Pipe organs measure pitch in "feet". Bigger number = lower pitch. The 
number is not /directly/ related to the physical size of the pipes, 
although generally bigger numbers mean bigger pipes.

A "normal" organ stop has 8' pitch. The pipes controlled by the peddles 
are normally 16' pitch (i.e., one octave lower). Most organs will also 
have 4' and 2' pitches, and unless it's a really small organ, there's 
usually at least one 16' stop.

Now, a *cathedral* pipe organ will have at least one 32' stop, and a 
really powerful one might have several of them.

There are exactly two pipe organs in the entire world which have a 64' 
stop. And here's why:

http://www.sydneyorgan.com/STH64.mp3 [Sydney Town Hall]
http://www.die-orgelseite.de/audio/atlanticcity_64ft.mp3 [Broadwalk Hall 
Auditorium Organ, New Jersey]

(Many organs have a 64' stop which actually generates /harmonics of/ a 
64' pitch, but only these two actually have true 64' pitch pipes.)

Worth it... :-P

Then again, the organ at Liverpool Cathedral has a 32' Double Open Bass 
which the organ's designer referred to as "the expensive draft". When 
played, it makes a vague fluttering sound. The louder 32' stops make a 
more definite sort of noise. (As best as I can tell, from video 
recordings made with professional equipment...) If 32' isn't that 
useful, why bother with 64'?

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> Then again, the organ at Liverpool Cathedral has a 32' Double Open Bass
> which the organ's designer referred to as "the expensive draft". When
> played, it makes a vague fluttering sound. The louder 32' stops make a
> more definite sort of noise. (As best as I can tell, from video
> recordings made with professional equipment...) If 32' isn't that
> useful, why bother with 64'?
>

Nigel Tufnel: The numbers all go to eleven. Look, right across the 
board, eleven, eleven, eleven and...
Marty DiBergi: Oh, I see. And most amps go up to ten?
Nigel Tufnel: Exactly.
Marty DiBergi: Does that mean it's louder? Is it any louder?
Nigel Tufnel: Well, it's one louder, isn't it? It's not ten. You see, 
most blokes, you know, will be playing at ten. You're on ten here, all 
the way up, all the way up, all the way up, you're on ten on your 
guitar. Where can you go from there? Where?
Marty DiBergi: I don't know.
Nigel Tufnel: Nowhere. Exactly. What we do is, if we need that extra 
push over the cliff, you know what we do?
Marty DiBergi: Put it up to eleven.
Nigel Tufnel: Eleven. Exactly. One louder.
Marty DiBergi: Why don't you just make ten louder and make ten be the 
top number and make that a little louder?
Nigel Tufnel: [pause] These go to eleven.


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> (Many organs have a 64' stop which actually generates /harmonics of/ a
> 64' pitch, but only these two actually have true 64' pitch pipes.)
>

And then, the harmonics of 64 are:
32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....

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On 25/04/2011 20:23, Alain wrote:

> And then, the harmonics of 64 are:
> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....

I love how the harmonics look like completely randomly chosen numbers, 
with no obvious pattern at all.

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> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

64/1 = 64
64/2 = 32
64/3 = 21 1/3
64/4 = 16
64/5 = 12 4/5
64/6 = 10 2/3
64/7 = 9 1/7
64/8 = 8
64/9 = 7 1/9
64/10 = 6 4/10
...

Nope, no discernable pattern at all
;)


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>> I love how the harmonics look like completely randomly chosen numbers,
>> with no obvious pattern at all.
>
> 64/1 = 64
> 64/2 = 32
> 64/3 = 21 1/3
> 64/4 = 16
> 64/5 = 12 4/5
> 64/6 = 10 2/3
> 64/7 = 9 1/7
> 64/8 = 8
> 64/9 = 7 1/9
> 64/10 = 6 4/10
> ...
>
> Nope, no discernable pattern at all ;)

Exactly. I mean, unless you happen to be able to compute 64/7 mentally, 
which normal humans can't.

If it was notated some other way, the pattern might be more obvious. But 
as it is...

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> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

Harmonics are integer multiple of the base frequency, or integer 
quotients of the base wave length having integer quotient of the power.

Armonic 1 is the base signal.
Armonic 2 have twice the frequency, or half the wave length, and half 
the amplitude. For 64, it gives 32.

Nothing random here, not even a bad pseudo-random. It's totaly 
deterministic.



Alain

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On 04/05/2011 00:21, Alain wrote:

> Nothing random here, not even a bad pseudo-random. It's totaly
> deterministic.

So is a psuedo-random number generator, and yet it still *looks* random.

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>>> I love how the harmonics look like completely randomly chosen numbers,
>>> with no obvious pattern at all.
>>
>> 64/1 = 64
>> 64/2 = 32
>> 64/3 = 21 1/3
>> 64/4 = 16
>> 64/5 = 12 4/5
>> 64/6 = 10 2/3
>> 64/7 = 9 1/7
>> 64/8 = 8
>> 64/9 = 7 1/9
>> 64/10 = 6 4/10
>> ...
>>
>> Nope, no discernable pattern at all ;)
>
> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
> which normal humans can't.

You're not that much younger than me, so maybe there's something 
fundamentally different between the school system in the UK vs. Canada, 
but in the 2nd or 3rd grade, we had to learn our multiplication tables 
by heart.

Normal humans should remember that 7 * 9 = 63.

Or if they don't, they should be able to guestimate that since 64 is 
rather close to 70, there's a good chance that 64/7 would be just a bit 
less than 70/7, which is easy to compute.

If not, I weep for humanity.

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>> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
>> which normal humans can't.
>
> You're not that much younger than me, so maybe there's something
> fundamentally different between the school system in the UK vs. Canada,
> but in the 2nd or 3rd grade, we had to learn our multiplication tables
> by heart.

This is almost universally regarded as one of the most useless things 
you learn in school. I haven't studied this statistically, but I suspect 
the majority of adults long since forgot all this stuff.

> Or if they don't, they should be able to guestimate that since 64 is
> rather close to 70, there's a good chance that 64/7 would be just a bit
> less than 70/7, which is easy to compute.
>
> If not, I weep for humanity.

Start weeping. This kind of reasoning is apparently far beyond the 
ability of most average people.

Even if it wasn't, standing there for five minutes computing tables 
isn't very immediate. If, instead of notating note pitches as 
wavelengths, they were noticed as, say "K * 7" or something, it would be 
far more instantly obvious what the relationship is, without having to 
perform complex mental arithmetic.

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