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Wide Mirrored 4ths - A Journey by Stick
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Author:  DavidWS [ Thu Dec 22, 2022 8:49 am ]
Post subject:  Wide Mirrored 4ths - A Journey by Stick

Having spent the best part of a year with the usual 4ths melody & 5th bass tuning & still not feeling any thing like at home with 5ths, after I had the good fortune to land a bamboo 12 string Grand my thoughts started to turn to what some refer (I hope jokingly!) to as the Dark Side of the Fourths...

I was particularly take by what Rob Martino & Jayesskerr have written on the topic (this post viewtopic.php?p=118103#p118103 especially). I was reminded of how I came to choose 'All Fourths' tuning (EADGCF) as what I use on all my guitars.

To dip my toes (or rather fingers!) in Mirrored 4ths, I I started with a simple experiment that essentially reversed what Emmett did all those years ago when he to started with fifths. He raised a string by a tone, left the next lower string un-changed, then dropped the next lower by a tone. I did the opposite with the 3 lowest RMR bass strings so E2 A1 D1 became D2 A1 E1. Only 3 strings to work with, but enough to feel that I liked the idea & wanted to take the experiment futher.

While waiting on a set of Mirrored 4th strings from SE, I decided to see what I could achieve on my Graphite 10 string (then set up for Full Baritone) using strings I already had to hand.

My first try involved switching the Baritone melody strings from the melody side to the bass then tuning them down a semitone, and re-fitting the Classic 10 melody strings that had been on the Stick when it arrived then tuning them up a semitone.

That gave a 'Mirrored 4ths' arrangement, i.e. octave inlay correspondence over 5 frets (e.g. bass 2 to melody 7), and lowest melody as a 'virtual' extension of the bass 4ths.

Code:
G#3 D#3 A#2 F2  C2      G2  C3  F3  A#3 D#4


That worked but didn't feel quite right, so I retuned all strings down semitone so that the melody side was unadjusted 'Classic 10', and the bass side was a whole tone below the melody side of Baritone melody. That made the arrangement equivalent to 'Mirrored 4ths', but a 5th higher.

Code:
G3  D3  A2  E2  B1      F#2 B2  E3  A3  D4


I really liked that. The mirrored fourths arrangement immediately felt more natural to my hands and my brain. :)

I'm sure someone must have done that tuning before, but if so I've not found it, so in the absence of another name I called it 'Baritone Mirrored 4ths 10' (hence the first attempt became 'High Baritone Mirrored 4ths 10').

I know that people say that Mirrored 4ths really needs 12 strings, but to me the 'Baritone Mirrored 4ths 10' arrangement gives a very usable range of possibilities in the guitar range of tones & I was planning on leaving the Graphite in that tuning.

Once the 'proper' Mirrored 4ths for the Grand arrived, I fitted them and set making it my 'home'.

The absence of the lower bass end of Classic (C1) & RMR (D1) was a pity, but I had in mind that maybe when, in due course, my 'built to order' Grand arrives from SE (it could easily be another 6 months) I might try a dropping all strings a 4th on the older Grand (I've not seen a name for that arrangement, so maybe 'Deep Mirrored 4ths 12'?), but other than that I had no plans for change...

After a month or two with normal Mirrored 4ths I felt that I wasn't getting a lot of use out of the low melody string, especally so at the lower end, so I started musing on the possibilities.

Around that time I happened to revisit Rob's video about his custom 7 bass & 5 melody Mirrored 4ths Stick, & was reminded that limited use of string 6 was part of his reason for ordering the 7 + 5 Stick. However I didn't see a 5+7 as where I wanted to go (even it was possible & practical). Options for widening the interval between low bass & low melody seemed like a good subject for study.

An early thought was to put an extra 4th between the two sides. Dropping the bass side by inserting a B0 that could be either a 'Classic' or MR low bass dropped a whole tone, or a Dual Bass Reciprocal low bass, gives

Code:
C3 G2  D2  A1  E1  B0      B1  E2  A2  D3 G3 C4


i.e. a straight 'reflection' but with an octave between the two low strings. If that arrangement doesn't already have a name, how about 'Matched Mirrored 4ths 12'?

'Matched Mirrored 4ths 12' doesn't give any useful full inlay correspondences, but it does include a 5 string octave inlay correspondence over 5 frets, e.g. bass fret 2 (8-12) to melody fret 7 (6-2). Spotting that 5 string correspondence gave me an idea...

If the interval between low bass & low melody is increased by a whole tone to a 9th by putting Classic 12 melody on the melody side and 'Matched Mirrored 4ths 12' bass on the bass side it gives

Code:
C3 G2  D2  A1  E1  B0      C#2 F#2 B2  E3  A3  D4


That arrangement had several features that appeared interesting to me.

a) Double octave inlay correspondence over 10 frets, e.g. bass fret 2 to melody fret 12

b) 5 string octave inlay correspondence over 5 frets, e.g. bass fret 2 (7-11) to melody fret 7 (5-1)

c) String 6 (the 'extra' melody string that isn't part of the 5 string octave inlay correspondence over 5 frets) is the 'low 5' of string 5. So with a bass root on the bass low string and a harmonising octave block an inlay away on strings 5-1, string 6 allows easy access to the 'low 5' & 'low 6' of the octave, notes which feature in countless melodies.

d) The overall range of the tuning is comparable to that of 'normal' 4ths/5ths Stick tunings, albeit with less overlap.

e) Since low melody is the 9th of low bass, it provides alternative access to an octave for a 1 5 octave power chord, or a 10 for a different 1 5 10 open triad. I'm not sure how useful that might be in pracctice, so probably minor, but the scope is there.

f) The melody side is back to good old Classic 12 / RMR 12. :)

In the absence of another name I call this arrangement 'Wide Mirrored 4ths 12'.

Once again I started my experiment with my Graphite 10 string. Instead of making that just the inner 10 of the ablve, I found I could ge a 4th higher 10 string equivalent by leaving the melody side as it already was (Classic 10 melody) and using the lowest 5 bass strings from my spare 'Mirrored 4ths' set on the bass side, giving

Code:
C3 G2  D2  A1  E1      F#2 B2  E3  A3  D4


and calling it 'Baritone Wide Mirrored 4ths 10'.

I liked what I found. It gives me (pretty much) the range of a normal 4 string bass & 6 string guitar on a single 10 string instrument, with most of the 'Wide Mirrored 4ths 12' benefits listed above. I think it has enough difference & appeal that it will still get played even with the 12 string version available.

I'm now converting the #5826 bamboo Grand to 'Wide Mirrored 4ths 12'. I've done the re-stringing and intonation. Next thing is to work on the action. Then I need to get back to learning to play...

I have 'fretboard map' illustrations of all the above tunings (i.e. the 'thought experiments' as well as the actual trials) if anyone is interested?

I've attached the 'Wide Mirrored 4ths 12' map.

Attachment:
Wide Mirrored 4ths 12.pdf


Edited to correct a typo.

Author:  DavidWS [ Thu Dec 22, 2022 10:12 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

DavidWS wrote:
I've attached the 'Wide Mirrored 4ths 12' map.

And, since it's also current & soon to be mentioned in my sig here's 'Baritone Wide Mirrored 4ths 10'

Attachment:
Baritone Wide Mirrored 4ths 10.pdf

Author:  WerkSpace [ Thu Dec 22, 2022 11:07 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

The Stick is a very versatile instrument. I love what you are doing.

I'm curious how are you calculating the stresses on the instrument?
Each string must reach the desired tone while minimizing it's tension.
https://tension.stringjoy.com/

If this was all done in MIDI, then changing tunings
could be done in an instant, (by selecting a different patch)
without ever having to physically change any string tensions.

Author:  DavidWS [ Thu Dec 22, 2022 2:24 pm ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

WerkSpace wrote:
I'm curious how are you calculating the stresses on the instrument?

I'm not. I'm just using appropriate existing strings of the same gauge (light) at or very close to their design pitch, and trusting that SE aim for a similar stress balance across all sets?

None of the experiments have deviated from design pitch by more than a semitone sharp or a whole tone flat.

With the current tuning the strings are all at design pitch, except for the B0, which is a C1 from a 'Classic' set down a semitone. The only 'official' SE B0 is in the Dual Bass Reciprocal set & I don't have one of those.


I have visited that site in the past (probably some other time when you posted it?), but not on this occasion.
Thanks for the reminder. Maybe I will take a look sometime & cross check to see what results it produces with this tuning?

Author:  robmartino [ Fri Jan 06, 2023 9:36 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

Interesting thought process here, maximizing the pitch range while maintaining some inlay relationships. Every once in a while I miss that deep B or C bass string from my first time playing the Stick. As my repertoire developed over the years I gravitated more towards the higher end of the bass range- at this point I find 7 bass strings in 4ths starting at low bass E up to Bb so helpful for chord voicings that I could imagine some kind of 14 string instrument with a low bass B and adding back the melody B an octave higher (8 bass, 6 melody) but then it might be getting into overkill territory (how often would I actually use those strings) and an impractically wide fretboard.

Author:  DavidWS [ Sat Jan 07, 2023 3:35 pm ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

Thanks for your thoughts Rob.
robmartino wrote:
maximizing the pitch range while maintaining some inlay relationships.

Early days yet, but I'm finding both the octave partial (5 string) relationship over one inlay & double octave full relationship over two
appealing in different circimstances.

And with all these string & tuning changes I think I'm finally getting somewhere with setting up a Stick. Nowhere near SE standards I'm sure, but I now have the action lower than I've ever managed before.

I look forward to my brand new Stick arriving
sometime this year (hopefully!) and being able to compare that to my efforts.

robmartino wrote:
at this point I find 7 bass strings in 4ths starting at low bass E up to Bb so helpful for chord voicings

Thanks for that bit of info. I wasn't sure how you have your 7 + 5 set up, & was thinking of asking sometime.

Author:  AnDroiD [ Sun Jan 08, 2023 8:55 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

What is the "built to order" Grand configuration? (and what is it wood, inlays, tuning pegs, pu) Also Rob posted about the new 7/5 Stick. Somewhere.

Author:  robmartino [ Sun Jan 08, 2023 8:58 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

Here's the thread on my 7 bass/5 melody instrument, which includes a link to a YouTube video I also made:

viewtopic.php?f=2&t=15549

Author:  DavidWS [ Sun Jan 08, 2023 11:24 am ]
Post subject:  Re: Wide Mirrored 4ths - A Journey by Stick

robmartino wrote:
Here's the thread on my 7 bass/5 melody instrument, which includes a link to a YouTube video I also made

Thank you Rob. I think I'd watched the video, but I don't recall spotting the thread. :D

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