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

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.

 

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....

 

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.

 

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.

 

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.

 

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:

 

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.

 

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.

 

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

 

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

 

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.

 

- 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.