The present unequal temperament - albeit with a possibly infantile “name”
- is based on sound keyboard tuning traditions found in central and southern Europe between ca. 1680 and
1760.
Like the contemporary temperaments by Werckmeister, Kirnberger,
Valotti and Neidhardt - - which are all typical “well-tempered” or sixth
comma mean tone
temperaments, this one also emphasises purer rendition of the central keys and
becomes gradually fresher as one modulates into
distant keys with progressively widening major thirds.
But as this temperament can be systematically varied in all of its parameter – easier than the above-mentioned historical ones – gentler
or sharper varieties of these transitions can be obtained ad libitum. The tuning can therefore be deliberately set to suit any concert
programme - for quite simple reasons: The purer
the outset – the more dissonant the
distant keys will become – or the opposite: if the opening thirds beat
faster - the more tolerable the distant keys will come out, as a consequence.
However, all major and minor keys will in any setting sound pronounceable
different from one another and the tuning will also comply with the Affektenlehre principles described by Mattheson.
Hence, it will work very well in all solo repertoire as well as in
continuo application; though it works - in its non-too extreme variety -
particularly easy intonation-wise with i.e. Viola da Gamba, since it does not necessarily have to be extremely polarised.
Although the more extreme settings would still allow the most distant keys to
be used (admittingly, with some modesty), such
settings would naturally focus closer on earlier, 17th century
repertoire, since an approach towards Mean Tone tuning is gradually taking over.
The setting is both easy and practical: the first steps consists of
tuning the two major thirds - c#' and f' - these will later become control
notes - directly from the pitch notes - a’- a;
then tuning three main groups of fifths and fourths: c#’– f’/
f’ – a’ / a’ – c#’, where the intervals are
matched to each other in related interference
groupings. The setting ranges from a to b-flat', setting it in a deeper octave would tend to make interval
interference less clear to detect. An interesting aspect to this temperament: it
is actually irregular in some places: the intervals of Group I are tempered with narrow 4ths and wide 5ths. and therefore goes
beyond pure interval settings.
Start by tuning a' – a in the desired pitch
– then proceed as follows:
|
Group |
Interval |
Tuning |
Options |
Remarks |
|
Start |
a –
c#’ and
a’
–f’ |
wide, ca.
3 – 4 beats p.s. |
5 – 7
b.p.s. *) |
The width of these two 3rds will be decisive for the rest! |
|
I |
c#’ – g#’ |
wide 5th, ca. 1 b.p.s. |
pure
**) |
Irregular tuning. |
|
|
f’ – bb’(+bb) |
narrow 4th, ca. 1 b.p.s. |
as above |
Match the eb’ equally |
|
|
eb’ – g#’ |
narrow 4th ca. 1 b.p.s. |
idem |
between
g#’ and bb’ |
|
|
eb’ – bb’ |
wide 5th ca. 1 b.p.s. |
idem |
control note =
f’ |
|
II |
f’ – c’ |
wide, ca. 2 b.p.s. |
slightly less |
Regular tuning. |
|
|
c’ – g’ |
narrow, ca. 2 b.p.s. |
out of phase
***) |
Match all the
intervals in group II |
|
|
g’ – d’ d' - a' |
wide, ca.
2 b.p.s. narrow, ca. 2 b.p.s. |
(ca. 2
b.p.s.) |
and III to each
other, so that they give the same impression
of |
|
III |
a’ – e’ |
wide,
but slightly less |
as for
gr .II, but |
temperament..
Control notes are |
|
|
e’ – b |
wide, as above |
even
slightly |
a' and c #',
respectively. |
|
|
b – f#’ |
narrow, as above |
purer. |
|
|
|
f#’ – c#’ |
wide, as above |
|
Gr.III - slightly
purer 5ths
& 4ths |
*) Beats per second; **) As the initial two maj. 3rds are tuned wider, the 5ths
and 4ths in group I
become pure.
***) The intervals in these two groups will sound less out of phase for the same
reason.
© Prof. Ketil Haugsand