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 Theoretical Tuning 
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Post Theoretical Tuning
"Root 2 Symmetry"

I have imagined a very different tuning for the Chapman Stick.

The standard tunings seem quite similar, just shifting things up or down a fret or two for the most part, keeping the 5ths (7 semi-tones) on the bass side and 4ths (5 semi-tones) on the melody side. This makes sense, tweaking a successful layout.

What about changing to 6 semi-tones on both sides? Something like C, F#, C, F#, C on both sides. The difference between two adjacent strings along the fret would be square root of two, and they would not sound good together. However, going up or down a fret would yield the 4ths and 5ths, and going across another string would give the octave.

I would love to hear different ideas on the pros and cons of such a tuning.

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Fri Oct 16, 2015 5:57 pm
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Post Re: Theoretical Tuning
It's always fun to consider the implications of tunings.

The main disadvantages I can see for your idea are that perfect 4ths and perfect 5ths are very common occurrances in common diatonic harmony. Tritones only occur once in any modal scale, but 4ths and 5ths occur three or four times. This has the advantage of making patterns easier to see on the 4th/5th grid, and easier to play as well, as there are repeating patterns across the strings (3 notes per string for 4ths and 4 notes per string for 5ths, for tritones, you would have to alternate 3 and 4 to cover a position.

Also, each finger's reach is expanded through the availability of double stops in 4ths and 5ths.

I can't think of anything good about the tuning you suggest. Since it doesn't increase the number of tones available to the hand in a given position,the way a closer tuning, like 3rds, would, it has no net benefit for chord formation compared to 4ths.

I've tried many different tunings, including major and minor 3rds, which was very interesting for chords but severely range-limiting, and very confusing melodically, It always comes back to how the patterns fit the fingers and the hand.

Just my 2 cents.

Still, if you have a burning desire to try it out, The Stick's fully adjustable hardware make such experiments very easy to do.

This one is easier than most as you don't have to tune the string up or down by much to make it work. I would not recommend trying to tune the high D melody string any higher, though!

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Fri Oct 16, 2015 6:43 pm
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Post Re: Theoretical Tuning
Dear Greg,

thank you very much for taking the time to think about this and give your expert opinion. You have already taught me something I did not know - that it is common to use one finger to sound two notes on the same fret (assuming that's what "double stops" means).

Obviously, I am an absolute novice when it comes to music. I had to look up what a tritone is! Coming from the perspective of mathematics and physics, I don't really get the "tritones only occur once in any modal scale", as I just see 12 semi-tones per octave, and any pair 6 semi-tones apart should sound equally awful together!

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Fri Oct 16, 2015 8:35 pm
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Post Re: Theoretical Tuning
My pleasure.

Yes, double stops, triple stops, there is even a point in the scale where you get a quintuple stop if you want to use it ( ex. C G D A E B) which gives you all the notes of a Maj13th chord, but out of order (1st, 5th, 9th, 13th, maj3rd, maj7th).

The only instance in the major scale where you have a tritone is between the major 7th and the perfect 4th (B to F for C major). so a double-stop in the configuration you cite is not as useful.

So bring on the 5ths and 4ths!

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Sun Oct 18, 2015 5:34 am
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Post Re: Theoretical Tuning
Welcome to the Stick world.

Unless you have very specific musical goals that would be better accommodated with a different tuning, I’d also suggest starting with one of the standard 4/5 tunings.

I’d recommend you start by simply listening and not thinking too much about the math or theory behind the sounds. Once you get a feel for what sounds good to you, then go look up the math, physics, and music theory behind it. I found this online, which has some info on the physics behind music. There are probably many more resources like this out there.

Jolyon wrote:
Obviously, I am an absolute novice when it comes to music. I had to look up what a tritone is! Coming from the perspective of mathematics and physics, I don't really get the "tritones only occur once in any modal scale", as I just see 12 semi-tones per octave, and any pair 6 semi-tones apart should sound equally awful together!

From a musical perspective, not all tones within the octave are equal (unless you’re working with 12-tone music). Music is generally based around a key, which will determine which tones within the octave are more “important”. That’s what constitutes scales/modes.

In terms of basic music theory (from a historical Western music theory perspective, there are many options outside of that):
- Scales are typically based on 7 notes. It is rare to refer to all 12 tones in an octave, it’s usually pared down to 1 (root), 2, 3, 4, 5, 6, 7.
- The root/octave is the most important.
- Modes are either major or minor, determined by the 3rd.
- The 4th and 5th are referred to as “perfect”, they do not change between modes.
- The 2, 3, 6, and 7 can be major or minor.
- Your friend the tritone (6 semitones) doesn’t even get its own number, it’s a #4 or b5. This note generally comes up as a part of a melody/harmony that leads back to the key/mode, to provide tension and resolution (listen to the Simpsons theme or Maria from West Side Story for obvious examples).
- The only mode where the tritone exists compared to the root is Lydian.

Greg posted an excellent guide on modes as they relate to the Stick which includes visual info that should help you understand how this correlates to the Stick tuning.

BTW, the tritone has a beautiful visual symmetry in the standard tuning (same in both the melody and bass):
Code:
|---|---|---|---|---|-X-|
|---|---|---|---|-X-|---|
|---|---|---|-X-|---|---|
|---|---|-X-|---|---|---|
|---|-X-|---|---|---|---|
|-X-|---|---|---|---|---|


Sun Oct 18, 2015 10:40 am
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Post Re: Theoretical Tuning
Claire,

thank you very much for your time and trouble, not to mention excellent links and explanations. I had already found the physics behind music link, but the link to Greg's website was new and most helpful to me.

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Tue Oct 20, 2015 5:13 am
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Post Re: Theoretical Tuning
To sum up - this particular theoretical tuning is a bad idea, and is not recommended by the most expert Chapman Stick players, for good reasons.

Emmett's response was very gentle:
Quote:
Your tuning sequence of flatted 5ths is interesting but would pose some problems when playing modes and scales. With a 4-fingered melodic technique, you'd be shifting up a fret in pitch at every other string. Using 3 fingers, you'd be shifting in the other direction, down a fret in pitch.

You'd have the advantage, however, playing the symmetrical scales, that is, the whole tone and 8-tone diminished scales (alternating whole steps and half steps).

Your choice but there are musical reasons why stringed instruments are tuned in 4ths and 5ths.

I thought it worth asking this publicly to save any other novice the trouble of looking quite so foolish!

My order of RMR tuning is unaltered following such clear feedback. Thank you Emmett, Greg and Claire.

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Tue Oct 20, 2015 5:28 am
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Post Re: Theoretical Tuning
Just in case anyone is still reading, I do have another question. Hopefully slightly less dumb than the first!

I see an alternate tuning of all 4ths, but not one of all 5ths. Why not an all 5ths alternate tuning?

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Tue Oct 20, 2015 5:32 am
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Post Re: Theoretical Tuning
Good question, and one that I dont think I can answer....but I'll take a stab. It would be mighty difficult I think to play the melody in fifths due to the wider intervals, both in the chord and scale realm.

cheers,
kev

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Tue Oct 20, 2015 11:58 am
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Post Re: Theoretical Tuning
As Kevin said, it’s mostly to do with your options for scales and chords. There’s an article by Rob Martino that outlines the mirrored 4ths tuning really well.

The reason you might not want 5ths in the melody is the same reason some people don’t want it in the bass. As an example, you wouldn’t be able to play close-position chords (with one hand).

If you’re wondering why go with 5ths in the bass, here’s a video from Greg that goes over it.


Wed Oct 28, 2015 9:35 pm
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