# relative vs. absolute (UNCLASSIFIED)

Mullins, Bill AMRDEC Bill.Mullins at US.ARMY.MIL
Mon Jun 8 16:04:59 UTC 2009

```Classification: UNCLASSIFIED
Caveats: NONE

>
> I think you're missing my point: *Pitch is a phenomenon of human
> perception.
> Frequency is a phenomenon of physics. They are not the same.
> *Describing
> pitch with an interval scale makes sense, because we're describing our
> perceptions.
>
> Let me return to the definitions and examples I gave earlier, which I
> think
> we agree on:
>
> Interval: The values are ordered and can be subtracted, but not added,
> multiplied or divided. The interval between Sept. 12, 2000 and Sept.
> 12, 2009 is 9 years, but "Sept. 12, 2000 + Sept. 12, 2009" is
> meaningless. Similarly,   Jan. 1, 2000 isn't twice as (anything) as
> Jan. 1, 1000,   100 degrees Fahrenheit isn't twice as hot as 50, and
> 40 degrees west longitude isn't four times as west as 10 degrees west,
> except as measured from their scales' arbitrary zeros.
>
> Ratio: The values can be treated as numbers: meaningfully subtracted,
> added, multiplied or divided. \$6 is twice as much as \$3,   300 degrees
> Kelvin is three times as hot as 100, and a person of 60 is twice as
> old as a person of 30.   40 degrees north latitude is twice as far
> north as 20 degrees north (and the equator, unlike the Greenwich
> meridian, is not arbitrary).
>
> Pitch has intervals -- a fifth from C to G, a semitone from A to Bb.
But it
> doesn't have ratios. What is 3 * C, or even 3 * middle C, or middle C
/ 2?
> To a musician, the question is meaningless. Pitch has no zero point.
Middle
> C is a point to measure from, like the Greenwich meridian or the
freezing
> point of water, and equally arbitrary. You can call it zero if you
like, and
> describe the other notes as so-and-so many semitones above or below
it, but
> you still can't can't add middle C to G-above-middle-C, or divide
middle C
> by 2, any more than you can do it with longitudes or Celsius
temperatures.
>
> Pitch does have a ratio aspect in its cyclical, or rather helical,
nature.
> Go up one octave and you've climbed in one dimension, but in another
you've
> come back to where you were. All C's share an identity relation for
which I
> can think of no analogue in temperature or earthquakes or dB or any of
the
> other phenomena we've discussed in this thread.
>
> Which puzzles me, now that I think of it. Perhaps we should consider
the
> musical scale as something different from these others, eligible for
that
> distinction because it is describing perception rather than physics.
>

Agree fully with your last paragraph, and it is a good restatement of
most of what
I was trying to say.
Classification: UNCLASSIFIED
Caveats: NONE

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