The Henry Ward Poole 100 note scale

This is a true historical curiosity, described in some detail in one
of Ellis' appendices to Helmholtz. It is something of a monstrosity,
but I'd suggest adding it to the Scala depository on historical
grounds; it doesn't seem to be there already. This should be correct,
as I made my list and checked it twice, etc. Ellis gives cents values,
including a wrong one for Ebb.

! poole100.scl
Henry Ward Poole's 100 note 7-limit scale, Helmholtz page 474
100
!
32805/32768
2240/2187
28/27
8505/8192
20480/19683
25/24
137781/131072
256/243
135/128
2187/2048
7168/6561
35/32
800/729
567/512
65536/59049
10/9
18225/16384
9/8
295245/262144
280/243
7/6
76545/65536
2560/2187
75/64
32/27
1215/1024
19683/16384
896/729
315/256
100/81
5103/4096
8192/6561
5/4
164025/131072
81/64
35/27
21/16
688905/524288
320/243
675/512
4/3
10935/8192
177147/131072
8960/6561
112/81
2835/2048
81920/59049
25/18
45927/32768
1024/729
45/32
729/512
28672/19683
35/24
3200/2187
189/128
40/27
6075/4096
3/2
98415/65536
1120/729
14/9
25515/16384
10240/6561
25/16
413343/262144
128/81
405/256
6561/4096
3584/2187
105/64
400/243
1701/1024
32768/19683
5/3
54675/32768
27/16
140/81
7/4
229635/131072
1280/729
225/128
16/9
3645/2048
59049/32768
35840/19683
448/243
945/512
50/27
15309/8192
4096/2187
15/8
492075/262144
243/128
35/18
12800/6561
63/32
160/81
2025/1024
2

have you cracked the code on this one?

Gene Ward Smith wrote:

>This is a true historical curiosity, described in some detail in one
>of Ellis' appendices to Helmholtz. It is something of a monstrosity,
>but I'd suggest adding it to the Scala depository on historical
>grounds; it doesn't seem to be there already. This should be correct,
>as I made my list and checked it twice, etc. Ellis gives cents values,
>including a wrong one for Ebb.
>
>! poole100.scl >Henry Ward Poole's 100 note 7-limit scale, Helmholtz page 474
>100
>!
>32805/32768
>2240/2187
>28/27
>8505/8192
>20480/19683
>25/24
>137781/131072
>256/243
>135/128
>2187/2048
>7168/6561
>35/32
>800/729
>567/512
>65536/59049
>10/9
>18225/16384
>9/8
>295245/262144
>280/243
>7/6
>76545/65536
>2560/2187
>75/64
>32/27
>1215/1024
>19683/16384
>896/729
>315/256
>100/81
>5103/4096
>8192/6561
>5/4
>164025/131072
>81/64
>35/27
>21/16
>688905/524288
>320/243
>675/512
>4/3
>10935/8192
>177147/131072
>8960/6561
>112/81
>2835/2048
>81920/59049
>25/18
>45927/32768
>1024/729
>45/32
>729/512
>28672/19683
>35/24
>3200/2187
>189/128
>40/27
>6075/4096
>3/2
>98415/65536
>1120/729
>14/9
>25515/16384
>10240/6561
>25/16
>413343/262144
>128/81
>405/256
>6561/4096
>3584/2187
>105/64
>400/243
>1701/1024
>32768/19683
>5/3
>54675/32768
>27/16
>140/81
>7/4
>229635/131072
>1280/729
>225/128
>16/9
>3645/2048
>59049/32768
>35840/19683
>448/243
>945/512
>50/27
>15309/8192
>4096/2187
>15/8
>492075/262144
>243/128
>35/18
>12800/6561
>63/32
>160/81
>2025/1024
>2
>
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning-math@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> have you cracked the code on this one?

No, and it's a pretty strange-looking scale, with all those
schisma intervals in it. By far the most obvious way to temper it is
garibaldi, the 41&53 temperament. That boils the whole thing down to
Garibaldi[43], which is a hell of a big difference from a 100 note
scale. But with 43 notes out of 94, you could just go to the 94 and
you'd still have fewer notes than the 100 you started with.

i made a graphic of it here, for a webpage which i
intended to flesh out but never finished.

http://sonic-arts.org/monzo/poole/poole.htm

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> This is a true historical curiosity, described in some detail in one
> of Ellis' appendices to Helmholtz. It is something of a monstrosity,
> but I'd suggest adding it to the Scala depository on historical
> grounds; it doesn't seem to be there already. This should be
correct,
> as I made my list and checked it twice, etc. Ellis gives cents
values,
> including a wrong one for Ebb.
>
> ! poole100.scl
> Henry Ward Poole's 100 note 7-limit scale, Helmholtz page 474
> 100
>
> <snip>

it looks like 5 -22 tone pythag. seperated by other just intervals

monz wrote:

>i made a graphic of it here, for a webpage which i
>intended to flesh out but never finished.
>
>http://sonic-arts.org/monzo/poole/poole.htm
>
>
>
>-monz
>http://tonalsoft.com
>Tonescape microtonal music software
>
>
>
>--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> >wrote:
> >
>>This is a true historical curiosity, described in some detail in one
>>of Ellis' appendices to Helmholtz. It is something of a monstrosity,
>>but I'd suggest adding it to the Scala depository on historical
>>grounds; it doesn't seem to be there already. This should be >> >>
>correct,
> >
>>as I made my list and checked it twice, etc. Ellis gives cents >> >>
>values,
> >
>>including a wrong one for Ebb.
>>
>>! poole100.scl >>Henry Ward Poole's 100 note 7-limit scale, Helmholtz page 474
>>100
>>
>><snip>
>> >>
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles