Why are pianos never in tune?
Reddit contributor “CheapBastid ” writes:
It is kinda mind-blowing when you dig into it. Our modern ears have grown accustomed to the ‘sparkly’ fast beating quality of ‘slightly out of tune’ Equal Temperament tuning. In the old days every Key had a certain ‘flavor’ to them that we’ve lost with the utilitarian/cross-key choice.
Long story short: modern/western/equal tuning is a compromise to allow a piano to play in every key.
This is because using ‘just tuning’ (keeping notes most pleasantly/mathematically related to their neighbors) going up a scale in a key will eventually result in a comma pump that starts to drift sharp.
The ‘idea’ in Equal Temperament (used on modern pianos) was to chop up the octave into 12 equal parts.
When you do so, you almost imperceptibly miss every Just Tuned note (notes that are tuned in the most harmonically pleasant way).
So one ends up slightly ‘out of tune’ note to note in a way that lets you play more easily key to key.
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 :
Pythagorean versus equal tempered scales
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.
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.”
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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.
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,
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