# Black hole music thread in other forum

1. Feb 5, 2004

### marcus

LPF, you suggested starting a thread on BH ringing modes
and/or natural units.
I started a thread in "Stellar Astrophysics" forum

2. Feb 5, 2004

### 8LPF16

Marcus,

The thread starter you left brings up first question:

Is this Stellar Astrophysics, or LQG, or??

Other questions:

2. The closest I come to 1855 (A440tun.) is at 1864, which is an A#.
Where is the discrepancy?

Yes, I would like to know the more precise version of "Sun's mass/5 = 2 octaves".

LPF

3. Feb 6, 2004

### marcus

You like numbers and precision. So let's be more precise and you do some of the calculation. One thing at a time though :)

You know what the planck mass unit is, in kilograms (its at the NIST site)
and suppose I tell you the sun's mass in kilograms. (having just checked in a couple of handbooks)
1.99 x 1030 kilograms.

would you be willing to get us the sun's mass in planck units?

4. Feb 6, 2004

### 8LPF16

Marcus,

I was hoping for a few Q & A's before testing but...

If this question is "elementary", then I give 9.1433e37. If it needs conversion, then I am not there yet.

(my next series of questions included planck units)

Every once and a while, my location provides splendor of high order.
This morning, as I attempted this answer, the Moon set into a band of magenta and peach behind the snow capped Mission Mountains to my right. Moments later, the Sun's rays scattered blues and yellow so white they lose individuality, through the trees of "the Bob" to my left. Normally, my desk is rather boring!

LPF

5. Feb 6, 2004

### marcus

fantastic scenery! where are the Mission Mountains?

I am happy with M = 9.1433e37

Do you want to do the next step as well? You asked about a more accurate value of the frequency (and consequently the pitch) of a solar mass BH. this is (one way) how to get it.

plug that M into the formula

$$\frac{log3}{8\pi M}$$

the log is the natural logarithm, sometimes people write it "ln" for "log natural", and reserve "log" for base-10. Does your calculator have a "ln" key? Or anyhow, can you calculate this.

It will give the frequency and we can then find out how many octaves and musical halfsteps it is from middle D.

6. Feb 6, 2004

### 8LPF16

Marcus,

1. (on roads) 3 hrs. S of Glacier Ntl. Park & 4 hrs. NW of Yellowstone.

2. 4.78080e-40 ?

(I should get one question answered with every correct response!)

LPF

7. Feb 6, 2004

### marcus

South of Glacier and NW of Yellowstone sounds like
living among the splendors of nature
I live among city lights and cant even see the stars at night, or not really well. the night sky is the umbilical for all the worthwhile thinking in the past 2500 years, I sometimes imagine, and we urbanites are cut off from it.

Well I'm happy with your 4.78e-40
-----------------------------------

Now I will calculate what A440 is, in planck terms, and you can calculate the ratio.

there are two conventional formats for frequency and when using hbar (to relate freq to energy) one always uses angular
this is puzzling when first encountered and I'm not sure I know how to help someone over it. angular format just works efficiently and has been used for over 100 years.

all frequency is counting events per unit time
and with a vibration the event can either be a CYCLE or it
can be passage thru a radian of phase. or turning by a radian of angle, if the oscillation is actually a rotation. it has been
found efficient (leading to clean formulas) over the course of a long time by many physicists to deal with frequency in the latter way.
what can I say? there are two conventions and the planck units that NIST lists and almost everybody thinks of as the planck units are based on hbar.

if we want to go to cyclic freq format then we need to change from hbar to h in all the formulas and we get different Planck units and we confuse all the people who are used to these ones

likewise if we take a totally new tack and define the event to be counted as "passage thru one degree of phase" that is 1/360 of a cycle. One could measure freq that way but it would mean changing all the formulas.

so even tho it is unintuitive and seemingly arbitrary I am going to say that A is 880 pi per second.

NIST says Planck time is 5.39121e-44 second

So I multiply the two and get that standard A is
1.490455e-40

Let's round that off a bit and call it 1.49e-40

Pythagoreans should not be surprised because I told you earlier that D was e-40
and A is a major fifth up from D ("do" up to "sol")
so you would expect it to be a higher freq by a factor of 1.5

the fact that it is 1.49 is just because the customary A440 is not
exactly planck. But actually the existing symphony orchestras each use their own tuning. Nobody really uses exactly A440, or so I have read. there is always some variation. So someday there may be an orchestra that uses planck tuning either accidentally or intentionally. this doesnt matter. only that I do not take the number 440, or (in angular format) 880pi, too seriously.
-----------------------------------

so now we have the pitch middle A is 1.49e-40

and we have your number 4.78e-40
for the solar mass black hole pitch

what is the ratio (by what factor is the BH pitch higher than A?)

Last edited: Feb 7, 2004
8. Feb 6, 2004

### marcus

LPF,

I am trying to respond to your questions as we go along.
Has anything been left out so far?

and official A in music is 1.49e-40

so please get their ratio so we can find out how many musical steps your frequency is above official A.
---------------------------

commentary:
what this is really about is appreciating the universe's intrinsic frequency which on the scale we are using is unity-----one.

It is a very high frequency.

Try to grasp it.

More and more people seem to think that Planck energy
is an intrinsic thing built into spacetime where new physics
begins to happen---something meaningful like the speed of light.

But to every quantity of energy E
there corresponds a frequency omega
such that E = hbar omega
(sort of core fact of quantum mechanics
energy steps correspond to frequency steps)

So since there is this intrinsic absolute quantity of energy
there is also an intrinsic frequency----the universe has a pitch

but it is very high
so that middle D (which I know because I can sing it) is e-40
on a scale where the universe frequency is 1.
--------------

however this commentary is not what matters
It seems to me what matters right now is to get the
ratio, if you would please indulge me in this I would
appreciate it.

then we will interpret the ratio as musical steps

9. Feb 6, 2004

### 8LPF16

Marcus,

Before we play any further, we need to get in tune.

It is not surprising that expressing this idea is easier (more convenient) in terms of rotation, nor counterintuitive. The model that takes this form is the only way to go. I am just not used to seeing "radian" tuning. Can you give me a way to translate? I know that a radian is 57.3, but I can't remeber the total "radians per rotation". (I know the formula uses pi in 4 increments)

LPF

ps. In my mind, 360 is good for the total, or "potentials" of angular movement, for determining frequency change one degree at a time. However, I feel that 57.3 is too large to accurately describe the resonant interval, so I worked out my own. One interval "period" is 27.6923, which is derived from the fixed number representing the interval: 13 (half steps) What do you think of that?

10. Feb 6, 2004

### marcus

2pi radians make a full cyle

11. Feb 6, 2004

### 8LPF16

Marcus,

Okay, so the whole cycle is 360.0265...

Does this give it 57.3 intervals of 2pi increments?

LPF

12. Feb 6, 2004

### marcus

The circumference of a circle is 2pi R.
A radian sector of a circle is like you take a radius of the circle made of rubber and bend it along the circumference.
(it covers 57 some degrees, the exact number of degrees is not too imporatant)
2pi radians make a full circumference.

-----------
conventions can be frustrating and irritating
I sympathize. It would be nice if we could make up our own language for describing rates of rotation and rates of oscillation

in physics classes up thru sophomore year the predominant format is cyclic

then (because it makes the formulas simpler or because nature seems to prefer it or something, maybe sheer irrationality) they gradually switch over more to angular format

so in UPPER DIVISION undergrad courses, and even more in the graduate courses, you see the symbol omega for frequency, which is your clue to the fact that every complete cycle or compete rotation is counted as 2pi.

Something real ordinary like A440 belongs to the lower division undergrad curriculum. So the frequency of A would always be
called
f = 440 cycles per second = 440 Hz.
but the frequency of a black hole is upperdivision or grad, so it
would be called
&omega; = 880 pi radians per second = 2765 per second.
doesnt that seem ridiculous?
----------------

There is a fracture in physicists language.
When you read a textbook you have to be alert and watch whether he
is using the symbol f
or the symbol omega
for frequency

If you see &omega; then one full turn is 2pi.
It is actually convenient in a lot of cases, like if there is a wheel turning with frequency &omega;
then the speed of a bug sitting on the rim is &omega;R
where R is the radius of the wheel.

Or if you are on a merrygoround turning at rate &omega;
then how fast you go is &omega;R
where R is your distance out from the axle of the merrygoround.

and your acceleration towards center, which feels like "centrifugal force" to you, is
&omega;2R

Angular format is the format that makes it easy to calculate what they usually want to calculate.

but it is hard to explain it to Freshmen and hard to get the
Engineering majors to accept it. So they hold off and introduce it later in the curriculum after the Engineer majors have left.

And then you see more and more of hbar
and less and less of h
because hbar goes with angular format
E = hbar &omega;

dont blame me. human language has lots of absurdities
this little inconsistency of physicists frequency-language is

Last edited: Feb 6, 2004
13. Feb 6, 2004

### marcus

the number 57.3 you mentioned is only an approximation

if you want a better approximation of the degrees in a radian
then take 360 and divide by 2pi

that is the same as taking 180 and dividing by pi

14. Feb 6, 2004

### marcus

I think you have been admirably patient and that I should
finish the problem up

15. Feb 6, 2004

### marcus

I should take over here.
The ratio of 4.78e-40 divided by 1.49e-40
is 3.2

so the pitch of the black hole is a factor 3.2 higher than conventional A (the A above middle C on the piano)

I have to say what note it is.

Well it is a factor 1.6 higher than the A above the A above middle C.

I am trying to figure out how many musical halfsteps corresponds to the factor 1.6, be back in a moment

16. Feb 6, 2004

### marcus

I got that it was 8 halfsteps above A (above A above middle C)

actually 8.137 halfsteps
but who can hear 0.137 of a halfstep in music, not me
so I just say 8 halfsteps

A BC D EF

It must be an F
because F is 8 halfsteps above A

So you go to the official A440 on the piano, the first one above middle C, and then you go one octave up to the next A
and then you go to F

and that is the note that a black hole with solar mass
would vibrate at

17. Feb 6, 2004

### marcus

now we have something reliable (not just a rough estimate)
the musical pitch of a solar mass black hole really is that F
we could write it on a staff, on music paper
or play it on the piano

I just went downstairs and played it on the piano
it is not the highest F on a conventional piano keyboard but
it is only one octave below the highest F

I dont think a soprano could sing it
sounds more like a bird than a human
cant imagine how a BH 3 kilometer in diameter could vibrate with that high a frequency,
incredibly rigid!

hope the weirdness of calculating such a thing did not freak you out.

if you have any questions a propos this please feel welcome to ask

18. Feb 7, 2004

### 8LPF16

Marcus,

I have a much better understanding now. So many specialists, so little communication.

How important is the use of musical note in this? Is it just a neat idea for a model?

When you say 2765 cycles/sec for 880 radians, that is its' vibratory rate per second. In our music scale, that would be indistinguishable from 2792 freq, or F three octaves up from mid C, yet your saying A. That's where I'm still wondering...

Music moves through 26 half-step intervals of 1.05946,
Mass (apparently) moves through 57.3 intervals of 6.28318 ?
to reach TWO full cycles.

(26 x 1.05946 = 27.54596 x 13 = 358.09748)
(57.3 x 6.28318 = 360.026214 / 13 = 27.6943...)
They are close, but I think after such large numbers in small increments, they wander "off tune".

I see that an interval of 1.065 would bring them closer (27.6926),
but would Mozart approve? What "equation" would give this interval, as 12th sqrt 2 gives 1.05946?

On the theoretical side, I have obtained these patterns from trying to envision the form of the photon. In this theory, a potential photon that is not "energised", is equal to a "gravitino". Maybe the proposed near speed of light speed of gravity could play into this (we are within 96-99%)

At any rate, I see a problem harmonizing a system that uses 13 as its' divisor, with a system that uses 57.3 [?]

LPF

Last edited: Feb 7, 2004
19. Feb 7, 2004

### 8LPF16

Marcus,

"Holy unlyrical lyrics Batman"...

Now I see that your on an F too!

And, upon further review, I see that 57.3/13=440 !!

Maybe we weren't so far off after all.

Thus concludes my first lesson in..(you never did tell me what this is).

LPF

20. Feb 7, 2004

### 8LPF16

Marcus,

I also see that your way (27.6943...)came closer to my predicted interval of 27.6923... than Mozart's of 27.54596.

And now, in perfect resonant form, the full Moon is rising out of my left window. Its' bright glow reflecting off snow covered ground casts the trees as the darkest objects in my perception; green does not exist in this world.