Neutral Thirds Tuning for Guitar and Bass

Introduction

Neutral thirds tuning is an alternate tuning for guitar and bass, making it possible to play quartertones on a guitar you already own.

This is the easiest way into microtonality for a guitarist, so grab an instrument and follow this quick and practical guide!

How to tune up

The diagrams below are interactive; click on them to hear the tuning. Tune your instrument to match what you're hearing.

On this page, pitches have been notated with ups and downs:

6-string guitar

String Pitch Frequency
Highest B↑3 254.178Hz
G♯3 207.652Hz
E↑3 169.643Hz
C♯3 138.591Hz
A↑2 113.223Hz
Lowest F♯2 92.499Hz

7-string guitar

String Pitch Frequency
Highest B↑3 254.178Hz
G♯3 207.652Hz
E↑3 169.643Hz
C♯3 138.591Hz
A↑2 113.223Hz
F♯2 92.499Hz
Lowest D↑2 75.567Hz

4-string bass

String Pitch Frequency
Highest E↑2 84.822 Hz
C♯2 69.296 Hz
A↑1 56.612 Hz
Lowest F♯1 46.249 Hz

5-string bass

String Pitch Frequency
Highest E↑2 84.822 Hz
C♯2 69.296 Hz
A↑1 56.612 Hz
F♯1 46.249 Hz
Lowest D↑1 37.784 Hz

A note about string gauges

This tuning is different enough from standard that you may notice a change in string tension. Specifically, the low strings are tuned higher so they may feel more tense, whereas the high strings are tuned lower so they may feel more slack.

Try the standard set of strings first and it might work fine for you. However if you do run into tension issues, you can swap out single strings for other gauges.

Chord and scale charts

This interactive chart explorer shows where various chords and scales can be played on the fretboard.

Note layout

This interactive note finder shows where all 24 pitches can be found on the fretboard.

Listening list

Table of intervals

Name Quartertones Semitones Cents
perfect unison 0 0 0
super unison, subminor 2nd 1 0.5 50
minor 2nd 2 1 100
neutral 2nd 3 1.5 150
major 2nd 4 2 200
supermajor 2nd, subminor 3rd 5 2.5 250
minor 3rd 6 3 300
neutral 3rd 7 3.5 350
major 3rd 8 4 400
supermajor 3rd, sub 4th 9 4.5 450
perfect 4th 10 5 500
super 4th, sub tritone 11 5.5 550
tritone 12 6 600
super tritone, sub 5th 13 6.5 650
perfect 5th 14 7 700
super 5th, subminor 6th 15 7.5 750
minor 6th 16 8 800
neutral 6th 17 8.5 850
major 6th 18 9 900
supermajor 6th, subminor 7th 19 9.5 950
minor 7th 20 10 1000
neutral 7th 21 10.5 1050
major 7th 22 11 1100
supermajor 7th, sub octave 23 11.5 1150
perfect octave 24 12 1200

Theory

Quartertones

The quartertone scale (also known as 24edo) divides the octave into 24 equal sized intervals. This is an exact doubling of the familiar 12-note chromatic scale.

In neutral thirds guitar tuning, the interval between each string becomes 7 quartertones, or 3.5 semitones, also known as a neutral third. This allows a guitar access to all 24 quartertones without any modification to the fretboard or needing to purchase a specialist microtonal guitar. In this system, each string has access to only 12 of the 24 notes. As you alternate through the strings, you alternate through these two sets of 12 notes.

Neutral diatonic system

Neutral diatonic is a tonal system that is particularly well suited to the physical limitations of neutral thirds tuned guitar. The open strings directly correspond to these scales, making them easy to learn and play.

While standard diatonic scales contain 5 wholetones and 2 semitones, neutral diatonic scales contain 3 wholetones and 4 ¾tones.

Each neutral diatonic scale is the average of two standard diatonic scales:

Diatonic modes As step sizes (semitones) Neutral diatonic modes As step sizes (quartertones)
Aeolian + Ionian 2 1 2 2 1 2 2 +
2 2 1 2 2 2 1
Neutral Lydian 4 3 3 4 3 4 3
Locrian + Dorian 1 2 2 1 2 2 2 +
2 1 2 2 2 1 2
Neutral Phrygian 3 3 4 3 4 3 4
Ionian + Phrygian 2 2 1 2 2 2 1 +
1 2 2 2 1 2 2
Neutral Dorian 3 4 3 4 3 4 3
Dorian + Lydian 2 1 2 2 2 1 2 +
2 2 2 1 2 2 1
Neutral Hypolydian 4 3 4 3 4 3 3
Phrygian + Mixolydian 1 2 2 2 1 2 2 +
2 2 1 2 2 1 2
Neutral Hypophrygian 3 4 3 4 3 3 4
Lydian + Aeolian 2 2 2 1 2 2 1 +
2 1 2 2 1 2 2
Neutral Hypodorian 4 3 4 3 3 4 3
Mixolydian + Locrian 2 2 1 2 2 1 2 +
1 2 2 1 2 2 2
Neutral Mixolydian 3 4 3 3 4 3 4

Each step of a neutral diatonic mode can be the root of a root-third-fifth triad. This results in 5 neutral triads, and two variants of diminished triad.

Maqam, Makam and Dastgah modal systems

Maqam, Makam and Dastgah are related modal traditions from the Arabic, Turkish and Persian worlds. While the size of the quartertones vary in practice, neutral thirds tuning provides an accessible entry point for exploring (24edo approximations of) these systems on guitar.

This page's scale explorer displays the pitch content extracted from maqamat but doesn't show you how to use them. If you're exploring these modal systems, don't simply rely on what is displayed on the chart and be sure to get further information from another resource such as Maqam World.

Semaphore scale system

The 9 note variant of semaphore is a powerhouse of subminor and supermajor chords. This scale is built from a sequence wholetones and quartertones. The symmetrical mode is T-q-T-q-T-q-T-q-T.

Harmonically, each of the 9 notes can be the root of two root-third-fifth style triads. The qualities of chord are subminor, supermajor, minor, major and two variants of diminished chord. This scale completely avoids neutral intervals.

Isomorphism

In standard tuning, chord or scale shapes that you learn in one position can't be moved arbitrarily across other strings. This is because standard tuning is not regular, using the intervals P4-P4-P4-M3-P4 between strings. Neutral thirds tuning is regular, using intervals n3-n3-n3-n3-n3, therefore it is isomorphic, meaning that chord or scale shapes you learn can be moved arbitrarily anywhere on the fretboard. This makes it easier to memorise shapes and more intuitive.

Intermodulation and the new power chords

Under distortion, playing two (or more) strings at the same time results in intermodulation. This adds additional frequencies to the signal which are highly dependent on the interval being played.

When an interval is close to a simple frequency ratio, the combination tones align and the resulting sound is clean. This is why intervals like the perfect fourth, perfect fifth and octave work so well under high distortion.

Intervals that are not close to a simple frequency ratio, such as the equal-tempered minor and major thirds, result in a mess of combination tones that make the sound muddy and unstable.

With neutral thirds tuning, you get two new power chords which are easy to play as double stops and work well on the high strings - the subminor third and neutral third. Both sound great as power chords, likely due to how well 24edo approximates the simple ratios of 15/13 and 11/9 respectively.

Disadvantages

While neutral thirds tuning makes some things easier to play (the new intervals) it also makes some things harder to play (major and minor chords among others). You need to work around the limitations.

Each string only has access to 12 of the 24 notes. Techniques such as trills, slides and hammer-ons require fretting a string that's already vibrating, therefore these techniques can't be used on the new 12 intervals, only the original 12.

The range of the guitar is reduced when using neutral thirds tuning. This is the tradeoff for higher melodic density.

Standard tuning
(6 string)
Neutral thirds tuning
(6 string)
Neutral thirds tuning
(7 string)
Highest note E6 B↑5 B↑5
Lowest note E2 F♯2 D↑2
Total range 4 octaves 3 octaves + 5.5 semitones 3 octaves + 9 semitones
Melodic density 12 notes per octave 24 notes per octave 24 notes per octave

Further reading

Beyond neutral thirds

There are yet more alternate tunings that let you play microtones on a standard fretted guitar.

The tunings given below deviate minimally from neutral thirds tuning, for ease of switching back and forth between the microtonal options on this page.

Alternating (near-just) major and minor thirds

Ixlramp suggests a string tuning which alternates (near-just) major and minor thirds.

6-string guitar

7-string guitar

4-string bass

5-string bass

Harmonic series subset

Try using a subset of the harmonic series as an open string tuning, such as 4:5:6:7:9:11:12 for 7 string or 4:6:7:10:11:12 for 6 string.

6-string guitar

7-string guitar

4-string bass

5-string bass

Glossary

cent
1/100th of a semitone.
down (↓)
50 cents flat.
interval
The distance between two pitches.
neutral
The quality of being half way between minor and major.
neutral third
An interval with size 350 cents, exactly half way between a minor third and major third. Two neutral thirds add up to a perfect fifth.
quartertone
An interval with size 50 cents, exactly half of a semitone.
semitone
An interval with size 100 cents. In standard tuning this is the smallest step size of the chromatic scale.
tuning (verb)
The act of setting up an instrument so that it can play desired pitches.
tuning (noun)
A set of desired pitches that an instrument can be tuned to play.
up (↑)
50 cents sharp.