True Temperament Curly Frets

[LouieAtienza]

Originally Posted by robj144

Wouldn't it help for one key though and one key only? For example, the perfect fifth is a 3/2 ratio of 1.5 in the natural scale. In the modern tempered tuning (of which the guitar is based) it's 1.498. This leads to the inherent or implicit intonation problems. The reason why it's 1.498 is because the interval between each semi-tone is 2^(1/12) which gives intervals close to the natural scale while having all the intervals the same which allows the guitar to be transposed easily. If the guitar is set up to have better intonation for a key (say exactly related to the natural scale), then it will sound very nice in that one key, but it won't be able to be transposed at all.

I checked ther websire out a while back. The electric guitar necks are optimized for 9-46 strings. The 12-fret even temperament neck is supposedly a closer model than straight frets. The Thidell Formula 1 and Well-Tempered necks supposedly play well in many different keys; the Thidell more biased toward blues and rock keys, with the Well-Tempered neck more towared jazz keys...

[robj144]

Originally Posted by LouieAtienza

I checked ther websire out a while back. The electric guitar necks are optimized for 9-46 strings. The 12-fret even temperament neck is supposedly a closer model than straight frets. The Thidell Formula 1 and Well-Tempered necks supposedly play well in many different keys; the Thidell more biased toward blues and rock keys, with the Well-Tempered neck more towared jazz keys...

They are still "optimized" for certain keys though. Not all 12 keys sound "good" in this system or even sound the same.

[robj144]

Originally Posted by bohemian

robj144

It is my understanding that tunings favor keys, or chords... or are a compromise.

This True tuning may go out of whack when you tune to an open tuning, and I'll bet it is not equally unexactingly tuned in all keys.

The natural scale is based on pure fractions for intervals like 4/3, 3/2, and 9/8. Using this scale, chords can be created which sound pure and the scale also sounds pure. However, while any note can be the root of the scale and thus form the key (key of C, which a natural scale of C, D, E, F, G, A, B, C without the sharps and flats), if one started in one key and use the same intervals to transpose to say E (from C), the E scale would not sound correct because the intervals their would be different than the base key of C. Now, some keys would sound better than others (the perfect fifth, a G scale would sound close to the base key of C). To correct this problem, the equal tempered was created where the flats and sharps were introduced and the interval between each note was equal. Hence, when transposed the intervals for any scale is the same as any other scale and thus all keys sound the same. However, the tempered intervals is a compromise to the natural scale where the intervals are pure fractions and the subsequent harmonic series have natural multiples with one another.

[LouieAtienza]

Originally Posted by robj144

They are still "optimized" for certain keys though. Not all 12 keys sound "good" in this system or even sound the same.

That's true, but typically in rock, there are keys that are more commonly used and that's what the Thidell Formula 1 neck is geared toward. Having all keys sound perfect is impossible of course, but if you don't play in every key then does it matter?

The 12-tone Even Temperament neck aims to get each note closer to the theoretical formula while taking into account string gauge (whichc the typical formula does not account for.)

The big thing for me is getting that major 3rd to sound good. Even when my guitars are intonated perfectly, I personally tune down my B string a touch, to guarantee I don't sharp that major 3rd

[bohemian]

robj144..
I appreciate the info, it was a nice brief review.

As I tune free reed instruments, some dating back to the 1880's, I am familiar with various tunings and the what and why.

I still have no clue what this "new" true tuning might be.

I find it would have limited appeal to me. Guitars sound fine with the TET
fretting. Millions of others may believe so as well.

Spending more for a little is not likely to make the "inventors" a commercial success.

[trion12]

Originally Posted by DanPanther

If you look closely at the neck, the G string is basically the one taking the most modification. I tune my G strings a few cents flat, and that seems to accomplish the same thing. The other strings are so close to right, that it's hard to notice the difference. But the G can be heard.
Dan

OK, I learned this stuff back many years ago when doing a music degree . . . let's see if I can remember it . . .

The issue of temperament is a function of the physics of a vibrating string. A string vibrates in whole fractions of itself and that is what produces the overtones that you hear when you pluck an open string. A string tuned to E produces a harmonic series (i.e. overtones) very different from a string tuned to Eb.

The reason that the G is the hardest to get in tune in standard tuning is because in standard tuning it is a 3rd against the low E string as the root. When you play an E major chord on the guitar the G# in the chord is 14 cents out from the harmonic series. This is noticeable to most of us and therefore requires some adjusting of the tuning of the G string to sound good when you play an E major chord. When you however play a G major chord guess what? That open G string will be in perfect tune without adjusting because it is the root of the chord and roots need no adjustment against the harmonic series.

That is the same on every tempered instrument not just the guitar. It is not the mechanics of the guitar that make tuning the G string the most temperamental (pardon the pun ;-) ), it is the fact that 3rds are the most out of tune note in a major triad between the harmonic series and the tempered version of that note.

As long as you stay in the key of E you are OK, but when you change to the key of Eb for example you would need a different instrument tuned to Eb to play in tune if not for equal temperament. This would clearly be very impractical and for that reason equal temperament was invented. i.e. to enable one instrument to play in all keys as in tune as possible by spreading the compromises required as evenly as possible across the instrument.
With equal temperament we are accepting a certain amount of "out of tuneness" for the convenience of being able to play in all keys on a single instrument. Most of us would agree that that is a good bargain, even if it means for e.g. that tuning the G string is always a royal pain.

This gets very technical (most of which I forgot long ago) but if you want the science behind it google the terms "harmonic series", "pythagorean comma", and "equal temperament"

Aaron