23 frets better?

Discussion in 'The Small Company Luthiers' started by Stike, Oct 31, 2005.

  1. Stike

    Stike Member

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    Stumbled upon this eggheadery you see below, thought it might make for an interesting discussion.


    Information Paper, May 23, 2005
    SUJECT: “The Optimal Number of Frets for an Electric Guitar with a 24.75” Scale”
    Problem Statement: We are building a 24.75” scale guitar, and wanted to choose the optimal
    number of frets to install on the guitar. The guitar will feature a korina body and neck, a flamed
    maple top, pao ferro fingerboard, and one humbucking pickup in the bridge position.
    1. First, we started with the physical construction of three of our favorite guitars. We examined
    three examples and took detailed notes on the construction and the tone of each.
    a. A 1963 Fender Stratocaster from a private collection. Guitar was completely stock and
    still had all hang tags and the sales slip in the case. Features a 25.5” scale, with 21 frets. Finish:
    Sonic Blue.
    b. A 1988 Fender HM Strat. Guitar was a new-old stock (NOS) find by a local music
    store. We believe this is the best sounding and playing 24-fret guitar ever made by a major
    manufacturer. This HM has one stock Dimarzio humbucker in the bridge position. Features a
    25.5” scale with 24 frets. Finish: Aqua.
    c. A 1991 Gibson Les Paul Classic. This is a genuine, stock “pre-historic” Classic, and is
    an extremely rare example because of the 1991 serial number and finish. This combination did
    not appear in Gibson literature until 1992. Features a 24.75” scale with 22 frets. Finish: Amber.
    d. All guitars feature rosewood fingerboards, and tone comparisons were made with a
    Bogner Überschall head with one matching 4x12 cabinet, a 1980’s Marshall JCM-800 and
    matching 80’s straight-front cabinet, and a 1997 Matchless Chieftain 2x12 combo. We used a
    George L’s cable, Ernie Ball Pink Slinky strings, and a Dunlop 1.00 mm Tortex pick for all
    testing.
    Assessment:
    Our assessment included playing individual notes on each string and a series of three chords: A
    in the second position, G in the third position, and an E in the first position. We played each
    guitar through each of the individual amps, using both clean and distorted tones on the Bogner
    and Marshall amps, and clean and natural distortion on the Matchless. We recorded each of the
    tones into our ProTools recording setup on an Apple G5 PowerMac and a MOTU Firewire
    Interface. We used a new Shure SM-57 even though we had a locker full of vintage mics
    available. We believed the Shure would provide a more “realistic” and familiar tone for our test.
    Conclusion:
    The vintage Strat had particularly strong tone in the upper register, and between the 17th and 21st
    frets, the clarity of the strings was astounding. The HM Strat sounded “strained” in the extreme
    upper register, and its 23rd and 24th frets were particularly unmusical. The Les Paul sounded
    “spongier” in the upper register, but the power chords were particularly clear and powerful.

    2
    Based on our sound test, we concluded that we needed to investigate a guitar with a Gibson
    24.75” scale with and extended fretboard.
    2. Second, we determined the exact placement of the frets for the 24.75” scale using our above
    examples. For illustration, we started at the 12th fret and worked toward the bridge. The purpose
    of this analysis was to determine the physical length of the string, regardless of scale, at various
    frets. Distances are measured from the nut to the top of the fret.
    Fret Vintage Strat HM Strat Les Paul
    Reference,
    Gibson Scale
    12 12.75 12.75 12.375 12.375
    13 13.466 13.466 13.07 13.07
    14 14.141 14.141 13.725 13.725
    15 14.779 14.779 14.344 14.344
    16 15.38 15.38 14.928 14.928
    17 15.948 15.948 15.479 15.479
    18 16.484 16.484 16 16
    19 16.99 16.99 16.491 16.491
    20 17.468 17.468 16.954 16.954
    21 17.919 17.919 17.392 17.392
    22 18.344 17.805 17.805
    23 18.746 18.195
    24 19.125 18.563
    Table 1. Distance of frets from the nut
    Based on our sound test, we came to an initial conclusion that a Les Paul could benefit from an
    additional fret that roughly corresponds, string length-wise, to the position of the 21st fret on the
    vintage Stratocaster, as well as the 22nd fret on the HM Strat.
    Initial analysis points to a 23rd fret, but not a 24th fret. The 24th fret on a Les Paul would roughly
    correspond to the 23rd and 24th fret on the HM Strat, and we already discounted them as unmusical.
    3. Finally, we used custom software to complete an analysis on the frequency response of each
    of the guitars in an effort to determine the optimal pickup placement, as well as the frequency
    response of each of our test guitars, as well as our “future guitar”. The frequency for each guitar
    string is shown below:
    Low E 82.41 Hz
    A 110.0
    D 146.8
    G 196.0
    B 246.9
    High E 329.6

    3
    Description
    Figures 1-5 on the following pages show the frequency response of our guitars. On top is a diagram
    showing a vibrating guitar string, a fingerboard with inlays, a nut on the left, a bridge on the right,
    and pickups. Two rulers above the string display the distance from the bridge in inches and the fret
    number.
    In the center is the resulting frequency response plot. The horizontal axis is a 20 Hz to 20,000 Hz log
    frequency scale and the vertical axis is a +10dB to -40dB amplitude scale. The horizontal red bar
    shows the pitch range of the fretted notes along the neck from the open string to highest fret. The
    gold vertical line marks the frequency of the currently fretted note. The actual position of the
    pickups, in inches from the bridge, is displayed below the pickup. The gold vertical line displays
    frequency of the current note on the response plot. For the test, all guitars were tested with the A
    string.
    The table at the bottom has a set of controls for each pickup; the pickup position (in inches from the
    bridge), the pickup magnetic aperture width (in inches), the pickup level (in dB) both as a value and
    as a slider control, the polarity of the pickup, and a button to remove that pickup.
    Things to look for
    The low-end response disappears as the pickup gets closer to the bridge. For a single pickup the
    response is the product of two "comb filters responses". A comb filter response contains a series
    of notches a constant number of Hz apart and looks like a comb. One of the combs is due to the
    position of the pickup, the distance the pickup is from the bridge while the other is due to the
    width of the pickup. Both will scale with the pitch of the open string.
    Symmetry
    A few players have pointed out that the frequency response curves for a single pickup ought to be
    identical when the pickup is placed at symmetrical locations about the center of the string. For
    example, the curve for a pickup 4.0 inches from the bridge ought to be the same as the curve for a
    pickup 4.0 inches from the nut. Yet the curves are very different.
    The frequency response plots are built by shortening the vibrating string length towards the bridge,
    effectively fretting notes up the neck. This corresponds to the formant filtering model (start with a
    flat response and filter it) that we are accustomed to hearing in acoustic instruments. But fretting the
    string immediately loses the symmetry of the pickup locations.
    The curves of symmetrically placed pickups are the same, however, at the specific frequencies of the
    open string and its harmonics.
    The most extreme case of this can be seen by comparing the response of a pickup placed right on the
    bridge to a pickup placed right on the nut. And sure enough, the frequency response of a pickup
    placed on the nut has nulls at all harmonics of the open string.

    4
    4. Frequency Response Plots. These represent the frequency response of the high E string fretted at
    the last fret closest to the bridge. The bridge pickup was used on all guitars.
    Figure 1. Frequency plot for vintage Stratocaster
    Note: Note the frequency at the 21st fret (under the right side of the red bar).
    Figure 2. Frequency plot for HM Stratocaster
    Note: Note the difference in harmonics at about the 5 khz range between the vintage Strat and
    the HM Strat. This is probably the reason for the strained response in our audio tests.

    5
    Figure 3. Frequency plot for Les Paul
    Note: Note the harmonics of the Les Paul in the 5-20 kHz range. The response is very similar to
    the HM Strat.
    Figure 4. Les Paul Scale with 23 Frets
    Note: The strong harmonics remain in the 5-10 khz range. Note the harmonics are extremely
    similar to the 22-fret Les Paul.

    6
    Figure 5. Les Paul Scale with 24 Frets
    Note: While the harmonics remain, they are more “compressed” than with the 23 fret guitar, or
    the 22-fret Les Paul.
    Comparison of Plots
    When reviewing these plots, it is important to remember that the differences in humbucking
    pickups and single coil pickups will manifest themselves in the sound of the individual guitars.
    Despite a lot of folklore, we believe the pickups will not generally affect the frequency response
    of the guitar’s strings.
    We reviewed each of the plots to determine which construction features would most accurately
    reflect the results of our subjective sound tests. Figure 6 on the next page graphically shows
    what we found. Based on the frequency response of the guitars and the physical length of the
    strings, we believe a guitar with a 24.75” scale and a 23 fret neck will most resemble the
    response of the vintage Stratocaster. Refer to the red line on the plots. See how closely matched
    the frequency response of the vintage Strat (upper plot) aligns with the plot for the 23-fret guitar
    (lower plot). This validates our analysis in Table 1.

    7
    Figure 6. Vintage Strat (upper) and 23-fret guitar (lower) plots
    Note: As stated above, refer to the red line on the above plots. See how closely matched the
    frequency response of the vintage Strat (upper plot) aligns with the plot for the 23-fret guitar
    (lower plot).

    8
    Conclusion
    Based on our subjective sound tests, as well as our objective scientific tests, we believe the
    optimal number of frets for a guitar with a neck scale length of 24.75” is 23.
    Additional Research
    To validate the research, our next step is to build our subject guitar with a 23-fret neck and
    compare it, both subjectively and objectively, to our test guitars.
    DISCLAIMER
    Disclaimer of Endorsement: Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer,
    or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the author. The views and opinions of
    author expressed herein do not necessarily state or reflect those of the sponsor, and shall not be used for advertising or product endorsement
    purposes.
    Disclaimer of Liability: With respect to the documents available, the author makes any warranty, express or implied, including the warranties of
    merchantability and fitness for a particular purpose, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness
    of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.
     
  2. Dave Orban

    Dave Orban Gold Supporting Member

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    A lot depends on the color... ;)
     
  3. Bryan T

    Bryan T Guitar Owner Silver Supporting Member

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    They seem to have put a lot of energy into an incredibly unscientific study.

    Bryan
     
  4. Lex Luthier

    Lex Luthier Member

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    It's like comparing apples to oranges.

    FWIW, Uli Roth had his Scorpions era '75 Strat modded with an extended fingerboard that added 2 more frets to 23, he used it on the Electric Sun stuff so he could hit some higher notes. The neck pickup remained in the same location.
     
  5. George Johnson

    George Johnson Member

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  6. Unburst

    Unburst Member

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    There ain't no money past the 5th fret.
     
  7. Schroeder

    Schroeder Member

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    I made a 23 fret guitar several years ago. However, I did not put quite as much thought/analysis into my decision! :D
     
  8. Schroeder

    Schroeder Member

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    Sort of reminds of the golf term, "Drive for show, putt for dough." I like it. Now THAT would be a different guitar. A seven fretter. Talk about eliminating a bunch of work (and potential fret buzz)!
     
  9. JPERRYROCKS

    JPERRYROCKS Member

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    Good God. I read about 15 seconds of that, and my brain shut down.

    How many frets are on a telecaster?
     
  10. fyler

    fyler Member

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    my guitar has 24...and a 25.5 scale...whatever works
     
  11. The Eristic

    The Eristic Member

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    You should build me one with with the first seven or nine frets, fretless for the rest of the board. ;^)
     
  12. smallbutmighty

    smallbutmighty Supporting Member

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    I can see it now.... "advertise your product here". It would be a whole new revenue stream..... and finally a way to make money beyond the fifth fret! :dude

    A
     
  13. tomteriffic

    tomteriffic Member

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    :confused:

    I asked those guys what time it was and they told me how to build a watch.
     
  14. cmatthes

    cmatthes Member

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    Well, you know, 22...23...whatever it takes.


    Seriously, I'm going to have to check snopes.com to see if that's real or not, Stike - has ANYBODY ever thought those old HM Strats were worth a dang?
     
  15. angelo

    angelo Member

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    THat's great! I love it.

    ....and I really hope not true:D
     

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