Yahoo Tuning Groups Ultimate Backup tuning Re: tuning system of Ramos/Ramis

>> [Mauel Op de Coul]
>> I looked it up and both spellings are right.
>> Ramos de Pareja Bartolomeo, or Ramis de Pareia Bartolome,
>> (1440-c.1491), Spanish theorist.
>
> [Paul Erlich, TD 381.9]
> And how did his 12-tone JI tuning differ from Ellis's duodene?

Ramos/Ramis:

[_Musica Practica_, Bologna, 1482]

4:3---1:1---3:2---9:8---27:16---81:64
D A E B F# C#
| | | |
| | | |
256:135---64:45---16:15---8:5---6:5---9:5
Ab Eb Bb F C G

[see Oliver Strunk, _Source Readings in Music History_,
W. W. Norton, New York, 1950: p 201-204. It's also on
p 83 of the copy of my book that you have, Paul.]

Ellis:

[Helmholtz, _On the Sensations of Tone_, Dover, New York, 1954
(reprint of 1885 2nd Edition of Ellis's English translation):
Appendix XX, section E, p. 461]

Note that Ramos, along with most medieval theorists,
called 1:1 'A', but Ellis, along with most modern theorists,
called it 'C'.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

Manuel Op de Coul wrote,

> 135/128 10/9 32/27 5/4 4/3 45/32 3/2 128/81 5/3 16/9 15/8 2/1

>Lattice:

> * * * * * *
> * * * * 0 *

Predictably enough, this can be construed as a Fokker periodicity block,
this time with unison vectors of a syntonic comma (4 -1) and a schisma (8
1):

|4 -1|
| | = 4*1 - (8*(-1)) = 4 + 8 = 12
|8 1|

| | | | * | | | | | | | |
| | | * | * | | | | | | |
| | * | | | * | | | | | | |
800| * | 100| | | * | | 225| 675| 2025 6075
*--/--400/-----/81-50/27-25/18-25/24*25/16-75/64---/-----/-----/1024-/--*
|729 |243 | | | | * | |128 |512 | * 4096
| | | | | | | * | | | * | |
| | | | | | | * | * | | |
| | | | | | | | * | | | |
| | | | | | | * | * | | |
| | | | | | * | | | * | | |
1280 | 160| | | * | | | | 135* 405| 1215
---/--320/-----/81-40/27*10/9---5/3---5/4--15/8--45/32---/--*--/256--/---
|729 |243 | * | | | | | | |128 * 1024
| | * | | | | | | | | | * |
| * | | | | | | | | | | *
* | | | | | | | | | | | | *
* | | | | | | | | | | * |
| * | | | | | | | | | * | |
1024 256* 128| | | | | | | * | | 243|
---/-----/--*--/81-32/27-16/9---4/3---1/1---3/2-*-9/8--27/16-81/64---/---
|729 |243 * | | | | * | | | | |128
| | | * | | | * | | | | | |
| | | * | * | | | | | | |
| | | | * | | | | | | | |
| | | * | * | | | | | | |
| | * | | | * | | | | | | |
4096 * | 512| 256| | * | | | | 243| 729|
*--/-2048/-----/-----/---64/45-16/15*-8/5---9/5--27/20-81/80---/160--/--*
3645 1215 |405 |135 | | * | | | | * |640
| | | | | | | * | | | * | |
| | | | | | | * | * | | |
| | | | | | | | * | | | |

Joe Monzo wrote,

>Ramos/Ramis:

>[_Musica Practica_, Bologna, 1482]

Just transpose the above by 6:5 to get these ratios in the FPB.

🔗Joe Monzo <monz@xxxx.xxxx>

> [Paul Erlich, TD 382.19]
>
> Predictably enough, this can be construed as a Fokker periodicity
> block, this time with unison vectors of a syntonic comma (4 -1) and
> a schisma (8 1):
>
> |4 -1|
> | | =3D 4*1 - (8*(-1)) =3D 4 + 8 =3D 12
> |8 1|
>
> <etc. ...>

Paul inadvertently skipped the 6:5 in the bottom row of his diagram,
and incorrectly shifted the last five ratios to the right.

The corrected lattice is:

| | | | * | | | | | | | |
| | | * | * | | | | | | |
| | * | | | * | | | | | | |
800| * | 100| | | * | | 225| 675| 2025 6075
*--/--400/-----/81-50/27-25/18-25/24*25/16-75/64---/-----/-----/1024-/--*
|729 |243 | | | | * | |128 |512 | * 4096
| | | | | | | * | | | * | |
| | | | | | | * | * | | |
| | | | | | | | * | | | |
| | | | | | | * | * | | |
| | | | | | * | | | * | | |
1280 | 160| | | * | | | | 135* 405| 1215
---/--320/-----/81-40/27*10/9---5/3---5/4--15/8--45/32---/--*--/256--/---
|729 |243 | * | | | | | | |128 * 1024
| | * | | | | | | | | | * |
| * | | | | | | | | | | *
* | | | | | | | | | | | | *
* | | | | | | | | | | * |
| * | | | | | | | | | * | |
1024 256* 128| | | | | | | * | | 243|
---/-----/--*--/81-32/27-16/9---4/3---1/1---3/2-*-9/8--27/16-81/64---/---
|729 |243 * | | | | * | | | | |128
| | | * | | | * | | | | | |
| | | * | * | | | | | | |
| | | | * | | | | | | | |
| | | * | * | | | | | | |
| | * | | | * | | | | | | |
4096 * | 512| 256| | * | | | | | 243|
*--/-2048/-----/-----/---64/45-16/15*-8/5---6/5---9/5--27/20-81/80---/--*
3645 1215 |405 |135 | | * | | | | * |160
| | | | | | | * | | | * | |
| | | | | | | * | * | | |
| | | | | | | | * | | | |

(be sure to view in a fixed-width font, such as Courier)

-monz