Re: Alternate harmonization of superpyth[7] leading to different ton

Mike wrote :

> I'm confused? I only see one 4:5:6:7 tetrad...

Apparently you haven't tried it, it has four of them plus two extra 4:6:7 in the ribbon sequence
It's easy to see from the number of notes of my main sequence.

! tapek-ribbon.scl
!
Eq-diff ribbon extension of Superpyth, made of two Tapek sequences
12
!
1777/1656 ! C#
627/552 ! D
173/138 ! E
4273/3312 ! E+
1465/1104 ! F
131/92 ! F#
104/69 ! G
3673/2208 ! A
945/552 ! A+
243/138 ! Bb
1043/552 ! B
2/1
! Tapek -c and triple h.eq-b recurrent sequence 3x^3 = x^2 + 8
! and Superpyth temperament (generator = 710.25498677616 c.)
! completed by the arithmetical mean ribbon y = (1 + x)/2,
! equal-differential frequencies of all [7:6:5:4] tetrads
! main sequence : 243 1465 69 13 627 945 4273/3 ... (C = 69)
! major third sequence : 3673 173 1043 393 1777/3...

It would be easy to extend the main sequence only, to have,
with 12 notes, nine [4:6:7] eq-b triads (or [6:7:8])
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Jacques

Mike wrote :

> > > Or perhaps "mesotonic," because they're middle sized scales, not
> > > haplotonic and not chromatic. Maybe that's the simplest of all.
> >

Just for info in case you don't know, "Mesotonique" is the french word for "Meantone temperament"...

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Jacques