#Electronic piano tuner manuals

(You can do this on a calculator by raising 2 to the power of 7/12.) That gives us a ratio of about 1.498307 instead of 1.5. Then, we multiply that by itself 7 times (because there are seven semitones in a fifth) to get the ratio of an equally tempered fifth. Since octaves are double, or a factor of 2, and an octave is comprised of 12 half-steps/semitones, we need to take the twelfth root of 2 to get an equally tempered semitone. Instead of a fifth being 3:2 (a frequency times 1.5), a fifth is defined as the twelfth root of 2 to the seventh power. That is why, in other temperaments, each key has its own flavor whereas, in equal temperament, all the keys are identical when you compare them relatively.Īll of them, by the same amount. Some fifths are (or are closer to) just/pure fifths while others are further apart. Other temperaments handle this differently. In this system, the same amount is taken away from all the fifths-hence it is called equal-so that the 12 fifths line up exactly with 7 octaves. So we've come up with many systems to fudge the difference. Nevertheless, there is a slight difference. One such point is seven octaves and twelve fifths. (I asked for a proof of this on the mathematics stack exchange and got several great answers.) But it so happens that there are a few points where a stack of fifths and a stack of octaves come pretty close to one another. That's correct because when you add up just/pure octaves and you separately add up just/pure fifths, they will never meet. However, when you divide each octave into 12 semi-tones, and tune it mechanically, there's going to be a problem with the fifths. Now that we have that basis, let's unpack your point #2. Either pitch would be the perfect 5th of A2, but only 165 Hz is the just/pure fifth. But in equal temperament, it's about 164.813778 Hz. 110 Hz is A2, so 165 Hz must be E3, right? In 'just intonation', yes, it would be. So, if you start at 110 Hz, for example, the just/pure fifth is 165 Hz. A just/pure fifth is always higher than the starting frequency by a ratio of 3:2. When we speak of fifths, however, just/pure fifths and perfect fifths are not necessarily the same. Descending octaves are always half the frequency. Ascending octaves are always twice the frequency of the starting note. When we speak of just/pure intervals, we are talking about the relationship between frequencies. Nevertheless, 'just', 'pure', and 'perfect' happen to be the same when applied to octaves. 'Just' and 'pure' are synonyms while 'perfect' has a different technical meaning in music. In equal temperament, octaves aren't merely perfect they are 'just' or 'pure'.

This may be true, but the practical reality for my cheap baby grand is that the backlash in the tuning pegs and the stability of each string's pitch doesn't allow such tiny adjustments to stay stable. I've seen claims that each unison should actually be slightly detuned, and that this affects the sustain of the tone. Over almost the entire keyboard, you can actually do fine just by tuning to an electronic tuner. The stretching of intervals is only desirable in the very high treble and very low bass, because those are the strings that have a significant amount of inharmonicity in their overtones. I believed these two claims until I actually started tuning my own piano. From a lot of the written descriptions you see out there, you'd imagine that (1) every interval on a piano was stretched by some fixed percentage, and also that (2) piano tuning has to proceed through a circle of fifths, tuning by ear using beats.

This is not nearly as complicated as a lot of people would have you believe. what, exactly? The distance between the notes in the lower half of the piano? to get the octaves and fifths to agree with one another), a piano tuner lengthens the. (I'm not sure: which fifths? Like, the tonic of the second octave and the fifth of the third octave? Or is it the fifths in the sense that you play a note and then go +5, and then again +5, and so forth?) If you then play the same C and any other C, it'll still sound perfect. To one's ear, it is essentially the same note. There's no conflict between the two notes. When you play an octave on the piano (say, a C and the C following it), it sounds perfect. I've been trying to make sense of it all, and now I find myself thoroughly confused.

#Electronic piano tuner manuals

I get the feeling that the actual explanation is a lot simpler than what the manuals and textbooks offer.