# Question about true temperament?



## Bearitone (Jan 9, 2016)

I know true temperament fret look all jagged because they offer perfect intonation across all strings.

What I don't understand is how it works if you change tuning. Wouldn't that mess everything up?

If I were to add true temperament to a guitar, wouldn't the frets be tailored to a specific tuning?


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## MoshJosh (Jan 9, 2016)

To my understanding, yes, it would be messed up if you change tunings.

As far as i know true temperament frets are designed with a single tuning in mind.

But I'm no expert.


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## KnightroExpress (Jan 9, 2016)

In the FAQ on TT's site, they say a half-step change is usually ok. Beyond that, yeah, you're leaving the design's functional parameters.


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## Ram150023 (Jan 9, 2016)

kindsage said:


> I know true temperament fret look all jagged because they offer perfect intonation across all strings.
> 
> What I don't understand is how it works if you change tuning. Wouldn't that mess everything up?
> 
> If I were to add true temperament to a guitar, wouldn't the frets be tailored to a specific tuning?



Look at it this way... Guitars have been around for centuries. And straight frets just as long. Why now, after all the years, all the artists, all the music... Does it need changing now?

Just looked at the site... Unless someone has MASSIVE OCD about the miniscule tone variances and has to have the absolute perfect tone every time he / she touches the fret board... theres no real benefit of installing that system.

Wont catch me spending $$ for that. But aa the old saying goes... "Opinions are like a$$holes... Everyone's got one."


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## OmegaSlayer (Jan 9, 2016)

Ram150023 said:


> Look at it this way... Guitars have been around for centuries. And straight frets just as long. Why now, after all the years, all the artists, all the music... Does it need changing now?
> 
> Just looked at the site... Unless someone has MASSIVE OCD about the miniscule tone variances and has to have the absolute perfect tone every time he / she touches the fret board... theres no real benefit of installing that system.
> 
> Wont catch me spending $$ for that. But aa the old saying goes... "Opinions are like a$$holes... Everyone's got one."



Have you tried one?
I didn't, and I think it's one of those features you understand only after you have tried it, like many many others.


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## Sumsar (Jan 9, 2016)

Well if you have tried to record guitar, especially with many harmonised parts then even high quality guitars out of Japan intonate like sh!t: You can set up the intonation correctly and tune the open string. Now try and play a note on the say 3rd fret while looking at a tuner; Not quite in tune is it? And if it is in tune, I can assure you you cannot do the same to the other stings. Yes it is a minor detail, and you can get by with standard frets, but I definatly see the reason why people would want this.

The thing is: If it has to be constructed for one tuning you can kinda never do production runs with these guitars, as every a-hole has his own weird tuning (myself included). Also when are you sure enough about your tuning that you will spend several thousands $ on a guitar that can only play in one tuning?
I would say that fanned frets seems to be a better way to cure some intonation problems, although that also has it own problems like tremolo, slanted non-standard pickups, price etc.


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## Bearitone (Jan 9, 2016)

Sumsar said:


> The thing is: If it has to be constructed for one tuning you can kinda never do production runs with these guitars, as every a-hole has his own weird tuning (myself included). Also when are you sure enough about your tuning that you will spend several thousands $ on a guitar that can only play in one tuning?
> 
> I would say that fanned frets seems to be a better way to cure some intonation problems, although that also has it own problems like tremolo, slanted non-standard pickups, price etc.



I think you're right in saying that most of us have our own weird tuning. I feel like TT frets are perfect for players that always, or at least a large majority of the time, play in one tuning. Their guitar with true temperament will be their main go-to guitar and their other guitars would be used for messing around in other tunings.

I feel like you could even take it a step further and Evertune that guitar and basically be forever, perfectly in tune and intonated to that one tuning.

It would be a MASSIVE commitment but, a hugely beneficial one if you found a tuning that you never left


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## Sumsar (Jan 9, 2016)

Yeah having just 1 TT frets evertune guitar, would be pretty awesome for recording.
I have played in the same tuning for a couple of years (standard 7 string tuned a half step up, so:CFBbD#G#CF), but I am considering going back to standard tuning, so yeah maybe in a couple of years it will make sense.


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## vansinn (Jan 9, 2016)

Ram150023 said:


> Look at it this way... Guitars have been around for centuries. And straight frets just as long. Why now, after all the years, all the artists, all the music... Does it need changing now?



Well, maybe because routing out grooves like this is quite a Bit more doable now than in earlier times.
I mean, a straight fret saw never was the best tool for non-straight cuts.. 

On a serious note, I personally wouldn't like a system fitting predominantly a single (+/- half step) tuning.
However, a few corrections here'n'there for the most severe off-pitch positions I would happily welcome.


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## Rusti (Jan 9, 2016)

As a luthier i like the concept of TT but i dont like like the fact you can't recrown nor refret them. You can level them when needed, but just imagine how you would go for tape-masking the fretboard with non-straight frets 
If they were to make TT out of ss it would be great.



Sumsar said:


> I would say that fanned frets seems to be a better way to cure some intonation problems, although that also has it own problems like tremolo, slanted non-standard pickups, price etc.



Fanned frets are not meant to fix the intonation problem, and they actually don't do that. They balance the string tension when using extender ranges instruments.


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## Nag (Jan 9, 2016)

Rusti said:


> you can't recrown nor refret them.



That, plus the "locked in one tuning" thing, should be enough to call the design... sliiiightly limited.

Fretted instruments NEVER had perfect intonation. It's just part of the design. Straight frets are just more versatile, and honestly, how many of you people can hear that the intonation is slightly off on straight fret guitars ? I doubt that upgrading to a design with so many limitations would be beneficial, unless you have perfect pitch and OCD. If you want to spend that kind of money, good for you, have fun, but I don't see this design ever get more demand than straight frets.


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## Chokey Chicken (Jan 9, 2016)

Never understood why people think fans fix intonation. That's why it irritates me when people blindly want to go fanned for reasons other than tension.

TT is a logical direction to head in, but I personally just don't give a damn. You can say the tuning is off all you want, but on a properly set up guitar, if you play along with a Synth that is in perfect tune, it will sound good. The slight inaccuracies don't make a large meaningful difference to how good something sounds.

Its a good idea, because perfection is always nice, but currently its not worth the price considering it forces limitations, and the problem it fixes is so negligible.


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## Lorcan Ward (Jan 9, 2016)

Ram150023 said:


> Look at it this way... Guitars have been around for centuries. And straight frets just as long. Why now, after all the years, all the artists, all the music... Does it need changing now?



You know people also gave out endlessly about the electric guitar and still do and even distortion had people raising their pitchforks when it was first used on a recording. 

A guitar is a very flawed instrument and thanks to the internet and modern travel methods where thousands of people can discuss and work on these issues we are now getting solutions. Multi-scales, true temperament, evertune, SS frets, hundreds of pickup options, endurnecks, amp modelling software/processors etc etc etc

Its a good time to be a guitar player and no matter what people say its only going to get more refined in the coming years. 



Nagash said:


> how many of you people can hear that the intonation is slightly off on straight fret guitars ?



I can hear the difference, its very noticeable on some guitars and on a lot of recordings. I transcribe a lot of music so it messes with my head a bit when a guitarist's intonation is out or he's using an instrument with poor intonation. I wouldn't get TT for a number of reasons but mainly since I've found a compensated nut will address a lot of the off frets.


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## Nag (Jan 9, 2016)

Chokey Chicken said:


> Never understood why people think fans fix intonation. That's why it irritates me when people blindly want to go fanned for reasons other than tension.



Depends what people mean. It doesn't fix intonation "fret by fret", but it helps with "overall" intonation because thinner strings need less adjustment than thicker ones in the same setup.


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## Manton Customs (Jan 9, 2016)

Rusti said:


> As a luthier i like the concept of TT but i dont like like the fact you can't recrown nor refret them. You can level them when needed, but just imagine how you would go for tape-masking the fretboard with non-straight frets
> If they were to make TT out of ss it would be great.



Why would you think that? The only difference is that you can't use a crowning file, a three corner file will work fine for re crowning. So they can be both refretted and recrowed. If refretting you'd obviously need to order the wire from TT.

In answer to the OP, I have built two TT instruments, see sig for one of them. With this one (in sig) the buyer was strongly considering having it tuned down a full step. So I made perfectly sure with TT that it would not be a problem to do so. It took a while waiting on the inventor to get back to us, as the guy who does the CNC work was not sure either. But he eventually got back to us and said it'd be no problem. Remember you still have full adjust ability at the bridge for intonation, just as you normally would with straight frets.

I can highly recommend the system, it sounds excellent with no real down sides other than tuning it (but you can buy a tuner to help with this, making it a non issue).

Any further questions feel free to get in touch.


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## Bearitone (Jan 10, 2016)

Manton Customs said:


> Why would you think that? The only difference is that you can't use a crowning file, a three corner file will work fine for re crowning. So they can be both refretted and recrowed. If refretting you'd obviously need to order the wire from TT.
> 
> In answer to the OP, I have built two TT instruments, see sig for one of them. With this one (in sig) the buyer was strongly considering having it tuned down a full step. So I made perfectly sure with TT that it would not be a problem to do so. It took a while waiting on the inventor to get back to us, as the guy who does the CNC work was not sure either. But he eventually got back to us and said it'd be no problem. Remember you still have full adjust ability at the bridge for intonation, just as you normally would with straight frets.
> 
> ...



I have a question! I noticed that True Temperament frets are made with Silicon Bronze and can't be made out of Stainless Steel (due to cost purposes). I tried to find comparisons between the two materials but all I could find was corrosion comparisons on boat building forums.

Is silicon bronze comparable to stainless steel as far as durability and corrosion resistance?


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## Manton Customs (Jan 10, 2016)

kindsage said:


> I have a question! I noticed that True Temperament frets are made with Silicon Bronze and can't be made out of Stainless Steel (due to cost purposes). I tried to find comparisons between the two materials but all I could find was corrosion comparisons on boat building forums.
> 
> Is silicon bronze comparable to stainless steel as far as durability and corrosion resistance?



I haven't seen any technical data on it, but from doing some minor touch up work on the TT frets I'd say they seem similar to regular Nickel silver frets in terms of hardness. But as mentioned before, it's not really so much of an issue as the fretwork on them can be done by any willing luthier. It's also certainly not so soft as to cause concerns. I think the main reason they don't offer SS frets is that the silicon bronze is very easy to cast...and as you mentioned, cheap!

For anyone too lazy to check out the thread, here are the two TT instruments we have done . The Echo (tele style) was a pre made TT neck and the 8 string was custom made by us.


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## Rusti (Jan 10, 2016)

Manton Customs said:


> Why would you think that? The only difference is that you can't use a crowning file, a three corner file will work fine for re crowning. So they can be both refretted and recrowed. If refretting you'd obviously need to order the wire from TT.



Any file doesn't fit the job for recrowning those frets. You can't reach most parts of the fret (on the beginning of the fretboard expecially since they need bigger intonation adjustments) being it so full of curves and angles. You would also have to work with the file from above in the direction of the fretboard in order to reach most of the spots, which gives you a very short stroke to file the fret (making it a very tedious process) and will make it easy to damage the fretboard, even if you tape mask it.
Also once it's time to refret, you pull out the fret, how do you clean that 0.6mm wide slot thats curved and angled as the fret itself? All the traditional tools are made for straight slots. A drill bit would be needed, but you can't follow that path by hand without enlarging it.
The amount of time needed would be insane, and the job will be imperfect for sure. Will it really be worth? I think you didn't consider it well enough


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## Manton Customs (Jan 10, 2016)

Rusti said:


> Any file doesn't fit the job for recrowning those frets. You can't reach most parts of the fret (on the beginning of the fretboard expecially since they need bigger intonation adjustments) being it so full of curves and angles. You would also have to work with the file from above in the direction of the fretboard in order to reach most of the spots, which gives you a very short stroke to file the fret (making it a very tedious process) and will make it easy to damage the fretboard, even if you tape mask it.
> Also once it's time to refret, you pull out the fret, how do you clean that 0.6mm wide slot thats curved and angled as the fret itself? All the traditional tools are made for straight slots. A drill bit would be needed, but you can't follow that path by hand without enlarging it.
> The amount of time needed would be insane, and the job will be imperfect for sure. Will it really be worth? I think you didn't consider it well enough



Sorry rusti, but I've considered my response to you well enough...in fact I didn't need to consider it too much, as I've done this work before! I in no way mean to sound rude, but it's obvious you have not done this work (on TT guitars) before. All it means is working in a slightly different way than you may be used to, which is a challenge us luthiers should welcome . If you can use a three corner file to crown frets it's not something you would struggle with, I'm sure. I'll also add that the majority of the frets are not so extremely wiggly as some people imagine. Quite a few aren't too far off straight, the most extreme being the first few.


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## shellsj (Apr 10, 2020)

I have two electrics and an acoustic with True Temperament fretboards/necks and I play open tuning. It can be done but you need a capo on the first fret. Reason being that the nut obviously is straight and the 1st fret is wiggly, so if you tune to the open nut, when you lay your first finger across the first (or subsequent frets) to play an open chord, everything will be off. If you think about it, in standard tuning, you don’t play an open chord on the nut - a G major chord would be the closest thing - but generally you’re always fretting something. So the TT necks are designed with E chord shapes and A shapes etc in mind. But for open tuning, if you slap a capo on the first wiggly fret and tune that, then you get the intonation benefits of TT - compensating for string thickness and tension at each fret - even in open tuning.

So, I tune the guitar to open-D and then slap a capo on the first fret and fine tune to open Eb. In this way, my strings are, low to high:
Eb, Bb, Eb, G, Bb, (Eb or C# - as I also tune to open Eb7).

That’s 1st, 5th, 1st, 3rd, 5th, (1st or 7th) - in terms of harmonics.

And I’m able to tune in harmonics in actual fact. I know that this is the great warning, even from True Temperament, not to tune with harmonics, but for strings 6, 5, 4 and 2 I can - and those strings and frets are in tune across the fretboard, I’m pleased to say. And I tune the first (7th) and 4th (3rd) strings in the normal way to the thinner string above them by matching at the third fret. Hope that makes sense. Anyway, in this way, it’s very in tune with itself in open tuning - and a noticeable improvement on a regular guitar. 

So you’re not stuck with standard tuning with True Temperament, but the trick is the capo. Until I realised that I was despairing but now I’m happy with it. Yes, you lose a fret - but I think of it as a zero-fret now.


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## shellsj (Apr 10, 2020)

Also, TT frets are no longer cast bronze. They’re now stainless steel. Don’t know how they manage that but should mean you’ll never need a fret job.

As far as other tunings besides standard and open tuning, Mattias Eklundh uses TT necks and uses something like 7 different tunings (including DADGAD) - he said in a video somewhere.


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## Winspear (Apr 10, 2020)

Without elaborating too much on the misunderstanding of TT (do a search, it's been discussed extensively on the forum),
the thing with using different tunings is that the temperament isn't actually operating anywhere near how it was designed anymore. Some chords may be better now, some may be worse. But in general the effect of TT is so subtle (just a few cents either way) that you can probably tune however you like and things will still be fine. But the company says it doesn't work in other tunings because, well, it isn't - you're left with a somewhat randomly intonated guitar but nothing too different to sound bad


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## shellsj (Apr 10, 2020)

@Winspear thanks - there are specific just intonation frequencies I’m trying to hit and, yes, it doesn’t hit them all, all the way up the neck. But it’s the closest I’ve got. I also tried the FreeNote necks, but that’s a lot of frets. In a few days, I’ll publish a table of the cent differences for each notes in my scale. In the end though, it sounds good to me. Each barre chord is in tune with itself all the way up the neck, and the other chord shapes as well. So, I’m happy. At some point, I suppose I could design my own bent fret system (I’ll call it “Frent”!) specifically for open tuning and the frequencies I’m after. Till then, this is better than straight frets.


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## ixlramp (Apr 11, 2020)

shellsj said:


> So you’re not stuck with standard tuning with True Temperament


Actually you are, even the company state this. Using non-standard tuning messes up the per-tone offsets from 12 Tone Equal Temperament, a capo does not solve this.


shellsj said:


> As far as other tunings besides standard and open tuning, Mattias Eklundh uses TT necks and uses something like 7 different tunings (including DADGAD) - he said in a video somewhere.


Mattias Eklundh may be a very talented guitarist, but based on his old and well known TT video he has many misunderstandings of TT.
He may be using different tunings, but when he does that he messes up the TT system. He may be happy to do this which is fine, but it does not mean TT can be used with non-standard tunings.

Detailed TT discussions here:
https://www.sevenstring.org/threads...tail-using-an-archive-of-the-old-site.337329/
https://www.sevenstring.org/threads...-summary-of-true-temperament-fretting.337522/

Good to see someone interested in Just Intonation, you may be interested in these threads:
https://www.sevenstring.org/threads/general-microtuning-thread.340098/
https://www.sevenstring.org/threads/microtonal-metal.202859/ 
(^ Actually a thread for any microtonal guitar content)
https://www.sevenstring.org/threads...al-guitar-by-restringing-and-retuning.335492/


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## shellsj (Apr 12, 2020)

@ixtramp - thanks, good stuff. I’ll provide a table of measured Hz cents offsets using my TT necks at each fret. It’ll be interesting to see how consistent it is with open tuning. Those other discussions are interesting - I’ve left some thoughts


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## ixlramp (Apr 16, 2020)

shellsj said:


> there are specific just intonation frequencies I’m trying to hit and, yes, it doesn’t hit them all, all the way up the neck. But it’s the closest I’ve got. I also tried the FreeNote necks, but that’s a lot of frets.


The TT threads give more details, but essentially, the TT guitar 'Well Temperament' only gets you, at best, roughly halfway to Just Intonation (JI) intervals, and only in half of the keys, at the expense of the other keys.
TT guitars are also very expensive due to the bent frets, i suggest they are not suitable for what you want.

I read about your guitar dilemma on your website. It seems what you really want is exact Just Intonation to have the closest relationship to a special tonic frequency, with full width frets, but are concerned about the high number of frets (24) used by FreeNote.
In fact, it is not necessary at all to have a large number of frets on a JI guitar.

Jon Catler has a long obsession with having harmonics 3, 5, 7, 11, 13 on a guitar, and this is why there tends to be so many frets in his systems. The '12 Tone Ultra Plus' system is the normal 12TET frets plus 12 JI frets, so it starts with 12 and adds more to that, which tends to result in a large number of frets. But the normal frets are not JI. The added frets are only there to add the JI intervals derived from harmonics 7, 11,13.
So i also consider the FreeNote system is not suitable for what you want.
The FreeNote system is also messy, awkward and difficult to use, as the available JI intervals vary from string to string, they are not consistently present across the range of the instrument as you would expect from an instrument. It is essentially a highly eccentric personal vision of Jon's.

Instead, for your needs it makes more sense to simply have the JI version of 12TET, and leave out the more dissonant and exotic JI intervals derived from harmonics 7, 11, 13.
I suggest that the JI system that is optimum for you might be '5-limit JI' or an almost complete subset of that. This is a highly consonant JI system that is orientated towards contemporary music harmony (major and minor triads etc.). It is a JI system derived from harmonics 3, 5 and is the JI version of 12TET.
https://en.wikipedia.org/wiki/Five-limit_tuning

A problem with TT and FreeNote is that their systems are fixed.
It would be better for you to order a guitar with a custom JI system and custom fret placement for your needs. This is something Metatonal Music do. The owner, Ron Sword, really knows his microtonal theory and could probably design a fretting system for you. The guitar or neck would also be cheaper than those from either TT or FreeNote. Many of the microtonal guitars currently in use came from Metatonal Music.
http://metatonalmusic.com/

Concerning the design of a JI fretting system with full width frets and not too many of them, this is something i was trying to do in this thread.
https://www.tappistry.org/post/just-intonation-for-tappers-10153805?highlight=just+intonation

And here is a webpage which discusses this exact topic.
http://jsnow.bootlegether.net/cbg/justintonation.html


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## JimF (Apr 17, 2020)

Seeing as this is where the temperament gurus live, I'm just wondering if I can get an answer to the following:

"True Temperament fret systems only work 100% correctly in standard tuning"
Now is this standard as in EADGBE, or standard as in the relationship between the strings? I.e. could I tune to B standard, and because the strings are all relative to each other the same as standard tuning, it would be fine, however tuning a guitar with standard TT to, for example, DADGAD, would sound like a pile of shit?
Could a standard True Temperament guitar handle drop D? 
If it could, and what I said about relationships between strings is correct, then surely it could handle Drop C (CGCFAD)?

Please excuse my lack of knowledge! I'm self taught and know very little music theory. Or at least I don't know the names of the parts of music theory I'm aware of, if that makes sense (harmonies etc). I've got confused in many of the temperament discussions here!

PS - I am one of the OCD people that can hear tuning issues on recordings, and I mainly do a lot of home recording so it drives me crazy. I'm getting an Evertune next to hopefully mask some of the issues, rather than fix them, but TT has always interested me.


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## bostjan (Apr 17, 2020)

JimF said:


> Seeing as this is where the temperament gurus live, I'm just wondering if I can get an answer to the following:
> 
> "True Temperament fret systems only work 100% correctly in standard tuning"
> Now is this standard as in EADGBE, or standard as in the relationship between the strings? I.e. could I tune to B standard, and because the strings are all relative to each other the same as standard tuning, it would be fine, however tuning a guitar with standard TT to, for example, DADGAD, would sound like a pile of shit?
> ...



Heh. I don't know if I can answer this, but I'll take a crack at it and say that tuning down to D standard should work just about perfectly fine, but if you go down to the point where you need a wound 3rd string, it won't work anymore.

Drop D (or drop C) will probably work if you are okay with "close enough," but if you are particularly discerning, it won't, in theory, at least, but I'm really skeptical that the miniscule changes in TT are worth all of the effort; mostly because the tuning system (or, more correctly, temperament system) is more concerned with marketing than with making sure to present factual information, and that sets of a huge red flag for me. I'd love to play around with the system, and will likely someday purchase something, but I have low expectations. For one, the deviations are significantly smaller than older WT systems, so it's a lot of effort for little change- and if there is little change, there is little potential for any significant gain in consonance. Secondly, I have already been working with other temperaments for decades and think that they just generally show more promise, depending on what you want to accomplish.


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## JimF (Apr 17, 2020)

I’m with you! Thanks. I understand. I think lol.


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## shellsj (Apr 17, 2020)

Here's a table I just finished for an Eb, open tuning on my TT electric. I accept that with attempts at JI, you can only expect to be in tune for 2 or 3 keys - so, the strings/frets marked in green are the main ones I'm trying to hit. For the most part, it's not bad on the green areas - except for D, which is consistently dissapointing. Note that my luthier was unable to quite get the saddle back far enough for the third string, so that ones out a bit anyway. I'll post one for standard D tuning, later. Yes, you can have up to 12-gauage strings and TT say it will still work.


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## shellsj (Apr 17, 2020)

Oh - the string at the bottom is the Eb equivalent of DADGAD for the 3rd string, FYI.


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## bostjan (Apr 17, 2020)

shellsj said:


> View attachment 79585
> View attachment 79585
> Here's a table I just finished for an Eb, open tuning on my TT electric. I accept that with attempts at JI, you can only expect to be in tune for 2 or 3 keys - so, the strings/frets marked in green are the main ones I'm trying to hit. For the most part, it's not bad on the green areas - except for D, which is consistently dissapointing. Note that my luthier was unable to quite get the saddle back far enough for the third string, so that ones out a bit anyway. I'll post one for standard D tuning, later. Yes, you can have up to 12-gauage strings and TT say it will still work.


Are the "actual" notes measured with a tuner or calculated?
Either way, I'm surprised by the end result. Interesting.


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## shellsj (Apr 17, 2020)

Measured - I used


bostjan said:


> Are the "actual" notes measured with a tuner or calculated?
> Either way, I'm surprised by the end result. Interesting.


Measured - I used the ClearTune app on my phone, which I've found reliable and which I can configure to pythagorean just for Bb. It's worth noting that its definition for C# (273.1Hz) and F# (364.1) are different from mine of 270 and 360 respectively - so, the the cent off-sets I've shown above are in relation to my definition of those notes, which makes it look worse than it is perhaps. I've put my full scale into Logic on my computer with offsets so I can hear them together, and they do go together nicely. My F# is a 3rd of my D (288), and my C# is a 3rd of my A. Here's the various alternative frequencies I considered for my Bb JI scale - based of 7.2 and 5.4 or 10.8 Hz.


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## shellsj (Apr 17, 2020)

ixlramp said:


> The TT threads give more details, but essentially, the TT guitar 'Well Temperament' only gets you, at best, roughly halfway to Just Intonation (JI) intervals, and only in half of the keys, at the expense of the other keys.
> TT guitars are also very expensive due to the bent frets, i suggest they are not suitable for what you want.
> 
> I read about your guitar dilemma on your website. It seems what you really want is exact Just Intonation to have the closest relationship to a special tonic frequency, with full width frets, but are concerned about the high number of frets (24) used by FreeNote.
> ...


Thanks @ixlramp - great info. Here’s a pic of my Catler guitar (which was stolen) - I ended up removing most of the “extra” frets.


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## shellsj (Apr 17, 2020)

shellsj said:


> Thanks @ixlramp - great info. Here’s a pic of my Catler guitar (which was stolen) - I ended up removing most of the “extra” frets.


. Here’s what it looked like to start with (with a bit of photo filtering to make it look cooler)

And here's a study I did of the Catler 24-fret Just neck. These are not measures though, but calculations based on his fret ratios. 24-frets per octave. The rows are different tunings for the string. The items in black are pretty good hits. The items in gray are misses. The idea was to find keys for the strings that would result in the most "hits". The best string tunings for my scale (with the most hits) are at the top of the chart, and it gets worse as you do down. I agree with you, having the straight frets, while fine in certain positions like his 14th fret, in other positions means the note "works" on one string on that fret, and doesn't "work" for another string on that same fret. I ended up marking up my fret-board to indicate which frets/strings not to play. You have to be a precise and focused player for this neck - whereas I prefer to hit a chord and play a run and not have to worry too much about it.


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## shellsj (Apr 18, 2020)

OK - now for standard tuning (not open-tuning): per this link, the best keys for the TT "Formula 1" which is the only one they seem to be making now are:

Major keys: E, F#, G, A, B, C, D
Minor keys: E, F#, G#, A, B, Eb
Being as those aren't the keys I want to play in, I tune down to standard-D (everything down a whole step), to give:

Major keys: D, E, F, G, A, Bb, C
Minor keys: D, E, F#, G, A, C#
In this way, I can use the standard chord shapes and get chords and notes more part of the Bb harmonic scale. Attached are the results. I'm actually pretty happy with this. Bearing in mind again that JI only works on 2 or 3 keys, I've marked in blue the string/fret positions that are part of my key - and those are hitting pretty well. For some of the open strings, I had to alter their tuning a bit in order to ensure that my main notes of Bb and F hit exactly (zero cents) on the neck, and I've highlighted those "tuning nodes" in yellow.

Most notes are pretty close. For G, I'm not too bothered because depending on how you determine it harmonically, G can be 384 or 388.8 in my scale, so 386 is a reasonable compromise. And my ClearTune tuner set to Pythagorean mode for Bb based on 460.8 Hz as the reference pitch gives C# and F# as 273.1 Hz and 364.1 Hz - where my harmonic determination of those is 270 and 360Hz - so, they don't sound as bad as 22-cents offset would suggest.

True Temperament does provide the tuning offsets from Equal Temperament - but my offsets are from JI, so it's not really apples-to-apples to compare them. Mine are, from 6th to 1st string:
0, -7.1, -8, 0, 10.4, 6

The other thing to bear in mind, when tuning with this sort of accuracy - point 1 here, point 3 there, is that after you've played the guitar a bit, it's shifted a bit. I think unless you had a guitar made of titanium, there would always be some shift - and that's what vibrato and whammy bars are for!


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## ixlramp (Apr 18, 2020)

JimF said:


> "True Temperament fret systems only work 100% correctly in standard tuning"
> Now is this standard as in EADGBE, or standard as in the relationship between the strings?


As in relationship between strings.
So you can take EADGBE and transpose it up or down a little.
However the system seems dependent on a small range of gauges. From the old TT site FAQ:

"*Do I need to use a particular string gauge?* 
Our concert pitch electric guitar necks are optimised for standard plain 3rd roundwound string sets from 0.009" - 0.046" & 0.010" - 0.046", to 0,011" - 0,050".

Using a wound 3rd is not an option if you have a True Temperament neck designed for a plain 3rd string."

https://web.archive.org/web/2014041...etemperament.com/site/index.php?go=4&sgo=0#A5
The new site FAQ is misleading and claims gauge is unrestricted.
The new site is dumbed-down and misleading in several places, for commercial interests, and contradicts their own old site.
It is essential to study the archive of the old site to get good information, links are here https://www.sevenstring.org/threads...tail-using-an-archive-of-the-old-site.337329/
Here is another important thread https://www.sevenstring.org/threads...-summary-of-true-temperament-fretting.337522/

Keep in mind that if you are using transposed EADGBE, the 'improved' keys (as listed in the previous post) are also shifted by the same amount.


JimF said:


> PS - I am one of the OCD people that can hear tuning issues on recordings, and I mainly do a lot of home recording so it drives me crazy.


Hmm, this depends what is bothering you, is it the errors from the standard tonal system called 12 Tone Equal Temperament (12TET), or errors from Just Intonation (JI)? This is the first thing to investigate.

If your ears want JI then Evertune will not help. TT will get you, at best, halfway towards JI, and only in half of the keys.
If your ears want perfect 12TET then TT is certainly not for you, as it intentionally offsets all tones away from 12TET by up to 4 cents to make some keys closer to JI.

So, amusingly and contrary to their misleading marketing, TT has worse intonation and is more 'out of tune' than a normal guitar. They are riding the wave of misunderstanding and misinformation for commercial reasons.
Some chords have improved harmony yes, but that does not mean intonation to 12TET is improved or it is more 'in tune' with 12TET, in fact it is the opposite.


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## ixlramp (Apr 18, 2020)

shellsj,
If you work through this thread https://www.tappistry.org/post/just-intonation-for-tappers-10153805?highlight=just+intonation
and use FretFind2D, you will be able to design your own JI fretting systems.

I recommend you do not work with frequencies when working with tonal systems, this is a bad habit many beginners have.
Everything will become simpler, easier and clearer if you work with 'intervals from tonic' instead, either expressed as JI intervals (in the form of frequency ratios, like '3/2' for the JI fifth), or expressed in 'cents'.
This also helps because what is important when working with tonal systems is 'relative frequency', not 'absolute frequency'.
Also, any interval that passes outside an octave should be transposed back into the octave, due to 'octave equivalence'.

This page is a good introduction to how to work with JI tonal systems https://www.kylegann.com/tuning.html
The whole site is a good source of JI information.


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## shellsj (Apr 19, 2020)

@ixlramp thanks - but if you look at my site, the one theme which must hit you, and as I’ve described above, is that I am using whole number harmonics, divisions of the starting frequency to give me the frequencies of the scale. And you need actual frequencies because if you’re using a tuner to tell if your instrument is in or out of tune, it doesn’t report on intervals and fractions, it reports on frequencies.


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## Winspear (Apr 19, 2020)

It's just a whole lot easier to work in cents because it is consistent and requires no reference. I need only know that my fundamental is 0 cents, then I know that 702 cents above is a 3/2, 386 cents above is a 5/4, 967c as the 7/4 and so on. It doesn't take long to memorize these transposeable intervals and pretty much any microtonalist will be extremely comfortable with them.
A 12edo tuner can be used programmed to the fundamental reference, and tuning with the goal of +2 cents on the fifth, -14 cents on the 3rd and so on as deviations from 12tet. Reading from frequencies without being intimately familiar with the users reference pitch of choice or extremely fast at mental multiplication is a nightmare, frankly  It's also incredibly hard to see how things deviate if analysing an imperfect tuning due to the logarithmic scale of frequency, as you have to have a perspective of how many cents a change in frequency would be at many different points in the spectrum.


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## shellsj (Apr 19, 2020)

Well, I did put cents on the chart. But I can add harmonic intervals too


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## shellsj (Apr 19, 2020)

shellsj said:


> Well, I did put cents on the chart. But I can add harmonic intervals too


And here’s a summary of the harmonic ratios for each note again:


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## JimF (Apr 19, 2020)

ixlramp said:


> As in relationship between strings.
> So you can take EADGBE and transpose it up or down a little.
> However the system seems dependent on a small range of gauges. From the old TT site FAQ:
> 
> ...




Thanks! Some good info there, I'll look into the differences between JI and TT and see which will help me! Essentially I hate how a guitar in tune for some chords is out of tune for other chords in different positions across the neck.


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## Winspear (Apr 19, 2020)

JimF said:


> Thanks! Some good info there, I'll look into the differences between JI and TT and see which will help me! Essentially I hate how a guitar in tune for some chords is out of tune for other chords in different positions across the neck.



JI is probably what your ear is after on each chord, but we can't achieve that correctness (387 cent major thirds, 316 cent minor thirds) on all chords. TT gets you a little closer for some popular chords, but we can't go all the way for any chord else we will break others. Indeed you should check if 0 cents on the tuner is actually what you want rather than -13 cent major thirds and +16 cent minor thirds - because if so, you should stay away from TT. But I would guess that you are looking for the JI thirds that one might tune an open chord to by ear and find the other chords broken.


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## ixlramp (Apr 20, 2020)

JimF,

The system of pitches the world currently uses for the large majority of its music and instruments is '12 Tone Equal Temperament' (12TET). In 12TET the octave is divided into 12 equally spaced pitches.
However, perfect 12TET inherently contains imperfect harmonies. The second, fourth and fifth are closely approximated to within 4 cents. But thirds, sixths and sevenths deviate by 14-18 cents from perfect harmony (perfect harmony is also called 'Just Intonation' (JI)).

So what your ears object to might be the inherent imperfect harmonies of 12TET. If so, it will make no difference how close to 12TET you get, using for example an Evertune bridge, or very careful setup and setting of intonation, or using refined technique.

You might be able to find out by playing chords on a synthesiser, which of course plays in absolutely perfect 12TET, and seeing if they still sound 'out of tune' to you.
Or on a guitar, carefully tune (using a good tuner, not a clip-on tuner) 2 adjacent open strings to be precisely 4 semitones apart (a major third), then play those open strings and see if it sounds 'out of tune'. Distortion is useful as it enhances the imperfect harmony of 12TET.
If chords only containing seconds, fourths and fifths sound ok, but chords containing thirds, sixths and sevenths sound wrong, this is another hint.

If your ears are after JI, prepare to go down a very deep rabbit hole of weird frets, microtonal guitars, tonal theory, limited usable keys etc. 12TET is very 'convenient', but the price paid is imperfect harmonies.


JimF said:


> Essentially I hate how a guitar in tune for some chords is out of tune for other chords in different positions across the neck.


Hm, if you mean one particular chord in various positions, this sounds possibly like poor setup, poor intonation, sloppy technique (very common for guitar). In 12TET, a particular chord has imperfect harmony, but the degree of imperfection does not change according to what root note you use.
To a degree, it is difficult to avoid intonation errors on guitar when playing and fretting various chords, strings often get pressed too hard or unintentionally bent. Evertune will help with that.


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## ixlramp (Apr 20, 2020)

shellsj said:


> I am using whole number harmonics, divisions of the starting frequency to give me the frequencies of the scale.


Sorry i find it hard to follow your tuning systems, this is partly because you approach it in an unusual way primarily using absolute frequencies.

So your target seems to be harmonic series JI intervals based on 7.2Hz Bb.
It seems quite common that people attach too much importance to the harmonic series.
If (as it seems) what you want is a system of JI intervals with the closest possible harmonic relationship to a tonic of 7.2Hz Bb, then it is important to not exclude intervals that are not part of the harmonic series.

For example, the JI fourth (freq ratio 4/3, 498 cents) is not part of the harmonic series of the tonic, but is still very closely and simply harmonically related to the tonic.
Same for the JI major sixth (5/3, 884 cents).
Harmonically, these is much more closely related to the tonic than the 7th, 11th, 13th etc. harmonics.


shellsj said:


> And you need actual frequencies because if you’re using a tuner to tell if your instrument is in or out of tune, it doesn’t report on intervals and fractions, it reports on frequencies.


Your tuner is unusual then, maybe because it is an app. Most real guitar tuners work with cents deviation from 12TET.
Almost everyone who tunes a guitar, either standard or microtonal, has no idea what the frequencies are and would just be confused by those. They work with intervals relative to tonic.

A quick note about pythagorean JI, it contains several complex and dissonant JI intervals. '5-limit JI' is, in a way, far more closely related to the tonic.


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## JimF (Apr 21, 2020)

ixlramp said:


> JimF,
> 
> The system of pitches the world currently uses for the large majority of its music and instruments is '12 Tone Equal Temperament' (12TET). In 12TET the octave is divided into 12 equally spaced pitches.
> However, perfect 12TET inherently contains imperfect harmonies. The second, fourth and fifth are closely approximated to within 4 cents. But thirds, sixths and sevenths deviate by 14-18 cents from perfect harmony (perfect harmony is also called 'Just Intonation' (JI)).
> ...



I guess I need to look into this further then, I don't want to be the equivalent of a man who's trying to buy a helicopter because he can't ride his bicycle!


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## bostjan (Apr 21, 2020)

Man, if I didn't have so much crap around the house that needs to be repaired this summer, I'd be trying to figure out how to turn my stimulus check into one of Ron's guitars with either some sort of JI fretting or maybe some sort of funky Bohlen Pierce-derivative scale.

If I had the funds, I wouldn't mind a couple of different options.

What do you guys think might be the best non-standard (micro) tuning for metal?


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## shellsj (Apr 21, 2020)

Well, I did just start playing DADGAD and it lends itself to all kinds of fun modal stuff, besides Kashmir, if that’s what you like. And, microtonally, because it’s tonic, fifths above and a fifth below, all the notes sit together nicer on the fretboard, than throwing in a 3rd or some other interval which seems to confuse the neck - if you get my meaning. Easier to design the fretboard around 5ths, consistently.


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## Winspear (Apr 21, 2020)

bostjan said:


> Man, if I didn't have so much crap around the house that needs to be repaired this summer, I'd be trying to figure out how to turn my stimulus check into one of Ron's guitars with either some sort of JI fretting or maybe some sort of funky Bohlen Pierce-derivative scale.
> 
> If I had the funds, I wouldn't mind a couple of different options.
> 
> What do you guys think might be the best non-standard (micro) tuning for metal?



Obviously I'm very into meantone as discussed in the other thread. I prefer 1/4 comma to 1/3 comma (i.e. 31 vs 19 edo) which is why I went for the uneven 19 subset of 31 on my current build rather than 19edo.
16 EDO seems cool in Last Sacrament but pretty limited in application.
I think 17 EDO is one to look at. It was brought to my attention here; https://twitter.com/bastard__wing/status/1246572842193305600?s=20
Great fifth. I like its minor focus, given that the minor triad is less dissonant than the neutral and major. The leading tone is a nice size too. A very playable size for guitar too which is definitely a consideration for metal.
Play
Certainly more xen than meantone stuff though!
22 also seems cool.


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## bostjan (Apr 21, 2020)

Winspear said:


> Obviously I'm very into meantone as discussed in the other thread. I prefer 1/4 comma to 1/3 comma (i.e. 31 vs 19 edo) which is why I went for the uneven 19 subset of 31 on my current build rather than 19edo.
> 16 EDO seems cool in Last Sacrament but pretty limited in application.
> I think 17 EDO is one to look at. It was brought to my attention here; https://twitter.com/bastard__wing/status/1246572842193305600?s=20
> Great fifth. I like its minor focus, given that the minor triad is less dissonant than the neutral and major. The leading tone is a nice size too. A very playable size for guitar too which is definitely a consideration for metal.
> ...



Has anyone done 22edo metal? I think I've seen photos of an 8 string 22-edo Ibanez RG, so someone must have tried it.

I am familiar with plenty of 24edo metal acts, and, of course, Ron's 16-edo and Jason/Iglashon's 15-edo and 17-edo stuff, which all sounds great in metal context, to me.

When I started really playing out and whatnot with 19-edo, a lot of non-micro-type people commented on how it sounded either "odd" or "middle-eastern," both of which took me by surprise, since I was trying to keep from spamming the weird notes.

I guess something like BP would sound too weird with tons of saturated distortion?


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## ixlramp (Apr 26, 2020)

shellsj,
I kept thinking about your table of desired frequencies, so i eventually worked through it and understand it now.

Here is a table derived from yours that clarifies your tone system by stating it as JI intervals from tonic, and stating the intervals in cents. In this form it is clear to microtonal / tuning geeks:




I checked your stated frequencies, they are all correct.

By '3rd of' you mean freq * 5.
By '5th of' you mean freq * 3.
By '9th of' you mean freq * 3 * 3.

Example of how i worked through each tone:
"3rd of 9th of 5th" means 'tonic freq * 5 * 3 * 3 * 3'
5 * 3 * 3 * 3 = 135
Divide by the next smaller 2^n to bring it down the necessary number of octaves and back into the first octave:
135/128
This is the JI interval, by convention stated as a frequency in fractional form assuming the tonic has frequency 1.
Then convert the JI interval to cents use the formula on https://www.kylegann.com/tuning.html
If the JI interval is 'n / p' then:
cents = log (n / p) * 1200 / log 2

I have also drawn out the harmonic lattice.
Your tone system is of type '5-limit Just Intonation' (meaning 'derived from the 3rd and 5th harmonics') but is unusual because, apart from 4/3 it consists entirely of 'harmonic series' intervals, harmonics 3, 5, 9, 15, 25, 27, 45, 75, 135, 225.

'A' being 432 Hz is interesting but is an unsurprising numerical coincidence that arises because 432 is based on 3s, the helek frequency is based on 3 and 5, and the tonal system is generated by repeated multiplication or division of frequency by 3s and 5s.

432 looks like a complex number, but turns out to be 27 * 16.
Due to octave equivalence we can ignore powers of 2 and consider this to be 27. 27 is 3 * 3 * 3.

If the helek period is taken as 3.333rec s (and i doubt it is exactly this):
Helek period = 10 / 3 s.
Helek freq = 3 / 10 Hz = 3 / 5 * 1 / 2 Hz.
Due to octave equivalence we can ignore powers of 2 and consider this to be 3 / 5.

For the tritone of your scale we are multiplying the helek frequency by 5 * 3 * 3:
= 5 * 3 * 3 * 3 / 10 Hz
5 / 10 becomes 1 / 2
= 3 * 3 * 3 * 1 / 2 Hz
= 27 * 1 / 2 Hz
Up an octave
= 27 Hz
Up a few more octaves
27 * 16 = 432 Hz

More coming later ...


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## shellsj (Apr 27, 2020)

@ixlramp - thank you for reviewing and translating this - and making it clear how the community views cents (in relation to the starting frequency). 
Just a few things on your table regarding which of my alternate pitches sound best in combination:

For G, 388.8 Hz (9th of 5th of 5th) seems to sound sweeter than 384 Hz
For B, 486 sound sweeter than 480
I entered these frequencies a while back as cent offsets in Apple Logic and tried them with a keyboard - and that combination seems to sound nicest together.


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## ixlramp (Apr 27, 2020)

So once i had the JI intervals it was easy to throw these into FretFind2D to get a fretting diagram.
http://www.ekips.org/tools/guitar/fretfind2d/

I chose to tune the open strings to: tonic, fifth, tonic, fifth, ..., which are the 2 most important tones in your system.
This open tuning also makes the fretting as simple as possible and minimises partial frets.
As Eb is a suitable highest string, i chose a tuning of (low to high): Bb Eb Bb Eb Bb Eb. This gives you roughly the range of a 7 string guitar.

The correct formatting for the scale is:
First line: Scale name.
Second line: Number of tones.
Following lines: The JI intervals, excluding 1/1 (tonic) but including 2/1 (octave).

Formatted text for copy-pasting:

shellsj
12
135/128
9/8
75/64
5/4
4/3
45/32
3/2
25/16
27/16
225/128
15/8
2/1

The other data to enter for a typical 25.5" scale 6 string electric guitar:




Result (enlarge to view):




A good result, compared to many JI frettings. In each octave only 3 places need partial frets, as i know you want to minimise those.
These are quite easy to create: Cut a full width slot and insert partial frets.


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## shellsj (Apr 28, 2020)

Wow @ixlramp - that is truly great stuff and I really appreciate it! So, is that formatted text essentially the “scala” file? I haven’t worked with these before. I’d like to try it with 9th or a 4th for the third string (a fifth of a fifth, and a 5th below, respectively) - which are two tunings I quite enjoy.

Now I just need to find a way to fabricate it with curved frets. Someone suggested printing the neck - but I suspect most 3D printing materials are not very durable- so, maybe find someone with a CNC and some titanium 

But like you say, it would be easy enough for a luthier to put straight fret partials in- and I’ll use the wang bar for bends 

Just noticed you’re also in the U.K. Whereabouts? I’m in SW London. 

Going to be tough to tune a regular guitar down to Bb, but I do have a Steinberger baritone and it goes down to Bb easily. It has a phenolic fretboard, but I expect something could be done.


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## Winspear (Apr 28, 2020)

Alternating 4th/5th tunings are very effective for maximizing straight-fret JI indeed! It's a shame I don't get on with them well musically in terms of available fingerings/voicings.

I would say it is questionable whether curved frets are the best approach or certainly the easiest - depending on the tuning of course. Perhaps simple enough for the few partial frets on the above design at least in the treble range 

Viewing that tuning in cents is very helpful , and it looks like a great tuning. I love how each key has a mix of thirds from 275/294/315 and 386/408/427. I've never been a fan of supermajors but the rest are very flexible.
Honestly, I don't think I have seen a JI 12 that is nearly as key flexible as this before?

Fretfind is a fantastic tool. You can link designs from the URL too 

When I pursue a JI guitar I think I will try a tuning that collapses in the trebles like the harmonic series does, to allow some more voicing flexibility above R5 barres.
For example this version tuned to R5R35b7 

Perhaps we should migrate the discussion to the micro thread?


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## shellsj (Apr 28, 2020)

@ixlramp once again - thank you! I'm getting my head around trying it with a slightly amended scala file - for the B and G - but I don't see how it let's you import or paste those values into the "calculation method" window of the fretfind2D tool. Here's what I have now, and I also wanted to explore what the neck would look like with the 3rd string as a 9th or a 4th. I do agree that they way you did it is pretty clean - with the only broken frets at the 1st, 9th and 10th frets - but I would like to see the other possibilities:

shellsj
12
135/128
9/8
75/64
81/64
4/3
45/32
3/2
405/256
27/16
225/128
15/8
2/1

FYI, I see the thing with the 1 beat per Helek thing matching 307.2 Hz as an interesting coincidence - but the real money is on the Bb and the F - as they were the two tones I discovered. But Eb at 307.2 fits exactly as a 4th below my Bb of 460.8 - so that's cool - and Eb is a workable tension for normal guitar necks, so that's another reason to go with itl. Ideally though, I think I would do a baritone comprised of Bb, F, and C (5th, 5th, 9th (5th of 5th)).


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## shellsj (Apr 28, 2020)

Winspear said:


> tuning that collapses in the trebles like the harmonic series does


 - yes, I do agree. I've been using a straight harmonic series approach of:
1. 7th (x7)
2. 5th (x6)
3. 3rd (x5)
4. octave (x4)
5. 5th (x3)
6. tonic

And it's almost eerie how, to me anyway, the way the notes on the higher strings are closer, make it easier to pick out the notes for soloing, while the lower strings are further apart which makes it easier to chord. And with this particular tuning, the notes just seem to sit under your fingers, just where you want them - if you're a pentatonic kind of guy like me, anyway. Ideally, I would tune my JI guitar to something like this - but it seems, if we don't go the bent frets route, the trick is to tune the strings in some semblance of 5ths - and that way they're more likely to join up. The 7th harmonic of course is a a kind of a dead-end harmonic - so I find other ways of calculating it - (9th of 3rd of 3rd, in the example above). I think that's why God rested on the 7th day, cos you just can't go anywhere from there 

I don't know about moving threads - but happy to go along with whatever you think.


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## shellsj (Apr 28, 2020)

ixlramp said:


> good result, compared to many JI frettings


 - OK, I got it to work. And I think your solution may the most practical. Except I'm going to have to learn to play guitar again, but that does seem to be an optimal lining up of frets. I tried the 4th and 9th and it was bit more bits and pieces. Here's a link to my version of the model - which is now the same as yours. Although, I did try my alternative fractions for G and B, I didn't see the frets move on the diagram as a result - perhaps the difference is too small in this cents-based tool?


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## ixlramp (Apr 29, 2020)

I was wrong about the helek, it is indeed exactly 10 / 3 s. Makes sense because units of time tend to be the Earth day repeatedly divided into 'round number' of divisions, so differing time units often have simple numerical relationships.


shellsj said:


> Going to be tough to tune a regular guitar down to Bb


Nah not at all. 25.5" is a little short for 7 string guitar B1 but it still sounds good.


shellsj said:


> Now I just need to find a way to fabricate it with curved frets.


Bent frets are difficult to create, and string bending on one results in unusual and inconsistent pitch changes because the string length varies as you bend.
Bent frets are only really suitable for small offsets as on TT, on these JI fretboards the offsets are much larger, which would make bending even more weird, it does not seem worth it to me.


shellsj said:


> and Eb is a workable tension for normal guitar necks, so that's another reason to go with it


Tension is not the limitation, you carefully choose custom gauges for the desired tuning to make sure the tensions are optimal.
The only limitation is how low you can go before losing a lot of tone quality due to the stiffness of the large gauge lowest string on a short scale. Going down to around B1 on a 25.5" scale is practical and still sounds good.
There really is no reason to think the lowest string must be somewhere around standard E2.

I thought G alt and B alt were rejected because they were red, named 'alt' and the red Eb alt was clearly rejected.

G alt
"9th of 5th of 5th"
freq * 3 * 3 * 3 * 3
81/64
408 cents
388.8 Hz
This is the 'Pythagorean major third'. Much less consonant than 5/4 when used in harmony, but is often preferred for melody.

B alt
5/4 of G alt
"Harmonic sequence" description is wrong, should be
"3rd of 9th of 5th of 5th"
freq * 5 * 3 * 3 * 3 * 3
405/256
794 cents
486 Hz


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## Winspear (Apr 30, 2020)

Indeed, try the slider on the link on my website. It will suggest you gauges based on an input such as a 46 E.


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## shellsj (Apr 30, 2020)

ixlramp said:


> I was wrong about the helek, it is indeed exactly 10 / 3 s. Makes sense because units of time tend to be the Earth day repeatedly divided into 'round number' of divisions, so differing time units often have simple numerical relationships.
> 
> Nah not at all. 25.5" is a little short for 7 string guitar B1 but it still sounds good.
> 
> ...


Yes - correct on both of those frequencies. I’ll keep experimenting with the fret finder app on the best tone for the third string and get back to you.


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## Spicypickles (May 3, 2020)

Any time @ixlramp posts my eyes immediately glaze over and I regret not finishing college. 

I’m just not smart enough to read the posts.


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## shellsj (May 3, 2020)

View attachment 80285


shellsj said:


> Yes - correct on both of those frequencies. I’ll keep experimenting with the fret finder app on the best tone for the third string and get back to you.



@ixlramp wanted to share this diagram - it's DADGAD using the following scala with Eb as the zero. I was looking for a way to play some sort of open tuning with a minimum of disruption of the straight frets, and this does it pretty well - at least on the lower frets:

shellsj
12
135/128
9/8
75/64
5/4
4/3
45/32
3/2
405/256
27/16
225/128
15/8
2/1

This is the flattened G you had suggested (5/4) with my preferred B (405/256). I did experiment further with Apple Logic this weekend and found that in some associations the 5/4 G sounds better, and in others the 81/64 one sounds better.  The answer will be to have both on a JI instrument - but for now, this ain't bad.


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## shellsj (May 3, 2020)

Also, for an open tuning that seems to best follow the contours of the True Temperament frets approximately, this open D-minor tuning does quite well - at least up to the 8th fret - which is quite handy. low to high: DADFAD



At least the main TT kink on the 3rd string corresponds with the "kinks" in this tuning, rather than being opposed to it, or something. This tuning actually sounds really nice on my True Temperament acoustic. I think this is the tuning I'll use for all of my True Temperament necks, as shown below.







Meanwhile, I have some other guitars with straight frets (a 5-string - for an F tuning, and a baritone - for Bb). I've found some tunings that will work quite well with new JI straight frets if I can convince my luthier friend.


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## ixlramp (May 4, 2020)

That DADGAD neck is impressively simple, looks like you carefully chose the open notes to keep the split frets high up the fretboard.
Good to see you are now fully able to design JI systems and frettings.


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## shellsj (May 5, 2020)

ixlramp said:


> That DADGAD neck is impressively simple, looks like you carefully chose the open notes to keep the split frets high up the fretboard.
> Good to see you are now fully able to design JI systems and frettings.


 yes, I generated quite a few of those fret finder neck diagrams, stored them as pictures and just went through them thinking how to minimise the gaps. That fret finder tool makes it possible. Thanks for giving me the link and how to do the scala thing. What I discovered is that major thirds are hopeless, but 4ths (as in DADGAD), fifths, 9ths go well - so it’s those combinations I looked into. 

Minor thirds pull the frets down, which is what happens on the True Temperament neck. It makes sense that F A D would work with TT for the top three strings as that’s just a normal guitar tuned down a whole step. So I think I got a glimpse into why the TT frets have that kink on the frets at the third string - for the minor third. But incorporating those strings as a minor DADFAD is a lovely and flexible tuning - like Albert Collins but down three frets.


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## ixlramp (May 8, 2020)

You should not compare your fretting designs to TT frets.
TT is a 'Well Temperament', so is a complex set of offsets from 12TET, it is not really offsets towards a particular JI tone system.
Also, the JI tone system TT is trying to emulate is the somewhat standard 'Ptolemy's 5-limit JI', very different from your JI tonal system.
Any comparisons to TT or apparent similarities to TT are mistakes or coincidences.


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