Re: Mohajira sequence (was Bradley's Easter Eggs)

Bravissimo, Gene !
176/7 applies perfectly the Mohajira mapping, and is indeed a remarquable attractor for a series of 16 mohajiras, that I didn't noticed.
What it suggests to me is that if you double this 11/7 interval :
49 : 77 : 121 you make a jump of 32 mohajs this means it's just one too much for a 31 tones scale -
and since 36 : 44 : 54 : 66 : 81 : 99 : 121 would be a -c correct ending,
it certainly is an inspiring frame at least for 31 tones.

We can remark also that 49 is a very precise semififth between 40 and 60, who bring now 5 into the scene.
So 40 : 49 : 60 : 73.5 : 90 : 110 : 135 : 165 : etc. could be a good start, transposing the ending scale by 5/4 (and introducing a second mapping for 5 which would be -23, in addition to +8...) .

Now 63 is 11/9 lower the middle point 77 and and with 40 it suggests another attractor for a series of 16 mohajiras, with 126/5 (441/440 higher). This gives a larger fifth of 1.496838922 or 698.3027739 c., but interestingly, cycling even better in 55 tones (32 steps of 55 = 698,181818...c.).

Between all these coincidences it seems possible to make simple enough 11-limit (??) performant -c versions of 31, and 55 tones scales.
- - - - - - -
Jacques

--- In tuning@yahoogroups.com, "bplehman27" <bpl@...> wrote:

> See, for example, my page about various sizes of regular (or "meantone") temps:
> http://www-personal.umich.edu/~bpl/larips/meantone.html

I draw the attention of Michael, who hates the 11/7 interval, to the description of the good 11/7s in 1/5 comma meantone as being useful "Easter eggs" which benefit the tuning. I also draw attention to the fact that the (176/7)^(1/8) fifth of 697.8115 cents is extremely close to the 697.8252 cents "Mohajira squared" fifth which is the root of
f^5-f^4-f^2-1/4 and which appears in the Mohajira tuning we've been discussing lately which uses x^5-x^4-1/2 as a generator. The point of the "Mohajira squared" fifth would presumably be you could use a linear recurrence relationship to define a rational intonation which would give results very close to it. Whether that has any potential uses for people who actually tune things I can't say.

Gene>"I
draw the attention of Michael, who hates the 11/7 interval, to the
description of the good 11/7s in 1/5 comma meantone as being useful
"Easter eggs" which benefit the tuning."

Actually I digress... my mind has changed on that. Turns out the "octave inverse" of 11/7 is 14/11...and the 1/1 11/7 2/1 chord is not a bad one at all. It seems a great example of "the whole is greater than the sum of its parts".

-Michael