what's with the new temperaments?(x post)

[Ron Koval]

ric M wrote about the Broadwood's Best being ET:

I think you are referring to an opinion of a modern writer.  If
James Broadwood in 1811 claims to be tuning equal temperament, why
not accept that?
"...the old system of temperament is now deservedly abandoned, and
the equal temperament generally adopted.."  James Broadwood, 1811.
The only controversy here is what he meant by "old system".  I
think it was Meantone
<snip>

Ah, now I'm beginning to understand.....

The danger in studying history, is to believe that what they wrote is 
true....  It reminds me of the early experiments with the Edison recording 
tubes; remember those scratchy, tinny, direct mechanical linkage to the horn 
recording/ playback devices?  People wrote that when they heard the playback 
it was as if the person/musician was in the room with them.  Now, I can 
still tell the difference between a recording of a piano, and a real piano 
playing in the room.  Are we to assume that with all of our modern recording 
and playback equipment, that we've lost the technology of the past, because 
how good it must have been to sound "just" like the musician?  I think not.

Or even take the example of trying to "transcribe" the EBVT.  Mr. Bremmer 
wrote the steps he used, and then other people tried to translate that to 
offsets.  The trouble was, his words were interpereted literally, (equal 
beating means the beats between comparison intervals must match, pure means 
an absolute pure interval) and there were many revisions, with the sideways 
well and everything inbetween, until the realization that some intervals 
weren't quite pure, or some equal beating intervals didn't quite match.

So, back to the Broadwood.... Yes, that was the ET of the day, in comparison 
to what had come before.  The instrument could be played in all keys, yes? 
But, compared to what we accept as ET, this is not even close.  In modern 
ET, we look for beat-rates of the thirds to smoothly increase over the range 
of an octave, where the beat-rate roughly doubles.

So a spread sheet example from C to C, in chromatic order looks like:

10.4
11
11.6
12.3
13
13.8
14.7
15.5
16.5
17.5
18.5
19.6
20.8

The numbers represent the beats/second for the major thirds.  Even spacing 
between all steps.  Contrast that, with what we expect to hear with the 
Broadwood's Best, in the same octave:

4.9
14
9
14
17
8.7
19
8.5
20.2
18.8
17.1
25.5
9.8

Hmmmm. not very smooth, and some intervals that are equal beating....  Look 
at the first interval of CE, it's beating at about the speed we'd expect to 
see an octave lower in ET!  This is where we can hear the unexpected 
smoothness in some of the keys.  Yet, all keys are still playable, no 
"wolves" to run from....

ET?  Nope, not in my book!

Ron Koval





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