I wrote:
>>(...)This effectively means that they are in some kind of just tuning:
>> the ratio of the frequency of each note to the drone frequency is a
simple
>> fraction with fairly low denominator. (...) It's close to the even
tempered
>>ale for the fifth
>> and third, not so close with the second, for instance. (15-17 cents
And Simon Wascher replied:
I> disagree strongly! the just third is quite far from the equaltempered.
a>nd the fifth is really different too.
>
Sorry, I was going from memory, and had the second and third
reversed. Here is the table someone posted to the UP list. (Made up, I
am sure, with a hand calculator, not a tuner on a set of real pipes.)
Anyway, the second is reasonably close and the third is not, as you say,
but the fifth on the other hand is quite close. (There's an interesting
choice for the G#: the two possibilities differ by 35 cents.)
Note Just Ratio (to D) Equal tempered fraction Difference in cents
---- ------------- ----------------------- ---------
D 1:1 1.00 0
D# 16:15 1.0595 +12
E 9:8 1.1225 +4
Fnat 6:5 1.1892 +16 (!)
F# 5:4 1.2599 -14
G 4:3 1.3348 -2
G# 7:5 or 10:7 1.4142 -17 or +18
A 3:2 1.4983 +2
A# 8:5 1.5874 +14
B 5:3 1.6818 -16
Cnat 9:5 1.7818 +18
C# 15:8 1.8878 -12
D 2:1 2.0
Cheers,
John Walsh
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