A rather ambitious way to test the "rare intervals"/"tritone hypothesis"

Hi all,

Mavila is an interesting tuning system in that mavila[7] contains the
same step patterns as meantone[7], but the pattern of whole steps is
flipped. Instead of there being a dissonant tritone, there's a
dissonant augmented fifth. The "anti-Ionian" mode contains minor i,
iv, and v triads, and the "anti-Aeolian" mode contains major I, IV,
and V triads. This might be review for most of you.

What is really interesting about Mavila is that all of the comma pumps
in Meantone also work if you turn every major chord into a minor chord
and vice versa.

For example (using Meantone notation for all just to avoid having to
define a new notation)

Meantone: Cmaj -> Am -> Dm -> Gmaj -> Cmaj (Ionian)
Mavila: Cm -> Abmaj -> Dbmaj -> Gmaj (same as Gb) -> Cmaj
(Anti-Ionian*) - the Dbmaj -> Gmaj is motion by 4/3

Meantone: Cm -> Gm -> Dm -> Fmaj -> Cm (Dorian)
Mavila: Cmaj -> Gmaj -> Dmaj -> Fm (same as F#m) -> Cm (Anti-Dorian) -
the F#-A from the Dmaj becomes equal to the F-Ab in Fm

Meantone: Cm -> Ebmaj -> Bbmaj -> Fm -> Cm (Aeolian)
Mavila: Cmaj -> Em -> Bm -> Fmaj (same as F#) -> Cmaj (Anti-Aeolian) -
the Bm -> Fmaj is motion by 4/3

Meantone: Cm -> Ebmaj -> Bbm -> Fm -> Cm (Phrygian)
Mavila: Cmaj -> Em -> Bmaj -> Fmaj (same as F#) -> Cmaj
(Anti-Phrygian) - the Bmaj -> Fmaj motion is by 4/3 (whooooo yeah!!!!)

You get the picture - so all of existing common practice music should
be able to be translated into this "alternate universe" and comma
pumps should still work. Furthermore, the pattern of steps should
remain the same, and there should still be a dissonant interval in the
right place, except now it's an augmented fifth rather than a
diminished fifth.

-Mike

*The "anti-" prefix means that the pattern of steps are identical to
the meantone counterpart, e.g. anti-Ionian is ssLsssL, identical to
Ionian's LLsLLLs.

Sorry, it looks like the last paragraph didn't get sent through properly -

So where I need advice is - I predict that using a mavila tuning with
a fifth flatter than POTE optimal will yield better results than the
optimal one, since with the optimal mavila fifth, the augmented fifth
will be about 721.166 cents, which I don't think will be dissonant
enough at all. I wanted to try exploring 16-equal, perhaps 25b-equal,
and maybe even 9-equal. So I need to find a way to make a generalized
mavila "score" and then pick a specific tuning. Can anyone recommend
an efficient way to do this? Might using Lilypond be good for this
purpose?

Lastly, I need a piece to try out. Something with lots of comma pumps
that is still clearly tonal would be nice. Any suggestions? :)

-Mike

On Thu, May 19, 2011 at 9:20 AM, Mike Battaglia <battaglia01@...> wrote:
> Hi all,
>
> Mavila is an interesting tuning system in that mavila[7] contains the
> same step patterns as meantone[7], but the pattern of whole steps is
> flipped. Instead of there being a dissonant tritone, there's a
> dissonant augmented fifth. The "anti-Ionian" mode contains minor i,
> iv, and v triads, and the "anti-Aeolian" mode contains major I, IV,
> and V triads. This might be review for most of you.