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Why are there 7 discrete notes? A possibly stupid question aboutsound...

Why are there 7 discrete notes? A possibly stupid question aboutsound... - Physics Forum

Why are there 7 discrete notes? A possibly stupid question aboutsound... - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


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  #1  
Old 05-15-2004, 06:29 PM
Michael Levin
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...



I'm a biologist, with no background in music and limited physics, so excuse
me if this is a stupid question. Why are there 7 discrete notes? The pitch
we hear is a function of frequency, which is a continuous, not discrete
quantity. So, at first I thought it was kind of like light and colors - we
make up arbitrary names for sections of the spectrum, but in fact there are
an infinity of colors (or however many the human eye can distinguish within
the EM spectrum). So, maybe each note is just an arbitrary part of the
frequency spectrum which people have agreed to divide into 7 sections. But
one thing bothers me: why does it "wrap around"? That is, on a piano
keyboard, after you've gone A,B,C,D,E,F,G, the next one is A again, one
octave higher, but in some sense, A again. How does this work? And, why does
it wrap around like that? If there is a real sense in which the sounds after
"G" are "A" again, does this mean that there is something to the "7 notes"
beyond just convention? Is there any discreteness in the sound spectrum
which is real (a real feature of the physics as opposed to arbitrary
convention)? I am interested in special numbers which come up in various
areas of math and science. Is the "7" here real, in the sense that the value
of Pi is "real" and not simply arbitrary human convention? Probably not, but
I would appreciate an explanation of where I've gotten confused. How do the
7 notes and the octaves relate to the continuous spectrum of air wave
frequency? Thanks in advance for any info.

--

Mike Levin
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  #2  
Old 05-15-2004, 06:44 PM
Robert J. Kolker
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...



Michael Levin wrote:


Hello? What about the 12 tone scale? The human ear is capable of
discerning more than seven notes in an octave. And what is sacred about
octaves?

Bob Kolker

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  #3  
Old 05-15-2004, 06:55 PM
John T Lowry
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...

Well, I used to be a biologist (geneticist) too. But somewhere back in
the 60's I (and a few others) started playing the guitar. There's
nothing special about our scale; I've heard the ear can fairly readily
distinguish intervals only about one-fourth the size of our current
semitones. Now an octave has real meaning in that going up an octave the
frequency precisely doubles.

An interesting fact I can up with (likely not original) is that the
circle of fifths (which means -- illiterate musicians! -- up FOUR whole
notes, 7 semitones) works because there are 12 (now) equally spaced
semitones and 7 (and 5, going down) are relatively prime to twelve. The
others (2, 3, 4, 6, 8, 9, 10) divide 12 or have common factors with 12.

HTH

John
--
John T Lowry, PhD
Flight Physics
5217 Old Spicewood Springs Rd, #312
Austin, Texas 78731
(512) 231-9391
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"Michael Levin" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
excuse
pitch
discrete
colors - we
there are
within
But
one
why does
after
notes"
spectrum
various
value
not, but
do the


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  #4  
Old 05-15-2004, 06:56 PM
Sam Wormley
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Default Why are there 7 discrete notes? A possibly stupid questionaboutsound...

Michael Levin wrote:

Try: [Only registered users see links. ]
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  #5  
Old 05-15-2004, 07:45 PM
Dirk Van de moortel
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...


"Michael Levin" <[Only registered users see links. ]> wrote in message news:[Only registered users see links. ]...

The simple explanation goes back to the Pythagoreans...

Start from C, take a quint (frequency of C times 3/2) and go to G.
This C and G sound great when played together, or one after the
other.
Now take another quint from G and go to D, then to A, then to E,
then to B, then to F, and finally back to C - You now have 4 times
the frquency of your original C.
C x 3/2 x 3/2 x 3/2 x 3/2 x 3/2 x 3/2 x 3/2 = 17.09 C
That is slightly over 16 C, i.o.w. you now span 4 octaves.
Now collapse them all together in one octave by taking half of
the frequencies of all the ones that didn't end up in the first octave.
That is your scale.

Not quite - It would be nice if (3/2)^7 were 16.
Now, do we have some other way of producing a power of 2
by taking a power of 3/2?
Yes.... try (3/2)^12 = 129.75 =~ 128.
Does 12 ring a bell?

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[Only registered users see links. ]

hth

Dirk Vdm


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  #6  
Old 05-15-2004, 08:30 PM
Michael Levin
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Default Why are there 7 discrete notes? A possibly stupid questionaboutsound...

On 5/15/04 2:55 PM, in article
BItpc.1514$[Only registered users see links. ].pas.earthlink.ne t, "John T Lowry"
<[Only registered users see links. ]> wrote:


Ah! That answers my question exactly. The number of notes in an octave is
indeed arbitrary, and the octaves wrap around because the ear detects
doublings of frequency as similar notes. Makes sense. Thanks!!

--

Mike Levin
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  #7  
Old 05-15-2004, 09:00 PM
Don Pearce
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...

On Sat, 15 May 2004 20:30:35 GMT, Michael Levin <[Only registered users see links. ]>
wrote:


The notes in the scale aren't really arbitrary. They are based on
harmonic relationships that make many of the overtones coincident. In
some cultures, this results in a very limited scale, with just five
notes. Play C, D, E, G, A on a piano to get the idea. Western music
has simply extended the scale to fill in all the blanks, so to speak.

d

--
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  #8  
Old 05-15-2004, 09:05 PM
Franz Heymann
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...


"Michael Levin" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
excuse

In European music, there are 12 logarithmically equally spaced notes
to the octave, not 7.
In some Asian music, there are up to 24 notes to the octave.
A violin can play a complete continuum.

discrete
colors - we
there are
within
the
sections. But
one
sounds after
notes"

THe "7 white notes" is a cultural convention. The relationship
between a note and its octave is what matters as far as your question
goes.
Take a pure sinewave note and one an octave higher. Play them
together. The second one now simply sounds the second harmonic of the
first. In the process, it loses its indentity as far as the listener
is concerned. It simply sounds as if it has modified the timbre of
the first note.

[snip]

Franz


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  #9  
Old 05-15-2004, 10:45 PM
Prai Jei
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Default Why are there 7 discrete notes? A possibly stupid question about sound...

Michael Levin (or somebody else of the same name) wrote in message
<[Only registered users see links. ]> thusly:


May I refer the interested reader to the article
[Only registered users see links. ] by contemporary American
composer David Stybr, which sets out the rationale behind the diatonic and
chromatic scales, simply but systematically.

--
Paul Townsend
I put it down there, and when I went back to it, there it was GONE!

Interchange the alphabetic elements to reply
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  #10  
Old 05-15-2004, 11:43 PM
Old Man
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Default Why are there 7 discrete notes? A possibly stupid question aboutsound...


"Michael Levin" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
excuse

There's also sharp and flat, and "atonal" music has been around
for centuries. There's no accounting for harmonious taste.

[Old Man]



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