John Pike Mander's Adlington-Hall organ tuning

according to John's Nov.2004 specifications,
overtaken from
http://www.mander-organs.com/discussion/index.php?showtopic=66&st=0&p=440&#entry440
it is actually

! J_P_Mander.scl
!
John Pike Mander's Adlington-Hall organ tuning
!
!C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B -1/6 F# -1/5 C# -1/6 G#
!Ab +2/3 Eb 0 Bb 0 F 0 C
!
12
!
78.0 ! C#
192. ! D
294. ! Eb
384. ! E
498. ! F
578. ! F#
696. ! G
775. ! G#
888. ! A
996. ! Bb
1080. ! B
2/1
!

Some samples
http://www.baroquecds.com/21Web.html
http://www.baroquecds.com/samples.html
http://www.baroquecds.com/Adlington.html

the organ
http://www.adlingtonhall.com/
http://www.cduniverse.com/search/xx/music/pid/1074762/a/Organ+At+Adlington+Hall.htm

Quest
How would the neo-Baroque experts in that group here
tune that old instrument for coeval G.F.Haendel recordings ?
not to mention J.S.Bach ?

bye
A.S.

A very brief excerpt of the the Aldington Hall organ was broadcast on the BBC on Saturday morning. The presenters commented that the tuning was not 12-tET, but no more detail. I looked it up on the web only to find that A.S. had covered it a year ago (see below).

(Note however the PC fractions don't seem to add up - F#-C# is stated to be "-1/5" but it needs to be "-1/12" to add up - A.S. seems to have made this change for us.)

Link to BBC programme (but NB it was a very short excerpt!):
http://www.bbc.co.uk/programmes/b00s4w8d

Steve M.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...> wrote:
>
> according to John's Nov.2004 specifications,
> overtaken from
> http://www.mander-organs.com/discussion/index.php?showtopic=66&st=0&p=440&#entry440
> it is actually
>
> ! J_P_Mander.scl
> !
> John Pike Mander's Adlington-Hall organ tuning
> !
> !C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B -1/6 F# -1/5 C# -1/6 G#
> !Ab +2/3 Eb 0 Bb 0 F 0 C
> !
> 12
> !
> 78.0 ! C#
> 192. ! D
> 294. ! Eb
> 384. ! E
> 498. ! F
> 578. ! F#
> 696. ! G
> 775. ! G#
> 888. ! A
> 996. ! Bb
> 1080. ! B
> 2/1
> !
>
> Some samples
> http://www.baroquecds.com/21Web.html
> http://www.baroquecds.com/samples.html
> http://www.baroquecds.com/Adlington.html
>
> the organ
> http://www.adlingtonhall.com/
> http://www.cduniverse.com/search/xx/music/pid/1074762/a/Organ+At+Adlington+Hall.htm
>
> Quest
> How would the neo-Baroque experts in that group here
> tune that old instrument for coeval G.F.Haendel recordings ?
> not to mention J.S.Bach ?
>
> bye
> A.S.
>

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> (Note however the PC fractions don't seem to add up
> - F#-C# is stated to be "-1/5" but it needs to be "-1/12" to add up > > - A.S. seems to have made this change for us.)

In deed Martin,
at that time I thought, that little change as convenient, in order to get rid of the somewhat unclear specification on Mander's own web-site, :

http://www.mander-organs.com/discussion/index.php?showtopic=66&st=0&p=440&#entry440
quote:
" C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B ...
... B -1/6 F# -1/5 C# -1/6 G# +2/3 Eb 0 Bb 0 F 0 C "

Guess:
Maybe here got the fractions of the SC and PC mixed or even confused?
because SC^(13/12)=~PC or PC^(11/12)=~SC.

bye
A.S.

--- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@...> wrote:
> quote:
> " C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B ...
> ... B -1/6 F# -1/5 C# -1/6 G# +2/3 Eb 0 Bb 0 F 0 C "
> Guess:
> Maybe here got the fractions of the SC and PC mixed or even confused?
> because SC^(13/12)=~PC or PC^(11/12)=~SC.

Yes that makes sense - if he meant SC then two of the M3's are 5/4, and we can assume that the "+2/3" is an approximation.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> (Note however the PC fractions don't seem to add up - F#-C# is stated to be "-1/5" but it needs to be "-1/12" to add up - A.S. seems to have made this change for us.)
>
> > http://www.mander-organs.com/discussion/index.php?showtopic=66&st=0&p=440&#entry440
> > ! J_P_Mander.scl
> > !
> > John Pike Mander's Adlington-Hall organ tuning
> > !
> > !C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B -1/6 F# -1/5 C# -1/6 G#
> > !Ab +2/3 Eb 0 Bb 0 F 0 C
> > !
> > 12
> > !
> > 78.0 ! C#
> > 192. ! D
> > 294. ! Eb
> > 384. ! E
> > 498. ! F
> > 578. ! F#
> > 696. ! G
> > 775. ! G#
> > 888. ! A
> > 996. ! Bb
> > 1080. ! B
> > 2/1
> > !

Hi Martin,
but a closer look into J.P.Mander's specification on his web-site
allows to deduce clearly, that Mander intends to divide the SC
instead of the the PC, as once I had supposed wrongly.
Hence here comes the corresponding subdivision of the SC=81/80.
The reanalysis yields now:

!J_P_Mander_SC.scl
!
John Pike Mander's Adlington-Hall organ tuning compiled by A.Sparschuh
!
! C -1/4 G -1/4 D -1/4 A -1/4 E -1/4 B -1/6 F# -1/5 C# -1/6 G# ...
! ... Ab +2/3 Eb 0 Bb 0 F 0 C as all in fractions of the SC=81/81
!
12
!
78.9165045 ! C# ! (135/128) / (81/80)^(-1/4 -1/6 -1/5) >~chroma 25/24
193.156857 ! D ! (9/8) / (81/80)^(1/2) standard meantonic whole-tone
32/27 ! Eb ! Pythagorean minor-3rd from pure 5ths Eb-Bb-F-C
5/4 ! E ! just-major-3rd as in meantonics
4/3 ! F ! just-4th: C-F
581.262762 ! F# ! (45/32) * (81/80)^(-1/4 -1/6) tritone
696.578428 ! G ! (3/2) * (81/80)^(-1/4) ordinary meantonic-5th
777.842470 ! Ab ! (128/81) / (81/80)^(+2/3) minor-6th
!777.28712 ! G# ! (405/256) * (81/80)^(-1/4 -1/6 -1/5 -1/6)
889.735285 ! A ! (5/3) * (81/80)^(1/4) ordinary meantonic-6th
16/9 ! Bb ! just diminished-7th due to pure 5ths: Bb-F-C
1082.89214 ! B ! (15/8) / (81/80)^(1/4) ordinary meantonic-7th
2/1
!
! Attend the tiny 'enharmonic' difference inbetween Ab - G# of about
! 777.842470 - 777.28712 = ~ +0.555346...Cents only.
!
![eof]

Now that corrected version makes i.m.h.o. more sense
than the obsolete PC-variant with an enharmonic-difference
of about more than an schisma.

bye
A.S.