. A432 does not from what I understand is not as malleable as A415 as it's odd (and many find it assaulting or hard to listen to since it does not conform to A440).
Heh, I don't like tabs or sheet music-- I prefer piano roll data. Like this:
C5, B4, A#4, A4, G#4, G4, F#4, F4, etc
https://entertainyourpc.files.wordpress ... o-roll.png
So that's all we need to figure out. Then David's Psalms can get mechanically popped into a piano roll and analyzed if any "musical" result is produced. Unlikely, but worth a shot. I would get a huge kick out of 'listening' to the Hebrew characters even if they're not musical.
I AM THAT I AM *insert jingle from corresponding hebrew words here*
Tuning your guitar to A415 doesn't put it into meantone temperament. The temperament specifies the tuning *between* the notes, whereas the diapason or master pitch, identifies what 'A' will be. So temperaments actually explore pitches that aren't touched by equal temperament @ 440 Hz. The 'in-betweens'. If you stop and think, there are many pitches we don't take advantage of on an 88-key keyboard. But more can be achieved once you start playing with the tuning.
For example, here's a video with pianoteq that uses A440, but goes through the different temperaments:
(listen to how meantone changes the colour of the chords versus equal). See... meantone can sound 'very bad' (dissonant) on certain chords, but sounds 'twice as good' on others. I am not sure how the Bach-Lehman tuning interacts with it since I just have not had time to go in depth with it, but get the general understanding. Ah, but sometimes the dissonance is good.
Pianoteq is the software I use for piano and harpsichord modelling (it can do other 'string' things as well). It is cross compatible with the tuning software 'Scala' (they may have used some parts for the tuning engine, I forget). I should get a PCMCIA MIDI card for a laptop running Linux to experiment with sending meantone MIDI signals (basically it uses the 'detune' signal to approximate an unequal temperament). I never got Scala working under Windows.