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Re: Concert Pitch (a second try)

From: Hans Aberg
Subject: Re: Concert Pitch (a second try)
Date: Tue, 7 Apr 2009 10:26:18 +0200

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.


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