Retune to play quartertone scales. Microtonal beginners guide

ixlramp

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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.

neutralsuperfourthscalepatterntext.gif




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

neutralsuperfourthscaletextflat.gif




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

2octaverun9string.gif




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

runup2stringsarrows-1.gif




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

fretboard3octaverunarrows.gif




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.

sussuperfourth.gif




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

neutraltriad.gif




Suspended neutral second chord, susn2

suspendedneutralsecondchord.gif




Suspended superfourth neutral seventh chord, sus^4 n7

sussuperfourthneutralseventhchord.gif




Suspended superfourth supermajor seventh chord, sus^4 ^7

sussuperfourthsupermajorseventhchord.gif




Suspended superfourth subminor ninth chord, sus^4 vb9

sussuperfourthplussubminorninthchord.gif




Suspended superfourth neutral ninth chord, sus^4 n9

sussuperfourthplusneutralninthchord.gif




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

neutralseventhchord.gif




Neutral triad supermajor seventh chord, n ^7

neutralsupermajorseventhchord.gif




Neutral triad subminor ninth chord, n vb9

neutralplussubminorninthchord.gif




Neutral triad neutral ninth chord, n n9

neutralplusneutralninthchord.gif




Suspended neutral second neutral sixth chord, susn2 n6

suspendedneutralsecondneutralsixthchord.gif




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

neutralninthchord.gif




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

neutralninthsupereleventhchord.gif
 

ixlramp

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Creating and visualising scales

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

scalepatternmasterwide.gif




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 ...

scalepatterntilingex.gif




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.

scalepatternmaster78.gif




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.

scalepatternmaster56.gif




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

failshredder

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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.
 

ixlramp

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Thanks guys.

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 ;)
 

ixlramp

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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).

universaloctave7string386c314cmajor.gif




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.

universaloctave7string386c314cminor.gif




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.
 

Waelstrum

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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?
 

ixlramp

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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.

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.
 

ixlramp

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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.
 

ElRay

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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
 

BigPhi84

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

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

ixlramp

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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.
 

Hemi-Powered Drone

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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"?
 

Hollowway

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:bowdown: 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!
 

Behaving_badly

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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
 

ixlramp

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Thanks guys for the positive comments.
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.
 

ixlramp

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

ixlramp

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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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