Retune to play quartertone scales. Microtonal beginners guide

[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.

 

[ixlramp]

No problem

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.

 

[chrisrivas1]

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!

 

[101101110110001]

ixlramp, thanks man!

 

[ixlramp]

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

 

[Mr. Big Noodles]

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.

 

[sleightest]

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

 

[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.

 

[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

 

[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.

 

[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

 

[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.

 

[ixlramp]

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

 

[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¢

 

[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).

 

[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

///////

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

///////

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

 

[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.

 

[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.

 

[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).

///////

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.

///////

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

 

[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.