# True Temperament fretting in detail (using an archive of the old site)



## ixlramp (Jul 23, 2019)

The 'True Temperament' (TT) fretting system was recently discussed in a Facebook microtonality group, and an archive of the old TT site was discovered.

There is a lot of misunderstanding of TT, and the old TT site was far more informative, so the intention of this thread is to link to the archived pages, reproduce the most important information, explain, clarify and discuss, such that this thread becomes the best reference for TT in this forum so far.

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I'll be adding extra posts later, to start, here are the links to the most important archived pages.
Each page of the old TT site was archived at different times, so simply navigating from the archived homepage very often results in missing pages and results in being redirected to the current TT site.
Some of the pages of the old TT site were never archived, such as 'Low Tune Guitar' and 'Bass Guitar', however, these are covered in the FAQ.

Product menu https://web.archive.org/web/20140414222828/http://www.truetemperament.com/site/index.php?go=1&sgo=0

'Thidell Formula 1' fretting https://web.archive.org/web/20111109073758/http://www.truetemperament.com/site/index.php?go=1&sgo=1

'The Well Tempered Guitar' fretting https://web.archive.org/web/20120419041637/http://www.truetemperament.com/site/index.php?go=1&sgo=2

'12 Tone Equal Tempered' fretting https://web.archive.org/web/20101020100111/http://www.truetemperament.com/site/index.php?go=1&sgo=3

FAQ (very informative) https://web.archive.org/web/20140415135226/http://www.truetemperament.com/site/index.php?go=4&sgo=0

Technical Details pdf https://web.archive.org/web/2015081....com/site/gfx/documents/Technical_Details.pdf

Prices and Options pdf (shows bass guitar to be Thidell Formula 1) https://web.archive.org/web/2012013...ent.com/site/gfx/documents/Prices_Options.pdf

Technique https://web.archive.org/web/20100507105726/http://www.truetemperament.com/site/index.php?go=9&sgo=2

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Here's the Technical Details pdf in image form (click to enlarge).


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## ixlramp (Jul 23, 2019)

For simplicity i will phrase my posts in the context of the old site, as if TT are still offering the same products.
They have a new site now, and may well have gone through changes, however the new site is so dumbed-down and lacking in detail it's not clear what they offer now. Even 'Well Temperament' is barely mentioned, if at all, so it's not made clear what their tonal systems actually are.

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Often i see people on forums using the words 'True Temperament' as if this is a tonal system, often they seem to be trying to refer to 'Just Intonation', which is a tonal system. 'True Temperament' is a brand name and nothing else.

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One of TT's Well Temperament fretting systems is called 'The Well Tempered Guitar' and is derived from a Well Temperament called the 'Bach/Lehman Temperament'.
For a long time i assumed, from that name, that this was known to be the Well Temperament used by J.S.Bach, and that Bach created it together with a contemporary called Lehman.
In fact, we do not know what exact form of Well Temperament J.S.Bach used. Bradey Lehman is a current day musician who claims to have 'decoded' the exact form of J.S.Bach's Well Temperament from ... a decorative doodle drawn by J.S.Bach.

I do not doubt Mr. Lehman's talents, and am sure that this Well Temperament he has created is a very good one, and suited to J.S.Bach's music. But this decoding is no more than speculation, and i dislike how this has been called the 'Bach/Lehman Temperament', implying that J.S.Bach was certainly involved. It's also seems an ego trip to have your name next to Bach's in a temperament name.
It should just be called the 'Lehman Temperament'.

TT's attitude is unjustifiably certain, from the FAQ:
"The first-named is adapted for the guitar from Dr. Bradley Lehman's brilliant reconstruction of the temperament used by J.S. Bach in "Das Wohltemperirte Clavier", Book 1."


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## Stevie_B (Jul 23, 2019)

This new hype might have something to do with Paul Davids and Adam Neely doing a video on the subject.

Wow, xlramp!

I was just going to post the following:


True Temperament Clarification

Hey guys!

I registered here to touch on "True Temperament", as I too spent quite some time wrapping my head around what it actually is and how it works.

It is definitely not Just Intonation.

It is in fact a mild unequal temperament (when compared to 12 Tone Equal Temperament) and is designed to favor certain "guitar keys".

That means that every key is different.

Every key has its own "key color" like it used to be in the old days of piano tuning and like it is still done today in organ tuning.

What is now marketed as "True Temperament" is actually the "Thidell Formula 1" - one of multiple temperaments designed by Anders Thidell who gave birth to True Temperament in the first place.


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## Stevie_B (Jul 23, 2019)

I am going absolutely insane, beacause this site won't let me post properly.
I can't post because of links, allthough I removed them again.

Please.
Let me just post this giant post I wrote....


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## Stevie_B (Jul 23, 2019)

Just like ixlramp wrote, there is a lot of confusion surrounding this topic.

High profile players buy and use the system, but often don't understand what it is.

I haven't seen any efforts by the company to clear up the confusion and I believe that, by now, it might actually be better, marketing-wise, to just keep selling the system as "sounds more in tune" or "perfectly intonated" than to tell people that what they're buying ist a remodelled, century old approach, that is not (perfectly) compatible with instruments that are layed out in an equally tempered fashion.

I don't have any behind the scenes knowledge, but it seems to me that the TT-company kind of maneuvered itself into this odd position where they have the atention of the public eye as doing and being something special, but at the same time not wanting to confuse any prospective buyers with too much information.

And let's face it. Most guitar players don't know anything about piano tuning systems of the 17th century.

Interestingly enough, there are a bunch of those out there right now playing and enjoying an unequal temperament without actually knowing.

At least there is quite a lot of approval for the system.
I tried to contact the people behind TT but didn't get any answers.

Seeing the serious lack of knowledge in the guitar community I decided to compile information on all of the above mentioned and am starting to put it in one place to create a collection of information, maybe in the way of a curriculum, starting from the laws of physics to the building process of a new prototype, be it acoustic, or electric.

Last year, as fate would have it, I found a modified Gibson SG on ebay which had been refretted in their Stockholm workshop.


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## Stevie_B (Jul 23, 2019)

So I got it and have been using it for a few months now and I have to say that it really does sound great!

The added "per-string per-gauge per-fret finer adjustments", like ixlramp called them, might already make a big difference by themselves, without the influence of the actual temperament.

There are old pictures online of Anders Thidell measuring and testing exactly that.

He built a special jig for it and tested every note individually with multiple string sets to account for the varying mass in commercially available strings.

This is why simply calculating the fret positions is not enough to achieve what he achieved.

He then marked the positions, made individual fret models by hand and later made molds to cast the frets in bulk. They used silicon bronze until recently, which some people think is going to wear too quickly and have recently come out with a stainless steel version.

Just like all of you I wasn't satisfied with the information I could find on the actual musical system, so I took the "cromatic offsets in cents from equal temperament" table, that can be found on their website under "how to tune", to map out the whole temperament.

E -2, F 0, F” -4, G +4, G” -4, A 0, Bb -4, B -1, C +2, C”-4, D +2, Eb -4

Let's take the major third interval from C to E as an example:

The table shows you, that C is raised by 2 cents and E is lowered by 2 cents.
This shortens the distance between these two notes by 4 cents.
In Equal Temperament, the major third interval ist 13,69 cents higher than the pure, justly intonated one.

13,69 minus 4 equals 9,69.

This makes the major third in the key of C 4 cents "cleaner" than the equally tempered one, and leaves it 9,69 cents sharp.

I made graphs for every interval in every key, which I can not post untill tomorrow because of this link posting issue with my new account...
So, tomorrow the following will be relevant:

The dark columns represent Thidell Formula 1.
The light colums represent 12 Tone Equal Temperament.
Their extensions up or down represent their respective deviation from the justly intonated (pure) equivalent.
Below the graphs:
Green stands for: "closer to Just Intonation than Equal Temperament"
Red stands for: "further away from Just Intonation than Equal Temperament"
Grey stands for: "the same as Equal Temperament"
The first number under the colours represents the deviation from Just Intonation in cents.
The second number in ( ) represents the deviation from Equal Temperament in cents.
You will notice, that I left out the Tritones.
Well, I wasn't sure which "just ratio" to pick, so I left it blank for now.
Maybe some of you know better.


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## Stevie_B (Jul 23, 2019)

While cooking my brain drawing these graphs, I talked to Tolgahan Cogulu, Professor at the Istanbul Technical University and responsible for the microtonal department over there.

You guys might know him through his YouTube content around microtonal guitar stuff.

He also did a video on the history of the microtonal guitar.

He ist a very nice and knowledgeable person and I presented the idea of creating a small and comprehensive curriculum style summary of how temperaments work and how they can be applied to the guitar.
He was interested, but I couldn't follow through until now out of time constraints and the sheer overpowering of this stuff to my brain.

This is also pretty tough to write because English is not my native language.


So if anyone on this forum is interested to join at some point, you're more than welcomed!

ixlramp you seem to know a lot about this! How did you acquire all this knowledge?

Hope this is of some value to at least a hand full of people.


Have fun with it!

Stevie




(If this is relevant to some other thread on here, please share this or tell me. I haven't properly navigated through the forum yet...)

EDIT: Sorry, if some of this information was already posted an hour ago.
I just wrote all of this and have been waiting to finally post this.
Links will be added, when the forum lets me and the bulk will be reduced.


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## ixlramp (Jul 24, 2019)

Stevie_B that's good input, it's good to have another member in this forum with an understanding of this.

Concerning related threads, another one that might interest you is https://www.sevenstring.org/threads/microtonal-metal.202859/ which has become this forum's 'microtonal guitar and microtonal music' thread, and not just microtonal metal.

About me ...
I'm a qualified physicist and in 2008 i became very interested in microtonal guitars and alternative tuning systems. I spent a lot of time researching on the web and learning about Just Intoantion, historical and alternative tuning systems. I have a guitar and bass i converted to quartertone fretting.

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From the TT archived FAQ:

"*What does “True Temperament” mean?*
The True Temperament Fretting System is a revolutionary new way to construct guitar fingerboards which tune accurately along the whole neck.

True Temperament does not imply Just Intonation. It is physically impossible to implement Just Intonation in more than one specific key (and its relative minor) on any instrument with only 12 intervals in the octave. (Except perhaps for computer-controlled instruments using electronically generated sounds.)

What we mean by True Temperament is that our fretting system will give you super-accurate intonation over the whole fingerboard in the particular temperament it is constructed for, whether this be standard 12-tone Equal Temperament or any of the other temperaments we offer."

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This is an important point, 'accurate intonation over the whole fretboard' is perhaps the most widely known feature of TT, it actually means the pitches of the played frets will be very close to the intended tonal system.
It does not mean 'perfect harmony chords over the whole fretboard', and i suspect this is a source of misunderstanding. 'Intonation' seems to be wrongly used by many to mean 'how perfect the harmony of the chords are'.
The misunderstanding is that TT enables 'perfect harmony chords over the whole fretboard', which of course would then mean 'in every key'. But of course that is impossible as stated by the FAQ. If it was possible there would be no need for most of the world to use the imperfect harmony of '12 Tone Equal Temperament' (12TET).

(The commonly known tonal system offered by TT is actually a historical tonal system known as 'Well Temperament', it was used by late Baroque and early Classical music, J.S.Bach was one of the first to use it. It was the tonal system used before the modern 12TET.)

So a guitarist may try a TT guitar and play triads in some rather commonly used guitar keys, and of course due to what is being played the triads have a noticeably more perfect harmony. The guitarist may then end up thinking something like 'all chords are perfect in all keys!'.

The truth is, only the minor and major thirds have slightly more perfect harmony, and only in 6 keys.
Of the other 6 keys, in 2 the harmony is no worse than 12TET, and in 4 the harmony is worse than 12TET.
This is discussed, and see diagram, here https://sevenstring.org/threads/intonation-debate.320112/#post-5030261
This was of course not a problem for late Baroque and early Classical music, this music was mostly triads played in a rather predictable keys.
Modern guitarists who don't just play triads in the common guitar keys will end up with no total chord harmony gain using TT, because harmony improvements in some keys inevitably result in worse harmony in others.
The only benefit would then be 'key colour'.


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## Stevie_B (Jul 24, 2019)

Here is the link to the graphs I made:
http://www.temperedguitar.com/true-temperament
If you spot a mistake please tell me!

The explanation is in my post above.
I just put it on the domain I got a while ago to publish other projects that are still in the making.

Remember that these are only calculations based on the numbers provided on the TT-website. To get a perfect picture you would have to check every fretted note individually, provided you are using the exact same instrument setup that was used in the measurement and production process of the TT-frets.

Paul Guy's website that I mentioned above:
http://www.guyguitars.com/truetemperament/eng/tt_faq.html#diff12tetwell

A pretty personal article about the whole thing from 2009:
http://www.furious.com/perfect/truetemperament.html

Old pictures of the production process:
https://s73.photobucket.com/user/jgrossnas/library/True Temperament?page=1

Tolgahan Çoğulu's video about the history of the microtonal guitar:


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## Hollowway (Jul 25, 2019)

This is HUGELY helpful. I am one who previously thought TT meant JI, and that “chords all over the FB would be perfectly in tune.” 

@Stevie_B those graphs (and your post) seem to show that, when considering all 12 keys, and when considering all intervals, TT is not any more “in tune” that ET. Is that correct? 
And, can I make the statement that a given interval in one key in ET is going to be the exact same amount “in tune” compared to the same interval in any other key? 
And that any two given intervals (within and individual key) in TT or ET will not be the same amount of “in tune”? But, by definition, all keys and all intervals will be in tune equally in JI, correct?

I sound like a lawyer here, lol, but I want to know if I’m understanding this.


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## Stevie_B (Jul 25, 2019)

HollowwTay said:


> @Stevie_B those graphs (and your post) seem to show that, when considering all 12 keys, and when considering all intervals, TT is not any more “in tune” that ET. Is that correct?
> And, can I make the statement that a given interval in one key in ET is going to be the exact same amount “in tune” compared to the same interval in any other key?
> And that any two given intervals (within and individual key) in TT or ET will not be the same amount of “in tune”? But, by definition, all keys and all intervals will be in tune equally in JI, correct?



When considering all 12 keys and all intervals, *as a sum*, TT will yield the same result as Equal Temperament, because all the changes happen within one octave.
But that's an impractical (or too mathematical) way to look at it.
The octave stays the same size, no matter how you rearrange the intervals "inside"
This being said, the *differences between keys* are rather noticeable.

In Equal Temperament all 12 keys sound the same with regards to interval quality, or interval distance/size.
The difference lies in pitch.
This is why you can easily transpose songs to a different key in Equal Temperant to accomodate different singers with different vocal ranges.

Intervals in True Temperament sound either slightly more in tune, or slightly less in tune (depending on the key) than their counterparts in Equal Temperament.
When you analyse the system, like I did with my graphs, you can potentially always be more in tune than in Equal Temperament, if you modulate wisely and place either more or less emphasis on certain intervals in certain keys. (The green ones in the graphs)
You don't have to, because even the less in tune ones are not that much worse than in Equal Temperament.

*Just intonation* refers to ratios, which can be created from any frequency.
Those ratios then become your intervals in relative relationship to your base frequency.
For example:
440 hz is what most of the musical world agrees to call "A".
Twice the cycles per second would be 880 hz and what we cal an octave.
These two frequencies are "in unison".
The ratio is 2:1

Throughout human history, people have discovered certain ratios to sound and feel "good".
Another strong and obvious ratio is 3:2, which we call a perfect fifth interval.
The western world has been content with 12 of these ratios for a while now.
Indian classical music distinguishes 22(!), called shrutis.
This is how so called microtonal music is commonly approached.
It is all about ratios.

Looking at these ratios, you can see, that their relative distances to each other are not consistent.
https://www.researchgate.net/profil...-Their-Size-in-Semitones-the-Ratio-of-the.png

This means that if you keep the frequencies that you built through calculating the ratios* around one base frequency* and then decide to take one of those frequencies, other than the base/root and make it your new base/root, the other ones will not sound harmonious relative to it.
This action would be what we call key change or "modulation".
You would have to calculate *new relative ratios *relative to the frequency you want to hear as the base/root.
If you stay within a single key in Just Intonation, all intervals can be perfect.
Changing to a different key would obviously be very impractical, if not impossible to achieve within the limitations of a single (non digital) instrument.

So, quite a ong time ago, smart people started tweaking those ratios/intervals.
Keep in mind that if you play in more than one key, every note can be a different interval relative to another note.
Those people accepted certain imperfections of certain intervals to be able to modulate to other keys, which was not possible before that.
This tweaking of smart imperfections is called "Temperament", or tempering.
Each temperament has its strengths and its weaknesses.
Throughout musical history, different intervals were favored at different time.
It started out with fifths, which neglected the thirds, and later moved on to "repair" (some of) the thirds.

Over the course of many centuries the musical world ended up with "12 Tone Equal Temperament", which devides the octave in 12 equally sized parts. We call them semi tones.
This makes the intervals' relative distances equal, but changes the relative distance to the base/root compared to the "Just"-Ratio.
The differences han be seen here:
https://i.stack.imgur.com/eMCQP.png
I based my calculations on this chart.

One might say we sacrificed melody to gain harmony.


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## Winspear (Jul 25, 2019)

Great to see this discussion , thanks for the hard work! Echoing a lot of my thoughts, as you know


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## Winspear (Jul 25, 2019)

Cool to see they _did _have a 12edo board that does what most people think todays TT does! I would be curious to A/B that against my most perfect setup, given the discussion had the other day about how I feel normal guitars can achieve perfect 12edo


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## Hollowway (Jul 25, 2019)

Stevie_B said:


> When considering all 12 keys and all intervals, *as a sum*, TT will yield the same result as Equal Temperament, because all the changes happen within one octave.
> But that's an impractical (or too mathematical) way to look at it.
> The octave stays the same size, no matter how you rearrange the intervals "inside"
> This being said, the *differences between keys* are rather noticeable.
> ...



This is one of the best explanations of anything musical I’ve ever read. Thanks for taking the time to write it out! It’s really fascinating to learn about all of it.


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## ixlramp (Jul 26, 2019)

Hollowway said:


> when considering all 12 keys, and when considering all intervals, TT is not any more “in tune” that ET. Is that correct?


In Well Temperament / TT fretting, every improvement of an interval in a key causes an equally sized worsening of an interval in another key. So in total, WT/TT is no closer to JI, no more 'in tune'. The benefits only occur in roughly half of the keys, in the 'commonly used guitar keys'.


Hollowway said:


> can I make the statement that a given interval in one key in ET is going to be the exact same amount “in tune” compared to the same interval in any other key?


Yes. In all keys of 12TET a major 3rd is always 400 cents and 14 cents sharp of the JI major 3rd.


Hollowway said:


> any two given intervals (within and individual key) in TT or ET will not be the same amount of “in tune”?


Mostly correct, depending on the WT, certain intervals in certain keys may still have the same size in cents.


Hollowway said:


> But, by definition, all keys and all intervals will be in tune equally in JI, correct?


Well ...
In a JI tonal system, because the tones are unequally spaced, when you move to a different key most of the intervals change in size, they will all still be JI intervals, but different JI intervals and usually less consonant ones (more complex frequency ratios).
Because they are JI intervals, they are all perfectly 'in tune', so 'will be in tune equally in JI' makes no sense.

This is all assuming that by 'in tune' you mean 'perfect JI harmony'.


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## ixlramp (Jul 26, 2019)

Stevie_B said:


> One might say we sacrificed melody to gain harmony.


I would say, we sacrificed harmony to gain modulation.
Indian classical music chose to not do this, Ragas do not modulate and the intervals are either JI or very precisely and intentionally played non-JI intervals.


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## c7spheres (Jul 26, 2019)

- Every great song ever written in any style of music ever has not used this. Ok, there's probably exceptions. There is nothing wrong with it, but many players played out of tune very often (Hendrix, Page, B.B., etc.). Slightly out of tune and out of temperament has been the rule for a long time and nobody seems to care that much. 
- I see a correlation between this and tube amps and Vinyl etc. Tubes and Vinyl are technically inferior to solid state and digital etc, but they are preferred because of their imperfections. I think the same goes for tuning and temperament. Instruments need those rough edges, unless there's a specific need for perfection on a specific piece of music. The current imperfect way of doing things with equal temperament is just fine. People slightly detune or change fret hand pressure etc and get the results they want still. I could see True Temperament and an Evertune system working working wonders though, especially in the studio. What both those systems seem to change however is energy output. They seem to kinda flatten/neutralize everything. 
- No matter what temperament or tuning method someone uses, even on a perfect instrument, the fret hand pressure will always be a factor causing slight imperfections in the tuning stability. People do not play with perfect pressure at all times like robots (well most people). They play with dynamics, and the fret hands dynamics are a huge factor, which players seem to ignore for some reason. This may be what people are talking about when they say that tone is in the hands. 
- I'd like to see this system brought to 7 string Ibanez wizard necks.I think Vai had that going on but that may have been a 6 string. Either way. It needs to happen.


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## ixlramp (Jul 26, 2019)

Does anyone know for certain what fretting systems TT offer now? The new site suggests only 'Thidell Formula 1' is.

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From the archived TT FAQ:

"Most guitars tend to play a little sharp in the lowest frets, a little flat in the 5th - 10th frets, and fairly accurately around the octave. Up above the 15th fret anything at all can happen!"

Well, lowest frets sharp means lowest frets out of tune with the nut, and is due to how the nut is cut and positioned. A well cut nut, maybe a nut with horizontal compensation (per-string or otherwise) can fix this. Without that attended to, intonating a guitar will inevitably end up with a less than optimal intonation.
The statement about 'above the 15th fret' is ridiculous (except on thick strings, which have unavoidably worse intonation on high frets, but they also have a poor tone and inharmonicity so wouldn't be played up there anyway). Maybe many guitars have poor intonation on the high frets because they use the imprecise intonation method i have criticised, which doesn't check the pitches of the highest frets.

The FAQ does not mention that TT fretting restricts you to standard tuning EADGBE or it's transpositions.


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## ixlramp (Jul 28, 2019)

I've looked at the current TT site again.

They've dropped the 'Well Tempered Guitar' temperament and the 12TET fretting, it seems everything is 'Thidell Formula 1' (TF1) now.
TF1 is offered for 6, 7, 8 string, low tuned (B standard) 6 string, steel and nylon acoustics, and 4 string bass.

In the FAQ, TF1 is referred to as a temperament, and that it has offsets from 12TET, these offsets are stated briefly, with no explanation, hidden away at the end of the 'how to tune' section.
Apart from this, there is absolutely no explanation of what the TF1 temperament is, what effect it has, how it works, or even that it is a 'Well Temperament' tonal system. This seems odd.


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## ixlramp (Jul 29, 2019)

Here's the guyguitars TT site, this is very similar to the old TT site, with similar information http://www.guyguitars.com/truetemperament/eng/tt_index.html

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Now to attend to *that* video:



'True Temperament - Mattias Eklundh Guitar Lesson' youtube video present on the homepage of True Temperament's website.

Pausing the video on a close-up, the fretting system is clearly not the subtle 'perfectly intonated 12TET' system that TT used to offer, so it is TT's WT.
On the videos page of TT's current site, the description of a slightly earlier video is:
"Mattias IA Eklundhs Caparison AH8 8-string signature model features a True Temperament Thidell Formula 1 fingerboard with 27 frets."
So it's fairly certain he uses TT's WT that is called 'Thidell Formula 1'.

"The natural harmonics [...] are now the same as the frets, or, the notes on the fretboard"
He plays a D harmonic at fret 3 on G string: 6th harmonic, 2 octaves plus a JI fifth.

Firstly, the only harmonics in tune with 12TET are the octave harmonics 2, 4, 8 etc.
However, this is a Well Temperament, most tones have been offset from 12TET, so the fretted pitches will usually be even further out of tune with the harmonics.

The D 6th harmonic on the G string is a JI fifth, 702 cents, above G.
In TT's WT, the offsets are G +4, D +2, each fretted D is 698 cents above G.
Difference is 4 cents.

"And you can play a barre chord with a major third, and it's in tune in every possible position"
He plays a barre chord in 6 consecutive positions.
The whole point of a WT is that the harmony of a particular chord will vary significantly on different root notes. The chord he plays will have better harmony on the (non-consecutive) root notes C D E G A B but worse harmony on 4 root notes. The harmony of these consecutive chords he plays will be actually be varying more than on a 12TET guitar.

Amusingly, many people commenting on the video have their minds blown and are claiming to hear perfection even though it is not actually occuring in most of the demonstrations. That's the power of suggestion from someone considered trustworthy.

The video gives the impression that TT's system creates perfect intonation to 12TET, which is also the impression the website gives, unless you read the FAQ and 'how to tune' page, and notice the stated offsets from 12TET and references to 'Thidell Formula 1' temperament.

So almost all of this video is incorrect.
The video seems to be used 'because it's Mattias Eklundh and people will trust him', even though it is clearly incorrect as TT will no doubt know.


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## Winspear (Jul 29, 2019)

^ Thank you! This video has always triggered me so hard particularly because It's Mattias who is a guy who is into his harmonics, difference tones etc. so I was particularly double baffled by some of those false statements


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## Fred the Shred (Jul 30, 2019)

Mattias, like most players, will use vibrato and subtle corrections to improve the inharmonic nature of some intervals on the guitar - it's subtle, but you actually notice you do that when you play a TT instrument, as the offsets will throw you off and force you to stop compensating in your usual fashion as it doesn't work as intended anymore, especially since we mostly go for the good old common major triads that typically sound worse without some form of compensation as a way to test this sort of thing. 

I think the power of suggestion, as pointed out, applies to him as well, seeing as he's pretty nimble when it comes to adjusting the pitch to his liking and has excellent control to boot. The chordal bit will be different, of course, and I do believe the difference can be refreshing enough to supercede actual accuracy in terms of how pleasant the chord will sound to one's ears.

The system's advantage, to me, is really how certain key "colours" will be a thing, which may produce interesting results. That, of course, is also its major disadvantage given that we're not exactly playing just triads as a chordal foundation, and the popularity of different tunings makes it so that the whole thing is basically useless the moment you start having different intervals in the same positions.


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## ixlramp (Aug 1, 2019)

Quick addition to video criticism:

".. and even crappy stuff like fifths ... sound good all over the place"
He plays a chromatic sequence of fifths in 18 positions, implying all these fifths have better harmony.
In TT's Well Temperament, the sizes of the fifths actually varies per root note as follows (from Winspear's analysis):

Root note. Size of fifth (semitones)

C 7.02
C# 7.00
D 6.98
D# 7.00
E 7.01
F 7.02
F# 7.00
G 6.98
G# 7.00
A 6.98
A# 7.04
B 6.97

4 of these have worse harmony than 12TET.
The 12TET fifth is 7.00 semitones, the perfect harmony JI fifth is 7.02 semitones.


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## Winspear (Aug 2, 2019)

Indeed, I was surprised he even brought that up - I mean does anyone actually have an issue with 700c fifths? I consider myself picky with tuning and am more than happy with the fifths. Indeed some of the ones in TT are drifting a little too far away


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## danielerphy (Apr 3, 2022)

Stevie_B said:


> Here is the link to the graphs I made:
> http://www.temperedguitar.com/true-temperament
> If you spot a mistake please tell me!
> 
> ...



Hello Stevie_B, I wonder if you can share again the graphic from this link (http://www.temperedguitar.com/true-temperament) unfortunately the link is not working. Thanks.


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## jco5055 (Apr 5, 2022)

I just grabbed a Strandberg TT guitar, since with their return policy it was risk free to try TT, and I gotta say I'm not really a fan. I don't like how it offsets/makes worse half the keys/intervals...why did they stop making their version of a more accurate 12 Tone ET? That would be ideal.


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## bostjan (Apr 5, 2022)

jco5055 said:


> I just grabbed a Strandberg TT guitar, since with their return policy it was risk free to try TT, and I gotta say I'm not really a fan. I don't like how it offsets/makes worse half the keys/intervals...why did they stop making their version of a more accurate 12 Tone WT? That would be ideal.


WT as in "Well Temperament?" I think that's the same basic idea if that is the case.


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## jco5055 (Apr 5, 2022)

bostjan said:


> WT as in "Well Temperament?" I think that's the same basic idea if that is the case.


My mistake, I meant ET not WT.


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## bostjan (Apr 5, 2022)

Gotcha. Have you tried their old ET fretting? I have not, but my gut tells me that it maybe wasn't generally considered worth the added effort/cost.

FWIW, I think the TT corrections don't go far *enough*. If the idea is to sweeten certain keys at the expense of others, dive into that. If not, ET already works. Trouble is that people in the 21st century don't want WT - they want the convenience of ET, but with sweeter keys across the board (halfass pun), which is mathematically impossible unless you introduce other unwanted compromise aspects (like you could just go full-on 60-EDO, and all keys would sound a little better, but then you have to account for 60 notes instead of 12). I think the spokespeople for TT, whether sanctioned by TT or not, have made promises that are just unrealistic, and people calling them out for it were ignored by the masses in favour of the hype.

I love playing in 19-EDO. I didn't invent 19-EDO, and I certainly don't think it's definitively better than 12-EDO. I just think it's got some cool intervals in it, fifths still sound okay enough, major and minor thirds sound markedly better, major seconds sound good enough if you don't dwell on them too much, it's not a ridiculous number of notes to manage, and it's an ET, so there's all the conveniences that go with that. But, if I wanted to sell 19-EDO fretboards to people, and somebody was out there hyping it to lead people to believe that 19-EDO made every note sound better, I know I wouldn't be too excited about interrupting them to correct their statements. And I think that's about what it is with TT. There is no perfect tuning. Everything will always be a compromise either making technique more difficult, making certainly things sound worse, or whatever. It looks like TT started off being marketed as a nifty alternative idea complete with its warts, but, slowly, the information that made it clear that it had its flaws started disappearing and around the same time its proponents were getting more vocal and leaning harder into the misinformation around it.

Oh well, ultimately, it's still an interesting alternative, and all of the hype allows it to continue to exist, so I shouldn't be all that upset. I'm just predisposed to be irritated by inaccurate claims involving science and mathematics.


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## ixlramp (Apr 7, 2022)

bostjan said:


> Have you tried their old ET fretting? I have not, but my gut tells me that it maybe wasn't generally considered worth the added effort/cost.


Yeah, i consider it not worth implementing.
A well set up guitar (perhaps with a compensated nut) can have very good intonation (when played carefully). The primary causes of pitch errors on a guitar are:
* Fingers unintentionally pushing strings out of tune.
* Strings slipping back and forth across a nut (if no double-locking system).
* Pitch rise on note attack on large gauge low tension strings.
None of which can be fixed by a True Temperament fretting.
So the old discontinued TT Equal Temperament fretting has little benefit, but still has all the disadvantages of a TT system.

The TT ET system does not have the 'wow factor' that the currently marketed TT Well Temperament system does. TT WT system a makes an impression because a guitarist trying it out hears the improved harmony of 50% of the major and minor keys ..... of course, only if they are playing the improved keys, but the chances that a guitarist will play a major scale or chord in keys CGDAEB are high, which is why many are impressed by TT.

Ironically, due to the sloppy and misleading way TT is currently being marketed and hyped, many are probably misled into thinking they are getting near-perfect Equal Temperament.


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## ixlramp (Apr 7, 2022)

@Stevie_B not sure if you are active here anymore.
Your grid diagram that combines all your results is very useful and exactly what people need to understand exactly which harmonies TT improves. Perhaps you could include it in a post in this thread?
It looks like your TT analysis website has gone down, perhaps intentionally.


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## Hollowway (Apr 28, 2022)

@ixlramp or anybody - have you heard of this? https://freenotemusic.com/product/freenote-24-fret-just-intonation-neck/. I haven’t thought too much about it yet, but I’m not sure I understand how this is looking like an ET microtonal neck, but still gives JI intervals.

Found some more info - and a super cool methodology to try to that the crazy thing playable! https://harmonicsofnature.com/just-intonation-instrument-design/

This is a super cool read, too: http://jsnow.bootlegether.net/cbg/justintonation.html


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## Winspear (Apr 28, 2022)

Hollowway said:


> @ixlramp or anybody - have you heard of this? https://freenotemusic.com/product/freenote-24-fret-just-intonation-neck/. I haven’t thought too much about it yet, but I’m not sure I understand how this is looking like an ET microtonal neck, but still gives JI intervals.
> 
> Found some more info - and a super cool methodology to try to that the crazy thing playable! https://harmonicsofnature.com/just-intonation-instrument-design/
> 
> This is a super cool read, too: http://jsnow.bootlegether.net/cbg/justintonation.html


It's a case of extras - which is why there are frets quite closely bundled together. 


https://freenotemusic.com/wp-content/uploads/2020/11/12-TUPnecks_DS_012113.jpg


It keeps the original 12 tone notes, and adds the JI options for various ones alongside them (so as a guessed example - say you're in C and want a perfect 5/4 ratio E third, it will have that available just under the regular E so that you can still use the regular E as another root and have all its normal stuff and not get thrown out by JI inequivalences).
As a sidenote I've heard the quality of these is really quite bad for anyone that is guitar quality critical (most micro guitarists don't seem to be). Have head similar critiques on Sword though not as frequent.


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## ixlramp (Apr 28, 2022)

Hollowway said:


> have you heard of this? https://freenotemusic.com/product/freenote-24-fret-just-intonation-neck/. I haven’t thought too much about it yet, but I’m not sure I understand how this is looking like an ET microtonal neck, but still gives JI intervals.


It is not an ET neck. It has full-width frets placed at exact JI positions.
Winspear: It is a different fretting to their much more well known '12 Tone Ultra Plus' fretting which is exact 12TET plus extra JI frets.

Contrary to their claim, due to the full-width frets, using standard tuning would result in the possible intervals being different on almost every string. Awkward to use and does not function like most instruments do: a scale being playable throughout the range.
Open tunings are a little better. Alternating fifths and fourths (CGCGCG) would be optimum.

Catler is the most well known and most celebrated microtonal guitarist, but has the most awkward microtonal guitar system and is enthusiastic about the '528Hz cosmic frequency' pseudoscientific nonsense (a very similar thing to 432Hz).

"Also perfect for C 528hz cosmic tuning." 


Hollowway said:


> Found some more info - and a super cool methodology to try to that the crazy thing playable! https://harmonicsofnature.com/just-intonation-instrument-design/


Beware that site, it has a lot of mistakes and nonsense, especially in that approach to Freenote guitars. I had a slightly grumpy discussion/argument with the site author forum member 'shellsj' in this thread https://www.sevenstring.org/threads/general-microtuning-thread.340098/

The Jim Snow site is trustable.


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## Winspear (Apr 28, 2022)

Whoops my mistake - only knew him for the 12ultra plus and that was indeed what I was describing and the image I linked. 
Seconded that CGCGCG is better for that kind of thing.


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## bostjan (Apr 28, 2022)

Hollowway said:


> @ixlramp or anybody - have you heard of this? https://freenotemusic.com/product/freenote-24-fret-just-intonation-neck/. I haven’t thought too much about it yet, but I’m not sure I understand how this is looking like an ET microtonal neck, but still gives JI intervals.
> 
> Found some more info - and a super cool methodology to try to that the crazy thing playable! https://harmonicsofnature.com/just-intonation-instrument-design/
> 
> This is a super cool read, too: http://jsnow.bootlegether.net/cbg/justintonation.html





Winspear said:


> As a sidenote I've heard the quality of these is really quite bad for anyone that is guitar quality critical (most micro guitarists don't seem to be). Have head similar critiques on Sword though not as frequent.



I own a freenote 19EDO neck. The neck is good quality. I've been rocking it for 17 years with no issues. That said, maybe quality has gone down hill sometime since then.

I'm somewhat familiar with 12 tone ultra plus - that one is pretty nifty, if maybe a bit limiting in application. I have no idea what this JI/ET frankenstein thing is (other than the thorough explanation on the other site you link, which I have't read yet). It seems like two things that can never go together to me. The description of it does nothing to help me understand it. JI tuning cannot mesh with ET, nor with "any tuning you want will work," nor with straight full-width frets, so I'm thinking it must be some sort of 12-tone ultra plus variation. 12-tone genuine drought? IDK.

If it fell in my lap, I'd mess with it, but IDK about paying $900 just for the neck.

Catler and Sword are both alright in my book. I don't want to discount anyone else's opinion, when they aren't here to share their story, but I've had good experiences myself.

I'd love to get a real ET neck made some day, but, ATM, my finances are far too focused on things like houses and cars. Maybe after my next microtonal music release goes viral. 

As a side note from me: I'm impressed. Years ago, people were complaining that this sort of stuff was far too theoretical. Now there are tons of micro artists out there raking in the micropennies on Spotify. Stuff like TT is pretty mainstream (even if, to make it appeal to this large of an audience, it has been washes of it's microtonal context). At any rate, I've found tons of music I think is pretty rad.


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## ixlramp (May 7, 2022)

Stevie_B said:


> You will notice, that I left out the Tritones.
> Well, I wasn't sure which "just ratio" to pick, so I left it blank for now.
> Maybe some of you know better.


See the 'Twelve-tone scale' section of https://en.wikipedia.org/wiki/Five-limit_tuning
The Just Intonation (JI) system that best represents Equal Temperament and standard (classical/pop/rock) harmony, is called '5-limit JI'.

In 5-limit JI, there is a choice of 2 tritones: 45/32 and 64/45.
45/32 is chosen because:

1. It has a simpler ratio so is more consonant.

2. It results from playing a JI major 7th chord with the chord root on the fifth, it is the 'major seventh of the fifth'.
The other tritone does not result from the chords of standard harmony.

The JI intervals that best represent Equal Temperament and standard harmony, are:

Freq Cents

15/8 1088
9/5 1018
5/3 884
8/5 814
3/2 702
45/32 590
4/3 498
5/4 386
6/5 316
9/8 204
16/15 112
1/1 0



Stevie_B said:


> https://i.stack.imgur.com/eMCQP.png
> I based my calculations on this chart.


I noticed you used the 'Pythagorean minor seventh', 16/9, 996 cents.
It is better to choose the '5-limit minor seventh', 9/5, 1018 cents, because:

1. It has a simpler ratio so is more consonant.

2. It results frequently from playing a JI minor triad with the chord root on the fifth, it is the 'minor third of the fifth'.
The Pythagorean minor seventh only results when playing a JI suspended fourth chord with the chord root on the fourth, it is the 'fourth of the fourth'.
So 9/5 is the more desirable interval to choose for the minor seventh.

The 583 cent tritone on that chart is the 'Septimal tritone' 7/5. 5-limit JI does not contain intervals derived from 7s, so this is not used for the tritone. It cannot result from the chords of standard harmony.

Your analysis is still very useful, only your minor seventh results are affected and not in a way that alters the important observations.


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