Ramos's tuning as a periodicity block

© 1999 by Paul Erlich


Onelist Tuning Digest 382
Message: 19
From: Paul H. Erlich
Sent: Friday, November 05, 1999 6:13 PM
To: 'tuning@onelist.com'
Subject: RE: [tuning] tuning system of Ramos/Ramis

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|

Joe Monzo wrote,


 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
 


Just transpose the above by 6:5 to get these ratios in the FPB [Fokker periodicity-block].

[Note from Monzo: In other words, the lattice given by Manuel and redrawn by Paul uses C = 1/1 as the reference. But Ramos actually used "A" as his reference, as in my diagram and the one like Paul's which would result from the transposition by 6:5.]


Back to where you were: Paul's A Gentle Introduction to Fokker Periodicity Blocks, part 2



Updated: 2000.1.20
By Joe Monzo

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