[CAUT] mean tone tuning- help!

[Fred Sturm]

Don McKechnie's numbers being different from Chip Miller's, I did a  
quick calculation (thanks to Thomas Donahue for giving me the  
understanding to be able to do this). The syntonic comma is about 21.5  
cents. Hence, 1/7 comma is about 3.1 cents, which I round to 3 cents  
to make my life easier. Starting with A at 0, and noting that all ET  
5ths are already narrow by about 2 cents, I simply tune (virtually)  
5ths down from A and up from A until I reach the standard E-flat in  
one direction and G# in the other. Results: pretty close to Chip.
C 3
C# -4
D 1
D# 6
E -1
F 4
F# -3
G 2
G# -5
A 0
A# 5
B -2
C 3
	In spite of this, I'd go with Don's numbers, as they seem to be "from  
the horse's mouth" and have satisfied the customer. And they are a bit  
milder, which is probably a good thing. I'd say they were more like  
1/8 or 1/9 comma. The wolf 5th is 8 cent wide, as opposed to 11 in my  
calculation (meaning 2 bps rather than 3 bps). In mine, all M3s are 4  
cents narrow of ET, all diminished 4ths (the "bad" M3s) are 8 cents  
wide of an ET M3. (Note that D# should be named E-flat, A# B-flat). In  
Don's (Tim Farey's), the sizes are irregular, which shows pretty  
conclusively that it is in error, strictly speaking in mathematical  
terms (mean tone is always regular). I am also curious about the F3  
+4.5, F4 +2.9 (I would probably peg the input number for F at 3.5, and  
let the ETD take care of the stretch). I guess I suspect that TIm did  
an aural tuning of this and recorded it. In any case, it is  
essentially the right overall shape, and in the ballpark.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu



On Feb 24, 2009, at 3:56 PM, Donald McKechnie wrote:

> Aaron,
>
> Peter performed twice last year here at IC. Both times I tuned the  
> 1/7th comma modified mean-tone he requested. I received the numbers  
> from a technician out in the mid west who's name I cannot remember.  
> I put the numbers in my RCT and all worked well. Peter was very  
> appreciative.
>
> F3 +4.5
> F# -3.4
> G +2.2
> G# -3.7
> A 0
> A# +3.7
> B -1.5
> C +2.2
> C# -2.9
> D +.7
> D# +4.4
> E -.7
> F4 +2.9
>
> Don