Grab a cup of coffee, put on your thinking cap, and start working through this video from Minute Physics, which explains why guitars, violins and other instruments can be tuned to a tee. But when it comes to pianos, it’s an entirely different story, a mathematical impossibility. Pianos are slightly but necessarily out of tune.
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“In tune” … “out of tune.”
What does this even mean?
Rod,
“In tune” means the harmonic sequence(s) associated with the strings align and resonate with the highest possible energy [or equivalently with the least amount of dissonance]. While the video was algebraically correct, as a musician and mathematician, the presentation lacked informative value.
Check out wiki: https://en.wikipedia.org/wiki/Harmonic_series_(music)
Regarding the article, the author has made a fundamental [small joke] error. The guitar strings can all be harmonically tuned using the fourths and major third, but every chord that involves using frets will be out of tune. Why? Because the frets are spaced using the ratio of the equal temperament system — just like the modern piano.
J.S.Bach was a major proponent of equal temperament which allowed him to compose in all keys. For a fabulous explanation and historical overview, see Ross Duffins’ “How Equal Temperament Ruined Harmony”.
What surprised me about this clever video was that there was no mention of Bach’s Well Tempered Clavier. In composing The Well Tempered Clavier, Bach had as one of his motives a practical demonstration that one could compose and play in all keys on an instrument whose tuning was necessarily tempered.
The video is factually incorrect. It suggests that the piano can’t be ‘tuned’. This is a nonsense statement. It can’t be tuned to simple integer ratios, but a 12-note octave, which is what is used in Western music, comprised of note related by simple interger ratios is a mathematical impossibility and NOT the tuning system used in western anyway. Musical tunings are cultural inventions and vary, as can be seen with Gamelan and Thai music. There is no universal standard for ‘in tune’ and the Pythorean model explaibed in the video was abandoned hundreds of years ago.A guitar can be tuned using harmonics but doing so will make it out of tune with itself because tuning strings to the interval of a fifth by eliminating beating makes it out of tune open with equal temperament, which is the tuning system it is made for.
As Jeff Daniels said above, the guitar (and all stringed instruments) are tuned to the equal tempered scale, the same as a piano.
I thought this article (video) was going to be about Stretch Tuning, which is done on a piano due to the inharmonicity of the strings, especially the thick wound ones in the bass.
The bass notes are tuned progressively flatter, and the treble strings are tuned sharper so that the out of tune harmonics of the lower notes do not clash with the fundamentals of the higher notes.
A long stringed piano ( e.g. a concert grand) needs much less stretching than smaller pianos like a console or spinet.
Correction: I should have said FRETTED stringed instruments in my post above.
Dissonance? Consonance?
Highest possible “energy”
equating with the least dissonance.
What century is this?
Can you tuna fish?