Yahoo Tuning Groups Ultimate Backup tuning EDOs 4 to 49

Here's the new list with EDOs 25 to 49 covered showing the good intervals that occur within 6.776 cents (256/255) accuracy.

EDO4...none

EDO5...none

EDO6...9/8,

EDO7...none

EDO8...11/6,

EDO9...7/6, 12/7, 13/7,

EDO10...none

EDO11...9/7, 11/8,

EDO12...9/8, 4/3, 3/2,

EDO13...11/8, 9/5,

EDO14...9/7,

EDO15...6/5, 5/3,

EDO16...8/7, 7/4, 11/6,

EDO17...4/3, 3/2, 11/7,

EDO18...9/8, 7/6, 12/7, 13/7,

EDO19...6/5, 5/3, 13/7,

EDO20...11/7, 9/5,

EDO21...8/7, 7/4,

EDO22...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,

EDO23...9/8, 7/6, 6/5, 11/7, 5/3, 12/7, 11/6,

EDO24...9/8, 4/3, 11/8, 3/2, 11/6,

EDO25...5/4, 9/7, 7/5, 10/7, 8/5, 11/6,

EDO26...8/7, 11/8, 11/7, 7/4, 9/5,

EDO27...7/6, 6/5, 7/5, 10/7, 5/3, 12/7, 9/5, 13/7,

EDO28...5/4, 9/7, 11/8, 8/5, 13/7,

EDO29...9/8, 4/3, 7/5, 10/7, 3/2, 11/7, 13/7,

EDO30...9/8, 6/5, 9/7, 5/3,

EDO31...8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6,

EDO32...8/7, 7/6, 11/7, 12/7, 7/4, 9/5, 11/6,

EDO33...9/7, 11/8, 7/5, 10/7, 9/5, 11/6,

EDO34...6/5, 5/4, 4/3, 3/2, 11/7, 8/5, 5/3, 9/5,

EDO35...9/8, 11/8, 7/5, 10/7, 11/7,

EDO36...9/8, 8/7, 7/6, 9/7, 4/3, 3/2, 12/7, 7/4, 13/7,

EDO37...8/7, 5/4, 11/8, 7/5, 10/7, 11/7, 8/5, 7/4, 13/7,

EDO38...6/5, 5/3, 13/7,

EDO39...9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 9/5, 11/6, 13/7,

EDO40...9/8, 7/6, 5/4, 11/7, 8/5, 12/7, 9/5, 11/6,

EDO41...9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6,

EDO42...9/8, 8/7, 6/5, 9/7, 5/3, 7/4,

EDO43...5/4, 4/3, 7/5, 10/7, 3/2, 11/7, 8/5,

EDO44...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,

EDO45...7/6, 6/5, 7/5, 10/7, 5/3, 12/7, 9/5, 13/7,

EDO46...9/8, 8/7, 7/6, 6/5, 5/4, 4/3, 11/8, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7,

EDO47...9/8, 8/7, 5/4, 9/7, 7/5, 10/7, 8/5, 7/4, 9/5, 11/6, 13/7,

EDO48...9/8, 8/7, 4/3, 11/8, 3/2, 7/4, 11/6, 13/7,

EDO49...7/6, 6/5, 5/4, 9/7, 7/5, 10/7, 11/7, 8/5, 5/3, 12/7, 11/6, 13/7,

31EDO has 13 good intervals occurring and both 41EDO and 46EDO have 16 (out of a possible 19) good intervals occurring.

As I said before, 25 and higher EDOs have adjacent notes that are less than 48.18855 cents apart which I consider to be illegal in melody (see msg 96914). So if I were to use an EDO between 25 and 49 inclusive I would select a subset of the notes such that no two notes selected are less than 48.18855 cents apart.

John.

🔗Mike Battaglia <battaglia01@...>

🔗Jake Freivald <jdfreivald@...>

John O'Sullivan said:
> > EDO12...9/8, 4/3, 3/2,
...and...
> > EDO19...6/5, 5/3, 13/7,
...and...
> > EDO22...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,

..to which Mike responded:

> If you think that 12 and 19 are useless for 5-limit harmony, or that
> no useful representation of 6/5 or 3/2 exists in 22-tet, then
> something about this formula needs to be reworked.

I think he's right, John. For decades, you and I never knew that the fourth frets on our 12-EDO guitars were out of tune; now that you've defined a new version of what "in tune" means, we can't just wholly turn our backs on our history and think we've been playing terrible-sounding notes. I love too much music that has "crows" in it to believe that they're "illegal".

I don't necessarily think you need to go back completely to the drawing board. Personally, I just feel -- and this is really gut instinct talking here, not anything more objective -- that the rules (e.g., difference from just =< 256/255 means "good", > 256/255 means "bad") are a little too arbitrary to be hard-and-fast. For instance, I'm starting to think that other things, like scale structure, context, musical attitude, and so on, matter more to how we hear consonance or dissonance than simple ratios do.

Regards,
Jake

🔗john777music <jfos777@...>

Hi Jake,

certainly intervals that are more than 6.776 cents (256/255) out of tune are acceptable to most ears but I'm aiming at perfection or close to it and am therefore pretty strict. The less strict I am the more good chords are "legal". I think that within my strict bounds the number of good chords available is more than adequate and worth the "srictness".

John.

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> John O'Sullivan said:
> > > EDO12...9/8, 4/3, 3/2,
> ...and...
> > > EDO19...6/5, 5/3, 13/7,
> ...and...
> > > EDO22...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,
>
> ..to which Mike responded:
>
> > If you think that 12 and 19 are useless for 5-limit harmony, or that
> > no useful representation of 6/5 or 3/2 exists in 22-tet, then
> > something about this formula needs to be reworked.
>
> I think he's right, John. For decades, you and I never knew that the
> fourth frets on our 12-EDO guitars were out of tune; now that you've
> defined a new version of what "in tune" means, we can't just wholly turn
> our backs on our history and think we've been playing terrible-sounding
> notes. I love too much music that has "crows" in it to believe that
> they're "illegal".
>
> I don't necessarily think you need to go back completely to the drawing
> board. Personally, I just feel -- and this is really gut instinct
> talking here, not anything more objective -- that the rules (e.g.,
> difference from just =< 256/255 means "good", > 256/255 means "bad") are
> a little too arbitrary to be hard-and-fast. For instance, I'm starting
> to think that other things, like scale structure, context, musical
> attitude, and so on, matter more to how we hear consonance or dissonance
> than simple ratios do.
>
> Regards,
> Jake
>