



A review of roots and powers for the music student who wishes to understand frequency relationships in equal temperament.
You do not need to use powers and roots to discuss music unless you want to talk about frequency relationships. They are particularly useful when discussing equal temperament. (See
Tuning Systems .)
Powers are simply a shorthand way to write "a certain number times itself so many times".
Roots are the opposite of powers. They are a quick way to write the idea "the number that, multiplied by itself so many times, will give this number".
Roots and powers are relevant to music because equal temperament divides the octave into twelve equal half steps. A note one octave higher than another note has a frequency that is two times higher. So if you divide the octave into twelve equal parts (half steps), the size of each half step is "the twelfth root of two". (Notice that it is
not "2 divided by twelve" or "one twelfth". For more on this, see
Equal Temperament .)
Using a scientific calculator, find
 The frequency ratio of a half step (the twelfth root of 2), to the nearest ten thousandth (four decimal places).
 The frequency ratio of a perfect fourth (five half steps, or the twelfth root of 2 raised to the fifth power), to the nearest ten thousandth.
 The frequency ratio of a major third (four half steps), to the nearest ten thousandth.
 The frequency ratio of an octave.
 1.0595
 The twelfth root of 2, to the fifth power, is approximately 1.3348
 The twelfth root of 2, to the fourth power, is approximately 1.2599
 The twelfth root of 2, to the twelfth power, is 2
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Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Sound, physics and music. OpenStax CNX. Jan 06, 2005 Download for free at http://cnx.org/content/col10261/1.1
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