Atomic notation again

Here is what we find if we want to take it up to the 23-limit:

3: [19, 1] 1:32805/32768, 5632/5625
5: [28, -7] 7: 126/125
7: [34, -16] 16: 56/55
11: [42, -25] 25: 36/35
13: [43, 72] 72: 6561/6050
17: [47, 105] 105: 260/231
19: [50, 50] 50: 128/121 ~ (36/35)^2
23: [52, 117] 117: 416/363

Atomic is a strong temperament up to the 11-limit, which is therefore
where this scheme works best. Here is a list of what we would need to
notate all the 11-limit consonances. Dave tells us that 5632/5625,
441/440, 126/125, 99/98, 56/55, 50/49 and 36/35 already have symbols;
the rest we could get, if in no other way, by combining these.

1 5632/5625
2 441/440
7 126/125
8 15625/15488
9 99/98
16 56/55
17 28672/28125
18 50/49
25 36/35
26 22528/21875
27 567/550

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Here is what we find if we want to take it up to the 23-limit:
>
> 3: [19, 1] 1:32805/32768, 5632/5625
> 5: [28, -7] 7: 126/125
> 7: [34, -16] 16: 56/55
> 11: [42, -25] 25: 36/35
> 13: [43, 72] 72: 6561/6050
> 17: [47, 105] 105: 260/231
> 19: [50, 50] 50: 128/121 ~ (36/35)^2
> 23: [52, 117] 117: 416/363

Gene,

Puhleeease put some column headings on these lists. Is your time
really so much more valuable than that of your readers?

I haven't a clue what you're on about here.

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > Here is what we find if we want to take it up to the 23-limit:
> >
> > 3: [19, 1] 1:32805/32768, 5632/5625
> > 5: [28, -7] 7: 126/125
> > 7: [34, -16] 16: 56/55
> > 11: [42, -25] 25: 36/35
> > 13: [43, 72] 72: 6561/6050
> > 17: [47, 105] 105: 260/231
> > 19: [50, 50] 50: 128/121 ~ (36/35)^2
> > 23: [52, 117] 117: 416/363

> I haven't a clue what you're on about here.

The [19, 1] for 3 says that you need 19 semitones, or 1900 cents
exactly, plus a schisma to get to 3. The 5632/5625 says this will
serve as a schisma. We have [19, 1] = [19, 0] + [0, 1]. The rest of
the primes are the same. It indicates what complexites and what kind
of 13-limit versions of n schismas it takes to get to the primes up to 23.