[r-t] Summary falseness of royal methods
Richard Smith
richard at ex-parrot.com
Sat Feb 3 16:18:42 UTC 2007
Don Morrison wrote:
> When applying the well known false course head "group" letters to
> royal methods some changes are needed, since the partitioning into
> sets of related false course heads was designed for major. Well known
> is that the in and out of course chunks that are always present
> together in major need not be together in royal; and that some of the
> in course chunks divide into two chunks which no longer have to appear
> together.
Of the 25 tenors-together falseness groups (A-U minus J and
Q, together with a-f), L, P and U (in-course), and K, N and a
(out-of-course) each split into two chunks.
L splits: 126543; 136245, 142563
P splits: 154326, 164352; 156342, 164523
U splits: 134256, 135426, 142356, 143652, 152436, 163254; 135264, 142635
K splits: 134526, 146352, 152346, 164253; 154362, 164325
N splits: 153264, 162435, 135462, 143625; 152634, 165234, 135624, 145632
a splits: 123465; 123546, 126453
> Is it also true that some of the chunks that in major can appear
> separately, in royal will always appear together? For example, is it
> true that in royal the in course B (24365) and D (32546, 46253) chunks
> will always appear together? If so, what other bits, potentially
> separate in major, coalesce in royal?
This is true, and it is the only (tenors-together) example
of two groups coalescing in this manner.
> I guess another way to ask this, is in royal there really is a
> different partitioning into false course head groups than in major.
> Closely related, but different. What is it?
There are 40 tenors-together falseness groups, and another
646 solely splits tenors (i.e. equivalent to X, Y, Z on
eight).
Of the 25 major groups, 15 are already single-parity
(if you ignore split tenors fchs): A, G, I, L, M, P, R, S,
U, a, b, c, d, e, f. This leaves only ten which split
through parity: B, C, D, E, F, H, K, N, O, T. The six
further splits noted above occur, and the in-course
coalescence of B and D reduces the number by one.
25 + 10 + 6 - 1 = 40
> And what happens at higher stages? It appears the in course B and D
> are no longer coalesced there.
This is the only change. There are 41 tenors-together
falseness groups for maximus and all higher stages.
RAS
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