suggestions for alternate tuning order?

[Jberczel]

Originally Posted by Raggamuffin

No, I set it up as an optimization problem in Excel and solved it using Solver (the optimization software that comes with Excel). Solver has an evolutionary optimization engine (essentially a genetic algorithm) that works well of these types of problems. It also has a very convenient/efficient way of constraining the cells representing decision variables to be a permutation of integers from 1 to "n" -- which is perfect for this type of problem. Of course, since "n" is relatively small in this case, a brute-force (complete enumeration) approach is very possible as well.

I actually found the most challenging part of the problem to be calculating the "distance matrix" needed to summarize how many half-step changes are required to go from tuning i to tuning j. Once I had that, Solver made the rest of it pretty easy.

thanks for clarification. this problem was a lot of fun. i did it using ruby programming language (brute-force since n was relatively small), but i'd like to hack on it a bit more.

for the "distance matrix", i just had a lookup array (1 - 12 notes), and i'd look for the difference between their indices, and it were greater than 6 (farthest distance if you loop to next octave), subtract by 12 to get the closer distance.

i double-checked your analysis and got the same results

Low E to high e string:

1. e a d g b e -> next tuning is 2 half-steps
2. d a d g b e -> next tuning is 1 half-steps
3. d a d g c e -> next tuning is 3 half-steps
4. d a d g b d -> next tuning is 8 half-steps
5. c g# d# f c c# -> next tuning is 6 half-steps
6. c# g# e f# b d# -> next tuning is 5 half-steps
7. d a e f c e -> next tuning is 5 half-steps
8. d a c# e b e -> next tuning is 4 half-steps
9. d a c# d a e

Total half steps for tunings: 34

[SantaCruzOMGuy]

Your guys response is far more sophisticated an answer than I even thought was possible ! Is it too much of an over-simplification to approach it the following way, with the goal being the least back and forth overall tension on the guitar? I got some string tension analysis from an ibanez forum that led me to conclude overall every string puts the same approximate tension on the guitar. Here is my attempt IN WHOLE STEPS AND HIGH TO LOW:


tuning - high to low # drops # raises Change
E,B,G,D,A,E (Standard) 0 0 0
E,C,G,D,A,D 1 0.5 -0.5
E,C,F,E,A,D 2 1.5 -0.5
E,B,G,D,A,D (Drop D) 1 0 -1
D,B,G,D,A,D 2 0 -2
D#,B,F#,E,G#,C# 3 1 -2
E,B,E,C#,A,D 3 0 -3
C#,C,F,D#,G#,C 5 1 -4
E,A,D,C#,A,D 5 0 -5

Strings:
Light 0.012 0.016 0.024 0.032 0.042 0.053


Tension Analysis:
E: .012" [PL] = 23.35 pounds
B: .016" [PL] = 23.30 pounds
G: .020" [PL] = 22.93 pounds
D: .032" [NW] = 28.10 pounds
A: .042" [NW] = 26.31 pounds
E: .054" [NW] = 24.18 pounds

Total Tension = 148.18 pounds

My apologies for not being able to get the table to format no matter what I tried.
Is this a valid approach if the goal is least back and forth stress on the guitars neck?

[SantaCruzOMGuy]

I guess I should also point out that the least back and forth on each string string the better, because thats when i've had them break - if i go up/down/up/down....

So My goal is not the least amount of re-turning work, but instead the least back and forth on the 1) individual string 2)overall tension on the guitar. It becomes a give and take, where each string has an obvious order, but then you put another string out of order like a rubix cube. So what tuning order results in the least overall back and forth....

[Raggamuffin]

Please help me understand what you mean by the amount of "back and forth" on an individual string. How would you quantify the total amount of "back and forth" on, say, the high E string and the low E low string in the following ordering of tunings?

EBGDAE (Standard)
EBGDAD (Drop D)
ECGDAD
DBGDAD
D#BF#EG#C#
C#CFD#G#C
ECFEAD
EBEC#AD
EADC#AD

[SantaCruzOMGuy]

Originally Posted by Raggamuffin

Please help me understand what you mean by the amount of "back and forth" on an individual string. How would you quantify the total amount of "back and forth" on, say, the high E string and the low E low string in the following ordering of tunings?

EBGDAE (Standard)
EBGDAD (Drop D)
ECGDAD
DBGDAD
D#BF#EG#C#
C#CFD#G#C
ECFEAD
EBEC#AD
EADC#AD

Ok, so for the standard turning B string with the progression above, its tuning changes are as follows:

Starts as B, half step up to C, half step back down to B, half step up to C, half step down to B, whole step down to A.

In a perfect world you could just go from C down to B down to A, or as another commenter suggested tune "up" to avoid string slip, and start from A and work your way up to C for that string. The trickiness is that you can't style the order for just that string, since every order throws off a particular string more than another. So the quest is, in what order does the most compromise between all of the strings occur, resulting in fewest overall tension changes back and forth on the neck - so perhaps start with the least bit of tension, and tune "up" adding tension all the way back to standard tuning. Does that make sense?

[Jberczel]

Originally Posted by SantaCruzOMGuy

Ok, so for the standard turning B string with the progression above, its tuning changes are as follows:

Starts as B, half step up to C, half step back down to B, half step up to C, half step down to B, whole step down to A.

In a perfect world you could just go from C down to B down to A, or as another commenter suggested tune "up" to avoid string slip, and start from A and work your way up to C for that string. The trickiness is that you can't style the order for just that string, since every order throws off a particular string more than another. So the quest is, in what order does the most compromise between all of the strings occur, resulting in fewest overall tension changes back and forth on the neck - so perhaps start with the least bit of tension, and tune "up" adding tension all the way back to standard tuning. Does that make sense?

if i understand correctly, you want to order the tunings from least tension back to standard tuning? so with each tuning change you'd add a little more tension until eventually getting back to standard?

i could take a crack at ordering them based on the tension (using standard as base tuning) unless ragmuffin has a better idea.

[Raggamuffin]

I believe that just involve sorting the tunings from the least tension to highest, no?

If so, I think this is what you'd end up with...

Tension Tuning
131.74 EADC#AD
137.61 C#CFD#G#C
140.09 EBEC#AD
145.71 DBGDAD
147.59 D#BF#EG#C#
150.48 EBGDAD (Drop D)
153.32 ECGDAD
156.02 ECFEAD
156.09 EBGDAE (Standard)

I used the following site to get individual string tensions...
http://www.mcdonaldstrings.com/stringxxiii.html

[SantaCruzOMGuy]

cool link and thanks so much for the help. This is great tool. So much of my goal is to be able to have a practice routine on my songs that is not causing strain on the guitars.