Long scale length, low tuning, string tension, flexibility, construction, and inharmonicity

Discussion in 'Extended Range Guitars' started by Hollowway, Nov 1, 2017.

  1. bostjan

    bostjan MicroMetal Contributor

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    Bass strings, in general, are lighter than guitar strings. It's because of the geometry of the wrapping - there are more voids in bass strings, by design, typically.

    For guitar strings, take a 0.056" as an example:

    Stainless unit weight: .00060297 lb/in (Say this is 100% for reference)
    Nickel Plated Steel: .00057598 lb/in (95.5%)
    Phosphor Bronze: .00063477 ib/in (105.3%)
    Chromes (Stainless flat wound): .00059075 lb/in (98.0%)
    Bass: .00053791 lb/in (89.2%)

    For an electric guitar, the best you're going to get with a D'Addario product, in terms of tension, is the Stainless Steel.

    Of course, if you made a plain steel .056", it'd have a unit weight of about .000695 lb/in (115.3%), but you'd need a torch or at least a dremel to trim the end of the string. :lol:

    When I worked as a tech, I had a couple of customers who played acoustic guitars with plain G strings on them. I actually blunted a pair of diagonal cutters the first time. :p
     
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  2. vansinn

    vansinn ShredNeck into Beck

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    I see what you mean, and agree.
    My suggestion would be a slight alternative:
    Derive the math needed to express not which string [construction, materials, tension, stiffness] to use for a wanted tuning at a wanted scale, but rather, which combination of scale and string is the most efficient for a wanted tuning.

    Some form of argumentation:
    I had a 26.5" Riot 8, which did not at all work for me on the 8th string - too short scale, and it didn't matter which different string gauges, types of steel, tension, I tried.
    Before this, I'd tried a couple 25.5" guitars, which were absolutely horrible.
    I'd also tried an Ibanez 27", which worked somewhat better.

    On the Riot 26.5", I found thicker strings to work worse than thinner - which in return felt too loose.

    My [too] few experiments with 8-stringers and strings has led me to believe somewhere between 27.5" and 28.5" will be ideal for most normal 8-string tunings, utilizing not too thick, not too thin/slinky strings.

    On bass, I've worked with 34" and 35".
    My Wolf 35" 7-stringer worked almost fine with the stock Titanium-coated .125 B-string.
    An Ernie Ball .130 did not at all make things better, sounding too dull/dark.
    A D'Addario .135 XL worked much better, feeling just right in tension, but didn't sound as good/crisp as the stock .125; interesting..
     
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  3. bostjan

    bostjan MicroMetal Contributor

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    Here's a suggestion/question:

    What if you took your 0.142" and tuned it up from G# to whatever arbitrary tuning feels good?

    Let's say you tune the G# up, without using a tuner, just riffing on the single string, and it still feels too slack for your liking, then you keep going, and finally, at some tension T, it finally feels "good." Now grab a tuner and see where you landed.

    For example, let's say you landed on A#0. That's what. 33.7 lbs? So, then choose a string which provides similar tension at G#0, like a 0.158". It won't feel exactly the same, because the string will have a little more mass and a little less "stiffness," but it's the same scale length and it should be close enough for government work.

    Tuning up to B would be like G# at 0.166". Tuning up to C would be sort of like 0.174", and tuning to C# gives a little more tension than you'd get with a G# with a 0.182", but you'd pretty much be at the biggest string available at that point, plus you'd be tuning up an entire fourth at that point.
     
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  4. PBC

    PBC Composition Ontology

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    The math is important, but it can't answer all of the questions you ask of it. See below

    In a short answer the 2" won't help much with that and I'll explain.

    Oh boy @Hollowway, this will be long one. Unfortunately, my knowledge is woefully minuscule compared with @bostjan and @ixlramp compared to the actual equations in strings but I do have some observations from my own dealings with ERGs. Regrettably, this takes the form of "personal testimony" in which the actual experience can lack the necessary empirical understanding of the subject to give significant insights; but I'll attempt it. To be clear this isn't a rant (nor is it hard fact), I want my tone to come across as if this is a friendly chat over tea.

    I break this down into several categories of specification (including tuning), personal bias, and strings.
     
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  5. PBC

    PBC Composition Ontology

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    Starting with Specification(Scale Length and Tunings):

    Here's a common statement: "The longer the scale length the thinner strings you need to reach the same tuning/tension"

    This statement is mostly a half-truth because it greatly reduces the complexity of the situation into a suitable maxim.

    As most of our fellow ERGers have observed at some point it seems that you need to up the gauge of the string in order to reach the desired tension. As the scale length increases, the amount of energy sent over the strings has a greater distance to travel. Some of you have probably noticed that if you tune to low tension on a longer scale instrument it seems that oscillations of the string cause it to behave awkwardly when attempting to play. Therefore, it seems logical to increase the tension to counteract the extraneous sinusoidal behavior of these strings; however, as we already stated it seems like it gets even worse even as the strings have thicker gauges and become more stiff.

    My hypothesis is that the string is having trouble with, if this is the correct unit, the amount of Joules produced by striking the string. @Hollowway , when I tried a .142 on my 10 string I found it to be one of the worst experiences in so far as playing goes. Because of the string spacing on the guitar, it was super close to the next string (also pretty thick), so there is barely enough space for solid up picking. This led to some odd sympathetic vibrations between the lowest strings (hard to mute). With it's tension and mass, I found that each strike I was counteracting my previous picking of the string (fighting myself). It also appears that the string greatly needs a longer scale length to get the correct flexibility; the equivalent experience is attempting to stuff an atlantic salmon into a fishbowl.

    On the subject of inharmonicity, as stated by others, there are too many unknown variables to precisely map this type of problem to an equation at the moment. However, we can break it down into several sections. As these members know, each note response differently depending on the scale length presented to it. Eventually after theoretically changing the scale length there are diminishing returns for every inch you add to the instrument.

    To add another component before continuing. It's important to note that high tension players, e.g. @Hollowway and @Winspear, start with a severe inharmonicity handicap. Each string and note, has different levels to how effectively the inharmonicity can be reduced. This is too difficult to explained in words because it comes from personal experimentation with strings and observing the numbers on the string calculator I created with @bostjan 's inharmonicity formulas (which aren't 100% perfect), for hours. Let's take a practical example (done with Kalium tension):

    You tune to B standard your second harmonic(overtone) is (123.48hz):

    For a 25.5" scale:

    .049 : 12.2 lbs : 127.26hz
    .053 : 15lbs : 128.94hz
    .061 : 18.48lbs :129.48hz
    .065 : 21.07lbs : 130.26hz

    Now for 27":

    .049 : 13.62 lbs : 126.49hz
    .053 : 15.88lbs : 127.37hz
    .061 : 20.72lbs : 128.25hz
    .065 : 23.62lb- : 128.87hz

    Now for 30":

    .045 : 14.38lbs : 125.13hz
    .049 : 16.88 lbs : 125.45hz
    .053 : 19.60lbs : 125.81hz
    .061 : 25.58lbs : 126.61hz
    .065 : 29.16lb : 127.02hz

    Let's crank it up for the last one 34"

    .045 : 18.47lbs : 124.48hz
    .049 : 21.69 lbs : 124.68hz
    .053 : 25.18lbs : 124.89hz
    .061 : 32.86lbs : 125.38hz
    .065 : 37.46lbs : 125.63hz

    There are several things to take note of here. First is that depending on the scale and the note itself, a lighter gauge string will have the same harmonic content as a higher gauge string on a longer scale. Second, there are diminishing returns when the scale length gets extremely long with respect to the note being played. Third (this applies to most situations), a higher gauge string player will get most inharmonic reduction by increasing the scale length (look at .065 vs .051) , however, they will always be outmatched by lighter gauge string players for harmonic content.

    The ideal goal is to be able to get to the scale length where increasing in tension and gauge has small bearing on the overall harmonic content. As an example, look at the difference for the 34" scale, you can increase the tension by almost 7lbs and only change the harmonic content by .5hz.

    From my personal perspective, each note has different Zones associated with this. The zones, if you think of them as a spectrum, have a range of string gauges within the spectrum that are permissible for harmonic content and playability. Generally, there is a zone that effects little of inhamonicity but usually outside the realm of playability; these would be wound gauge strings with less than 10lbs of tension. There is the second tier of strings that fall in the realm of playability where you can slightly increase the gauge without dramatically affecting the inharmonicity , yet, there is a soft cap where after a unknown threshold there gets to the third tier of stiff strings, big tension change per small increases in gauge, and large inharmonicity. The goal then is to figure out the correct combination of scale length, tuning, and player technique so that it'll allow you the higher possible gains. Lastly, this spectrum changes in regards to each scale length and note; they have their own "Zone" where things work well. This is extremely difficult to describe, because you must try out a whole host of different strings on all types of scale lengths as well continuing looking at calculations for patterns and trends.

    A couple last points for this section.
    The math is good gauge of seeing the results of certain strings on certain guitars. However, there becomes that point where you question: How much is this tuning worth? What is 10hz of inharmonicity really? Will it be that much better for me if I reduce the tension in order to drop the second harmonic by a semitone? This is where the math fails, and practical experience (more like routine failure) comes into play. I have bought a ton of strings over the last 4 years. I set it up, play, then check the inharmonicity, followed by a guitar on a shorter scale to A/B the two. With a handwave towards pickups, construct method, and those other hotly debated topics, this method allows my ears to differentiate the "worth" of the inharmonicity. Of course this worth is subjective. Generally I tend to follow my ears first, then adapt my playing, because nothing is as satisfying as clear note definition and separation.

    Lastly, each note is different (obviously). To elaborate, while you may increase the scale length on an instrument, there comes a point (to me), where the scale length is not even close to be where it needs to be for the note to ring true. For example, you have a subcontra bass guitar. This is tuned to C#/Db0

    Frequencies for root and 2nd harmonic (17.32/34.64):

    34" Bass:
    .190 : 23.71lbs : 104.05hz (Yes that's A2 for second harmonic)
    .210: 28.85lbs : 119.77hz
    .232: 35.50lbs : 137.70hz
    .254: 43.31lbs : 158.87hz (E3)

    39.55" Quake:

    .166 : 24.67lbs : 63.37hz (B1)
    .190 : 32.08lbs : 72.55hz
    .210 : 39.04lbs : 81.14hz
    .232: 48.03lbs : 90.93hz (F2)

    So as we see here, the Quake offers a massive increase in harmonic content but it's nowhere close to the actual 2nd harmonic of 34.64hz. As we've already established: strings tension coupled with scale length is not a linear affair, it's exponential. Therefore every half step you tune down requires more scale length and potentially tension than it took for the previous note. To get close for this note would require something close to 60" scale length (a la Kalium Skip's Rim). This would probably look like a .166 (56.86lbs) with 40.06hz (D#/Eb1) second harmonic.

    Here's a personal bass example (instrument is a Brice 735, 35" scale, I'll just highlight the bottom strings):

    A1 (55.00hz) (110.00hz) : .049 : 18.24lbs : 111.20hz
    E1 (41.20hz) (82.40hz) : .067 : 18.74lbs : 85.45hz @ixlramp I from a random post on talk bass that you've used a .070
    B0 (30.87hz) (61.74hz): .090 : 18.26lbs : 69.21hz - This B is slightly better harmonically than the .118 that C3 used in the Quake NAMM 2017 video, of course that string is much more playable at 40lbs of tension
    F#/Gb0 (23.12hz) (46.24hz): .118 : 17.74lbs : 63.63hz

    These strings are extremely light (even for me), I much rather prefer something akin to 23-25lbs for my basses, however one of the issues in the search for tone is that you cannot unhear the clarity of a note once you hear it. The F# is clear enough that I can hear its sound well acoustically on the bass however this is an example of a note and string on the edge of a Zone, because in order to get it to 25lbs in would require going for a .142, so I'm still playing this type of instrument until I can get the funds to commission at 40.25" bass. If I were to go to 37" I'm okay with this note's definition as is, I'll increase my gauge to .130 that would increase the tension to 23.90lbs keep the same inharmonicity (63.4hz) but allow for better playability. On the long scale bass my goal on that is to have a

    .124 : 25.83lbs : (23.12hz) (46.24hz) : 57.25hz

    for the string that way it'll be a bit more playable (but again decreasing the gauge this time).

    Lastly, it's important to keep in mind octaves when looking at data like this since each octave follows a pattern of (N(Octave) * 2^N). In plain english, octave 3 covers ~ 110-220hz, octave 2 is 55hz-110hz, octave 1 22.5-55hz. So as you get lower the notes become closer together from a frequency perspective. If you can sacrifice 1lb of tension for a half step in inharmonicity decrease, it could very well be worth it.
     
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  6. PBC

    PBC Composition Ontology

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    Personal Bias:

    Recall that we start out with the gauges and tension that are dictated by the string companies. So while basses usually have 30-40lbs it doesn't always have to be the case. Therefore you tend to have this internal anchor of how much tension is considered "normal", this is okay, everyone has it. Yet, if you take the time to experiment on different instruments, you'll find that they can handle a much larger range of tension then what seems to be "normal". As above, a 34"-34"bass can actually handle about a 25lb range difference (15lbs-40lbs+).

    Naturally this brings into the question of your playing. Do you tend to want your guitar to handle how you play or are you willing to adjust technique to string tension changes. Neither methodolgy is wrong. I found that for me as I got better at guitar, I settled into my gauges. Started with .007s to start (trouble cramping with fretting hand), then when I got better (stronger) ended up with .010s, but then my picking improved still (followed my ear) and now I'm pretty much settled on .008/0085 -.040 for E standard on 25.5" and I've experimented enough so that I know how to maintain this feel on baritone guitars. @Winspear mentioned above that if you keep your picking the same distance from the bridge as on a short scale, it'll feel almost exact from the fretting hand.

    The technique can be improved, I suggest you try experimenting with different picks and pick angles. I reduced my usually pick down to a .6mm or even lower (there's a carbon fiber .2mm pick) when I decided on using light gauge strings for ERGs. Once I understood that feel, I changed over to my normal picks 2mm Nuclear Cheese and my favorite 8mm Winspear's and trained my picking to match the feel of the lighter pick.

    Strings:
    While we can't calculate the difference between core shape, core diameter, number of wraps, wrap alloy (most likely proprietary), we all know that these factors have a contribution. After several years trying different brands, I realized that Kalium's are the best, personally, for ERGs and ERBs. They have superior flexibility in their material as well as higher mass, so they have greater tension at gauges compared to other brands.

    Currently, the strings seem to be the greatest obstacle in getting better clarity and tension. There are several technologies that can be used to enhance the mass while hopefully increasing or maintaining the same flexibility. There has been discussion on TalkBass of using the Alloy 52 strings, which uses combination of Nickel and Iron, have higher magnetic output as well as other "marketing" terms, but nevertheless have some dedicated users for bass. I've yet to try these out but they intrigue me, unfortunately, like most music technology, it's present where it seems it'll do the least impact. Standard 9-42, 10-46, 10-52 ect. We ERGers are left in the cold again.

    I'm still hoping that potentially D'Addario will use their method of creating Orchestra Strings and start producing Tungsten guitar strings, Tungsten has almost twice the ounce per cubic foot that Nickel. However, I don't know how flexible the string would be (depending on the core) and another issue with different metals for strings is if magnetically they can work with current pickups. @bostjan, mentioned this in one of the other threads we had made. There was another thread around here somewhere when someone was debating buying one of D'Addarios Low F Cello strings to put on their 8 string; that would be an interesting experiment,

    The general consensus among ERGers here is that we prefer Progressive Tension sets; it gradually increases in tension from plain strings before peaking on the bottom most string. I've found that the best for ERGs, past 7 strings (potentially 8), is that the best solution is something I call Parabolic Tension. These string tension reaches a peak in the middle before lowering for the bottom most string. This allows the lower string tension to couple with the decreased mass for low tuned string, as observed and detailed above, to behave more accordingly with the scale length it currently is strung at; as opposed to the atlantic salmon .142 string.

    Furthermore, this parabolic tension creates balanced flexion; where as each string has the same stiffness across the entire board. It can be a bit odd to have your lower wound strings bend like your top ones but you get used to it. Although I don't have numbers for this, the decreased in tension, especially on the bottommost strings, helps counteract that relationship that @bostjan mentions between stiffness and mass.

    My suggestion to you @Hollowway is to try something like this (assuming 10 string guitar at 30" scale):
    Kalium -

    E4: .008 : 14.42lbs
    B3: . 0105 : 13.94lbs
    G3: .0135 : 14.51lbs
    D3: .018 : 14.48lbs
    A2: .027w : 17.26lbs
    E2: .037 : 17.48lbs
    B1: .051 : 18.21lbs
    F#/Gb1: .067 : 17.35lbs
    C#/Db1: .086 : 15.84lbs
    G#/Ab0: .110 : 14.35lbs

    I know these gauges seem preposterous but having a slight parabola seems to give the best evenness across all the strings. If I were to create this set, I'd probably max out at 16.5lbs the apex of the parabola (that's the F#-A2 gauges above down one from their current gauge) that way it would feel more even, but I know you like your tension, so I increased it a little bit. A note, the inharmonicity of the G# string will be about 75.8HZ (D2) compared to 51.92 as the actual 2nd harmonic. In order for you to get close to this inharmonicity with a .142, you'd need to increase the scale length to 35", in which they are about even.

    My tunings are variations on G my ten strings right now are, L to H:
    I use these both on my 25.5-28.625 and 30-27 fanned scales.

    GDGCFBbEbGCF -- Top String is F4
    GDGDGCFADG --- Top string is G4

    For the Drop G (C) Standard variation I use (25.5-28.625)

    .114 : 12.48lbs
    .079 : 13.26lbs
    .061 : 13.97lbs
    .045 : 13.65lbs
    .033 : 13.07lbs
    .024 : 12.70lbs
    .018 : 12.72lbs
    .0135 : 11.07lbs
    .010 : 11.61lbs
    .008 : 11.69lbs

    Yes, pretty light strings. On the 27-30 I might decrease the last two strings to .076 and .106 respectively, but that's rare. I know you like your action low @Hollowway, just for clarity's sake. I use 2.25 at the 12th for the 7th string, while at the plains I got to 1.65-1.75, with the nice radius of the guitar I'm able to increase my action to 3.0 for the 9th string and 3.5 for the 10th while still having them lower than 7th and 8th if you look at the curve of the strings.

    A more exaggerated version of
    [​IMG]

    My goal this year is to commission a 30-33 fanned fret ten with GDGCFBbEbGCF. By using tests from my basses, I'm planning on using a .102 gauge string for that low G. Of course, clips ahoy for the NGD when the time comes, that's the plan.

    In summary:
    If you are a high tension person who like to keep the feel, you'll find yourself not changing your gauges much at all and increased scale length won't necessarily help as much as you think (although your harmonic content will increase, potentially substantially). 9 and 10 string guitar scale lengths are not remotely close to the tunings that they are trying to achieve. Doesn't that raise the question, aren't we all just used to the inharmonicity of strings? After all guitar is a flawed instrument. The short answer is yes, however, that doesn't mean we have to settle. We can keep trying to improve it as much as possible.

    This novel/post took a while. Hopefully it's of some use.
     
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  7. Hollowway

    Hollowway Extended Ranger

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    Thanks for all of your input, you guys. And, just to make it clear, I am not as much worried about finding out what gauge I can put on my instrument to work well for me. I know that I can do it by experimentation, or, as bostjan suggested, tuning the lowest string up to a comfortable tension, figuring out the pitch, then tension, then applying that. I did that, and figured the .100" is good for the C#1, and therefore the G#0 would be about .136". (Oddly, the .100" string on there for G#0 currently is close to the .102" that Kalium makes, and they don't even list that tension in their calculator, because it is considered too low to be useful.)

    But what I mainly mean is that there must be some sweet spot, between scale length and string diameter. In other words, increasing the scale length to, say 60" would obviously allow a much smaller string diameter for a given tension (at pitch). But the inherent length of the string will drastically increase the floppiness of the string (i.e. decrease the stiffness). So, to compensate, you'd need to in turn increase the thickness. So the question is, at what point is the increasing scale length starting to backfire, and increase diameter of the string, beyond the usefulness of increasing the length to allow for a smaller diameter at pitch? Certainly there is a way to figure that out. We don't typically do it, because history, evolution, etc., of the guitar has shown us that guitars function well around 25", as opposed to 10 inches or 40 inches. But tuning a stringed instrument to G#0 and below is fairly uncharted territory. And I think it would be cool to figure out what this sweet spot in scale length is. It will be different from person to person, of course, but it beats the trial and error of what we've been doing the last few years.

    One potential solution I thought of was to look at pianos. Pianos require a certain tension because of the way the hammers work. You can't have a super floppy bass string and have it work correctly. So, piano makers have, over time, worked this out, and now have some guidance about what works best. That's why there are no 2' 0" petit baby grands. At some point someone figured out it's impractical, and sounds like crap. So I'm wondering, if we were to pop open a baby grand, measure the A0 string, diameter (mine is .25") and length, plot it as a point, and then do it for a grand piano, parlor grand, concert grand, etc., would we be able to extrapolate what we could do down at our length.

    Essentially what I'm saying is that there are two competing issues: Increasing scale length allows us to choose a thinner string for a given tension. But increasing scale length also REQUIRES a thicker string, because a higher tension is required due to the decreased stiffness. So, it's a sliding scale, and there is going to be a sweet spot in there somewhere, and I'd like to know what it is, irrespective of everything else (like how practical it is, why don't I just buy a piano, no one makes a string that long, etc.).


    Here are links to a couple of things I've been reading...
    http://www.cs.ioc.ee/~stulov/appl08.pdf
    https://books.google.com/books?id=x...page&q=grand piano A0 string diameter&f=false
     
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  8. ixlramp

    ixlramp SS.org Regular

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    We discussed bostjan's inharmonicity formulas when we discussed your calculator, there's something very wrong with them because they give inharmonicity results (difference between perfect frequency and actual frequency for a particular harmonic) that are far too high and would be cleary audible as dissonant beating.
    What are the Hz values? They're not the 2nd harmonic (around 35Hz) are they the 3rd harmonic? If they are the inharmonicity shown here is ridiculously high and would make these strings unusable.
    How do the results indicate 'harmonic content'? and what do you mean by that? Harmonic content (brightness of tone) has nothing to do with inharmonicity.
    Again inharmonicty is far too high. My .070 tuned to E1 on 35" is extremely clear and harmonic.
    The difference between 85.45Hz and 82.4Hz for the 2nd harmonic is 63cents, 2/3rds of a semitone, this amount of mistuning would create very intense dissonant beating (not even chorus, far beyond that).

    It's best to clear your head of this inharmonicity formula and all thoughts that arise from the results.
     
    Last edited: Nov 3, 2017
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  9. bostjan

    bostjan MicroMetal Contributor

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    You won't hear beats between different harmonics.

    When you pluck a theoretically perfect string, you get the harmonic series of frequencies: Say the fundamental is 100 Hz. The harmonics would be 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1000 Hz, 1100 Hz, 1200 Hz, and so on ad nauseum.

    If you introduced inharmonicity of, say 10% per harmonic, the fundamental would still be 100 Hz, but the harmonics would be 220 Hz, 420 Hz, 1060 Hz, 1300 Hz, etc. There's no way you'd hear a specific beat pattern in that mess, so I'm not sure where that thinking comes from. It's not like the inharmonicity only applies to one overtone out of the series or applies an offset linear amount to each overtone.

    With heavy strings, you can see that the harmonics are a mess by performing an FFT on a .wav file recorded from clean guitar. Trying to quantitate that to compare with the theory is not trivially simple.

    But we did have a conversation about those estimates. It turns out to be an upper bound based on assumptions on the density and elastic moduli of the strings. But the lower limits are certainly not more than an order of magnitude off.

    In other words, an inharmonic string doesn't make a tone like two detuned unison strings, it sounds more like a percussive instrument with shifted harmonics, a la Malimba or xylophone.
     
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  10. PBC

    PBC Composition Ontology

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    I misused the term harmonic content, the actual definition doesn't fit within the context of the sentence.

    I do recall the conversation on the calculator. Per this discussion, I must apologies to @Hollowway and rest of the members here for promoting intellectual dishonesty in the posts above. Please disregard those posts.

    Do you have any recommendations @ixlramp to fix the formulas? Do you know of the correct Young's Modulus of some strings or a completely different equation to calculate inharmonicity? It takes little effort to observe something as incorrect. We can't necessarily take into account the core shape as well as the different alloys but can we get somewhere close if we decide we get a standard core + material density? There are bright members on this forum. Looking at the equation, the most of the errors are occurring in regards to variables being raised to various powers. I'm not a material engineer, so if someone knows more, please speak up.
     
  11. ixlramp

    ixlramp SS.org Regular

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    Correct, that wasn't the right word to use.

    PBC hey no problem.
    I wouldn't know how to model such a complex structure as core plus wrap layers, with a certain wrap tension, linear stretch, inter-layer friction, then get a result for inharmonicity. The difficulty of doing this is perhaps why bostjan's initial formula came up with such extreme values. Maybe somewhere on the internet there is an approximation.
     
  12. bostjan

    bostjan MicroMetal Contributor

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    Perhaps a best place to start is with actual measurements of elastic moduli for ERG strings, instead of the crude extrapolations I used
     
  13. vansinn

    vansinn ShredNeck into Beck

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    Have any of you tried D'Addario's FlatTop/Polished strings on longer scales?
    I didn't get around to it when I had the Riot 8, but were thinking that, as those are build with a slightly thicker core, followed by ordinary wrappings which gets grounded flat-top, they do carry a bit more tension than ordinary XL's.
    Might be interesting with lower tunings..
     
    Hollowway likes this.

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