System for Just Intonation on guitar with standard frets (improved minor thirds version)

[ixlramp]

This thread is related to my earlier thread https://sevenstring.org/threads/jus...al-guitar-by-restringing-and-retuning.335492/
A new thread has been started because the system is now using a superior minor thirds base tuning, and because i am presenting the system in a new simpler, more concise, but also more detailed way.
The earlier thread is verbose and messy, and contains variations of the system, so a new thread is needed to make a fresh start, create a focus on the new base tuning and improved presentation, and avoid confusion.
It is not necessary to read the earlier thread, i actually recommend you avoid the presentations of the system it contains until you understand the presentation in this thread.

I will very soon submit 2 posts in this thread with a document in each.
Then a 3rd post will contain the documents in useful image forms.
I ask forum members to please wait until all 3 posts are posted before adding your own posts, just to keep the presentation unbroken.

One document is for scales with mostly major intervals, the other is for scales with mostly minor intervals.
These 2 documents belong together as a pair, and will often be used together, for the reason explained in the documents.
However, each document is a complete presentation of the system.
At first, i recommend choosing and working through one document.

+14 cents and -14 cents are not the only pitch offsets that can be used, there are 3 more primary offsets that i might present in future, that allow playing the more tonally unusual 'septimal' and 'undecimal' Just Intonation intervals.

 

[ixlramp]

___'Offset Twelves' system for Just Intonation on guitar with standard frets___
___By Ixlramp (Menokefug Sonataris)___
___Document for the -14 cent offset for major intervals___


___Introduction to the system___

I developed this system in 2011.
Every second string has its pitch offset by the same small amount.
Various pitch offsets can be used. Each offset makes a particular set of Just Intonation intervals playable, from which many Just Intonation scales can be formed.
The offset can be easily changed by a slight retuning of the strings.
To make the system playable, a minor thirds tuning is used.

Unlike a conventional Just Intonation guitar with special fretting, a Just Intonation scale can be modulated to any key.
Most examples of standard guitars retuned to Just Intonation are limited. My system functions like a standard instrument with all scale degrees playable in all octaves.


___Tuning of the open strings___

1) Start with all intervals between the open strings being 3 semitones (300 cents), a minor thirds tuning.
A string set with custom gauges is necessary for suitable string tensions.
2) Divide the strings into 2 types: 'Non-offset strings' (N) and 'Offset strings' (O), where N and O strings alternate with each other: NONONO... or ONONON...
3) Flatten the O strings by 14 cents (approximately one sixth of a semitone). Can be done in 2 ways:
A) Use a tuner with a cents graduation on the display, a cents readout, or a cents setting.
B) This method is not easy and might require practice.
Tune by ear a Just Intonation major third interval (3.86 semitones, 386 cents) between a fret on a N string and the next higher fret on the adjacent higher pitch O string.
To tune a Just Intonation interval, listen for the smoothest and purest harmony. Using distortion might help by enhancing the harmony.


___List of playable Just Intonation intervals___

The Just Intonation intervals listed are approximated by this system to within 4 cents.
Half are on the N strings, half are on the O strings.
The root note is always on the N strings.
From these intervals a subset is chosen to create a Just Intonation scale.



___Some playable Just Intonation scales___

Just Intonation Major (R M2 M3 4 5 M6 M7)
Just Intonation Mixolydian (R M2 M3 4 5 M6 p7)
Just Intonation Lydian (R M2 M3 st 5 M6 M7)
Just Intonation Lydian Dominant (R M2 M3 st 5 M6 p7)
Just Intonation Dominant Bebop (R M2 M3 4 5 M6 p7 M7)

Many more combinations of the intervals are possible.
For the major second there is the option of using the slightly flatter S2 instead of the M2.


___Fretboard maps___

These interval maps are used to construct scale maps and find chord shapes.
R can be the tonic of a scale, or the root note of a chord.
R can be positioned on any fret of the N strings.

The interval map shown below shows the positions of the playable Just Intonation intervals relative to a root note 'R'.
25 frets are shown to contain all possible transpositions of the 1 octave length needed to construct a scale map.



The interval map shown above is constructed from the repeating 4 string interval map shown below.
The best way to construct a scale map is to choose a 1 octave length from the 4 string interval map and repeat it horizontally and vertically.



The fundamental repeating element of the interval map is shown below, it repeats vertically and diagonally.
This element clearly shows how to play through a scale across the strings.
This element also clearly shows the chord shapes for chords whose root notes are on the N strings.



___Instant transition to a +14 cent offset___

Without altering the tuning of the open strings, the root note of scales or chords can be placed on the O strings. The O strings become N strings and the N strings become O strings with a +14 cent offset. The document for the +14 cent offset applies.
Therefore modulation to Just Intonation scales with minor intervals is possible.


(c) ixlramp 2022
Licensed under CC BY-SA 4.0

CC BY-SA 4.0 Deed | Attribution-ShareAlike 4.0 International | Creative Commons

creativecommons.org

 

[ixlramp]

___'Offset Twelves' system for Just Intonation on guitar with standard frets___
___By Ixlramp (Menokefug Sonataris)___
___Document for the +14 cent offset for minor intervals___


___Introduction to the system___

I developed this system in 2011.
Every second string has its pitch offset by the same small amount.
Various pitch offsets can be used. Each offset makes a particular set of Just Intonation intervals playable, from which many Just Intonation scales can be formed.
The offset can be easily changed by a slight retuning of the strings.
To make the system playable, a minor thirds tuning is used.

Unlike a conventional Just Intonation guitar with special fretting, a Just Intonation scale can be modulated to any key.
Most examples of standard guitars retuned to Just Intonation are limited. My system functions like a standard instrument with all scale degrees playable in all octaves.


___Tuning of the open strings___

1) Start with all intervals between the open strings being 3 semitones (300 cents), a minor thirds tuning.
A string set with custom gauges is necessary for suitable string tensions.
2) Divide the strings into 2 types: 'Non-offset strings' (N) and 'Offset strings' (O), where N and O strings alternate with each other: NONONO... or ONONON...
3) Sharpen the O strings by 14 cents (approximately one sixth of a semitone). Can be done in 2 ways:
A) Use a tuner with a cents graduation on the display, a cents readout, or a cents setting.
B) This method is not easy and might require practice.
Tune by ear a Just Intonation major third interval (3.86 semitones, 386 cents) between a fret on an O string and the next higher fret on the adjacent higher pitch N string.
To tune a Just Intonation interval, listen for the smoothest and purest harmony. Using distortion might help by enhancing the harmony.


___List of playable Just Intonation intervals___

The Just Intonation intervals listed are approximated by this system to within 4 cents.
Half are on the N strings, half are on the O strings.
The root note is always on the N strings.
From these intervals a subset is chosen to create a Just Intonation scale.



___Some playable Just Intonation scales___

Just Intonation Natural Minor (R M2 m3 4 5 m6 m7)
Just Intonation Phrygian (R m2 m3 4 5 m6 m7)
Just Intonation Locrian (R m2 m3 4 lt m6 m7)
Just Intonation Locrian Natural 2 (R M2 m3 4 lt m6 m7)
Just Intonation Aeolian Sharp 4 (R M2 m3 lt 5 m6 m7)

Many more combinations of the intervals are possible.
For the minor seventh there is the option of using the slightly flatter p7 instead of the m7.


___Fretboard maps___

These interval maps are used to construct scale maps and find chord shapes.
R can be the tonic of a scale, or the root note of a chord.
R can be positioned on any fret of the N strings.

The interval map shown below shows the positions of the playable Just Intonation intervals relative to a root note 'R'.
25 frets are shown to contain all possible transpositions of the 1 octave length needed to construct a scale map.



The interval map shown above is constructed from the repeating 4 string interval map shown below.
The best way to construct a scale map is to choose a 1 octave length from the 4 string interval map and repeat it horizontally and vertically.



The fundamental repeating element of the interval map is shown below, it repeats vertically and diagonally.
This element clearly shows how to play through a scale across the strings.
This element also clearly shows the chord shapes for chords whose root notes are on the N strings.



___Instant transition to a -14 cent offset___

Without altering the tuning of the open strings, the root note of scales or chords can be placed on the O strings. The O strings become N strings and the N strings become O strings with a -14 cent offset. The document for the -14 cent offset applies.
Therefore modulation to Just Intonation scales with major intervals is possible.


(c) ixlramp 2022
Licensed under CC BY-SA 4.0

CC BY-SA 4.0 Deed | Attribution-ShareAlike 4.0 International | Creative Commons

creativecommons.org

 

[ixlramp]

The 2 documents in the previous 2 posts are attached to this post in image form.

___Document for the -14 cent offset for major intervals___



___Document for the +14 cent offset for minor intervals___

 

[ixlramp]

The initial presentation is complete, discussion is now welcome.

 

[Hollowway]

So, I FINALLY understand this. I just reread the old thread, and understood it all. I was on my phone, so I sat down, and searched the thread so I could respond on my laptop, but found this updated thread. A couple of qestions:

1) Since each of these can modulate to the other (i.e. major can modulate to minor by moving the root to the offset strings) does that mean that if you start in the major tuning, and then move the root up to the O string you get those intervals (like the large tritone)? It would seem like that's the case, if I'm understanding it. Because it's just flipping the 14 cents to either + or -.

2) If I'm correct in #1, then the only advantage one has over the other is if you want the lower notes for that particular scale/song/chord, right?

3) In practice, do you think one is better than the other, in terms of every day use? (Assuming an open F as the lowest note.)

 

[ixlramp]

So, I FINALLY understand this.

Ahh ... well done The original thread is a mess and does not present the system particularly well.
I recommend reading the documents in this thread, as they explain the full capabilities of the system (Each offset makes a unique set of 10 intervals playable, the combinations of these intervals result in many scales. It is not just a case of major and minor scales).

1) Since each of these can modulate to the other (i.e. major can modulate to minor by moving the root to the offset strings) does that mean that if you start in the major tuning, and then move the root up to the O string you get those intervals (like the large tritone)?

Yes.
You probably realise this, but to be clear, when you move the root note to the offset strings, the offset strings and non-offset strings swap positions. The non-offset strings are defined as the strings which have the root note ('non-offset' and 'offset' are not defined by which strings are offset from standard A4=440Hz Equal Temperament).

It would seem like that's the case, if I'm understanding it. Because it's just flipping the 14 cents to either + or -.

Exactly.

2) If I'm correct in #1, then the only advantage one has over the other is if you want the lower notes for that particular scale/song/chord, right?

That is one advantage, but there will sometimes be other reasons to choose or change the absolute open tuning of the guitar.

3) In practice, do you think one is better than the other, in terms of every day use?

Which is best for you depends on the requirements of the situation.

Here's a suggestion for choosing the absolute open tuning of the guitar:
1. Choose which strings will be non-offset and which offset, perhaps decided by which intervals you want the lowest notes of the guitar to be.
2. Choose +14 or -14 cents for the offset strings, depending on which scales you are most interested in (see the documents in this thread for which scales result from which offsets).

For beginners, or in the absence of any reason to choose, i suggest making the lowest string non-offset, as this is more intuitive, and the user is perhaps more likely to prefer the lowest notes on the guitar being the Tonic, Major 2nd, 4th, 5th of the scale, such that the lowest chords have their root notes on the Tonic, Major 2nd, 4th, 5th.

 

[Hollowway]

Ahh ... well done The original thread is a mess and does not present the system particularly well.
I recommend reading the documents in this thread, as they explain the full capabilities of the system (Each offset makes a unique set of 10 intervals playable, the combinations of these intervals result in many scales. It is not just a case of major and minor scales).

Yes.
You probably realise this, but to be clear, when you move the root note to the offset strings, the offset strings and non-offset strings swap positions. The non-offset strings are defined as the strings which have the root note ('non-offset' and 'offset' are not defined by which strings are offset from standard A4=440Hz Equal Temperament).

Exactly.

That is one advantage, but there will sometimes be other reasons to choose or change the absolute open tuning of the guitar.

Which is best for you depends on the requirements of the situation.

Here's a suggestion for choosing the absolute open tuning of the guitar:
1. Choose which strings will be non-offset and which offset, perhaps decided by which intervals you want the lowest notes of the guitar to be.
2. Choose +14 or -14 cents for the offset strings, depending on which scales you are most interested in (see the documents in this thread for which scales result from which offsets).

For beginners, or in the absence of any reason to choose, i suggest making the lowest string non-offset, as this is more intuitive, and the user is perhaps more likely to prefer the lowest notes on the guitar being the Tonic, Major 2nd, 4th, 5th of the scale, such that the lowest chords have their root notes on the Tonic, Major 2nd, 4th, 5th.

Ok, cool, thanks for taking the time. The really cool thing here is that I could do this on an 8 string as well, and effectively circumvent the whole idea of wanting to mess with the true temp frets just to hear what it sounds like. I’ve never played in any tuning other than standard and dropped, so the thirds will be interesting, but likely also inspiring, as by definition I won’t be able to fall into a rut playing.

 

[waitati]

I am wondering about the advantages and disadvantages of different tunings to achieve:

1. The most diatonic notes in the first octave
2. the physical closeness (ease of play) of different intervals and chords under a just tuning

It seems that, by design (the closeness of TET12 scale to Just Scale for certain intervals), there will
always be tones close (within 4 cents) to just tones in the TET12 fret scale under many reasonable tunings.
For instance, below I show the 'Close to Just Tones' for a 4ths tuning from standard tuning and
it has quite a number of tones close to just tones. Can we say anything more quantitative about
issue (1) or (2) for particular tunings, or provide other guidance about how to choose a tuning?
Criterium (2) is really about the 'distribution' of the diatonic scale within the fret board. I am
particularly interested, as the example shows, for 6 string guitars where we tune the
open strings to a just frequency. For instance, in the example
E2 = 81.76 Hz, A2 = 109.01 Hz, D3 = 147.16 Hz, G3 = 196.22 Hz, B3 = 245.27 Hz, E4 = 317.03 Hz.

Thanks for any thoughts on this discussion area.

 

[waitati]

The last two frequencies should be:
C4 = 261.63, F4 = 348.83 Hz for
the Just 4ths Tuning and E2 = 81.79.

 

[ixlramp]

@waitati i replied in another thread here https://www.sevenstring.org/threads/general-microtuning-thread.340098/post-5501109
Although your posts are closely related to my system and not offtopic (it is fine for you to post them here), that thread seems a better place for discussion that might follow, because it is not specifically about my system.

 

[ixlramp]

The previous documents i have posted in this thread are very concise, but i have realised that a document is needed that is a slightly more gentle 'introduction' to this system This document will also give me space for discussion of some aspects of the system.
The next post in this thread (which will be posted very soon) will be this introduction document.
People who are new to this system might find it helpful to read the introduction document first.

I am also preparing a document with gauge suggestions for minor thirds tuning, for those who are not confident with designing a custom string set.

 

[ixlramp]

___An introduction to my system for Just Intonation on guitar with standard frets___
___By ixlramp___


~~Short description of my system~~

I created this system in 2011.

A conventional Just Intonation guitar has a fretboard with unusually positioned frets, often including partial width frets.

My system enables the playing of a large variety of Just Intonation scales on a standard guitar with standard frets. This is done by setting up the guitar with a custom string set in a special tuning.

My system is cheap (the cost of a string set), reversible, and it is much easier to obtain than a conventional Just Intonation Guitar.
My system can play a larger variety of Just Intonation scales than a conventional Just Intonation guitar, and has several other advantages.


~~How retuned strings can play Just Intonation scales~~

In Equal Temperament (the standard pitch system), the interval sizes of the Minor scale are:

(1 semitone = 100 cents)

Interval       Interval
name           size
               (cents)

Minor seventh  1000
Minor sixth    800
Fifth          700
Fourth         500
Minor third    300
Major second   200
Unison         0

The interval sizes of the Just Intonation Minor scale are slightly different, often diverging from Equal Temperament by approximately 16 cents (approximately one sixth of a semitone):

Interval       Interval
name           size
               (cents)

Minor seventh  1018
Minor sixth    814
Fifth          702
Fourth         498
Minor third    316
Major second   204
Unison         0

To play the Just Intonation Minor scale, it seems necessary to have a special guitar with frets placed in unusual positions. So how can the Just Intonation Minor scale be played on a guitar with standard frets?

These Just Intonation intervals can be divided into 2 groups:

The first group are all very close to Equal Temperament pitches (to within 4 cents):

Interval       Interval
name           size
               (cents)

Fifth          702
Fourth         498
Major second   204
Unison         0

The second group are all very close to being 14 cents sharp of Equal Temperament pitches (to within 4 cents):

Interval       Interval
name           size
               (cents)

Minor seventh  1018
Minor sixth    814
Minor third    316

If we take a guitar tuned to any Equal Temperament tuning and sharpen some of the strings by 14 cents we can play the first group of intervals on the non-sharpened strings, and play the second group of intervals on the sharpened strings.

Playing the intervals this way might sound awkward. However, i have designed my system to make it surprisingly and reasonably practical and playable.

This way, all the intervals of the Just Intonation Minor scale can be played, and they are all very closely approximated to within 4 cents. 4 cents is a very small tuning error that is not discordant, it only creates a subtle, slow and desirable 'shimmering' effect.

Interval       Interval  Interval size
name           size      on guitar
               (cents)   (cents)

Minor seventh  1018      1014
Minor sixth    814       814
Fifth          702       700
Fourth         498       500
Minor third    316       314
Major second   204       200
Unison         0         0

~~Playing other Just Intonation scales~~

In a similar way to the explanation above, the Just Intonation Major scale can also be played on a guitar with standard frets, this is done by flattening (instead of sharpening) some of the strings by 14 cents.

My system is not limited to playing the Minor and Major Just Intonation scales. The following list is some of the other Just Intonation scales possible:

Mixolydian
Lydian
Lydian Dominant
Dominant Bebop
Phrygian
Locrian
Locrian Natural 2
Aeolian Sharp 4

Also, by retuning some strings by different small amounts (for example -31 cents, +31 cents, +/-50 cents), a much larger variety of Just Intonation scales can be played, including ones with more exotic sounding intervals.
Therefore, my system can play a larger variety of Just Intonation scales than a conventional Just Intonation guitar.

Because some strings of the guitar are only retuned by small amounts (no more than half a semitone), string tensions change only slightly, so strings remain familiar and playable.
Because the total string tension changes only slightly, the setup of the guitar (neck relief, string action, intonation) is not significantly affected.
Therefore, a single guitar can quickly and practically switch between a large variety of Just Intonation scales (and of course, can switch back to Equal Temperament).


~~Alternating retuned strings~~

One design consideration is which strings on the guitar are retuned.
In my system, alternating strings are retuned.
For example on a 6 string guitar this could be either strings 1, 3, 5 or strings 2, 4, 6.
For example on a 7 string guitar this could be either strings 1, 3, 5, 7 or strings 2, 4, 6.

Alternating retuned strings is optimum for 2 reasons:
1. All the Just Intonation scale intervals are playable across the entire range of the instrument.
2. Anywhere on the fretboard there will always be a retuned string and a non-retuned string next to each other, this ensures that all the Just Intonation scale intervals are within close reach.


~~Minor thirds base tuning~~

Another design consideration is which 'base tuning' to use.
The 'base tuning' is the initial Equal Temperament tuning before alternating strings are retuned.
Technically, my system functions with any Equal Temperament base tuning, but some base tunings are much more practical than others.

It is optimum to make the base tuning uniform across the guitar to make the system uniform and therefore simpler.

Understandably it will be tempting to use an 'all-fourths tuning' (for example EADGCF) because a standard string set in standard tuning can be easily retuned to all-fourths by tuning up the high BE strings by a semitone. But this makes the system awkward to play.

By mapping out scales and chords for different base tunings, i have discovered that the optimum base tuning is 'all minor thirds' (3 semitones between adjacent open strings).
With this base tuning, scales and chords map out across the strings in a beautiful and reasonably playable way.
A standard string set cannot be used for a minor thirds tuning, a custom string set is required.

A minor thirds tuning reduces the range of a guitar.
Playing a large variety of Just Intonation scales on a standard guitar in a reasonably playable way is, of course, an impressive achievement. Naturally this must come at some kind of cost, that cost is the reduction of range.
A 6 string guitar will still have a reasonable range. However, to compensate for the reduction in range a guitar with 7, 8 or more strings could be used. Alternatively, two 6 string guitars could be used, one with a higher tuning, the other with a lower tuning.


~~Other stuff~~

* Modulating Just Intonation

A 'conventional' Just Intonation guitar cannot modulate a Just Intonation scale to other keys (for example modulation from C Just Intonation Minor to G Just Intonation Minor). This is a disadvantage of most Just Intonation instruments.
Because my system uses a standard fretboard, modulation of a Just Intonation scale to 12 keys is possible.
Also, by shifting the tonic note to an adjacent string, it is possible to instantly, for example, modulate between Minor and Major keys.

* Playing in Equal Temperament

As well as playing various Just Intonation scales, the guitar can also be quickly and practically retuned back to the Equal Temperament base tuning of minor thirds.
Equal Temperament minor thirds tuning creates interesting new chord possibilities and is optimum for playing keyboard style 'closed position' chords.

* Playing this Just Intonation system in Equal Temperament music

With a guitar retuned to play in Just Intonation, there are ways it can be used in Equal Temperament music, for example when playing with other musicians.
The non-retuned strings are normal Equal Temperament strings. By only playing the non-retuned strings, the guitar effectively has a tritone tuning.

My system makes it possible to play Just Intonation chords which have their root notes on any Equal Temperament pitch. So Just Intonation chords could be added to Equal Temperament music. These chords would have their root notes and fifths in tune with Equal Temperament, but the other pitches (thirds, sixths, sevenths) would have the perfect harmony of Just Intonation.

* Playing quarter-tones

The 'Quarter-tone' or '24EDO' pitch system is the octave divided into 24 equal size intervals, it is the pitches of 12 Tone Equal Temperament (the standard pitch system) plus 12 additional pitches each halfway between the standard pitches.
My system can play the Quarter-tone pitch system by retuning alternate strings up or down by 50 cents. The retuned strings then provide all the quarter-tone-sharp/flat pitches.

* Advantages of standard frets

A conventional Just Intonation guitar has unusually positioned frets and/or partial width frets in different positions on each string. Some frets can be very close together.
Compared to this, standard frets have several advantages:

1. Standard frets are familiar. The player can apply their existing technique and 'fret position memory'.
2. Shapes and patterns are easier to visualise and memorise on the consistent grid of standard frets.
3. There are no frets that are very close together.
4. Standard frets are full width, there are no partial width frets that limit or prevent string bending.

* Stealth Just Intonation

Because my system uses a guitar with standard frets, the guitar looks normal.
This creates interesting possibilities by not visually alerting people to something unusual.


(c) ixlramp 2023
Licensed under CC BY-SA 4.0

CC BY-SA 4.0 Deed | Attribution-ShareAlike 4.0 International | Creative Commons

creativecommons.org

 

[waitati]

Looking forward to the string gauge set recommendations!

 

[ixlramp]

___Suggested gauges for minor thirds tuning___
___By ixlramp___

To use my system for Just Intonation on guitar with standard frets, the first step is to set up a guitar in a minor thirds tuning.

Ideally, an internet tension calculator would be used to design a custom string set. But for those not comfortable doing that, here are some suggested gauges.


~~Suggested gauges~~

Gauge  Tuning example

.008p  G4
.009p  E4   standard high E
.011p  C#4
.013p  A#3
.016p  G3   standard G
.022w  E3
.026w  C#3
.032w  A#2
.038w  G2
.044w  E2   standard low E
.052w  C#2
.062w  A#1  standard low B - 1 semitone
.074w  G1   standard F# + 1 semitone

p = plain steel string
w = wound string

The 'tuning example' is the minor thirds tuning that results in 'medium tension' on a 25.5" scale length.

The minor thirds tuning that results in 'medium tension' depends on scale length as follows:

24"-25.5": The 'tuning example'.
27"      : The 'tuning example' transposed down by 1 semitone.
28.5"    : The 'tuning example' transposed down by 2 semitones.
30"      : The 'tuning example' transposed down by 3 semitones.

In this document 'medium tension' means the approximate tension of a .009-.042 string set tuned to standard tuning EADGBE on a 25.5" scale length.


~~How to use this data~~

From the sequence of suggested gauges the guitarist chooses a sub-sequence according to the number of strings on the guitar and the desired pitch range.

The information above about which tuning results in 'medium tension' is not a list of recommended tunings, this information is used as a guide: Knowing which tuning results in medium tension allows the guitarist to approximately judge which tuning will result in their preferred tension.
For example: 1 or more semitones higher for 'high tension', 1 or more semitones lower for 'low tension'.

Once the guitar is strung up, the guitarist can then experiment, slightly raising or lowering the tuning to choose the tuning with the optimum tension.


~~Relative tensions~~

The relative tensions of the 'suggested gauges' are as follows:
Plain strings having approximately equal tensions.
Wound strings having approximately equal tensions.
Wound strings having slightly more tension than plain strings.

Obviously, these relative tensions will probably not be optimum for the guitarist, these gauges should be considered a starting point for modifications.