RE: equal and just tuned harmonicas

[Pat Missin <pat@xxxxxxxxxxxxx>]

Stephen Molitor wrote:

>I would also point out, as I'm sure Pat knows, 

Of course! :)

>that this is not just a
>'harmonica' issue. Players of other fixed pitch instrument with sustained
>notes have struggled with the same problem. That's why you can buy
>accordions, concertinas, etc. in just (or 'compromise just' -- sorry for the
>bad terminology Pat) tuning. Players on these instruments also notice the
>rough chords with ET tuning.

The piano accordion is almost invariably tuned in 12TET (except when
Pauline Oliveros is playing it) and tends to have a somewhat harsh
sound as a result - as in "welcome to Hell, here's your accordion".

Diatonic accordions, like harmonicas, were usually tuned in JI (if you
listen to old recordings of Cajun squeezebox, you can hear the
characteristically flat 4th note of the scale, much like 5 draw on a
JI harmonica) for similar reasons to the harmonica - ie, as they play
different notes on push and pull, there are certain note combinations
that cannot be played simultaneously. Also like harmonicas, in recent
years diatonic boxes have had a variety of tempering schemes applied
to them.

English concertinas were traditionally tuned in meantone temperament
(see below) with a scale of 14 notes per octave with separate buttons
for Eb and D# and Ab and G#. However, the last time I had the chance
to check the tuning of a 'tina, it was in 12TET with the Ab and G#
buttons and the Eb and D# buttons tuned the same.

>As Pat pointed out, within the 'fixed pitch sustained notes' instrument
>category, the harp has it fairly easy as the combination of notes that can
>be played at the same time is fixed. You can't play a draw and a blow note
>at the same time. 

Well, you could do that trick of covering the back of the harp and
blowing really hard to force the air out through the draw reeds...

>The organ has it the worst, as any two notes can be played at the same time.
>That's why virtually all baroque organs, and many modern pipe organs, are in
>fact *not* tuned to ET (or modern piano tuning either), but to some
>compromise tuning. 

Usually some form of meantone tuning. In its basic form, meantone
gives pure major thirds and slightly flat fifths. This is almost the
opposite of 12TET, which gives rather sharp major thirds and fifths
that are very nearly pure. I use meantone on harmonica tunings that
feature several fifths in a row, such as the various Sprial-type
tunings.

>Contrary to popular belief, Bach almost
>certainly did not play on ET tuned organs. Or so I've been told -- I'm no
>expert.

There was no practical method of accurately tuning 12 Tone Equal
Temperament in Bach's day. So even if he wanted to play in ET, he
would have been unable to do so. It is often claimed (even by many
authorities that should know better) that he wrote the Well Tempered
Clavier to demonstrate the advantages of Equal Temperament. In fact,
the WTC would have originally been played on a keyboard instrument
tuned in one of the systems generally referred to as Well
Temperaments. Hence the name Well Tempered Clavier, rather than Equal
Tempered Clavier...

>Another point: I've just started getting into amplified playing. At first
>I thought that JI vs. ET wouldn't matter as much when playing amplified,
>because your sound is so distorted anyway. But I'm finding that it does
>matter a lot.

I find it amusing that players who can talk all night about
amplifiers, mikes and playing techniques, often seem to glaze over
when tuning is discussed. A large part of getting "that sound" is
having an appropriately tuned instrument.

>The amp really brings out 'undertones' sometimes, and those
>undertones can be way out of tune (completely different notes that don't fit
>in with the chord) with ET, but can sound cool with JI tuning. 

Strictly speaking, these are not "undertones", but difference tones.
Also known as lower combinational tones, resultant tones, Tartini
tones, etc., etc.

http://www.patmissin.com/ffaq/q26.html

>Of course
>you can dial the undertones out by tweaking the EQ, which might be desirable
>in some band situations. 

You can de-emphasise the difference tones with EQ, but you can't
eliminate them completely. With a well tuned harp, you wouldn't want
to eliminate them. If you play the major chord in the lowest draw
holes of a harp in JI, the difference tones (and the difference tones
of the difference tones) all converge on a pitch precisely two octaves
below the pitch of 2 draw. Running that through your amplifier gives
you a huge strong tone.

Doing the same thing with, say, an A harp in 12TET gives you a pair of
primary difference tones, one slightly sharper than the pitch two
octaves below 2 draw, the other slightly flatter. The beat rate
between these two tones would be, if my jottings are correct, about 8
times per second. You would also have secondary difference tones of a
G# about 1/3rd of a semitone flatter than equal (clashing horribly
with 3 draw) and a low B about 1/4 semitone sharper than equal
(clashing horribly with 1 and/or 4 draw). Put that lot through an
amplifier and it will sound rougher than a badger's fundament.

 -- Pat.