Larry is correct in what he says. By the way, I don't think he was contradicting you, maybe just saying things in a different way.
I heard a recording of a pipe organ that was tuned using the "just" system rather than the now standard "equal" system. I believe it was tuned so that in the key of C they had the mathematically correct ratios for all the white keys. They played a tune in C, which sounded perfect - in fact it sounded better than it did in "equal" tuning. Then, they transposed it to different keys. I think they went around the circle of fifths. As they got farther around the circle it began to sound worse and worse - like a broken down calliope!
In the equal system, every key is equally wrong, by a consistently small amount. A Cajun accordion only has notes for one key, therefore it is fine for it to be just tuned, which tends to make it sound a little better and maybe a little louder. I have been told that barbershop quartets sing in perfect "just" tuned intervals for the same reasons, and that some violin players might make small intonation adjustments in order to get perfect intervals.
In the spirit of being perfectly pedantic :-)
(and having some *fun* with this topic ..)
Being from an Engineering discipline, I recall
the evenly tempered scale as each note being
the twelfth-root-of-two higher than its predecessor.
And as Larry states, a piano is always out of tune,
because of this tempering. G-sharp and A-flat are
technically two different pitches depending what key
that you're playing in. Only a fretless instrument
can be played in tune!
(I always wondered why my guitar sounded like that!)
Further more, if you don't care what notes constitute
a specific song, yes you can play any song in any key
on a Cajun accordion
And wait .. there’s even more .. I was just talking
with Mark Savoy last week. He tells me that two
notes on the scale of the Cajun box are indeed tuned
15 cents flat.
How about that for confusing units .. pitch
in “cents”!
“Yes, can you please tune my accordion
a buck-two-fifty .. I think I'm 3 quid flat!"
Seriously though, thinking in the key of "push"
and the key of "pull" is a very good place to start
with the Cajun Accordion!
it is certainly possible to tune a piano
so that every interval is close enough to
the 12th root of 2 ratio
that;s how they do it - that;s 'the system'
if you do that, there is no reason for any
key to sound out of tune more than another
that is the very reason for the
'equal tempered' scale
[yes i know that is an irrational number
but the ear doesn;t have infinite resolution.]
[and yes i also know that on a piano, which
has a 7 octave range, the very highest and
lowest notes have to be made somewhat sharper
than 'correct' notes, because the actual
correct ones sound flat - but that;s not
what he was talking
about]
Thanks for all the replies. I guess I am like Ron since my world used to be a 5 string and a bass fiddle. Throw on a capo on the 5 string and play the same song in a different key.
So the bottom line here, if I am reading this right is, If you like a song, find out what key its in and then grab the box that can play in that key. If that is correct,what key boxes do you guys that perform have?
Thanks again for your patience in this matter as I dont have a lick of music training.