Decisions - scratch build 7 string, string spacing, scale length, pole-to-string and lots more..

[NickK-UK]

Just did a manual measurement for each fret frequency and mapped against a calculated correct frequency:



You can see my my G string (red) has a fret issue, and my top E has a problem with the frets causing two to be the same (known). The upper B string needs a little work I think.

I've seen guitar sites that explain a natural curve up to sharpness for guitars with 12 temperament and some guitar builds adjust if the person never uses the lower frets (lead guitarists) but in the end if the band is in tune/temperament then it will sound fine.

I will calculate the % error and try to identify frets with a >2% error.

 

[NickK-UK]

I found an error in my measurement (that was the red 7oclock above).

This is the % error deviation of the neuraldsp tuner measurement from the mathematically calculated correct string frequency at the given fret.


Colour Key:
Bottom Blue = Low B string
Grey = Low E sting
Yellow = A Sting
Red/Orange = D string
Purple = G string
Upper Blue = High B string
Green = High E string

Note that simply pushing harder will change the frequency in the order of a few Hz given they're jumbo stainless steel frets so small error may be due to measurement.
The points on the graph that I need to look at:
1. The Nut - this is showing a big jump between the nut and the first fret that then has an impact through the rest of the frets.
2. That's my duff high-E string upper fret due to a couple of lifting frets.
3. This looks like my B string being a little erroneous up the frets.
4. This small so it may be a measurement error.

Frets in even 12 temperament go sharp up the fretboard but there's obviously a couple of issues.
First that Nut needs attention - ideally we can remove fret 1 error entirely and that would remove from the rest of the fretboard.

Edit: easy test for observation #1 is to tune the first fret, ignoring the open string. Sure enough the rest of the fretboard has less error. Although the Low B still has issues, which may be a bridge issue. Barred chords sound nicer too.
I think this points to the nut being too far away from fret 1, so shortening the fret length.

 

[NickK-UK]

After testing the theory - tuning for fret 1 and ignoring the open string, the majority of the fretboard measurements are spot on. Needless to say the guitar sounds even better.

Next step then is a nut job, then intonation and finally sort out any remaining duff frets.

 

[NickK-UK]

Ahh so I've started intimating it and that seems to have solve alot of the issues.

 

[JimF]

This is well beyond my understanding but glad you're making progress!

 

[NickK-UK]

This is well beyond my understanding but glad you're making progress!

Basically all the notes should be the note it's designed to play at that fret. Oddly Gibson actually have an odd distancing for frets - slightly flat below 12th and slightly sharp above, so this defines the sound of the guitar quite a bit.

The process I've been following for intonation is:

1. Use the 1st fret - tune to the fret's designed pitch using the tuning pegs
2. Move bridge to tune the harrmonic of 12th being the right pitch for 12th fret.
3. repeat until both are in tune - then the nut is in tune.
4. repeat for the next string

Next stage will be to re-measure the fret frequencies to see incorrect my fretboard is

So far the process has corrected the majority of string fret errors - I still need to finish the last three solid strings completely then remeasure the errors.

 

[NickK-UK]

Ok, freshly intonated.. gave it a blast and retuned.

First clean.. then there's me trying to find a good chug (skip to second video)..


Next the chug.. and you can ignore the comment and me playing with the neck pickup harmonics.


Did I say it sounded Brutal

 

[Hollowway]

It's cool you're making your own guitar, but honestly the intriguing thing is those graphs you're posting. I'm with @JimF in that I have no idea what's going on, but I'd love to know more about this (with respect to what you were saying about Gibson, your methodology, etc.) This reminds me of some of the stuff @ixlramp posts about tuning and microtonality, etc.

 

[NickK-UK]

So the graph shows how out of tune the frets are in terms of the pitch frequency (I'll just call it pitch so it relates to music).

1. Measure fret in Hertz (Hz), let's call that "m"
2. Subtract the designed fret Hz (let's call that "d" from the measured Hz = the amount of Hz error, let's call that "r". This can be a + or a - error.
3. % = 100*(calculated error Hz / designed Hz) = percentage out of tune it is, basically %=100*(r/d)

If the error is + then the measured fret pitch is above the designed pitch. The pitch is sharp as the string is too short between the fret and the bridge.
If the error is - then the measured fret pitch is below the designed pitch. The pitch is flat as the string is too long between the fret and the bridge.

Now because you have 24 frets and 7 strings, that's 168 measurements so I use a spread sheet todo the calculations and to display the error percentage in a graph where I plot the % error in the vertical for each fret on the horizontal. Using a stacked graph means each of the strings are stacked for each fret position.
The multiple colours in the stack (one for each string) gives some information - if the multiple colours are the same size then the fret wire is straight and perpendicular to the centre line. If the multiple colours differ in size then there is a problem, such as a trend of small to large size for each colour would indicate the fret is skewed and not perpendicular.

So in my case the sharp nature of all the readings means the fretboard is too close to the bridge. However the nut shows it's too far away hence flat - did I make a boo-boo and mess up my guitar? Well possibly.. the guitar isn't intoned yet.

Intonation, I think, is explained wrong.

Let's start with strings and pitch.
A pitch on a string (ie when you fret or open string) is a result of a number of things that then make the string vibrate at a number of times per second (also called Hertz or Hz). When played on a fretboard the pitch is basically a result of the string length (this includes the action as you push your finger on the fret) and the neck relief, the string gauge (the mass of the string), and the string tension (how tight the tuners are wound up). Change just one of these and the fretted pitch in the same position will change. This means either an error in the fretboard (oops!) can cause a problem with the desired pitch.
What do I mean by error on the fretboard? Well you have to cut each fret slot and fit each fret wire very very accurately. If the distance between the fret and the bridge is wrong for a single fret.. then all the other notes would be perfect and you could find a duff note (sharp or flat) that isn't the correct note (the horror).

Now Intonation is simply a way to take that ^^^ and adjust the both the string length and tension, so the bridge to 12th fret is the correct pitch for the 12th fret. However it assumes that all the other frets and nut position are correct #lightbulb. By changing the position of the 12th fret on the string - you also change the position of all the other frets, hence they go in or out of tune depending on the errors in positioning the fret.

I'm making a guitar - I can't assume my fretboard cuts and fittings are accurate. So I need to measure, analyse and then fix if need be.

If the fretboard is accurate then intonation should result in all the frets in tune (or very very low small error colours on a graph). It's made worse as you go up the fretboard, the more accurate you have to be to be in tune.

Now I'm going to ignore temperament (the error between playing the same note pitch on different strings). Let's ignore true temperament - it's too related to tuning, string gauge, action etc. You've been playing for years and it doesn't sound bad.. so moving swiftly on..

Now on researching this all.. as I'm a beginner.. I came across a few posts indicating that Gibsons fret pitch error was flat before the 12th and sharp after the 12th for an intonated guitar. Interesting - I'm not sure if that's due to action, neck warp, fretboard expansion, or simply design. However the author seems to indicate that it seemed to be common, hence contributing to the sound of the guitar as a standard. Not sure I totally see the logic - I would suspect the sound is the guitar scale, strings, pickup and wood.. to me a in-tune guitar is an in-tune guitar.
I could see if it sounds more pleasing, that the notes are either flattened or sharpened for standard tuning.. especially if it worked between with the guitar itself and any possibly the guitar amps and speakers of the time.

Anyway.. I need to remeasure after intonation and see the difference next. I did make a booboo on the description of the intonation (doh! tired) but in my case I wasn't simply trusting the nut due to the measurement error.. instead I was checking the fret tuning using the first fret. I switched back to standard intonation after going through the logic - simply getting the 12th fret right.. positions the fretboard.. and after that I can then test the 1st fret open and others for error. That's another hour or two in measuring and recording fret pitches into the spreadsheet. I may do that tonight and post the difference.

 

[NickK-UK]

Just finished measuring and calculating after intonation.



You can see my duff frets However the others have really calmed down. I have noted that the string pressure plays quite a role in reproducing the same frequency.

What is good is the majority are very close to to the desired frequency across all strings. At these % error, the difference can be finger pressure. I will check out the orange and the yellow strings (D & A). I'll also check out the nut, frets 1, 2, 15 and 23/24 across all strings - I think 15 20 & 21 are the raised frets IIRC).

 

[NickK-UK]

So continuing on the intonation. The reason is the tuning on the guitar takes time after adjustment to even the tension on the headstock and bridge. I've Intonated, gone back a day later and intonated again, and again..

The largest intonation errors on a fretted string are 0.28% (ignoring my duff lifted frets which will be redone). The only other figures for intonation across a fretboard seem to be about 1% error.
What I have noted is that it's now getting to the point where finger position behind the fret and pressure on the string will swing the results.

However the guitar sounds good and stays like that over night. So I think I can call that intonated for the time being.

Some ambient noodling.. (video may still be uploading/processing)

 

[ixlramp]

So the graph shows how out of tune the frets are in terms of the pitch frequency (I'll just call it pitch so it relates to music).

1. Measure fret in Hertz (Hz), let's call that "m"
2. Subtract the designed fret Hz (let's call that "d" from the measured Hz = the amount of Hz error, let's call that "r". This can be a + or a - error.
3. % = 100*(calculated error Hz / designed Hz) = percentage out of tune it is, basically %=100*(r/d)

This calculated 'percentage frequency error' is possibly inconsistent across the frets.
By 'inconsistent' i mean that, for example, a 0.5 semitone error will show up as a different 'percentage frequency error' depending on which fret it is.
An inconsistency would give a wrong impression on a graph. For example, your graph in post 122 might not actually be proof of increasingly sharp pitches as you go up the fretboard.

But anyway, whether it is inconsistent or not, it is much better, and much more meaningful, to consider pitch error in the units of pitch: semitones or cents.
Frequency and pitch are related but are different things, have different units, and behave differently mathematically.

If you cannot measure in semitones or cents, and can only measure in Hz, then you can convert 2 frequencies to an interval in cents as follows:

cents = 1200 * log(f / F) / log(2)

Where f and F are frequencies in Hz.

From https://robertinventor.com/software/tunesmithy/help/cents_and_ratios.htm

 

[NickK-UK]

So when I attempted for a smaller number of frets on the problem strings from the previous graphs:

cent = 1200 * log( measuredHz / calculatedHz ) / log(2)

So this is a ratio between the measured and calculated rather than error:



It's not clear in the definition if the ratio, but I took it as a ratio of error (ie if it was perfect it would be 61.7/61.7 = 1 for example)

I can see the cent is 12 temperaments and 100 devisions (ie 12*100=1200) and that it would be non-linear but I'm trying to understand how log(2) fits (it gets used for decay curves quite often but unless we're saying octave up = 2* and octave below is /2 which makes sense.
Sorry .. thinking out aloud.

In that case I think I still have some work but given 100 cent to a semitone (fret position) I think finger pressure etc is going make it difficult to get down to a 1 cent precision repeatedly - this aligns with my experience in measuring and the higher up the fretboard the more sensitive it becomes due to the higher pitch (100 divisions of a 24th fret is far more sensitive than 1st fret). I can see this also being more sensitive for smaller guitar scale lengths too but that's a different discussion.

One place indicates a spread of people that will retune if between 3-6 cents out.

 

[NickK-UK]

So I've decided to build a tube amp with the Robinette EF80 JCM800 as the basis. Simply put the plugins have some immediate appeal but just don't do 'it' for me from a configurability perspective. I'll cover the amp build here: https://www.sevenstring.org/threads...robinette-jcm800-ef80-switchable-mods.366211/ and I'm planning Fortin plus some additional mods such as an fx loop and power soak/reactive speaker load for silent DI operation.

So following the intonation I have a roughly 28.625" scale length - it's currently measuring 29" for the B string and well within the bridge adjustment zone.

Remaining tick box of tasks:
* Tidy up back - needs a lid on the electonics.
* Some tidy up of the volume knob angle.
* Resolve lifted frets (this is small be enough to cause a gap and buzz)
* Neck dress - frets, action, relief and nut.

 

[NickK-UK]

Here's an update on the guitar. DADGAD tuning - accoustic and amplified (sound rather than picture):