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# Why pianos are never in tune

### Imagine avoiding a leap year by tacking on a few seconds every day. This would mean that clocks would have to be a bit weird to ‘equalize’ over the day so we don’t have to have Feb 29th every four years.Or you can look at a color analogy :

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## Pythagorean versus equal tempered scales

Explaining the equal temperment, by Yuval Nov

Why are pianos never actually in tune? Reddit discussion

Why it’s impossible to tune a piano – MinutePhysics

Just Intonation vs Equal Temperament – Trippin’ on Cookies

## Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Examples of situations to consider could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water,

SAT subject test in Physics: Waves and optics

General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect

## Common Core Math Standards

#### Understand ratio concepts and use ratio reasoning to solve problems.

CCSS.MATH.CONTENT.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
CCSS.MATH.CONTENT.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger.”1
CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

http://www.corestandards.org/Math/Content/6/RP/

CCSS.MATH.CONTENT.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems

## Massachusetts Arts Curriculum Framework

2.1 Demonstrate and respond to: the beat, division of the beat, meter
(2/4, 3/4, 4/4), and rhythmic notation,

2.7 Identify, define, and use standard notation symbols for pitch, rhythm,
dynamics, tempo, articulation, and expression

5.1 Perceive, describe, and respond to basic elements of music, including beat,
tempo, rhythm, meter, pitch, melody, texture, dynamics, harmony, and form

5.13 Demonstrate knowledge of the technical vocabulary of music