On 7 Apr 2009, at 08:18, Peter Chubb wrote:
Here's my rough try at the three entries:
Concert Pitch:
Notes like a, b, c etc., describe a relationship between themselves,
not an absolute pitch. The nature of the relationship is the
so-called temperament (q.v.). To be in tune, a group instruments
must agree
on the relationship between pitches *and* the absolute pitch of one of
the notes. In recent times that pitch, `concert pitch' has been
defined as 440Hz for the A above middle C, with other notes arranged
according to the temperament being used.
The term "concert pitch", from what I looked up, can refer to two
different concepts: a non-transposing instrument, and a tuning
standard (like international A = 440 Hz).
I do not want to tie these concepts together, so that a transposing
instrument is becomes one that uses different tuning, because the
notational system is in fact more clever:
There is one set of notated pitches. All instruments must agree on
these pitches, otherwise they will sound out of tune when playing
together. This system of notated pitches are fixed by a tuning
standard which is one note set at a specific frequency. The other
notes in the notation system are set by choice of intonation. One
generally does not know what the frequencies of those are, as the may
be adjusted by musical context or stretch tuning.
Transposing Instrument: If an instrument is usually notated at a
pitch other than its sounding pitch (whether out of tradition, or for
the convenience of the player) it is said to be a *transposing
instrument.* Bes and A Clarinets, many brass instruments, and some
saxophones
are transposing instruments.
Then a transposing instrument is simply one that plays a different
pitch than the notated, but still in that notation system. The note
will comes out right, as it is transposed twice in opposite
directions: first by the composer who writes the sheet music, and then
the musician who plays the instrument.
Temperament: the relationship between different pitches in a scale.
In the simplest case, an *equal-tempered* system has notes whose
frequencies are in the ratio of the twelfth root of two. Such a
system always sounds out-of-tune, because thirds, fourths and fifths
are not exact ratios. However it is widely used because all notes are
equally spaced, regardless of the starting note of a scale.
Yes, E12 (which is the Scala name for a 12-ET notational system) is a
system that sounds equally bad in all keys :-). I think that
historically E12 like tunings were used early on lutes, but during the
Renaissance one used keyboards that approximated extended meantone
tunings (where the major second is close to the interval sqrt(5/4)).
If this is cut down to a meantone 12 keys per octave, it will have an
interval jump somewhere called a "wolf" due to the fact it sounds very
badly. The E12 keyboard solves that problem.
I have though used an extended meantone, or diatonic, keyboard layout
with Scala on my computer typing keyboard for several months now. It
works just fine playing in any key - as it is fully transposable,
there is only one fingering to learn for each scale or chord
regardless of key.
I might be usable for entering notes as well, as it does not apply E12
enharmonic equivalence, as piano keyboards do.
Hans
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