# Retune to play quartertone scales. Microtonal beginners guide



## ixlramp

This tuning allows you to play quartertone scales on a conventionally fretted guitar or bass guitar. The modification is cheap and reversible, only requiring a custom set of single strings. This is 'stealth microtonality', no-one would know by looking at your guitar it is microtonal.

*Introduction to 24EDO*

The quartertone scale is also known as: 24 Equal Divisions of the Octave (24EDO), 24 Equal Temperament (24ET), 24 Tone Equal Temperament (24TET) or just 24 equal. Use of the word 'temperament' is sloppy, the quartertone scale is not necessarily a temperament, so I use 24EDO. 24EDO is a division of the octave into 24 equal steps of pitch, each step being a quartertone = half a semitone = 50 cents. Our standard system of 12 equal temperament is contained within 24EDO. 24EDO is the standard tones plus 12 quartertones, each one added halfway between the standard tones.

When naming the new intervals, super = quartertone sharp, sub = quartertone flat, neutral = halfway between major and minor.

A popular ASCII notation is to use up and down arrows: ^ = quartertone sharp, v = quartertone flat.

Semitones - Interval name - Abbreviation - Notation example

12 ..... Octave .................................................. 8 ...................... C
11.5 .. Supermajor seventh ............................... ^7 ..................... B^
11 ..... Major seventh ........................................ 7 ...................... B
10.5 .. Neutral seventh ..................................... n7 ..................... Bv
10 ..... Minor seventh ....................................... b7 ..................... Bb
9.5 .... Supermajor sixth / Subminor seventh ...... ^6 / vb7 ............. A^ / Bbv
9 ....... Major sixth ............................................ 6 ...................... A
8.5 .... Neutral sixth ......................................... n6 ..................... Av
8 ....... Minor sixth ........................................... b6 ..................... Ab
7.5 .... Superfifth / Subminor sixth ..................... ^5 / vb6 ............ G^ / Abv
7 ....... Fifth ..................................................... 5 ...................... G
6.5 .... Subfifth ................................................ v5 ..................... Gv
6 ....... Augmented fourth / Diminished fifth ........ #4 / b5 .............. F# / Gb
5.5 .... Superfourth ........................................... ^4 ..................... F^
5 ....... Fourth ................................................... 4 ...................... F
4.5 .... Supermajor third / Subfourth ................... ^3 / v4 ............... E^ / Fv
4 ....... Major third ............................................. 3 ...................... E
3.5 .... Neutral third .......................................... n3 ..................... Ev
3 ....... Minor third ............................................ b3 ..................... Eb
2.5 .... Supermajor second / Subminor third ........ ^2 / vb3 ............. D^ / Ebv
2 ....... Major second ........................................ 2 ....................... D
1.5 .... Neutral second ...................................... n2 ..................... Dv
1 ....... Minor second ........................................ b2 ..................... Db
0.5 .... Subminor second .................................. vb2 .................... Dbv
0 ....... Unison .................................................. 1 ....................... C

*Neutral thirds tuning*

The intervals between the open strings are all neutral thirds of 3.5 semitones = half a fifth. Therefore chords and scales can be transposed to any position on the fretboard without changing shape, modulation to any key is possible. Although the pitch range of a guitar is reduced, there are now 24 usable tones per octave, so the total number of pitches actually increases.

Open string tuning
Semitones - Interval

12+5.5 ..... Supereleveth
12+2 ........ Ninth
10.5 ......... Neutral seventh
7 .............. Fifth
3.5 ........... Neutral third
0 .............. Unison

The tuning follows the conventional chord structure of root - third - fifth - seventh - ninth - eleventh. The strings alternate between standard tones and quartertones. Playing the open strings or chords straight across one fret creates neutral versions of the conventional chords: 3 adjacent strings create a neutral triad, where the major or minor third is replaced by a neutral third halfway between at 3.5 semitones. 4 adjacent strings create a neutral seventh, where additionally the major or minor seventh has been replaced by a neutral seventh halfway between at 10.5 semitones. 5 adjacent strings add a ninth to the these chords and 6 adjacent strings add a supereleventh to this neutral ninth chord.

*String gauges and restringing*

I have used the D'Addario tension charts to create a sequence of gauges suitable for this tuning and with a slight, steady fall in tension from lowest to highest string. This tuning reduces the range of the instrument so choose a sequence of gauges that covers the required range. Acoustic guitars have a fixed intonation bridge so you need to use similar gauges to an acoustic set, the closest match is 48 38 30 24w 17p 13p. Using strings thinner than the nut slots is not problematic as long as there is downforce at the nut and the slot floors retain their curvature.

Guitar
74 59 48 38 30 24w 17p 13p 10p 8p

Bass
125 95 75 60 45 35 25w 17p 13p 10p 8p

For example 6 string electric guitar equivalent to a 10-46 set:

10p D^
13p B (standard B)
17p G^
24w E
30 C^
38 A (standard A)

4 string bass equivalent to 40-100 set (FACE tuning)

45 Ev
60 C
75 Av
95 F

Since with these gauge sequences the lowest string is the tightest, restring the lowest string first and tune it up to the highest tension you are comfortable with, this will set the pitch of your tuning. Because the gauges have changed you will need to move the saddles to reset the intonation.

*Tuning the quartertone strings*

Most guitar tuners display pitch from -50 cents to +50 cents. -50 cents = quartertone flat , +50 cents = quartertone sharp. When correctly tuned to the quartertone midway between 2 semitones the display may jump back and forth from the lower semitone +50 cents to the higher semitone -50 cents, as these are the same pitch.

*Scale example 1 n2 n3 ^4 5 n6 n7 8*

This scale introduces all 4 neutral intervals and the superfourth / 11th harmonic.
Scales can be defined as the pattern of a 1 octave run played across the strings. Red circles are the tonics.









To cover the entire fretboard with the scale, first draw the tonics and use them to position copies of the pattern above.








A 2 octave run through the scale on a 9 string guitar, showing how to play across the strings.








2 octave run through the scale playing up the strings. This involves skipping between 2 strings.








A diagonal 3 octave run through the scale on a 6 string guitar.








*Chords*

Red circles are the root tones.

Suspended superfourth chord, sus^4. A fundamental chord combining the
superfourth / 11th harmonic and the fifth / 3rd harmonic.








Neutral triad, n. Precisely midway between a major and a minor triad.








Suspended neutral second chord, susn2








Suspended superfourth neutral seventh chord, sus^4 n7








Suspended superfourth supermajor seventh chord, sus^4 ^7








Suspended superfourth subminor ninth chord, sus^4 vb9








Suspended superfourth neutral ninth chord, sus^4 n9








Neutral seventh chord, n7 . A neutral triad plus a neutral seventh.








Neutral triad supermajor seventh chord, n ^7








Neutral triad subminor ninth chord, n vb9








Neutral triad neutral ninth chord, n n9








Suspended neutral second neutral sixth chord, susn2 n6








Neutral ninth chord, n9. A neutral seventh chord plus a ninth. A ninth can be added to all previous chords.








Neutral ninth suoereleventh chord, n9 ^11. A neutral ninth plus a supereleventh. A supereleventh can be added to all previous chords.


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## ixlramp

*Creating and visualising scales*

Here is the scale pattern master diagram with all 24 tones.








A scale can be defined by the pattern it creates within the black outline, the pattern is a 1 octave run played across the strings. For example ...








To cover the entire fretboard you 'tile' the fretboard with the shape outlined in black. I have added 2 tonics to the master diagram to help position copies of the pattern.

15 tones of 24EDO closely approximate a Just Intonation tonal system constructed from the 3rd and 11th harmonics (no need to understand what that means). The 15 tones contain 7 standard tones plus 8 quartertones.








If you choose your scale from the 15 tones shown the resulting scale will have a tonal consistency.

To narrow the choice further, here are the 11 most consonant tones of the Just Intonation system.








This is a good way to start designing scales and to acclimatise your ears to 24EDO. Choose your scale from the 11 tones shown.


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## failshredder

This is totally badass. You have any videos/recordings made with this? I'd love to see, and would be _really_ tempted to try it.


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## SirMyghin

That is a really cool idea and some great work you did there dude.


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## ixlramp

Thanks guys.



failshredder said:


> You have any videos/recordings made with this? I'd love to see, and would be _really_ tempted to try it.



Not yet. But then, listening to a clip is nothing like trying it for yourself


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## ixlramp

*Just Intonation*

I'll now quickly describe the ability of the 24EDO neutral thirds tuning to be slightly retuned to play Just Intonation (JI) scales. It's not essential to understand this additional theory as it is independent from the theory above.

This is the JI major scale on a 7 string guitar. Intervals between the strings are alternating JI major and minor thirds (to within 2 cents).








Moving the tonic to strings 2, 4 or 6 results in JI minor scales. Here the tonic has moved to the major third of the scale above.








So with this open string tuning it is possible to modulate between 12 JI major and 12 JI minor keys, within certain limitations.

Retuning the intervals between the strings to alternating 267 cents and 433 cents, septimal JI scales can be played (that include the subminor third and subminor seventh / 7th harmonic, 'blue notes' of jazz and blues). The strings never need to be retuned by more than a semitone either way to play different JI tonal systems. It's possible to tune the JI intervals using harmonics, so a special microtonal tuner is still not needed.

*Tuning by harmonics*

The root, fifth, ninth etc. strings are tuned normally using a guitar tuner or by tuning to the 7th fret. The strings inbetween, above each of those by JI thirds, are tuned using harmonics:

JI major third, 386c. Tune the 4th harmonic of the higher string to the 5th harmonic of the lower (frequencies in ratio 5:4).
JI minor third 316c. Tune the 5th harmonic of the higher string to the 6th harmonic of the lower (frequencies in ratio 6:5).

Septimal JI subminor third, 267c. Tune the 6th harmonic of the higher string to the 7th harmonic of the lower (frequencies in ratio 7:6).
Septimal JI supermajor third, 435c. Tune the 7th harmonic of the higher string to the 9th harmonic of the lower (frequencies in ratio 9:7).

*Possible JI modes*

Tuning 386c-314c-386c-314c or 384c-316c-384c-316c.
Ionian (major) 1 2 3 4 5 6 7 modulatable to Mixolydian 1 2 3 4 5 6 b7.

Tuning 316c-384c-316c-384c or 314c-386c-314c-386c.
Phrygian 1 b2 b3 4 5 b6 b7 modulatable to Aeolian (nat. minor) 1 2 b3 4 5 b6 b7.


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## Waelstrum

That is same mad stuff! That 24 EDO tuning would work great with one of Rondo's new nine string guitars. If I did that (in a fantasy world where rent and food is free) I'd probably tune A1 C#v2 E2 G#v2 B2 D#v3 F#3 A#v3 C#4. The thing I like about that 24 EDO tuning is that if you don't want to use the micro tones, you can just play it like a fifths tuned five string (if you're good at string skipping). I also like how the shape for a major second in fourths tuning gets you an subminor second, and using that you can get a really cool M.A.N style 24EDO chromatic style lick going.

Also, that just intonation tuning is inspired! It does lock you into only using the one shape for each scale, but I bet it sounds amazing. I do like the way that the major and natural minor scales use the same shape, though. Should make for some easy blues wanking. I am curious as to which string that you'd put the major 6 and 7 on for melodic minor. Would it be one fret up from the b6 and b7, or would you move one or both of them to the same string as the root note?


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## ixlramp

Waelstrum said:


> The thing I like about that 24 EDO tuning is that if you don't want to use the micro tones, you can just play it like a fifths tuned five string (if you're good at string skipping).


Also, the strings can be easily retuned to standard 12ET alternating major and minor thirds. A retuning of only 50 cents on every other string that shouldn't alter the tension on the neck much. So 12ET, 24EDO, JI and septimal JI are all playable with no more than a semitone of retuning.



Waelstrum said:


> I am curious as to which string that you'd put the major 6 and 7 on for melodic minor. Would it be one fret up from the b6 and b7, or would you move one or both of them to the same string as the root note?


Unfortunately JI melodic minor is not possible since the 6th and 7th change on ascent and descent. I guess you could make do with the out of tune 12ET major 6th and 7th if you're not a purist like me.


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## ixlramp

On the subject of M.A.N., in case anyone hasn't seen this yet, some 24EDO metal ...



It can sound sick, it can also sound exotic in a sultry Arabic way.


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## ElRay

ixlramp said:


> It can sound sick, it can also sound exotic in a sultry Arabic way.


IIRC, Greg Ginn from Black Flag used 1/4 tone (sharp) runs in "Damaged II" and "Police Story". I don't recall if they were bends or re-tuning.

Ray


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## BigPhi84

Whoa, this is very cool, although the graphics in the OP made me feel like I was playing a game of Othello.   The best strategy is to always try to get the corners! 

Thanks for sharing! I might try this some day with my beater guitar.


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## Tomo009

I REALLY have to try this out, looks awesome. The pattern looks basic enough as well so hopefully not too overwhelming.


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## ixlramp

*ERGs in the 24EDO neutral thirds tuning*

Open string tuning
Semitones - Interval

36+2.5 ..... 3 octave plus supermajor second
24+11 ...... 2 octaves plus major seventh
24+7.5 ..... 2 octaves plus super fifth
24+4 ........ 2 octaves plus major third
24+0.5 ..... 2 octaves plus subminor second .................. (8 strings)
12+9 ........ Major thirteenth or octave plus major sixth
12+5.5 ..... Super eleventh or octave plus super fourth
12+2 ........ Major ninth or octave plus major second
10.5 ......... Neutral seventh
7 .............. Fifth
3.5 ........... Neutral third
0 .............. Unison

So 8 strings are needed for the same range as a 6 string in standard tuning. This tuning would be perfect for 25.5" 8 string guitars like the ESP LTD SC-208.


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## Hemi-Powered Drone

I'm sorry if I seem like a noob, but can you put what the actual tuning is? I'm not sure if I'm getting it, but are you saying to tune the standard E string to A? Wouldn't you need a large string to tune that on 25.5"?


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## Hollowway

I don't know WTH you've got written there but I thanked the crap out of your post. You're like one part musician and two parts Beautiful Mind guy. You and Schecterwhore need to stay in different areas of the globe or the whole universe might collapse on itself!


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## Behaving_badly

WOW

thats all I can say, Ive been really interested in micro tonal music ever sense I began listening to little bits and pieces of eastern music


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## ixlramp

Thanks guys for the positive comments.


dragonblade629 said:


> I'm sorry if I seem like a noob, but can you put what the actual tuning is? I'm not sure if I'm getting it, but are you saying to tune the standard E string to A? Wouldn't you need a large string to tune that on 25.5"?


Hi, no problem. Actual tuning in terms of the notes each string is tuned to? The actual tuning depends on the number of strings, the range you choose to cover and your preferred tension.
I also posted this example tuning:

10p D^ ............................. E - 1.5 semitones
13p B (standard high B) ..... B
17p G^ ............................. G + 0.5
24w E .............................. D + 2
30 C^ ............................... A + 3.5
38 A (standard A) .............. E + 5

The low E is tuned up to standard A, not down. With the top E detuned to D quartersharp.
That tuning may not be low enough for many so here's a tuning starting 1 string lower:

13p Bv (quartertone below standard High B) ..... E - 5.5
17p G ........................................................... B - 4
24w Ev ......................................................... G - 3.5
30 C ............................................................. D - 2
38 Av ........................................................... A - 0.5
48 F (semitone above low E) ........................... E + 1

These are the recommended gauges for an acoustic.


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## ixlramp

A disadvantage of neutral thirds tuning is the reduction of range, this has been bothering me especially since i'm used to fifths tuning.

So here's the superfourth tuning that slightly extends the range of a fourths-based tuning. The interval between open strings is 5.5 semitones, close to the 11th harmonic at 5.51 semitones, therefore a standard string set can be retuned, extending the range of a 6 string by 3.5 semitones. However since this creates a light-bottom-heavy-top tension i recommend the gauges shown below. These have been chosen using D'Addario's unit weight values (http://www.daddario.com/upload/tension_chart_13934.pdf) to create a progressive fall in tension from low to high strings that is as gentle as possible. The bass gauges are constrained by gauges that step by .005, therefore having a steeper fall in tension.

The larger interval makes step by step runs through scales more awkward to play, involving string skipping and some large jumps, 2 handed tapping really helps with this.

Every other string can be tuned using the frets or a guitar tuner. It's then possible to tune the quartertone strings inbetween using harmonics. Tune the 8th harmonic of the higher to the 11th harmonic of the lower.

Superfourth quartertone tuning
open string tuning
semitones ..... interval

36+2.5 ..... supermajor second / subminor third
24+9 ........ major sixth
24+3.5 ..... neutral third
12+10 ...... minor seventh
12+4.5 ..... supermajor third / subfourth
11 ............ major seventh
5.5 ........... superfourth
0 .............. unison

Guitar
95 66 48 34 24w 16p 11p 8p

Bass
125 85 60 40 25w 16p 11p 8p


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## Infinite Recursion

If this uses quarter tones, do you still have the same full range of traditional 12EDO intervals or are they gone?


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## ixlramp

Infinite Recursion said:


> If this uses quarter tones, do you still have the same full range of traditional 12EDO intervals or are they gone?


I hope i understand your question correctly 
You can still play all the 12EDO intervals but also the 12 additional quartertone intervals that lie midway between the 12EDO intervals. The quartertone scale (24EDO) contains 12EDO.
So you now have 24 intervals per octave:

Semitones - Interval name - Abbreviation - Notation example

12 ..... Octave .................................................. 8 ...................... C
11.5 .. Supermajor seventh ............................... ^7 ..................... B^
11 ..... Major seventh ........................................ 7 ...................... B
10.5 .. Neutral seventh ..................................... n7 ..................... Bv
10 ..... Minor seventh ....................................... b7 ..................... Bb
9.5 .... Supermajor sixth / Subminor seventh ...... ^6 / vb7 ............. A^ / Bbv
9 ....... Major sixth ............................................ 6 ...................... A
8.5 .... Neutral sixth ......................................... n6 ..................... Av
8 ....... Minor sixth ........................................... b6 ..................... Ab
7.5 .... Superfifth / Subminor sixth ..................... ^5 / vb6 ............ G^ / Abv
7 ....... Fifth .................................................. ... 5 ...................... G
6.5 .... Subfifth ................................................ v5 ..................... Gv
6 ....... Augmented fourth / Diminished fifth ........ #4 / b5 .............. F# / Gb
5.5 .... Superfourth ........................................... ^4 ..................... F^
5 ....... Fourth .................................................. . 4 ...................... F
4.5 .... Supermajor third / Subfourth ................... ^3 / v4 ............... E^ / Fv
4 ....... Major third ............................................. 3 ...................... E
3.5 .... Neutral third .......................................... n3 ..................... Ev
3 ....... Minor third ............................................ b3 ..................... Eb
2.5 .... Supermajor second / Subminor third ........ ^2 / vb3 ............. D^ / Ebv
2 ....... Major second ........................................ 2 ....................... D
1.5 .... Neutral second ...................................... n2 ..................... Dv
1 ....... Minor second ........................................ b2 ..................... Db
0.5 .... Subminor second .................................. vb2 .................... Dbv
0 ....... Unison .................................................. 1 ....................... C


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## chrisrivas1

stupid question here

so this just gives us access to the microtones and the guitar does not have 24 frets per octave? im confusing myself and this is the only thing that makes sense. for some reason i thought that one would have to divide each fret in two for microtones. 

does my question make sense? and thanks.


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## ixlramp

No problem 


chrisrivas1 said:


> so this just gives us access to the microtones and the guitar does not have 24 frets per octave?


Correct. These tunings are for standard guitars or basses with 12 frets per octave.

Essentially strings 1 3 5 7 9 etc. provide the normal notes and the strings between provide the quartertones. It's a little awkward to play melodically but if one accepts it's limitations and works with them it's certainly usable. When i discovered microtonal music 3 years ago i was desperate to play a microtonal guitar, so i thought up this tuning and restrung my 6 string fretted bass. I'm sharing the theory because i want everyone to have the chance to experience playing microtones without committing to an expensive refretting of their guitar. I consider PITCH to be the forgotten, obvious and massive musical revolution waiting to happen, for 250 years now we've been using the same 12 equally-spaced frequencies.


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## chrisrivas1

ixlramp said:


> No problem
> 
> Correct. These tunings are for standard guitars or basses with 12 frets per octave.
> 
> Essentially strings 1 3 5 7 9 etc. provide the normal notes and the strings between provide the quartertones. It's a little awkward to play melodically but if one accepts it's limitations and works with them it's certainly usable. When i discovered microtonal music 3 years ago i was desperate to play a microtonal guitar, so i thought up this tuning and restrung my 6 string fretted bass. I'm sharing the theory because i want everyone to have the chance to experience playing microtones without committing to an expensive refretting of their guitar. I consider PITCH to be the forgotten, obvious and massive musical revolution waiting to happen, for 250 years now we've been using the same 12 equally-spaced frequencies.



very well put, indian pitch and rhythm (tablas master zakir hussain) are vastly superior to western music. thanks so much for sharing your knowledge!


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## 101101110110001

ixlramp, thanks man!


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## ixlramp

The first 2 posts in this thread are available as a pdf (attached below) in case anyone wants to print out the diagrams.


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## Mr. Big Noodles

chrisrivas1 said:


> very well put, indian pitch and rhythm (tablas master zakir hussain) are *vastly superior* to western music. thanks so much for sharing your knowledge!



There's no way that this could be construed as personal opinion, and it's perfectly reasonable that the two musics would be compared in such a way.


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## sleightest

ixlramp said:


> On the subject of M.A.N., in case anyone hasn't seen this yet, some 24EDO metal ...
> 
> 
> 
> It can sound sick, it can also sound exotic in a sultry Arabic way.




Dam that was sick ive never heard of them before lead vocalist reminds me of Phil Anselmo


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## ixlramp

24EDO bass and some microtonal riffs from the album.

See this thread http://www.sevenstring.org/forum/general-music-discussion/202859-microtonal-metal.html and search my posts for more microtonal stuff.


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## ixlramp

i discovered this video by goodcyrus, who has developed the same all-neutral third tuning for playing quartertone music on a standard guitar.
https://www.youtube.com/watch?v=E1FTC1VMXfM


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## ixlramp

Update with a better set of suggested gauges for this 'all neutral thirds' tuning.
Select a suitable sequence from these according to number of strings and desired pitch range.

The open string pitches are a suggestion that results in similar tension to the common standard 9-42 set.

Calculated for D'Addario guitar plain steel and nickel roundwound strings but will be approximately correct for any string brand.

The .085 G is marked '??' as it does not exist as a D'Addario guitar string.

A PL007
F#v PL0085 or PL009
D PL0105 or PL011
Bv PL013
G PL016
Ev NW022
C NW028
Av NW036
F NW046
Dv NW056
Bb NW070
Gv ??085

A suggested tuning for 6 string is 'F Av C Ev G Bv' roughly covering the range EADGB of standard tuning.
'v' after a note means 'quartertone flat'.

This sequence of gauges is also usable for the 'alternating Just Intonation major and minor thirds' system briefly mentioned earlier in the thread.
It is also usable for alternating 12ET major and minor thirds.


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## The Omega Cluster

This is cool. I was never fond of tuning semitone instruments in quartertones because I think it's less reliably-well tuned (that might only be an issue for my chromatic tuner) and the weird fingerings you get by having quartertones only on every other string. This is a nice thread though, makes me want to try again.

By the way, M.A.N. is awful (subjective opinion, I know), but their use of quartertones is totally just as passing tones (that's slightly more objective).

Alternative tunings like that could also help for playing sixth-tones, by tuning every second string 33.3¢ off, and every third 66.7¢ off. That only exacerbates the problem of finding the sixth-tones on three strings instead of two with quartertones.

Other tunings are possible, too. If you enter your ¢ offset (x) in this formula you can know how many strings (s) you'd need to have all tones of a theoretical tuning system.

s = 100/x

Examples

100/50¢ = 2 (with 2 strings you can play 50¢ increments by tuning alternatively)

100/(33.3) = ~ 3 (to play sixth-tones)

Alternatively, you can calculate how many ¢ is the offset you need by doing a ratio of the semitone fraction you want.

If you want sixth-tones, that's 2/6, or three microsteps in one semitone (1/3), times 100¢ (the gap of a semitone) = 33.3¢

If I'd want a 26-tone tuning with a normal 12-tone guitar, I'd need to tune my strings with 100(12/16) or 46.16¢ offset. And on top of that only my octave and tritone frets would be useable in the 26-tone tuning and I'd need 13 strings to have all microtones


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## ixlramp

I agree about M.A.N., i never much liked the music, 6 years ago i was just happy to see a somewhat popular metal band using microtones.

Although this thread is mostly about quartertones i am actually more interested in the ability of this thirds tuning to provide fairly precise Just Intonation scales (to within 4 cents), and being able to switch between classic 5-limit JI and 7-limit JI (blues/jazz intervals with 7/6 third and 7/4 seventh) just by retuning a few strings.
Because this is on a 12ET fretted guitar these JI scales are actually modulatable to a certain degree, which is very difficult to do on a guitar with JI fretting.

I'm planning to start a new thread about the JI abilities, as it was only briefly covered here.
Here's a preview of a JI major scale on 7 strings, the numbers on the left are the intervals between the open strings stated in cents.


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## ixlramp

Tuning a quartertone should be quite accurate with most tuners, retune until the tuner is constantly switching between 2 adjacent chromatic notes.


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## The Omega Cluster

I found that if you put your tuner at 449Hz and tune it up with a 15¢ tuning offset, you're within 0.05¢ of your goal.

That's the closest I was able to get mathematically within the options of my tuner. I don't like the idea of tuning when the tuner is constantly switching between two notes, I find this unreliable. I'll list some alternatives too:

To tune to A-half-sharp:

Concert pitch | Chromatic note | Tuning offset | Error margin

449 Hz | A | +15¢ | 0.05¢
439 Hz | A-sharp | -46¢ | 0.06¢
450 Hz | A | +11¢ | 0.09¢
438 Hz | A-sharp | -42¢ | 0.11¢
429 Hz | A-sharp | -6¢ | 0.17¢


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## ixlramp

Yes i guess it could potentially be unreliable depending on the tuner.

A way without needing a tuner is to use 2 strings that are tuned roughly 5-6 semitones apart, and tune the 8th harmonic of the higher string to the 11th harmonic of the lower (not easy), the interval will then be 551 cents (11th harmonic).


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## ixlramp

In this post i will describe the easiest and cheapest way to restring a 6 string guitar to a neutral thirds tuning.
(The same set of gauges is actually also optimum for alternating major and minor Just Intonation thirds).

Starting with a EADGBE string set, 4 strings from such a set can be used, plus 2 single strings, to retune to 12 Tone Equal Temperament (12TET) FACEGB (stated low to high).
FACEGB is alternating major and minor thirds, the intervals in semitones (stated low to high) are 4 3 4 3 4. This is very close to the neutral thirds tuning 3.5 3.5 3.5 3.5 3.5.

It is helpful to first tune to 12TET FACEGB tuning using a normal guitar tuner, then detune the A E B strings by quartertones to acheive neutral thirds F Av C Ev G Bv.
To detune by a quartertone (50 cents), detune the string until the tuner can't decide and is constantly switching back and forth between the pitch and the semitone below.
Or if your tuner shows deviations in cents it is more accurate to tune to -50 cents or to the semitone below +50 cents.

FACEGB is easy to remember, think "FACE Great Britain", i am in the UK so you are facing me as you learn this =)
(a 7 string extension of the tuning is DFACEGB heh).

Going from EADGBE to FACEGB:

The low E is tuned up to F, which works well because the low E is under-tensioned in traditional sets.
The top E is removed.
G and B are moved over by 1 string.
D is replaced with 2 new strings tuned to C and E, these are the 2 single strings you need to add.
9-42 set: Add 2 wound single strings .026 and .021 (or if a .021 is not available, a .022).
10-46 set: Add 2 wound single strings .028 and .022.

Details are below. I used the D'Addario String Tension Pro website to calculate tensions and choose the single string gauges.

///////////////////////////////////////////////////////

pitch / gauge / tension (lbf) / notes

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Standard tuning

9-42

E 9 13.1 remove
B 11 11.0
G 16p 14.7
D 24w 15.7 replace with C, E strings
A 32 15.5
E 42 14.4 tune to F

Alternating major and minor thirds
or neutral thirds

B 11 11.0
G 16p 14.7
E 21w 15.1 (or 22w 16.7)
C 26 14.6
A 32 15.5
F 42 16.1

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Standard tuning

10-46

E 10 16.2 remove
B 13 15.4
G 17p 16.6
D 26w 18.4 replace with C, E strings
A 36 19.0
E 46 16.9 tune to F

Alternating major and minor thirds
or neutral thirds

B 13 15.4
G 17p 16.6
E 22w 16.7
C 28 16.8
A 36 19.0
F 46 19.0


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## bostjan

Nifty. This could be a nice first step, then anyone who likes the effect could graduate to those adhesieve frets marketed by Tolgahan.

I just did a quick glance at the heavier bands and artists doing micro stuff, and the majority are 24-EDO, with 17-EDO making up most of the rest. I guess it should be no surprise.


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## ixlramp

Well meh i'm not impressed by Tolgahan's stick-on fret idea, as they have to be identical height to the frets on your guitar to be functional, but aren't, he has one height only.


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## ixlramp

The fretboard diagrams are now missing from the early posts in this thread, so i'm reposting some.
The horizontal lines are strings, the vertical lines are frets.
The red circles (for those colourblind, the empty circles) show the 'tonic' note of the scale.
The black circles show the other intervals of the scale and contain symbols.

The '12 Tone Equal Temperament' (12TET) intervals use conventional symbols:
2 = major second, 2 semitones.
4 = fourth, 5 semitones.
5 = fifth, 7 semitones.
b7 = minor seventh, 10 semitones.

The quartertone intervals use the following symbols:
n2 = neutral second, 1.5 semitones.
n3 = neutral third, 3.5 semitones.
^4 = superfourth, 5.5 semitones, the 11th harmonic of the tonic.
n6 = neutral sixth, 8.5 semitones.
n7 = neutral seventh, 10.5 semitones.

The 5 quartertone intervals listed above are the most consonant quartertone intervals so are a good place to start when choosing quartertone intervals to use in a scale.
(They are actually almost perfectly tuned 'Just Intonation' intervals, so although they sound unfamiliar they are very 'in tune', much more so than the thirds and sixths of 12TET).

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The 3 diagrams below show how to play through 1 octave of a few quartertone scales by playing across the neck.










Due to the intervals between the open strings being 3.5 semitones, the strings alternate between strings providing 12TET notes, and strings providing quartertone notes.

It is clear how 3.5 semitones is helpful in how it positions the intervals of a scale:
The fifth is very often present in a scale and is present 2 strings up on the same fret.
The octave is of course present in a scale and is present 4 strings up and 2 frets down.
(So root-fifth and root-octave chords are easily playable.)

Intervals can be moved between the 12TET strings and quartertone strings to create various scales.
For example those 3 diagrams show:
A major second becoming a neutral second.
A fourth becoming a superfourth.
A minor seventh becoming a neutral seventh.

The small intervals between the open strings help to keep the patterns fairly compact for any possible quartertone scale.
The alternative open string intervals are 2.5 or 4.5 semitones, the first would reduce the pitch range of the guitar too much, the second would make scale patterns cover too many frets.

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The 2 diagrams below take the 3rd scale from above and show:
An example of how to play it diagonally across the full range of a 6 string guitar.
How to play it up and down the neck using the minimum of 2 strings.









//////

Here is a diagram showing the positions of all 24 intervals relative to the tonic notes.
They are present within a 7 fret length of the fretboard.




Semitones ... Interval name ... Symbol

12 ..... Octave .................................................. 8
11.5 .. Supermajor seventh ............................... ^7
11 ..... Major seventh ........................................ 7
10.5 .. Neutral seventh ..................................... n7
10 ..... Minor seventh ....................................... b7
9.5 .... Supermajor sixth / Subminor seventh ...... ^6 / vb7
9 ....... Major sixth ............................................ 6
8.5 .... Neutral sixth ......................................... n6
8 ....... Minor sixth ........................................... b6
7.5 .... Superfifth / Subminor sixth ..................... ^5 / vb6
7 ....... Fifth ..................................................... 5
6.5 .... Subfifth ................................................ v5
6 ....... Augmented fourth / Diminished fifth ........ #4 / b5
5.5 .... Superfourth ........................................... ^4
5 ....... Fourth ................................................... 4
4.5 .... Supermajor third / Subfourth ................... ^3 / v4
4 ....... Major third ............................................. 3
3.5 .... Neutral third .......................................... n3
3 ....... Minor third ............................................ b3
2.5 .... Supermajor second / Subminor third ........ ^2 / vb3
2 ....... Major second ........................................ 2
1.5 .... Neutral second ...................................... n2
1 ....... Minor second ........................................ b2
0.5 .... Subminor second .................................. vb2
0 ....... Unison .................................................. 1


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## ixlramp

I love playing my guitars at home for my own enjoyment, but i do not consider myself much of a musician and rarely record. So i have been waiting for someone to use this system.

Finally it has happened, and microtonal metal too.
https://traumatriad.bandcamp.com/album/visceral-defects
The tuning system is not made clear on that page, but was explained by the artist in a facebook post.
The album comes with a document explaining the tuning system, and even guitar tablature.

I am impressed, and this shows how usable this system is, despite the unusual use of patterns on the fretboard.
Some of the quartertone-containing chords are surprisingly consonant ... weird but oddly consonant ... which is due to how some intervals of the quartertone system are extremely close to being perfect harmonies (Just Intonation). It is good to hear how these behave with distortion.


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