Tuning Deviations

http://cortaigne.mitb.net/deviation/

I would imagine this sort of thing is pretty self-explanatory to most (probably all) of you, and wouldn't be surprised if there are many other charts very similar to it, but I'm thinking of converting a beaten-up old electric guitar to 19-EDO and wanted to make sure that would be the best choice. (The green subsets section was an expansion merely out of curiosity; 34 caught my interest and I plan to explore that one soon, but not for the guitar.)

This chart is a compact version of what I started with, deleting unimportant EDOs, reducing from three decimals to one, formatting adjustments, etc. If anyone wants the big version for some reason, let me know, but I think this smaller one is a handier reference.

Any feedback or suggestions for improvement would be appreciated! :-)

On Tue, Apr 19, 2011 at 12:07 PM, Callahan White <cortaigne@...> wrote:
>
> http://cortaigne.mitb.net/deviation/
>
> I would imagine this sort of thing is pretty self-explanatory to most (probably all) of you, and wouldn't be surprised if there are many other charts very similar to it, but I'm thinking of converting a beaten-up old electric guitar to 19-EDO and wanted to make sure that would be the best choice. (The green subsets section was an expansion merely out of curiosity; 34 caught my interest and I plan to explore that one soon, but not for the guitar.)

34 is great. I wish that all of the people who get hung up on finding
a near-just 5-limit non-meantone EDO would get over 53 and just go to
34 instead. It has almost 20 less notes and is also very accurate in
the 5-limit, and in many respects I actually prefer it 53-EDO. Namely
because I really like the slightly sharp 17-EDO fifths, which I think
are bright and colorful and awesome, and judging from George Secor and
Margo Schulter's previous discussions on the matter I'm not alone in
this regard.

> This chart is a compact version of what I started with, deleting unimportant EDOs, reducing from three decimals to one, formatting adjustments, etc. If anyone wants the big version for some reason, let me know, but I think this smaller one is a handier reference.

So this is all with reference to 24-TET?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> 34 is great. I wish that all of the people who get hung up on finding
> a near-just 5-limit non-meantone EDO would get over 53 and just go to
> 34 instead. It has almost 20 less notes and is also very accurate in
> the 5-limit, and in many respects I actually prefer it 53-EDO. Namely
> because I really like the slightly sharp 17-EDO fifths, which I think
> are bright and colorful and awesome, and judging from George Secor and
> Margo Schulter's previous discussions on the matter I'm not alone in
> this regard.

Truth be told, I'm a fan of sharp fifths myself. In fact, my original idea was for a 17-EDO guitar, but having crunched numbers like these and also having played with subsets on my keyboard and full scales with ThumbJam on my iPod touch, I found myself with a slight preference for 19 overall (despite its flat fifth). The main reason mathematically is that every interval in the subset of 19 that approximates 12-EDO does so better than the equivalent subset of 17 -- and as a bonus, it really nails 6:5. Even before I figured that out, though, I thought it had a more pleasant sound than 17.

> So this is all with reference to 24-TET?

Functionally, that's the upshot, yes. The real idea was in reference to 12-EDO with the grey columns being the halfway spaces, so anything in those is sure to sound the most drastically unusual to the pinks. ;-)