[Dixielandjazz] Tuning, temperament, keys and colour

Anton Crouch anton.crouch at optusnet.com.au
Fri Oct 6 21:09:35 PDT 2006

Hello all

A useful, brief, article on this matter is re-produced below. The author is
Stephen Bicknell, an organ historian, designer and consultant. As noted,
the essay first appeared on the electronic mailing list Piporg-l

Those who are REALLY keen will find the following website useful, also.



A beginner's guide to temperament

This essay first appeared on the electronic mailing list Piporg-l

Temperament is one of those subjects that attracts a) buffs and b)
incomprehensible jargon. The usual explanations start with an analaysis of
the dreaded COMMA - whether Pythagorean or Syntonic - and most of us never
really get past the problem of trying to work out what on earth such a
thing might be.

I hope, kind readers, that you will allow me to come to your rescue, and
attempt to explain in simple terms what the temperament enthusiasts are on

There is a problem to be solved in tuning any musical instrument: the notes
cannot be made to fit into the octave, and some have to be de-tuned to make
sense. If you tune a circle of pure fifths......

c - g - d - a - e - b - f# - c# - g# - d# - a# - f - c

....the c you end up at is not exactly in tune with the one you started
with - a mathematical anomaly known as a comma.

In equal temperament all the notes in the scale are shifted by the same
amount in order to resolve the problem.

In all other tunings the notes in the scale are shifted by differing
amounts, giving each temperament a certain character. These can be arranged
in more or less chronological order: -

The earliest is PYTHAGOREAN tuning, which seems to have been in use up to
the end of the 16th century. Almost all the fourths and fifths are dead in
tune, and the entire comma is 'dumped' on one interval (according to Arnaut
de Zwolle between F and B flat), which is therefore unusable. This tuning
is easy to explain and to execute, but it leaves a lot of the notes of the
scale in quite odd positions. It is quite satisfactory for music written in
the old 'modes' that preceeded the major and minor scales, provided there
is no modulation whatever.

By the early 17th century MEANTONE temperament was the norm. In this
temperament the major thirds are perfectly in tune and the fourths and
fifths slightly compromised - except for one hideously catastrophic fifth,
usually between G sharp and E flat, the famous 'wolf'. However, this is now
a 'regular' temperament, for in keys with less than four accidentals the
notes of the major scale are in the same relative positions, the thirds all
pure. This, for the first time, allows the composer freedom to include
harmonic modulation in one direction or another, and to choose a key that
mirrors his thoughts. However, during the course of modulatory passages
there will be an audible 'shift' of tonality, rather like changing gear.
The appearance of a black note that is technically 'unavailable' in music
of the 17th century (they are A flat, A sharp, D flat, D sharp and G flat)
is a sure indication that a sudden clash was intended - rather like the
deliberate use of false relations. The more extreme accidentals (C flat and
onwards) barely ever appear. The occasional appearance in the mean-tone era
of keys like F minor suggests the dawning of an awareness of the
possibilities of key-colour: with four flats it has a very strange minor
third (G sharp, not A flat) and if the G flat is called for there is
further trouble in store. (Also known as QUARTER-COMMA MEANTONE)

The wolf in meantone tuning is so horrible and such an obstacle that, by
the later seventeenth century, it was being modified substantially in
MEANTONE, the latter sometimes also known as SILBERMANN TEMPERAMENT) is
probably the most appropriate temperament for most of the 'early' organ
music we now hear - even though Buxtehude and Bach were clearly among those
exploring new tuning systems, their compositional technique remains
informed by the meantone system. Simply put, the pure thirds of meantone
are de-tuned a little bit in order to try and lessen the wolf. Modified
meantone temperament was still being used by English organ builders,
including Willis, as late as the 1850s. Naturally it allows the composer to
modulate a little more freely and frequently, perhaps permitting an
occasional excursion into five sharps or flats before returning to a more
reasonable home key.

Late in the seventeenth century theorists started to experiment with
various WELL-TEMPERED systems, or CIRCULATING TEMPERAMENTS. The object was
to finally hide the wolf, making all keys usable. It is perfectly obvious
that this could be done by distributing the intervals equally acoss the
scale, but this was not the path they took (except as an academic
excercise). Why? The answer lies in the fact that these circulating (i.e.
no wolf) temperaments are those which allow the widest exploration of key
colour. There is every indication that musicians of the 18th century were
very happy with the expressive possibilities offered by writing in
different keys, and sought to exploit the quite different character of each
in their writing. Temperaments of this type include the various tunings by
WERCKMEISTER (organ expert, 1691), KIRNBERGER (Bach pupil, early 18thC),
NEIDHARDT (1724) and VALLOTTI (c1730). Of these systems, Werckmeister III
is notable for its purity in the best keys and its suitability for organs
with large quint mixtures (many of the fourths and fifths are in tune); but
it is irregular and bumpy in the way it deals with modulation and key
colour. Vallotti is smooth and regular, but the key colour is generally
rather mild . In all these systems it is possible to play in any key,
though the more remote keys may sound unpleasant, and enharmonic modulation
is not always happy. Other circulating temperaments have been devised in
modern times, almost all of them suffering from the grave defect that they
are difficult to commit to memory and therefore difficult to use in
practice (you can't tune an organ with a book in one hand).

Finally, EQUAL TEMPERAMENT. This very obvious solution has been known since
350 BC (!), but did not become widespread until the late 18th century
(50-100 years later in the English speaking world). The advantages are
obvious - all keys are usable without fear or favour, and full enharmonic
modulation is possible. The disadvantages are also clear: not one interval
is dead in tune (indeed in any major scale the thirds and leading notes are
extremely sharp), and there is no key-colour whatever. In organs, reeds
sound grittier and tierce mixtures begin to scream.

A few words on BACH and temperament. Bach did not at any time advocate the
use of equal temperament. He wrote two sets of pieces called Das
Wohltemperierte Klavier ('The Well-tempered Keyboard'), avoiding the German
term for equal temperament, which is gleich-schwebende temperatur. These
forty-eight pieces are designed to exhibit the full range of key-colour
available from a circulating temperament, and careful examination of the
texts shows that Bach varied his compositional technique according to the
key he was writing in.

All the rest of Bach's music falls into the more conventional patterns of
the day, most of it being quite well suited to modified mean-tone
temperament (even if it continually pushes at the boundaries of this
system). It is particularly noticable in the organ music that Bach uses
modulation as an expressive device, and dares to use the highly coloured
remote keys for periods of tension. Today we often wonder how seventeenth
and eighteenth century players could stand playing long pieces without
changing the stops from time to time. The answer is that the modulation
from one key to another during the course of the music was an audible
'event', a noticeable change - and is one of the factors that renders
registrational changes unnecessary. When Bach plunges from a passage in the
home key into a section of wild dissonance peppered with suspensions and
discords, he is deliberately invoking the colourful effects obtainable only
from unequal temperament.

Why, then, did Bach write such works as the Mass in B minor, in four
sharps? In this instance it is possible that the instrumentalists were
playing instruments tuned to chamber pitch, a whole tone flatter than organ
pitch. The organ continuo would be transposed by the player, who would be
playing in serene, no-accidentals, A minor. A quick check of the score will
show that, if this transposition is assumed to have taken place, then the
continuo player will have been able to avoid the G sharp - E flat wolf at
all times.

Today's instrument makers and theorists have always erred on the side of
caution and have avoided large scale use of meantone or modified meantone,
preferring to offer us more 'usable' and 'versatile' circulating
teperaments. My own feeling is that this is a great shame, for, despite
Bach's famous jokes at Silbermann's expense (he is supposed to have played
Gottfried Silbermann's organs in outlandish keys, until the builder was
forced to retire, 'his wolf howling in his ears'), his music is surely
centered round the meantone tradition and the many colourful possibilities
it offers.

Those who wish to hear large scale demonstrations of major works - Bach and
others - played on old unequally tempered organs, are recommended to try
Harald Vogel's recordings of the Schnitger at Norden and Ton Koopman's
recordings of Bach, especially on the G. Silbermann at Freiberg. Amongst
instrumental recordings I would recommend those of the music of Monteverdi
(Vespers et al.) made by Andrew Parrott and the Taverner Choir and Consort
(for which I tuned the Mander continuo organ in quarter-comma meantone).

Mention of Italian music brings us naturally to the question of
CHROMATICISM in early music. This is an area in which the Italians
excelled, but there are examples from many other countries, especially in
the seventeenth century, where the chromatic scale is used for special
effect. On equal temperament this is uniformly dull, and music of this type
fails dismally to engage the listener. However, in meantone tuning a quite
different picture emerges. The half-steps of the scale are all of differing
sizes, and the chromatic scale, far from being smooth and oily, becomes a
bumpy, eccentric and challenging affair. The harmony it brings with it
displays rapid, even kaleidoscopic, changes of key colour through constant
modulation, and the repeated build-up and release of harmonic tension is
characteristic and fascinating.

I would also mention one other genre especially suited to meantone - the
English Trumpet Voluntary. The acid whining of thirds and sixths in equal
temperament makes these pieces less than harmonious to the modern ear. Even
in a circulating temperament they fail to 'come across'. In meantone they
present a quite different picture, one that I tried to hint at in my
imaginary conversation with John Stanley, posted to the list a few months
ago ('Ye Olde Englysshe Tradicion' - see link on 'Essays' page).

I hope that this introduction will encourage some of you to listen out for
the many positive features of unequal temperament, even though the wide
range of the modern repertoire means that most new organs will (and
probably should) be tuned to equal temperament.

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