Thanks for joining us here for another video from Howard Piano Industries. I'm Steve Howard and we're here in the workshop of Howard Piano Industries and we're going to be talking today about inharmonicity, and it's a term we use in tuning. What it does is, it kind of describes, and as they define, and show you what inharmonicity is, it's going to show you why pianos need what are called what's called stretch to the octaves. Now we talked in a previous video about what partials are. They're basically overtones in any single piano key that you hear, that are present. You don't necessarily hear them real strongly but they are present in any tone or any note of a certain piano key or a piano. So what inharmonicity basically is, is if you can imagine, that any piano wire or piano string, when it's played, those partials are present in that string, and what those are, are segments which are divisions of that string. For example, the first partial is going to be half the length of the string. The second, the third partial, is going to be third of the length of the string ,and so forth. What happens is, all those partials are present because you get vibrations that are just portions of that string, and that creates whatever, those are called partials or overtones. What happens is, because the length of that string there was those shorter segments, which create the partials are stiffer because if you can imagine, as you have a piano wire or a string that is the same thickness throughout its entire length, as those segments get shorter they get stiffer, and what happens is, because they're stiffer than the entire length, it actually raises the overtone, or the partial. So for example, we've got here, let me just show you an example, and as you could imagine, a shorter segment of the same thickness of string is going to be stiffer. If we do the full length you can see that it will move fairly quickly, but if we're, fairly easily, but if we do a shorter section it doesn't want to move, so it, so yeah, you know, general logic would tell you that it's going to be stiffer if it's shorter, if the diameter is the same. For example, we talked about, here we're good. We got a three. The first partial is, or the second partial is going to be an octave higher. The third partial is going to be an octave and a fifth, and as we go higher with the partials, those are going to increasingly be a little bit sharp of what, theoretically, that partial should be. If everything were in a perfect world but because of that inharmonicity, which is created by the stiffness and what happens is, that stiffness, the ends don't want to bend as easily which causes the pitch to raise a little bit the higher the partials go. So that's basically what inharmonicity is and what that does is, as we get higher, partials are going to be higher. So for example, if we know that we've got partials all the way up here, maybe on a six and a seven we got partials in this note, of those notes and if by the time we get up here, these are 15, 20, 30 cents sharp, the partials for this note we have to tune, those notes, that many cents sharp, so that it matches the partials for this note, all the way down here, in case so basically we have to tune gradually sharper. We will usually start at A4 as zero cents sharp or flat from where it should be but as we get higher, from there though, we have to stretch, the stretch to the pitch a little bit higher to match those overtones or those partials that are in the notes below them, and as we go down below this obviously the stretch has to go lower because, basically unless we started at A0, but we don't, we start at A4, but if we started at A0 at being at pitch, then we'd have to gradually get higher, but that's not real practical, so we start with A4, and so gradually, as we go down, to a lesser degree, it's not, we don't stretch the bass and the lower end of the sections of the piano as much as we do the upper end. So the other thing is, it also depends, the amount of stretch is going to depend on the size and the model and scaling of each individual piano and in general, the taller or longer the piano is, longer in a grand piano taller in an upright piano, the less inharmonicity you have, and the reason for that is, if we look over here at the bass strings as you're probably familiar with bass strings, they're round with wound with copper windings, and the reason for that is because you have to be able to get the lower pitches and theoretically to keep thinner wire on the bass strings you'd have to have really, really, really, long bass strings so they wrap those with copper windings to make them thicker so that they can get the lower pitch without having to make the strings enormously long. So as you can imagine, a nine foot concert grand piano, it's not going to have as thick of strings all the way down here at A0 in this bass section as it does on like, for example this console piano or a baby grand piano that's only five feet long. So that's why you've got less inharmonicity in a taller or longer piano and that's why the bass sounds so much better on longer or taller pianos than it does on a shorter or not as long piano. So that's some general things and we'll talk more about inharmonicity and how it relates to tuning in a future video, but feel free to visit our website or ask us if you have any questions. Our website is howardpianoindustries.com