Saturday, October 29, 2005

Concert Pitch vs. Philosophical Pitch: Questioning the Foundation

I began to become interested in well-tempered tunings and early pitch standards back when I discovered Davitt Moroney's recording of J.S. Bach's Art of Fugue. His pitch standards and tunings are those of Bach - as closely as can be reconstructed - and the sound is so sublimely wonderful that listening to any other pitch standard and tuning has become something that grates on my nerves.

As a guitarist, there is nothing I can do to slide the frets around and get J.S. Bach's variant of the Kirnberger III tuning system, which is certainly designed around the Golden Mean, but tuning the guitar to the Philosophical Pitch of C= 256 Hz (A= 430.5 Hz), is a piece of cake. I had thought about doing that, but there were no A= 430.5 Hz tuning forks around, and my Lexicon's built-in tuner was set at A= 440 Hz, and there is no calibration adjustment for it. Besides, I had no rational compelling reason to lower my pitch standard. That all changed today.

As far as the tuning system is concerned, I am stuck with the guitar's admittedly compromised version of equal temperament (Guitar intonation is NEVER perfect - even by equal temperament standards - due to the fact that the different strings start out at their own set pitch and progress base-E, base-A, etc. individually through their own version of the temperament), but I had already solved that cosmic conundrum: Since I play electric nylon string the vast majority of the time, I simply apply 36% of pitch-shift chorus to every virtual acoustic environment that I program. Combined with the Hall Reverb and various phase, flange, and comb filter effects that I use, the inherant nastiness of equal temperament is nicely ameliorated (Not to mention that my sound is "awesome" according to many of my audience members).

But there is that A= 440 Hz "thing". I thought that the foundation of our tuning system was a convienience that simply didn't matter, but then I read this article and all that changed. I'm going to need to re-read it several times to internalize it all, but I got goosebumps reading it because I knew I'd discovered something profoundly fundamental to add to my musico-philosophical outlook. I suggest you read it and question everything: The only truth about "conventional wisdom" is that it's conventional, because it certainly isn't wisdom, or even the truth!

Turns out there is a cool little chromatic digital tuner that can callibrate the pitch A anywhere from 420 Hz to 460 Hz, and it's small enough and cheap enough that I can buy five of them and put one in each of my guitar cases and gig bags. Bingo. The guitar is inaccurate enough that 430 Hz versus 430.5 Hz isn't of any practical or practicable difference anyway. I love the results. It's impossible to explain, but the effect it has on me is that the instrument and the music "breathes" easier and just has an... indescribable "niceness" to it.

Good luck to all you pianists out there ;o).

UPDATE: "Heh", as Glen Reynolds would say.

My blog is worth $6,774.48.
How much is your blog worth?

Via Scott Spiegelberg, whose blog is woth much more than my little backwater.


Blogger Devin Hurd said...

Greetings Musical Monk and a hemi-demi-handshake,

As a strong advocate of alternative intonation schemes I can only encourage this path that has you so excited.

I remember the first time I encountered that Jonathan Tennenbaum article and it's always rubbed my unrepentant Helmholtzian brain the wrong way. The intonation world is filled with various strains of "fundamentalists" who like to make grand generalizations about how everything outside their proscribed system is "arbitrary" or "scientifically invalid" (or the really exhausting charge that 12-tone equal temperament is "facistic"). Statements like these are what makes intonation theorists seem "cultish" from the outside and it's best to steer clear of some aesthetic equivalent of a "Spanish inquisition" so to speak.

I would argue that any and every tuning system is inherently "arbitrary" and that's just fine by me. Tennenbaum attempts to define a non-arbitrary system by arguing that vocal music is the measure of non-arbitrariness. Or he at least assumes that the human voice possesses some divine property of "musical-ness" or whatever that one can build intonation around. Which is fine, but doesn't make it any less arbitrary in my book. The human voice isn't greater or less than any other means of sound production in a general sense.

It should be noted that Partch - an accomplished guitarist in his own right - pursued just intonation as a means of best replicating the intervals of spoken word and as such built his system with the human voice firmly in mind. And it was the discovery of Helmholtz's work that set him on his path.

Read the Helmholtz in addition to the Tennenbaum. Read Adrian Fokker's articles. Check out some issues of 1/1. And if you really want a trip try reading Jeremy Grimshaw's articles on LaMonte Young. And keep tuning that guitar. It sounds like you're on a good track.

1:26 AM  
Blogger Hucbald said...

Thanks Devin, and nice to chat with you again (And, I LOVE your profile pic: I played violin for a couple of years when I was that age. This is probably why we both like alternative tunings. LOL!).

There are some other factors for guitarists relative to relaxing the tension of the guitar's strings that makes me appreciate this approach. I'm certainly not buying Tennenbaums artcle "hook, line, and sinker" vis-a-vis the voice being the wellspring of proper pitch standards, but I have to admit, the "naturist" in me does like the idea.

Over the past 50-75 years - since catgut strings were replaced with nylon (Thank you DuPont!), and then since 1988 when carbon fiber was introduced as an even brighter sounding alternative to nylon - the trend in classical guitar strings has been toward higher and higher string tensions, and correspondingly higher playing actions to get a louder and brighter sound.

My personal luthier hero and mentor in that area, the late Anthony Murray, rejected the ultra-high actions and ultra-high tension string approach of modern "concert" classical guitars, because he (Practically and realistically) viewed the guitar as a chamber music instrument meant for salons and other intimate venues. As a result, his guitars are easier and more fun to play, and they have a compellingly gorgeous tone, but they are not overly loud.

By relaxing the pitch from A= 440 Hz to A= 430 Hz, the higher tension strings, which have inherantly more mass to them, can be used without over-stressing the guitar's top and bridge, or making the playing action overly hard, and the added mass of the strings combined with the lower pitch gives the tone more weight, or body. Interestingly, due to the exageration of these effects through the amplification system, this effect is actually in some ways enhanced on my electric nylon string guitar.

Of course, this will lead me - again - down the (expensive!) path of experimenting with every possible brand and tension of string. I would be lying if I said I don't look forward to this: Experiments are fun for the scientiffically-minded musician!

5:29 AM  
Anonymous Anonymous said...

Hi, I just wanted to share my recent experiences with alternate tunings. I had learned about Pythagoren tuning that uses A= 432hz, I play in a band, and so I tried it with our singer & she loved it! I proceeded to tune all of our instruments to this calibration(using an older Korg CA-30 tuner with a calibration range of 410hz - 480hz), intruments include guitar, bass, and a fender electric piano. About a year after, she was practiing on an acoustic guitar, and I noticed a range of tonal textures & qualities that I hadn't heard previously, so I checked the tuning, and found that it had dropped to A=430hz, so I wanted to see if anyone used this tuning and found your article. Needless to say, I was delighted to find that this 430.5 hz has a geometric/mathematical relation to the Universe. With the Pythagorean tuning I used his 2:3 ratio between 5ths as a starting point( since the relationship between octaves and 5ths has the most smooth and consonant tonal qualities, & because with the piano it sounded more in tune(execpt for a wolf interval between 3rd's) One of the arguments for the institution of 440 calibration has been stated as being due to difficulties in the manufacture of mass produced instruments, which I found to be untrue, since I was easily able to tune the Fender Rhodes to the 432hz cal.) I also discovered that the 440hz standard began in the 1930's with Nazi scientists who made the change based on experiments which had discovered damaging frequencies in experiments on prisoners of world war II !!! No wonder!!! Anyway, I just thought I would share some of my experiences with you.
Best Regards, Py

4:36 PM  
Blogger Kairologic said...

Hello there! I am so glad that you've brought this up in blog format. I was a proponent of 432hz tuning for years after I first learned about it's potential use for easing the strains of singers and for seemingly resonating with various "sacred geometrical" numerologies and art composition patterns found throughout time and across the world. However, I happened across the origins of the second hand complication in our modern timekeeping system and realized that the more prolific ancient standards were aligned with sectioning off the day into parts called "helek/helakim" or "barleycorn" that equate to the number of years in a Precession of Equinoxes. This changed my outlook dramatically. I decided to do some frequency conversions to that system to see what best resonates in such a "sacred" way, and found that equal temperament provided much confusion in the overall numbers. After some digging, it struck me: if the B note is dropped to 60hz (being a fractal of the 60 seconds in a minute, and abiding by Babylonian timekeeping fractioning), in 5-Limit Just Intonation (a bit more consonant than 12-TET), we automatically achieve the Philosophical Pitch of C256. A432 is obviated for something more important (and less bric-a-brac) here. Please have a look at my keynote presentation titled "A Horological and Mathematical Defense of Philosophical Pitch," linked from my domain I hope you take to it!

2:13 PM  

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