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Author: admin | Category: How To Learn Piano | 28.02.2016

It was Pythagoras who first discovered that notes which blend well together have frequencies of vibration that are related by simple fractions. Here are some building bricks laid out with lengths in the ratio of 3 to 2 - see how the pattern repeats regularly, and how the resulting composite pattern has an innate structure.
This structure is not so different from the regular pattern of vibration of the eardrum when a perfect fifth is sounded - the eardrum vibrates in a simple pattern, pleasing to the brain. When two notes do not have this sort of relationship, the pattern does not repeat for a long time, and the vibration of the eardrum changes constantly.
Suppose we start at bottom C on the piano, and go up in perfect fifths - C G D A E B F# C# G# D# A# F C.
But we've gone up exactly 7 octaves, and each has double the frequency, so we have gone up in frequency by 2 to the power 7, which is 128.

In musical terms, the beating between, say, C on the second string and G on the top string, is slower than once every two seconds. And so in guitar terms, tuning a chord to perfection instead of to "near perfection" will make another chord sound worse!
Here's an example - play the chord of E in first position, and you will find you can flatten the G string and the chord stays sounding nice. When I tune using a tuning fork, rather than a chromatic tuner, I double check my tuning by playing the chords of E and C, and also an open chord of D (just Ds and As). As indicated, the notes on a piano are named after the first seven letters of the alphabet.
Chords in natural minor keys follow the pattern, minor diminished major minor minor major major.

The following piano key chord chart shows all the triads in E minor as well as four note extended chords.
Indeed, the problem has been known to occupy whole books about tuning, but we can cut to the chase in one page. The layout of a piano keyboard consists of two black keys followed by two white keys, then three black keys followed by two white keys.

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