fokjack1

From: Gene Ward Smith (2004-09-16)
Subject: The seven 128/125 and ampersand Fokker blocks

The ampersand, of course, is the <-25 7 6| comma. If we put it
together with 128/125 we get seven Fokker blocks which are pretty
similar in character. The first on my list I give below on the grounds
it is inversely symmetrical; the others come in inversely equal pairs.

All of these scales have six major and six minor triads, and marvel
tempering gives five major and five minor tetrads; in comparison
Blackjack has eight major and eight minor tetrads. So far as tetrads
go we have something corresponding to Miracle[19]. I was hoping to get
something closer to Blackjack, since if we do the same sort of thing
with Fokker blocks for 81/80 and the ennealimma we get 45 note 5-limit
blocks which work fine as 5-limit versions of Ennealimma[45]; perhaps
the ampersand with a comma other than 128/125 would work.

! fokjack1.scl
First 128/125 and ampersand Fokker block
21
!
16875/16384
16/15
1125/1024
256/225
75/64
4096/3375
5/4
675/512
4/3
45/32
64/45
3/2
1024/675
8/5
3375/2048
128/75
225/128
2048/1125
15/8
32768/16875
2

From: Gene Ward Smith (2004-09-16)
Subject: The seven 128/125 and ampersand Fokker blocks

The ampersand, of course, is the <-25 7 6| comma. If we put it
together with 128/125 we get seven Fokker blocks which are pretty
similar in character. The first on my list I give below on the grounds
it is inversely symmetrical; the others come in inversely equal pairs.

All of these scales have six major and six minor triads, and marvel
tempering gives five major and five minor tetrads; in comparison
Blackjack has eight major and eight minor tetrads. So far as tetrads
go we have something corresponding to Miracle[19]. I was hoping to get
something closer to Blackjack, since if we do the same sort of thing
with Fokker blocks for 81/80 and the ennealimma we get 45 note 5-limit
blocks which work fine as 5-limit versions of Ennealimma[45]; perhaps
the ampersand with a comma other than 128/125 would work.

! fokjack1.scl
First 128/125 and ampersand Fokker block
21
!
16875/16384
16/15
1125/1024
256/225
75/64
4096/3375
5/4
675/512
4/3
45/32
64/45
3/2
1024/675
8/5
3375/2048
128/75
225/128
2048/1125
15/8
32768/16875
2

From: Gene Ward Smith (2004-09-16)
Subject: Re: The seven 128/125 and ampersand Fokker blocks

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

 I was hoping to get
> something closer to Blackjack, since if we do the same sort of thing
> with Fokker blocks for 81/80 and the ennealimma we get 45 note 5-limit
> blocks which work fine as 5-limit versions of Ennealimma[45]; perhaps
> the ampersand with a comma other than 128/125 would work.

One difficulty with this is that the 5-limit planar projection using
4375/4374 is a lot more like ennealimma than the marvel projection is
like miracle. If we project 2401/2400 to the 5-limit in 4375/4374
planar, we get the ennealimma, 19% larger than 2401/2400. If we
project 1029/1024 to the 5-limit using 225/224, we get the ampersand,
which is 409% larger than 225/224.

From: Gene Ward Smith (2004-09-16)
Subject: Re: The seven 128/125 and ampersand Fokker blocks

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> One difficulty with this is that the 5-limit planar projection using
> 4375/4374 is a lot more like ennealimma than the marvel projection is
> like miracle. If we project 2401/2400 to the 5-limit in 4375/4374
> planar, we get the ennealimma, 19% larger than 2401/2400. If we
> project 1029/1024 to the 5-limit using 225/224, we get the ampersand,
> which is 409% larger than 225/224.

I should have said 374% larger than 1029/1024, which is more to the
point. The 1/4-kleismic 1029/1024 is 77% of the JI version, so things
aren't so bad if we go ahead and marvelize, rather than looking at the
5-limit.