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For high school and above, a discussion of the relationship of musical intervals and frequency ratios, with examples and exercises.

In order to really understand tuning, the harmonic series, intervals, and harmonic relationships, it is very useful to understand a little bit about the physics of sound and to be comfortable discussing ratios, fractions, and decimals. This lesson is a short review of some basic math concepts for students who want to understand some of the math and physics principles that underlie music theory.

Ratios, fractions, and decimals are basically three different ways of saying the same thing. (So are percents, but they don't have anything to do with music.)

    If you have two apples and three oranges, that's five pieces of fruit altogether. you can say:

  • The ratio of apples to oranges is 2:3, or the ratio of oranges to apples is 3:2.
  • The ratio of apples to total fruit is 2:5, or the ratio of oranges to total fruit is 3:5.
  • 2/5 of the fruit are apples, and 3/5 of the fruit are oranges.
  • There are 2/3 as many apples as oranges, and 1 and 1/2 times (or 3/2) as many oranges as apples.
  • There are 1.5 times as many oranges as apples, or there are only .67 times as many apples as oranges.
  • 0.4 (Four tenths) of the fruit is apples, and 0.6 (six tenths) of the fruit is oranges.

You should be able to see where the numbers for the ratios and fractions are coming from. If you don't understand where the decimal numbers are coming from, remember that a fraction can be understood as a quick way of writing a division problem. To get the decimal that equals a fraction, divide the numerator by the denominator.

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    An adult is walking with a child. for every step the adult takes, the child has to take two steps to keep up. this can be expressed as:

  • The ratio of adult to child steps is 1:2, or the ratio of child to adult steps is 2:1.
  • The adult takes half as many (1/2) steps as the child, or the child takes twice as many (2/1) steps as the adult.
  • The adult takes 0.5 as many steps as the child, or the child takes 2.0 times as many steps as the adult.
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The factory sends shirts to the store in packages of 10. Each package has 3 small, 3 medium, and 4 large shirts. How many different ratios, fractions, and decimals can you write to describe this situation?

  • Ratio of small to medium is 3:3. Like fractions, ratios can be reduced to lowest terms, so ratio of 1:1 is also correct.
  • Ratio of small to large, or medium to large, is 3:4; ratio of large to either of the others is 4:3.
  • Ratio of small or medium to total is 3:10; ratio of large to total is 4:10.
  • 3/10, or 0.3, of the shirts, are small; 3/10, or 0.3 of the shirts are medium, and 4/10, or 0.4 of the shirts, are large.
  • There are 3/4 as many small or medium shirts as there are large shirts, and there are 4/3 as many large shirts as small or medium shirts.
  • If you made more ratios, fractions, and decimals by combining various groups (say ratio of small and medium to large is 6:4, and so on), give yourself extra credit.
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What has all this got to do with music? Quite a bit, as a matter of fact. For example, every note in standard music notation is a fraction of a beat, and every beat is a fraction of a measure. You can explore the relationship between fractions and rhythm in Fractions, Multiples, Beats, and Measures , Duration and Time Signature .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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