What does “True Temperament” mean?

What’s wrong with straight frets?

Which temperament should I choose?

Do I need to use a particular string gauge?

Can I tune down a half-step?

How do I tune these temperaments?

How do I adjust my guitar's intonation after installing one of these necks?

What do I do when the frets need dressing?

How do I get one of these necks refretted?

Why are there four different temperaments?

What is the difference between Equal Temper and Well temper?

What is the difference between Die Wohltemperirte Gitarre and Thidell Formula 1?

What happens when True Temperament guitars are used with other guitars, bass, piano etc?

What is Meantone Blues?

What about acoustic and bass guitars?

How does your system compare to the Buzz Feiten Tuning System®?

Can I buy a fretted TT fingerboard to put on my guitar?

Can your True Temperament frets be retrofitted to an existing guitar neck with standard frets?

Do you have a version for 7-string guitars/low tuned guitars/baritone guitars?

Do you sell complete guitars?

Can I have stainless steel TT frets?


Complementary texts for answers in the F.A.Q.:

Technical details - Die Wohltemperirte Gitarre / Thidell Formula 1

About Key Colour

Meantone Blues™

How is the Meantone Blues™ temperament tuned?

Tuning methods evaluated


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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What’s wrong with straight frets?
Standard equal tempered fret spacing is calculated from one single piece of information about the instrument - the scale length (the theoretical speaking length of the open strings). A divisor constant is used to determine the locations of the frets. The scale length divided by the constant gives the position of the first fret. The remaining length after subtracting the first fret, divided by the same constant, gives the position of the second fret, and so on.

The divisor used by all but a vanishingly small percentage of modern guitar builders is 17.817152, a figure arrived at by way of the logarithmic function "the 12th root of 2" (1.0594631). This results in precise mathematical fret spacing with the 12th fret at the exact centre of the calculated scale length. If the calculation is repeated for 24 frets, the distance from the 24th fret to the theoretical bridge saddle position will be exactly one-fourth of the calculated scale length. (The residual error is ridiculously small, less than one ten thousandth of an inch on popular guitar scales.) All very impressive. But this mathematical model is a gross oversimplification. It ignores virtually every physical parameter which governs the behaviour of vibrating strings, except one - speaking length. Tension and mass are not even considered.

The model assumes an "ideal" or "perfect" string - one which only exists in theory, not in the real world. It assumes, firstly, that the strings have no stiffness. Secondly, it assumes that all strings behave identically, regardless of their thickness, whether they are plain or wound, and the material they are made of. Thirdly, it assumes zero string height - and completely ignores what happens when the strings are pressed down on the frets!

The frequency of a vibrating string is determined by three factors: the speaking length, its mass, and the tension applied. All three of these factors are affected to varying degrees when a string is pressed down on a fret. Along the neck, the length and mass decrease by 50% per octave. Changing the length affects the stiffness. The tension is affected by fretting the string, as the string height is not zero. Pressing the string to the fret stretches the string slightly, increasing the tension and thus sharpening the notes produced.

The strings themselves vary considerably in diameter and construction (plain or wound), and thus react differently to being fretted. One single adjustment per string at the bridge ("intonation") cannot possibly fully compensate for all these parameters at once, as they all vary in different degrees on different strings.

The only way to fully compensate for all these parameters is to adjust each and every string-to-fret contact point on the fingerboard separately, until each and every note plays the target frequency exactly. This, which is impossible on a guitar with traditional, one-piece, straight frets, is exactly what we do with Dynamic Intonation™, and Curved Frets™.

Previous attempts at implementing non-standard temperaments on the guitar, or of adding extra intervals, have relied on adding extra frets, or splitting the frets into separate pieces. This makes it very difficult, if not impossible, to employ modern rock and blues playing techniques like stringbending.

Our Curved Frets™ let you play the way you are used to - not only in true Equal Temperament, but in any temperament you choose.

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Which temperament should I choose?

12-Tone Equal Temperament
This is the musical scale which "ordinary" guitars are constructed for - in theory. In reality, the best that can be achieved is a close approximation to Equal Temper, because the simple mathematical formula which is used to calculate the fret positions is based on insufficient information about the physical properties of vibrating strings. (See: "What's wrong with straight frets?") 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!

tt_12equal_lay.jpg

A True Temperament 12-Tone Equal Temperament neck has even and precise intonation throughout its register. It tunes the way the guitar is supposed to tune ­ according to the mathematical formula - but with much greater precision than ever previously achieved, Open strings can be combined with notes way up on the neck, right up to the last fret.

12-Tone Equal Temperament is a compromise which enables us to play all intervals, in every key, with the same relative accuracy. It is an artificial, mathematical division of the octave into twelve equal semitones, which conflicts with the natural tone row - the pure intervals in the overtones of vibrating strings. When two or more strings are played together, each string generates its own overtone series. Since neither the frets, nor the strings, are tuned in pure intervals, the overtones from the individual strings are way out of tune with each other. The beat frequencies which are generated between conflicting overtones are not musical. This is especially evident when playing major third, minor third, sixth and seventh intervals with distortion.

Not even a True Temperament neck can cure this problem, as the laws of Nature cannot be broken. But a 12-Tone Equal Temperament TT neck brings the guitar exactly into line with the human mathematical rules!

Well Tempered
Up until now, the guitar has always been shackled to equal temper, as this is the only practical alternative when you have twelve straight frets to the octave. But the equal tempered scale is far from being the one and only way to divide the octave into semitones - many hundreds of different temperaments have been documented through the centuries. The True Temperament system finally makes it possible for the guitarist to explore alternative, very musical-sounding temperaments. (The majority of modern keyboards and music software programs have this ability to switch temperaments built in - but sadly, few users ever make use of this feature.) Some of the most interesting of these temperaments are so-called "Well Tempered" schemes.

Well Tempered tunings are designed to favour different key signatures to different degrees. In the favoured keys, intervals tune closer to the natural tone row than in equal temperament, which improves consonance and reduces intermodulation and beating. The price for this is that consonance in the lesser-used keys is sacrificed a little. The best well-tempered schemes make all keys usable, however, with a good balance of tonal colours.

We offer two different Well temperaments. Which one you choose depends mostly on which keys you want to favour most.

Thidell Formula 1
If you mostly play in "guitar keys" then Thidell Formula 1 is for you. Formula 1 is specifically designed for the guitar. It is optimised for all the standard open and barre chord patterns. Major keys in Formula 1 which sound closer to the natural tone row are: E, F#, G, A, B, C, D. Minor keys which sound closer to the natural tone row are: E, F#, Ab, A, B, Eb.

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Die Wohltemperirte Gitarre
If you play a lot of "jazz" chords, in key signatures which brass players tend to favour, Die Wohltemperirte Gitarre is an excellent choice. Major keys in "Wohl" which sound closer to the natural tone row are: F, G, Bb, C, D. Minor keys which sound closer to the natural tone row are: E, F#, Ab, A, B, D.

For a detailed description of how these temperaments are constructed, see: Technical details

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The remaining key signatures in both "Wohl" and Formula 1 all sound harmonically acceptable to the ear, with varying degrees of tonal colour. Nothing sounds dissonant, but interesting, subtle effects are created which add harmonic "spice" to the mix. This applies to all well-tempered keys to some extent, and is a valuable tool which can add to the emotional "feel" of the music.

Before equal temperament came along in the mid 19th century, "Key Colour" - also known as "Key Character", or, in German, "Affekt" - was a familiar and generally accepted form of musical expression. "Key colour" is absent in equal temperament . As all its intervals are equal, the blend of intervals is the same in every key, so all keys sound alike. Well Tempered intervals are unequal, which gives each key its own unique blend of intervals and thus its own personality. Some keys sound sad or gloomy, some sound happy, some sound majestic, yet others frivolous.

Our well-tempered variants blend in well with "ordinary" instruments, the offsets from equal temper are not so severe that they sound dissonant. They have their own unique characters that never sound "wrong", but rather enrich the musical palette - they could be described as different dialects for the different temperaments.

For more on "Affekt", go here: About "Key Colours"

If you are in search of something really different, see: Meantone Blues

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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". We have found that normal intonation at the octave is enough to handle this range of gauges.

Our LOW TUNE model is optimised for 0.014” - 0.018” - 0.024” plain - 0.036” - 0.052” - 0.060” roundwound strings.

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

Our steel-string acoustic fingerboard (650mm scale) is optimised for standard 0.012” - 0.054” bronzewound strings with a wound 3rd.

We also have a version for 641mm scale steel-string guitar with a plain (0.018") G (as used by Steve Vai on his Ibanez Euphoria EP9 signature model).

Our nylon-string acoustic fingerboard (650 mm scale) is optimised for Savarez Corum Alliance strings (blue packet).

Our bass necks (34” scale) are optimised for standard roundwound 0.045” - 0.105” strings.

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Can I tune down a half-step?
You can tune down and/or change string gauges within sensible limits. A half step down works fine. The limitation on how low you can go before the intonation craps out is most often the (plain) 3rd string - anything thicker than a 0.018" usually sounds horribly "plonky" at, or close to, concert pitch, but thinner ones can become too floppy (and difficult to intonate) when tuned down - and again, using a wound 3rd is not an option if you have a True Temperament neck designed for a plain 3rd string.

We now offer a LOW TUNE, standard (25-1/2”) scale version for “fourth down” tuning (B - E - A - D - F# - B). Please see “Guitar & Bass Necks” for details.

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How do I tune these temperaments?
Where Equal Temperament is concerned, exactly the way you should be tuning now. Here is an in-depth analysis of correct and incorrect methods of tuning the equal tempered guitar, see Tuning methods evaluated.

The 5 - 5 - 5 - 4 - 5 fret method, or tuning with octaves, will always work with any of these temperaments. Specific instructions for tuning Das Wohltemperirte Gitarre™ and Thidell Formula 1™ temperaments, by ear or with an electronic tuner, including offset settings for progammable tuners, are here:

Die Wohltemperirte Gitarrre
Thidell Formula 1

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How do I adjust my guitar's intonation after installing one of these necks?
In exactly the same way you would intonate with a standard neck - by matching the open string notes to the octave (12th fret) notes.

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What do I do when the frets need dressing?
Fret levelling is done the exact same way as with standard frets. Re-crowning is more time-consuming than with standard frets, but any skilled luthier should be able to handle the job. (He will of course charge you considerably more than for standard frets!). We will be posting video on our website demonstrating the techniques and tools we use in our workshop, and will be happy to offer any help and advice we can. If you can't find a luthier who will take on the job you can send the neck to us for fret dressing at a reasonable rate.

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How do I get one of these necks refretted?
Refretting a True Temperament neck requires considerably more patience than refretting a standard neck, but uses essentially the same techniques. We can supply a new set of frets, and will be making a special fret press shoe available, which will fit Stewart MacDonald Guitar Shop Supply fret presses. (We will also supply individual frets for repair situations.) Once again, we will be posting video on our website demonstrating the techniques and tools we use in our workshop, and will be happy to offer any help and advice we can. If you can't find a luthier who will take on the job you can send the neck to us for refretting at a reasonable rate.

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Why are there four different temperaments?
There are literally hundreds of ways to divide an octave into 12 semitones, and equal temperament (“12-tet”) is only one of them - and not necessarily the most satisfactory to the ear. The beating of equal-tempered 3rds and 6ths can cause some quite unpleasant effects, particularly with an overdriven or distorted guitar signal. We offer a super-accurate 12-tet, plus several alternatives – two different Well temperaments, and an Extended Meantone temperament that we call Meantone Blues.

Beating and intermodulation between overtones, which steals energy from the strings, is significantly reduced with our well-tempered and meantone necks. This allows the overtones to multiply and sustain, instead of cancelling each other out. String separation is dramatically improved. Our two Well temperaments are Die Wohltemperirte Gitarre, modelled after Dr. Bradley Lehman’s reconstruction of the temperament used by Bach for Das Wohltemperirte Clavier, and Thidell Formula 1, constructed by our own Anders Thidelll. Formula 1 is the first temperament ever constructed specifically with the guitar in mind. Meantone Blues, also constructed by Anders Thidell, is for the more adventurous guitarist, as it adds two extra frets in the first octave to maximise the number of usable key signatures.

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What is the difference between Equal Temper and Well Temper?
Our 12-Tone Equal Tempered model tunes the way the guitar is "supposed" to tune - according to the mathematical formula - but much more accurately than with standard straight frets. However, the Equal Tempered scale is not the only way to divide the octave into semitones, historically hundreds of other systems have been devised. Many of these temperaments are available in software on most modern keyboard instruments and computer music programs, but unfortunately they are seldom used. Many of these are so-called "Well Temperaments", where certain chosen keys are favoured to different degrees. What this means is that intervals in these keys are closer to Just than the strict mathematical approach allows for, at the cost of sacrificing the purity of seldom used keys a little.

As a general rule, the closer to Just certain key signatures are tuned, the fewer playable other keys that are left - unless you are willing to add more intervals to the standard 12 to the octave. In good Well tempered systems all the key signatures are usable, with a good tonal balance between them.

The Equal Tempered scale, as its name implies, is made up of 12 equal intervals, which gives the same balance of intervals in all the key signatures. All the keys therefore sound the same. Well tempered intervals are not regular, and thus each key signature has its own unique blend of intervals. This gives each key its own personality, or "colour" - some sound happy or playful, while others sound sad and serious. These "Key Colours" were regarded as an important part of musical expression before the introduction of the Equal Tempered scale in the mid-1800's swept them away. J.S. Bach, for example, used choice of key signature very effectively to express emotional effects, see Key Colours

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What is the difference between Die Wohltemperirte Gitarre and Thidell Formula 1?
Die Wohltemperirte Gitarre and Thidell Formula 1 are both so-called "Well" temperaments. 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. ( See www.larips.com ) Thidell Formula 1 uses the same approach but is adapted to the unique features of the guitar.

The difference between Die Wohltemperirte Gitarre and Thidell Formula 1 is in the balance between different key signatures.

Major keys in "Wohl" which are closer to Just are F, G, Bb, C, D.

Minor keys: . E, F#, Ab, A, B, D.

Major keys in Thidell F1 which are closer to Just are E, F#, G, A, B, C, D.

Minor keys: E, F#, Ab, A, B, Eb.

The reason for this is that "Wohl" was originally constructed for keyboard instruments, while Formula 1 is exclusively constructed for the guitar.

For a more detailed description of how these temperaments are constructed, see Technical details.

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What happens when True Temperament guitars are used with other guitars, bass, piano etc?
Our 12-Tone Equal Temperament versions tune considerably better against keyboards than "ordinary" guitars. Against other guitars they can highlight the tuning problems which plague "ordinary" guitars - the problems which True Temperament was developed to solve. The effect is seldom disturbing, however, it manifests itself as a sort of "chorusing".

Our Well tempered versions work just fine together with "ordinary" instruments. The offsets from Equal Temper are not so severe that they normally create dissonance. Each Well temperament has its own unique personality which never sounds "wrong", on the contrary they enrich the musical interplay. One could describe them as different dialects of the same musical language.

Meantone Blues is a special case, and is not intended for use with instruments in other temperaments.

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What is Meantone Blues?
Meantone Blues is an adaptation for the guitar of the Meantone Intonation which was in general use from the 14th to the 17th centuries. (W.A. Mozart, for example, wrote his music in Extended Meantone Intonation.) In Meantone the major thirds are Just, and the minor thirds are almost Just. A general rule is that the closer to Just you tune certain key signatures, the fewer the number of other playable keys which remain, if you stick to the standard 12 intervals in the octave. Due to the very close to Just tuning of the thirds, it was necessary to add two extra frets to the Meantone Blues neck, to give for example Just F# major and G# major thirds .

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What about acoustic and bass guitars?
We presently offer fingerboards in the Thidell Formula 1 temperament for both steel-string (wound G) and nylon-string guitars with 650mm scale length. We also have a version for 641mm scale steel-string guitar with a plain (0.018") G (as used by Steve Vai on his Ibanez Euphoria EP9 signature model). We have 34" 4-string electric bass necks available in the Thidell Formula 1 temperament also.

Other versions will be made available according to demand. Contact us for information.

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How does your system compare to the Buzz Feiten Tuning System®?
We feel that, on guitars with traditional straight frets, the Buzz Feiten system offers a genuine and worthwhile improvement in chord consonance over standard intonation. However the improvement is limited, because you can only do so much with one tiny adjustment to the position of the nut and a little stretch tuning – you are trying to calibrate 132 fretted notes (on a 22-fret guitar) with only 7 adjustments (nut position + 6 offsets to the intonation points at the bridge). In common with other systems using nut compensation (either overall compensation, or individual compensation for each string) and “offsets” in the octave intonation, it is a compromise solution, albeit a better compromise than traditional intonation.

True Temperament calibrates each of those 132 fretted notes *individually*. No compromises.

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Can I buy a fretted TT fingerboard to put on my guitar?
Sorry, we do not supply fretted fingerboards. We tried this but it didn't work well. We have found that the only way to ensure optimal results is to fret the fingerboard after it is glued to the neck. Installing and dressing TT frets requires special tools and techniques, so the way we normally work with collaborating luthiers is either a) we supply them with a ready-slotted fingerboard which they install on their own neck, and then send the complete neck back to us for fretting, or b) they send us a complete neck with an unslotted fingerboard. We return the neck with the frets installed, dressed, and polished, ready for assembly to the body.

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Can your True Temperament frets be retrofitted to an existing guitar neck with standard frets?
Yes. But it is a very labour-intensive, and therefore expensive, procedure. There are two ways to do this:

a) Fill in the fret slots and rout new ones

b) Replace the fingerboard entirely.

Option a) is a very fiddly job that always leaves visible traces of the old fret slots. It also plays havoc with the machining. Moreover, the old position markers will not align correctly between the TT fret slots, and will also need to be moved. Not recommended!

Option b) is almost always less problematic and time-consuming than option a), so ends up costing less.

See our Custom Shop page for more details.

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Do you have a version for 7-string guitars/low tuned guitars/baritone guitars?
We now offer a LOW TUNE, standard (25-1/2”) scale version for “fourth down” tuning (B - E - A - D - F# - B). Please see “Guitar & Bass Necks” for details.

We are planning on doing 7-string and baritone (long scale) versions but it may take a while before we get to it, as we have to take things one step at a time.

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Do you sell complete guitars?
Yes, we can do complete instruments. See our Custom Shop page for more information.

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Can I have stainless steel TT frets?
No, sorry. The only practical way to make our frets in bulk is to cast them. Stainless steel does not lend itself to our supplier's casting methods. Our frets are precision cast in silicon bronze, chosen for its durability, low friction, and resistance to corrosion. It has also been certitied nickel-free by the Karolinska Institutet in Stockholm and, so is ideal for guitarists with a nickel allergy. (Stainless steel is *not* nickel-free. 60% of the world’s total nickel production is used in the making of stainless steel.)

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Technical details - Die Wohltemperirte Gitarre / Thidell Formula 1
Die Wohltemperirte Gitarre is adapted for the guitar from Dr. Bradley Lehman's brilliiant reconstruction of the keyboard temperament used by J.S. Bach for Das Wohltemperirte Clavier. Thidell Formula 1 is designed exclusively for the guitar.

Listening to the Wohltemperirte major thirds, we notice that the keys of F, C, and to an extent G, are the most favoured, which gives a tonal balance well adapted to keyboards where major keys are concerned (F major is a barre shape on the guitar, but uses only white keys on the keyboard). We have modified this a little to fit in better with its application on the guitar. Major keys which are more consonant than in equal temperament are F, G, Bb, C, D. Minor keys which are more consonant than in equal temperament are E, F#, Ab, A, B, D.

Formula 1 does not take F as most favoured major key, but keeps the third to A equal tempered. However the F - C fifth interval is Just. The tonal balance here favours the major keys of E, F#, G, A, B, C, D. Minor keys which are more consonant than in equal temperament are E, F#, G#, A, B, Eb.

One thing which is very similar about these temperaments is the open string offsets. (Specified in cents offset from equal temperament.)

Die Wohltemperirte Gitarre:
E A D G B E
-2 0 +2 +3,9 0 -2


Thidell Formula 1:
E A D G B E
-2 0 +2 +4 -1 -1


We see that an octave stretch is built into Formula 1 for the note E. One of the reasons for this is to make a better fifth interval to A.

The general open fourth increase serves to subtly push up the pitch for D and G so that the major third intervals from D - F# and G - B are larger and the minor third interval to E is smaller. This makes for thirds which are closer to Just.

Chromatic analysis, Die Wohltemperirte Gitarre:
E F F# G Ab A Bb B C C# D Eb
-2 +7,8 -1,4 +3,9 +0,2 0 +3,9 0 +5,9 +1,4 +2 +0,6
    (+2)   (+3,9)         (+3,9)   (+3,9)

Figures in brackets are the original Bach/Lehman figures, the upper row is the Lehman temperament as modified for the guitar. F# is lowered to give a good D major. G# is lowered to make E major more consonant. C# is lowered for a better A major. Eb is lowered for a better B major. These are all common guitar keys.

Chromatic analysis, Thidell Formula 1:
E F F# G G# A Bb B C C# D Eb
-2 0 -4 +4 -4 0 -4 -1 +2 -4 +2 -4


Study of this chromatic scale reveals that it has 7 fifth intervals which are purer than their equal tempered equivalents. If we add together the number of major and minor highlights we get 20. The equivalent number of highlights in Wohltemperirte is 15.

The remaining key signatures in both Wohltemperirte and Formula 1 all sound harmonically acceptable to the ear, with varying degrees of tonal colour.

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About Key Colour
"Key colour" is absent in equal temperament . As all its intervals are equal, the blend of intervals is the same in every key, so all keys sound alike. "Key colour" is a feature of temperaments with unequal intervals, like Meantone and Well Temper. Before equal temperament came along in the mid 19th century, "Key Colour" - also known as "Key Character", or, in German, "Affekt" - was a familiar and generally accepted part of musical expression.

"By Beethoven's day, the concept of "Key Character" (in which different keys conveyed specific emotional meanings), was much refined. A widely read and influential list of keys and their affective qualities, written by Christian Friedrich Daniel Schubart and published posthumously in 1806, contained the fashionable descriptions for all major and minor keys." from "Six Degrees Of Tonality - The Well Tempered Piano" by Edward Foote.

AFFECTIVE KEY CHARACTERISTICS
from Christian Schubart's Ideen zu einer Aesthetik der Tonkunst (1806)

C Major
Completely Pure. Its character is: innocence, simplicity, naïvety, children's talk.

C Minor
Declaration of love and at the same time the lament of unhappy love. All languishing, longing, sighing of the love-sick soul lies in this key.

Db Major
A leering key, degenerating into grief and rapture. It cannot laugh, but it can smile; it cannot howl, but it can at least grimace its crying.--Consequently only unusual characters and feelings can be brought out in this key.

C# Minor
Penitential lamentation, intimate conversation with God, the friend and help-meet of life; sighs of disappointed friendship and love lie in its radius.

D Major
The key of triumph, of Hallejuahs, of war-cries, of victory-rejoicing. Thus, the inviting symphonies, the marches, holiday songs and heaven-rejoicing choruses are set in this key.

D Minor
Melancholy womanliness, the spleen and humours brood.

Eb Major
The key of love, of devotion, of intimate conversation with God.

D# Minor
Feelings of the anxiety of the soul's deepest distress, of brooding despair, of blackest depresssion, of the most gloomy condition of the soul. Every fear, every hesitation of the shuddering heart, breathes out of horrible D# minor. If ghosts could speak, their speech would approximate this key.

E Major
Noisy shouts of joy, laughing pleasure and not yet complete, full delight lies in E Major.

E minor
Naïve, womanly innocent declaration of love, lament without grumbling; sighs accompanied by few tears; this key speaks of the imminent hope of resolving in the pure happiness of C major.

F Major
Complaisance & Calm.

F Minor
Deep depression, funereal lament, groans of misery and longing for the grave.

F# Major
Triumph over difficulty, free sigh of relief utered when hurdles are surmounted; echo of a soul which has fiercely struggled and finally conquered lies in all uses of this key.

F# Minor
A gloomy key: it tugs at passion as a dog biting a dress. Resentment and discontent are its language.

G Major
Everything rustic, idyllic and lyrical, every calm and satisfied passion, every tender gratitude for true friendship and faithful love,--in a word every gentle and peaceful emotion of the heart is correctly expressed by this key.

G Minor
Discontent, uneasiness, worry about a failed scheme; bad-tempered gnashing of teeth; in a word: resentment and dislike.

Ab Major
Key of the grave. Death, grave, putrefaction, judgment, eternity lie in its radius.

Ab Minor
Grumbler, heart squeezed until it suffocates; wailing lament, difficult struggle; in a word, the color of this key is everything struggling with difficulty.

A Major
This key includes declarations of innocent love, satisfaction with one's state of affairs; hope of seeing one's beloved again when parting; youthful cheerfulness and trust in God.

A minor
Pious womanliness and tenderness of character.

Bb Major
Cheerful love, clear conscience, hope aspiration for a better world.

Bb minor
A quaint creature, often dressed in the garment of night. It is somewhat surly and very seldom takes on a pleasant countenance. Mocking God and the world; discontented with itself and with everything; preparation for suicide sounds in this key.

B Major
Strongly coloured, announcing wild passions, composed from the most glaring colours. Anger, rage, jealousy, fury, despair and every burden of the heart lies in its sphere.

B Minor
This is as it were the key of patience, of calm awaiting ones's fate and of submission to divine dispensation.

Translated by Rita Steblin in A History of Key Characteristics in the 18th and Early 19th Centuries. UMI Research Press (1983).

Plagiarised from various (acknowledged) sources by Paul Guy

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Meantone Blues™
Put pure thirds in your chords!

This neck may look like something out of the Twilight Zone, but you don’t know how sweet - or how mean! - guitar chords can sound until you’ve heard this temperament.

mean1tone_new.jpg

For the truly adventurous guitarist in search of pure third intervals, we offer Meantone Blues, an adaptation for the guitar of the Meantone Intonation which was in general use from the 14th to the 17th centuries. (W.A. Mozart, for example, wrote his music in Extended Meantone Intonation.)

In Meantone the major thirds are Just, and the minor thirds are almost Just. A general rule is that the closer to Just you tune certain key signatures, the fewer the number of other playable keys which remain, if you stick to the standard 12 intervals in the octave.Due to the very close Just tuning of the thirds, it was necessary to add two extra frets to the Meantone Blues neck, to give for example Just F# major and G# major thirds .

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The extreme appearance of the frets is a result of providing the maximum number of available intervals on the minimum number of frets. Some old church organs tuned in Meantone, with up to 15 intervals in the octave, have been preserved. The "black keys" are split into two in three places in the octave, to increase the number of playable key signatures. "Power chords" with Just thirds sound really heavy on these instruments, just like the Meantone Blues neck.

Try this through your Marshall on 11!
This temperament will change your definition of the term “Power Chord” forever - adding the pure third to the root and 5th adds real power to the sound! Open chords, barre chords, chords way up above the twelfth fret - it’s like a choir singing, or a big string section. Of course there is a hitch. The price you pay for all this beautiful harmony is having to get used to using those two extra frets.

Meantone Blues is not intended for use together with instruments in other temperaments.

How is this temperament tuned?

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How is the Meantone Blues™ temperament tuned?
Any of the three "correct" tuning methods here Tuning methods evaluated can be used to tune the Meantone Blues temperament - just use an A on your tuner, or from another instrument, as your reference note, instead of an E.

Tuning the open strings - except for the A string - to an ordinary chromatic tuner will not work with Meantone Blues, as the open strings are not tuned in equal tempered intervals. But any tuner will work just fine if you tune any A note on each string: 5th or 17th fret on the E strings, open or 12th fret on the A, 7th or 19th fret on the D, 2nd or 14th fret on the G, and 10th or 22nd fret on the B.

Offsets (in cents) for programmable tuners for the open strings are as follows:

E6 A5 D4 G3 B2 E1
-2.6 0 +4.8 +7.2 -4 -2.6


If you are tuning by ear, you should always take an A note as reference when tuning to another instrument. Tip: the 5th fret harmonic on the A string, and the 5th fret note on the high E string, should both be A=440Hz (Or A=442Hz, etc, if that is what your band uses.).

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Tuning methods evaluated
by Paul Guy © 1990 - 2009

There are several popular methods commonly used to tune guitars. Some of them work well, others don't work at all. The following is an evaluation of the most common methods, and of the method that works best for me.

Correct methods
Incorrect methods
Tuning Tips
Unison method (4th/5th fret method) - Correct
The old faithful "4/5" method is perfectly correct in principle, since unison intervals are used. For those readers from Mars who aren't familiar with it, the method is as follows: one string (usually high E) is tuned to a reference frequency ("Oi! Fred! Gimme an E!").
The 5th fret E on the B string is tuned to match the open E,
the 4th fret B on the G string is tuned to match the open B,
the 5th fret G on the D string is tuned to match the open G,
the 5th fret D on the A string is tuned to match the open D,
finally the 5th fret A on the low E string is tuned to match the open A.

If you have tuned accurately the interval between the two E strings will be exactly two octaves - the 5th fret double octave harmonic on the low E should sound at the same pitch as the open high E. The problem with this method is that if you get one string wrong, the following strings will also be out. But if you have a well-adjusted guitar and a good ear, it can work well.

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Octave method - Correct
Any tuning method using octaves is correct in principle. There are many variations - one way is to tune the open B string one octave below the 7th fret B on the high E string, the open G string one octave below the 8th fret G on the B string, the open D string one octave below the 7th fret D on the G string, the open A string one octave below the 7th fret A on the D string, and - you guessed it - the open low E one octave below the 7th fret E on the A string.

But we're back to small errors affecting the following strings again. To avoid this, and because tuning errors become more obvious further up the fingerboard, make your comparisons using only fretted octaves between the 7th and 12th frets, and try tuning in this order:

  • Tune low E two octaves below high E.
  • Compare high E and D - tune D.
  • Compare high E and G - tune G.
  • Compare D and B - tune B.
  • Compare G and A - tune A.


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Recommended methods
If you tune all the strings to the same reference string, you can avoid a small error on one string affecting all the others.

Tune the high E string to a reference: compare
5th fret E on the B string: adjust B
9th fret E on the G string: adjust G
14th fret E on the D string: adjust D
7th fret E on the A string (one octave below); adjust A
5th fret harmonic on the low E string: adjust low E.

I have found this to be the easiest and most reliable way of tuning I have ever used. Since you are listening to the same note all the time, the ear "tunes in" to the overtones and an out-of-tune string sticks out from the rest like a sore thumb. It is also useful for tuning with electronic tuners of doubtful accuracy, as even the cheapest nastiest tuner will (usually) give the same readout for the same input frequency.

Another method which works very well - and which I still use as a cross check on the above (if I feel the need) is as follows:

(Tune high E to a reference:)
Tune 5th fret harmonic on low E to match open high E:
12th fret harmonic on low E / fretted 7th fret E on A string: adjust A
12th fret harmonic on A / fretted 7th fret A on D string; adjust D
12th fret harmonic on D / fretted 7th fret D on the G string;adjust G
12th fret harmonic on G / fretted 8th fret G on B string; adjust B
Check that 12th fret harmonic on B matches fretted 7th fret B on high E.

This method worked well for me - and for many of my customers - for many years. (It is also extremely effective at getting the best available results out of a poorly adjusted instrument.)

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5/7 Harmonics method - Does not work!
This method seems to have a strange attraction for many guitarists. Not least because it's such a convenient method, which leaves the fretting hand free to tune with, many guitarists cling stubbornly to harmonics tuning, despite the recurrent tuning difficulties it causes.

The simple fact is that the method cannot possibly work, as all harmonics are pure intervals, and the frets are placed to give equal tempered intervals. With the exception of the octave and double octave harmonics (octaves are pure in both the pure and the tempered scales) harmonics should not be used for fine-tuning.

The most common harmonics method is the "5/7" where the high E is tuned to a reference, and the 5th fret harmonic on the low E, to the open high E.
The 7th fret harmonic on the A is tuned to the 5th fret harmonic on the low E.
The 7th fret harmonic on the D is tuned to the 5th fret harmonic on the A.
The 7th fret harmonic on the G is tuned to the 5th fret harmonic on the D.
The 5th fret harmonic on the B is tuned to the 7th fret harmonic on the high E.

Many users of this method also delude themselves that the 4th fret harmonic on the G string should sound the same frequency as the 5th fret harmonic on the B string.

A guitar tuned this way will, quite simply, not play in tune. The reason is simple - the 7th fret harmonic on the A string sounds the note E, the fifth . But this is a pure fifth interval (to be pedantic, an octave and a fifth). The tempered fifth is lowered two cents from pure. The resulting open A note will therefore be two cents flatter than the tempered A we want. The interval between the low E and the A strings should be a tempered fourth, which is raised two cents from pure. Since the A string has been tuned two cents flat the E - A interval will be flat by the same amount.

Two cents isn't much but when you tune the D to the A the same way, the D ends up four cents flat. When you get to the G you will be six cents flat. Tuning the 5th fret harmonic on the B string to the (pure fifth) 7th fret harmonic on the high E leaves the open B sharp by two cents. The resulting open G to open B major third interval will be eight cents sharp.

Trying to tune the B string to the G by harmonics will really get you into trouble. The 4th fret harmonic on the G string sounds the major third of G - a B note. But again, this is a pure interval. The tempered third is raised fully 14 cents from pure. Tuning the 5th fret harmonic on the B string to the pure third on the G will leave the B 14 cents flat. Try it and then compare the 4th fret B on the G string to the open B - you'll see what I mean. It should be obvious by now that harmonics - other than octaves - are not to be trusted! They are useful for the initial coarse tuning, however, as the fretting hand is free to tune while both strings are sounding. Just don't try to use them to fine tune.

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Tuning pairs of open string by counting beats - Good luck!
All "by ear" tuning ultimately depends on the use of beats - the tremolo (regular variation in volume) produced by interference effects when two notes are played together - in unison or other intervals - and the interval is not precisely pure. The closer to pure, the slower this tremolo, until it disappears altogether when the interval is pure. The speed of this tremolo is also relative to the interval's absolute pitch - the higher the pitch, the faster the tremolo.

Inexperienced guitarists often try to tune the guitar by tuning for zero beats between pairs of adjacent open strings. For example, they play the open E and A strings together, and tune the interval so that the beats disappear. Next they play the open A and open D together, and so on. The problem with this method is exactly the same as with the harmonics method - i. e. that the intervals are being tuned pure, and the guitar must be tuned to tempered intervals. If the open E and A strings are tuned beat-free, the interval will be two cents too narrow. If the open G and B strings are tuned the same way, the interval will be fourteen cents too narrow. A guitar in exact equal tempered tuning sounds the following beats between pairs of strings:

String 6 5 4 3 2 1
Note E A D G B E
Interval Fourth Fourth Fourth Third Fourth  
Beats 0.3/sec 0.5/sec 0.6/sec 8/sec 1/sec  


It's easy enough to hear when the beats disappear, and to tune the intervals pure. It's much harder to learn to count the beats accurately enough to tune the guitar correctly by them. Most of us will find it much easier to use another method.

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Tuning to a chord - No way!
Tuning one chord so that it sounds perfect just causes all other chords to sound terrible. In tempered tuning all chords are slightly "out", but all by the same small amount. Remember that the tempered scale is a compromise that enables us to play all chords and intervals, in all keys, with the same relative accuracy. It therefore follows that there is not one chord on the guitar that tunes absolutely pure. Thus it is a total waste of time to tune the guitar to a chord and expect it to sound pleasing anywhere else. If you can't swallow these facts, then for your own peace of mind, you're probably better off if you give up the guitar and get a flute or a sax or something instead. With experience, though, you can develop an ear for even tempered tuning.

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Tuning tips
1. Learn to attach the strings to the machine heads properly!

2. Never try to tune down to a note - first tune below the target pitch, then stretch the string, then tune up to the note. (To avoid problems caused by the "play" in 99% of tuning machines.) Make a couple of deep bends (you don't have to actually play the note, just bend it to settle the tension) then fine tune.

3. Before tuning a string that you suspect is out, check it against both adjacent strings! Many guitarists make the mistake of tuning the wrong string! Oftentimes you think your G is sharp when in fact it's the D that's flat, for example. I do sometimes, and when I watch other people tuning, it seems to me that they do too...

4. When tuning a guitar with a vibrato arm, tune the string, give the arm a good shake, stretch the string, give the arm another shake, and fine tune. On the plain strings I also like to bend the string a whole tone a couple of times (somewhere around the middle) before fine-tuning.

5. Listen for the beats!

Those who find it difficult to hear whether an interval is in tune or not have usually just not learned the trick yet. It's like riding a bike, or swimming - once you've got it, it's dead simple. Learning to listen for the beats is the answer. Play the two notes together - say the open low E string and the E on the D string at the second fret - and let them ring.

If they are not precisely in tune you will hear a tremolo (regular variation in volume) produced by interference effects. This is called "beating". Tuning either one of the strings will either a) cause the beats to increase in speed, which means that you are going the wrong way, or b) cause them to slow down and eventually stop altogether when the two notes are perfectly in tune.

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