M3/m3 ratios (cross posted)

[Vanderhoofven]

Hi Ron,

Is Robert Wendell by chance going to be in Dallas this summer?  I would 
love to meet him.  If you know him, tell him that I have enjoyed the mild 
well temperament he created.  I also used his new Natural Well Temperament 
on a piano earlier this week and thought it sounded good.

Earlier this week I tuned a Steinway B for a music teacher using the new 
Wendell Natural Well Temperament.  The last two times I tuned, I used Ron 
Koval's version of the EBVT, and the piano owner was fine with that. This 
time I used the Wendell Natural Well Temperament using the figures posted 
below.  The piano was -12 to -25 cents flat because of climate, so I did a 
pitch correction and fine tuning at A-440, and got to play the piano for 
about 20 minutes.  It was interesting to compare the beat speeds of the 
major and minor thirds and hear how they worked together.  I will 
definitely use this temperament again.

Today I tuned a Steinway L using Jorgensen's Improved EBVT.  The pianist 
had an interest in knowing more about the theory of tuning, so I brought 
along Jorgensen's big red book "TUNING", and both of Ed Foote's CD's and we 
looked through them together.  Also, while at the appointment, I showed the 
pianist the rollingball.com web page and we discussed the difference 
between Equal Temperament and the various other temperaments.  We looked at 
about a dozen different tunings and discussed how they would be different 
from ET.  He chose the Jorgensen Improved EBVT, so I tuned and then we 
listened to the tuning while looking at the graph so we could see what we 
were hearing.  Then he played for a while and said he could hear the 
difference and that he liked the contrast.

I will have to try the Wendell Natural Well Temperament again when I have 
more time to listen to it critically.  Well worth trying again.

Sincerely,

David Vanderhoofven
Joplin, MO


At 02:59 PM 2/19/03, you wrote:

<snip>
>Along came Robert Wendell, who has the math skills to do a lot of 
>calculations in his head when creating temperaments.

<snip>

>Robert Wendell just discovered (his words) a temperament that has all the 
>M3/m3 ratios set to either 1.5 or 2.  He describes it as just falling into 
>place, once he got started, kindof working backwards from F#. (I don't 
>pretend to understand how he got there!)

<snip>

>For those of you willing to try this mild well temperament, here are the 
>offsets from equal temperament.
>
>Wendell Natural Well temperament:
>(M3rds range from 7.4 ­ 17.6 cents from pure thirds)
>
>C       4.24
>C#      -1.59
>D       2.41
>D#      2.32
>E       -2.08
>F       2.29
>F#      1.83
>G       3.74
>G#      0.37
>A       0
>A#      4.28
>B       -0.12
>
>Ron Koval
>Chicagoland