Hello,
John Walsh wrote:
In fact, the even tempered scale hasn't completely taken over. The
uilleann pipes are usually tuned against the drones, and I imagine that is
also true of the highland pipes and other instruments like the vielle
which have drones. (...)
To my understanding, there are two groups of tuning systems which both
are forming the basis of western music:
1) tempered intonation scales
Including everything from pythagorean to equal tempered. In this system
some or all intervals are made gradually imperfect to open a wider range
of chromatic changes more "playable" scales on a twelve key instrument
(like the piano). The common idea starts at one specific point of the
musical system: dealing with the difference between the octave and the
accumulation of twelve fifths. The dominance of the twelve keys per
octave instrument, which is in fact one of the major reasons for this
kind of tonal system, has historical reasons not entirely musical. These
tempered scales, in their notation system, note names, temper relations,
even the twelve tone system of semi tones still refer to the other group
of scale intonations the
2) just intonation scales (I do not really know if this is the right
term in english the german term is "Skalen mit reiner Intonation")
In this intonation the scale is assembled out of "perfect" simple ratio
intervals the specific characteristic of a scale based on the relations
of the used numbers. As an example two common scales of this type:
the scale used by the Alphorn which just uses the harmonics of one basic
note is constructed on the numbers
7 :8 :9 :10:11:12:13
b :c :d :e :f :g :a
as one can see these numbers differ strongly against equal temperament.
It is used today by traditional music, singers, fiddle players, not just
Alphorn players! in many european regions.
The scale most drone based instruments use (not just those):
24:27:30:32:36:40:45
c :d :e :f :g :a :b
this proportions are based on the ratios of only three numbers, the
first three indivisible numbers 2,3,5. This makes the scale more usefull
for music which contains harmonies because there are less beat-notes
(ger:interferenz-tne) than in the alphorn scale wich includes ratios of
many numbers such as 7:11
(...)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 scale
for the fifth
and third, not so close with the second, for instance. (15-17 cents
I disagree strongly! the just third is quite far from the equal
tempered. and the fifth is really different too.
not so close with the second, for instance.
In fact in those just intonation scales I know the perfect second is a
very stable nearly consonant sound, seen as fifth of the fifth.
Laura Conrad wrote:
"Phil" == Phil Taylor [EMAIL PROTECTED] writes:
Phil Yes and no. the expression "well-tempered" comes from the
Phil title of Bach's two volumes of preludes and fugues. (...)
No, I think most people these days believe that Bach's Well-tempered
keyboard was not equal tempered.
as far as I know it was well tempered following a system developed by a
man called werckmeister. In systems like this you chose a number of
consecutive fifths wich are about just intonation and divide the
divergence between 12 just intonated fifths and the octave between the
other fifths. As I remember, this specific system also includes a
correction for the thirds.
Simon Wascher - Vienna, Austria
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