OUT of tune Tuning - Question from new member

Greetings!

Im new to music theory and am intrigued by two questions that have
captured my imagination;

1.) A musician friend of mine told me, that if a band were playing
together and everyones instrument was in tune except for one person,
the one person with the out of tune instrument would really stand out.

Normally, the one person would get his out of tune instrument back in
tune. Alternatively however, a different approach could be used to
normalize the sound within the band, relatively speaking.

That is, all the other band members could re-tune their in tune
instruments to be out of tune the in same way the original un-tuned
instrument sounded. This way they would sound relatively the same,
tuning wise.

So - this got me thinking....

In the below table, there are four instruments. They could be guitars,
or something similiar.

Column (A) shows the frequency in hertz of four different notes,
intervals played on the instruments when they are in tune. Notes,
intervals, for example; b, diminished octave, C#, A#, all sound
the same way on each instrument.

Column (B) on the other hand, represents a scenario, where each of
the four instruments may be tuned quite differently from each other.

Here comes the first question...

We want to match two instruments to each other in accordance with
values listed in column (B)

The important instrument is 'INSTRUMENT # 1'.

Constraints;

We only get to play one note on 'INSTRUMENT # 1'. That is 496.15104
as shown in the table.

=====================================================================
Freq. in Hertz
COLUMN (A) COLUMN (B)
NOTE INTERVAL IN TUNE OUT OF TUNE
-----------------------------------------------------------------------------------------------------------
INSTRUMENT # 1 B Mjr 7th 495.00 496.15104
INSTRUMENT # 2 Dim. Octave. 501.6 504.1152
INSTRUMENT # 3 C# Enharmonic 270.34 269.15072
INSTRUMENT # 4 A# Aug. 6th 448.8 452.05248
=====================================================================
We can only play one note on instruments #2 through #4, likewise
those notes being the ones listed in column (B) for each instrument.

What simple rule, principle, formula, will allow us to determine
which instrument from #2 to #4 is tuned most closely to instrument # 1.

Further, by knowing ONLY INSTRUMENT #1's note listed in Column (B),
how can we derive the rest of its entire 'out of tune' scale?

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Hi Dan,

I'm not sure I understand your question. It looks like
the formatting in your table got off somehow. I will
say this:

If all instruments in a band were out of tune by the
same amount, it's true that none would stick out. But
would the audience know that they were out of tune at
all? That is, is 'in tuneness' relative, or is there
a fixed standard of it somewhere that people can actually
hear?

Perhaps that's the question we've been trying to answer
on this list for at least the last 10 years......

-Carl

The only person on earth who really knows if something is in or out
of tune is the performer. Is it what they intended, good or bad, or
a happy accident surpassing expectation? Then it's in tune. If not,
it's not.

In a way, there's no such thing as "out of tune". What is- is.

Other judgements require two or more people agreeing on premises-
this is the correct tuning, in this style thirds are consonant, in
another style they're not, etc. etc.

If "standing out", or sticking out like a sore thumb for that
matter, was the intention of the performer, it's in tune.

"Rembrant's shades of blue suck so hard, they're a totally different
shade than Da Vinci's!"

"No, they're just different."

"Okay... they don't suck, but they don't fit in this painting."

"No- that's just a different kind of painting now, take it or leave
it."

There is a way to state flatly whether something is in tune or not,
and that is based on assumptions of internal integrity, ie.
something must at least be true to itself. In a world flooded with
information and disinformation, it's probably a wise assumption- a
basic filter.

Shall we agree on this? Okay. Do you now concede that most of the
music of the Western world for the last couple of generations is at
best out of tune, and at worst deliberately dishonest? It is, if we
assume that something must be true to itself. Most Western music in
wide circulation is based on the idea that the tonic major triad is
a calm, or happy, or sweet, or stable, consonance, and in 12-tone
equal temperament this is audibly a mild dissonance, nervous
cheerfulness at best: it is out of tune with what it claims to be
(and what is taught to countless students, I was one of them).

Is this a theatrical deception? A resigned grimace masquerading as a
smile? An irony, a post-modern satire, or just a bumbling error?

Or maybe the difference between what the major tonic triad today
claims to be, and what it is, is an artistically sound mirror of a
culture based on lies? Hmmm..... that would mean that there would
probably be people living in the confines of the world of illusion,
but most hurt by it, who would directly address or attack that
fundamental bogosity. They'd probably do something like, I don't
know... play the false third, then bend it into an honest one, make
a real point of it... nah, that couldn't happen.

Anyway I think you're question is actually very good and interesting,
it addresses some eternal practical problems. It seems to me that
the best answer (we're assuming that the group and the soloist share
the same musical goals) is what's always been done- an interplay,
give and take. This is the hairy bitch of working with organs,
klaviatura, and most synthesizers- realtime accurate flexibility of
intonation is hard to do.

-Cameron Bobro