Re: quarter comma meantone on keyboard

To Paul Erlich or anyone else interested,
I'll explain a bit more about what I want to know. I plan to simulate what might be similar to quarter comma meantone tuning of several hundred years ago. I plan to select a 12 (plus 4 "split key") tone subset of 31 tones equal. (In my previous message I described the tones selected.) I would like to hear on my own (stringed) instrument what quarter comma meantone might have sounded like to those people several hundred years ago. I selected this one tuning from many other tunings that were used back then.
As I understand much of the tuning of 12 tone (plus "split keys") keyboards was done, effectively, by "ear." Based on this type of information from long ago has anyone more recently compiled a chart of frequencies (Hz) of the tones in quarter comma meantone scale? If so, I would like to see such a chart so that I could tune my modern instrument to simulate what they heard so long ago.
ALITA MORRISON

In-Reply-To: <00ba01c074a3$bb461f00$f25763d1@texas.net>
Alita Morrison wrote:

> As I understand much of the tuning of 12 tone (plus "split keys")
> keybo=
> ards was done, effectively, by "ear." Based on this type of
> information fr=
> om long ago has anyone more recently compiled a chart of frequencies
> (Hz) o=
> f the tones in quarter comma meantone scale? If so, I would like to
> see su=
> ch a chart so that I could tune my modern instrument to simulate what
> they =
> heard so long ago.

Ah, that's what you want! To convert an interval of n steps in 31 tone
equal temperament into a frequency ratio, do 2^(n/31). That means the B
above A=440 will be 440*(2^(5/31)) = 492 Hz. I think that makes it:

C 261
C# 272.9
D 291.9
Eb 312.1
E 326.4
F 349.0
F# 365.0
G 390.3
G# 408.2
A 436.5
Bb 466.9
B 488.1
C 522

But don't take my word for it, find a calculator!

Strict quarter comma meantone's a bit more difficult, as would be
predicting the frequencies that would be arrived at through tuning by ear.

Graham

Alita Morrison wrote

http://www.egroups.com/message/tuning/17068

>
> ... has anyone more recently compiled a chart of frequencies
> (Hz) of the tones in quarter comma meantone scale? If
> so, I would like to see such a chart so that I could
> tune my modern instrument to simulate what they heard so
> long ago.

Graham Breed posted a sensible response to this in the next
message, but as I think Paul Erlich already pointed out -- BEWARE!

The reference tuning of "A" varied *wildly* during the Renaissance,
Baroque, Classical, and Romantic periods, so in order to determine
the correct Hz for your tuning, you need to do some serious research
into what tuning for "A" was more-or-less standardized for the
year and geographical location under consideration.

The best reference I've ever seen to this question is the appendix
by Alexander Ellis in the back of Helmholtz's book _On the Sensations
of Tone_; it's in the current Dover reprint of Ellis's English
translation.

At some point in the past I sent a post to the Tuning List
about this. Check the archives... if it was during the Onelist
days (1999 - I think it was), it will be in the archive but
will not show up on the search engine.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'