How to retune a conventionally fretted guitar to play 24EDO (pdf document)

When I discovered microtonality in 2008 I was very keen to play a microtonal instrument. At the time my only instrument was a conventionally fretted 6 string bass guitar, so I thought up a slightly awkward 'double chromatic' tuning that allowed me to play the quartertone scale and a few simple Just Intonation scales. Some of you have seen my 'bichromatic tuning' thread on the Not Only Music forum.

Recently I improved the tuning to 'double chromatic thirds' and have been surprised by how usable the tuning is. When the intervals between the strings are all adjusted to neutral thirds of 3.5 semitones the quartertone scale can be played, also the fretboard becomes isomorphic: the shapes of scales, chords, melodies, intervals etc. are the same at any point on the fretboard.

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.

Download the pdf document here ...
http://micro.soonlabel.com/mat_cooper/Neutral%20thirds%20tuning%20for%20quartertones%20on%20conventionally%20fretted%20guitar.pdf

Thanks to Chris for hosting it ;)

MatC

Double chromatic thirds JI ...

Retuning every other string up or down by 35 cents creates alternating JI major third and JI minor third intervals between the strings. Chords straight across a fret become JI major and minor triads, sevenths, ninths. JI major and minor scales can be played in patterns similar to the scale example in the pdf.

Retuning to alternating 266 cent (7/6) and 434 cent (9/7) intervals, septimal JI chords and scales can be played.

Because the fretboard is 12EDO these JI scales can even be modulated to a limited number of keys.

MatC

... like this ...

http://img.photobucket.com/albums/v643/parramatta/universaloctave7string385c315cmajor.gif

With intervals between strings alternately tuned 385c and 315c the JI major scale can be played. I've squeezed the JI major and minor 3rds by 1 cent each to make their sum 700c.

MatC

Thanks for all the info Mat, I'll check this out. What you're doing here is
called "Compton" temperament, which was apparently at one point called
Aristoxenean, but then it wasn't, but Paul said it was still. If that sounds
confusing to you, it is to me. Either way, the basic idea is - 1/12 octave
period, just 5/4 generator. So it's like two chains of 12-tet that are
offset by a just 5/4. In that sense it's the next level up from blackwood
(which does this with 5-equal) and whitewood (which does it with 7-equal).

-Mike

On Mon, Apr 25, 2011 at 9:46 PM, ixlramp <ixlramp@...> wrote:

>
>
> ... like this ...
>
>
> http://img.photobucket.com/albums/v643/parramatta/universaloctave7string385c315cmajor.gif
>
> With intervals between strings alternately tuned 385c and 315c the JI major
> scale can be played. I've squeezed the JI major and minor 3rds by 1 cent
> each to make their sum 700c.
>
> MatC
>
>
>

[Non-text portions of this message have been removed]

Yep the strings are split into 2 groups, each group is a 12ET chromatic scale that closely (within 4c) approximates a pythagorean chain of 5 tones. The relative tuning of the 2 chains can be easily adjusted to any value by micro-retuning 1 group of strings. So it's possible to play a 10 tone JI tonal lattice constructed from fifths and 1 other freely chosen interval. I was playing the JI septimal subminor and supermajor scales recently on my 6 string bass.

MatC

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> So it's like two chains of 12-tet that are
> offset by a just 5/4.

--- In MakeMicroMusic@yahoogroups.com, "ixlramp" <ixlramp@...> wrote:
> Download the pdf document here ...

The 24EDO pdf is now out of date, the revised guide can be found in this thread at muzicforums ...

http://www.muzicforums.com/music-theory/53860-neutral-thirds-tuning-quartertones-conventionally-fretted-guitar.html

MatC

I just saw this post by Mike B., and was struck by how clear his explanation is.
I'm not trying to make work for you, but you're good at putting things simply,
in a way I can understand.

-c

________________________________
From: Mike Battaglia <battaglia01@...>
To: MakeMicroMusic@yahoogroups.com
Sent: Mon, April 25, 2011 9:49:46 PM
Subject: Re: [MMM] Re: How to retune a conventionally fretted guitar to play
24EDO (pdf document)

Thanks for all the info Mat, I'll check this out. What you're doing here is
called "Compton" temperament, which was apparently at one point called
Aristoxenean, but then it wasn't, but Paul said it was still. If that sounds
confusing to you, it is to me. Either way, the basic idea is - 1/12 octave
period, just 5/4 generator. So it's like two chains of 12-tet that are
offset by a just 5/4. In that sense it's the next level up from blackwood
(which does this with 5-equal) and whitewood (which does it with 7-equal).

-Mike

On Mon, Apr 25, 2011 at 9:46 PM, ixlramp <ixlramp@...> wrote:

>
>
> ... like this ...
>
>
>http://img.photobucket.com/albums/v643/parramatta/universaloctave7string385c315cmajor.gif
>f
>
> With intervals between strings alternately tuned 385c and 315c the JI major
> scale can be played. I've squeezed the JI major and minor 3rds by 1 cent
> each to make their sum 700c.
>
> MatC
>
>
>

[Non-text portions of this message have been removed]

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