Well-tempered != equal tempered

[mdlbear]

From this post by braider, we get this intriguing article by Bradley Lehman, who makes a good case for having figured out Bach's original tuning based on a decoration on the title page Bach's main copy of "The Well-Tempered Clavier".

There's more at larips.com, including video demos and sound clips.

C-E, F-A, G-B, and Bb-D are calmer and more resonant than in equal temperament; D-F# and Eb-G are the same as their size in equal temperament (size 7); F#-A#, Ab-C, A-C#, B-D#, Db-F, and E-G# are more active than in equal temperament.

Some subjective remarks about key character, when playing with this temperament: Music in sharp keys tends to sound increasingly crisp and brilliant with each added sharp. Music in flat keys tends to sound mellow and warm, with a vibrant glow at each added flat. C major and its nearby keys sound plain-spoken and resonant, similar to 1/6 comma meantone.

Music in the flat minors tends to sound dark, troubled, sorrowful, yet noble. Music in the sharp minors tends to sound intense and incisive, with forceful dominant tensions. Music in major keys tends to sound smooth, having fewer strong contrasts than in minor-key music.

As for me, I'd probably have to listen carefully several times to a side-by-side comparison of the same piece played in both this and equal temperament before I could tell the difference, but the math is right.

Comments

[technoshaman.livejournal.com]

From Bach? I'm not surprised... have to listen to the soundy bits when we get cflute's Polks hooked up. But Bach has always fascinated mathematicians as well as musicians...

[technoshaman.livejournal.com]

The irony is that cflute's piano, Claire, is with the tuner as we speak.

You can tune a piano, but you can't tuna fish. :)

[mdlbear]

A similar quote was in the man page for tunefs(8) on SunOS; it does not seem to be present in man tune2fs.

[technoshaman.livejournal.com]

Google sez it showed up in Mac OS X, too. Definitely BSDish.

[technoshaman.livejournal.com]

This (http://community.livejournal.com/unixhistory/1808.html) says it's definitely 4.2 BSDish, and was probably committed by McKusick or Bill Joy.

(I remember the similar tale that the original source code for vi contained


/* code code codity code */
/*
there was a haiku
in the source code for v-i
right in the middle
*/
/* code code coda code code */


Our TA made the mistake of telling us that as we were writing our own mini version of the editor for our term projects. I know for certain he got some.... interesting comment blocks... )

[mdlbear]

There was a time when I was using circular lists as data structures specifically so that I could put "One ring to rule them all..." in the comments.

[technoshaman.livejournal.com]

OK, that tops me... :)

[eleccham.livejournal.com]

That should probably go into the pth code; it uses them extensively. :)