Yahoo Tuning Groups Ultimate Backup tuning Handel's 16-tone meantone organ (was: 7:5 tritone in Common Practice JI ...)

Since Tom's original post about this concerned the music of Handel,
and since i've already written before about Partch's description
of Handel's 16-tone extended-meantone organ keyboard

http://tonalsoft.com/monzo/partch/et/partch-on-et.htm

i decided to create a complete interval list of all the
intervals available in Handel's tuning, using 1/4-comma
meantone.

(There was discussion of this here years ago when i first
made that webpage ... i don't recall it now, but it's in
the list archives for those who want to look ... just be
warned that Partch's description may not be entirely
accurate.)

I took the time to make this for several reasons:

* Handel's music was much more popular and influential in its
time than Bach's (with the single exception of the
_Well-Tempered Klavier_);

* Beethoven admired Handel very much, and considered him
to have been the greatest composer before himself, so there
was probably a strong influence of Handel's harmonic practice
on Beethoven;

* in general, "common-practice" harmony is based on the
assumption that notes written according to this set of sharps
and flats would be tuned this way, in practice at least up
to the early Beethoven (c.1800), and in theory all the way
up to c.1900.

(Hopefully those viewing this on the Yahoo web interface
can see it correctly by clicking the "Option" link which
appears in the upper right under the date, and then clicking
"Use Fixed Width Font".)

cents are rounded to the nearest 1/10-cent

CHAIN-OF-5THS:

+10 A# 965.8
+9 D# 269.2
+8 G# 772.6
+7 C# 76.0
+6 F# 579.5
+5 B 1082.9
+4 E 386.3
+3 A 889.7
+2 D 193.2
+1 G 696.6
0 C 0.0
-1 F 503.4
-2 Bb 1006.8
-3 Eb 310.3
-4 Ab 813.7
-5 Db 117.1

SCALE:

note cents

B 1082.9
Bb 1006.8
A# 965.8
A 889.7
Ab 813.7
G# 772.6
G 696.6
F# 579.5
F 503.4
E 386.3
Eb 310.3
D# 269.2
D 193.2
Db 117.1
C# 76.0
C 0.0

INTERVAL LIST:

notes in the interval are listed with the lower note
on the left

cents notes interval

1200.0 [all] perfect-8ve

1158.9 Bb:A# augmented-7th
1158.9 Db:C# augmented-7th
1158.9 Eb:D# augmented-7th
1158.9 Ab:G# augmented-7th

1124.0 C#:C diminished-8ve
1124.0 D#:D diminished-8ve
1124.0 E:Eb diminished-8ve
1124.0 G#:G diminished-8ve
1124.0 A:Ab diminished-8ve
1124.0 D:Db diminished-8ve
1124.0 F#:F diminished-8ve
1124.0 A#:A diminished-8ve
1124.0 B:Bb diminished-8ve

1082.9 Db:C major-7th
1082.9 Eb:D major-7th
1082.9 E:D# major-7th
1082.9 F:E major-7th
1082.9 G:F# major-7th
1082.9 Ab:G major-7th
1082.9 A:G# major-7th
1082.9 Bb:A major-7th
1082.9 B:A# major-7th
1082.9 C:B major-7th
1082.9 D:C# major-7th

1047.9 D#:Db double-diminished-8ve
1047.9 A#:Ab double-diminished-8ve

1006.8 E:D minor-7th
1006.8 F:Eb minor-7th
1006.8 G#:F# minor-7th
1006.8 A:G minor-7th
1006.8 Bb:Ab minor-7th
1006.8 C#:B minor-7th
1006.8 D:C minor-7th
1006.8 D#:C# minor-7th
1006.8 Eb:Db minor-7th
1006.8 F#:E minor-7th
1006.8 G:F minor-7th
1006.8 A#:G# minor-7th
1006.8 B:A minor-7th
1006.8 C:Bb minor-7th

965.8 F:D# augmented-6th
965.8 Ab:F# augmented-6th
965.8 Bb:G# augmented-6th
965.8 C:A# augmented-6th
965.8 Db:B augmented-6th
965.8 Eb:C# augmented-6th

930.8 D#:C diminished-7th
930.8 E:Db diminished-7th
930.8 F#:Eb diminished-7th
930.8 G#:F diminished-7th
930.8 A#:G diminished-7th
930.8 B:Ab diminished-7th
930.8 C#:Bb diminished-7th

889.7 F:D major-6th
889.7 A:F# major-6th
889.7 Bb:G major-6th
889.7 C#:A# major-6th
889.7 Eb:C major-6th
889.7 E:C# major-6th
889.7 F#:D# major-6th
889.7 G:E major-6th
889.7 Ab:F major-6th
889.7 B:G# major-6th
889.7 C:A major-6th
889.7 Db:Bb major-6th
889.7 D:B major-6th

848.7 Db:A# double-augmented-5th

813.7 E:C minor-6th
813.7 F:Db minor-6th
813.7 F#:D minor-6th
813.7 G:Eb minor-6th
813.7 G#:E minor-6th
813.7 A:F minor-6th
813.7 A#:F# minor-6th
813.7 B:G minor-6th
813.7 C:Ab minor-6th
813.7 C#:A minor-6th
813.7 D#:B minor-6th
813.7 D:Bb minor-6th

772.6 Bb:F# augmented-5th
772.6 F:C# augmented-5th
772.6 G:D# augmented-5th
772.6 Ab:E augmented-5th
772.6 C:G# augmented-5th
772.6 Db:A augmented-5th
772.6 D:A# augmented-5th
772.6 Eb:B augmented-5th

737.6 G#:Eb diminished-6th
737.6 C#:Ab diminished-6th
737.6 F#:Db diminished-6th
737.6 A#:F diminished-6th
737.6 D#:Bb diminished-6th

696.6 F:C perfect-5th
696.6 G:D perfect-5th
696.6 G#:D# perfect-5th
696.6 Ab:Eb perfect-5th
696.6 A:E perfect-5th
696.6 Bb:F perfect-5th
696.6 B:F# perfect-5th
696.6 C:G perfect-5th
696.6 C#:G# perfect-5th
696.6 Db:Ab perfect-5th
696.6 D#:A# perfect-5th
696.6 E:B perfect-5th
696.6 F#:C# perfect-5th
696.6 D:A perfect-5th
696.6 Eb:Bb perfect-5th

655.5 Ab:D# double-augmented-4th
655.5 Db:G# double-augmented-4th
655.5 Eb:A# double-augmented-4th

620.5 G#:D diminished-5th
620.5 A:Eb diminished-5th
620.5 C#:G diminished-5th
620.5 F#:C diminished-5th
620.5 G:Db diminished-5th
620.5 A#:E diminished-5th
620.5 B:F diminished-5th
620.5 D:Ab diminished-5th
620.5 D#:A diminished-5th
620.5 E:Bb diminished-5th

579.5 Ab:D augmented-4th (tritone)
579.5 A:D# augmented-4th (tritone)
579.5 Bb:E augmented-4th (tritone)
579.5 C:F# augmented-4th (tritone)
579.5 Db:G augmented-4th (tritone)
579.5 E:A# augmented-4th (tritone)
579.5 F:B augmented-4th (tritone)
579.5 G:C# augmented-4th (tritone)
579.5 D:G# augmented-4th (tritone)
579.5 Eb:A augmented-4th (tritone)

544.5 G#:Db double-diminished-5th
544.5 A#:Eb double-diminished-5th
544.5 D#:Ab double-diminished-5th

503.4 A:D perfect-4th
503.4 Bb:Eb perfect-4th
503.4 C#:F# perfect-4th
503.4 G:C perfect-4th
503.4 G#:C# perfect-4th
503.4 Ab:Db perfect-4th
503.4 A#:D# perfect-4th
503.4 B:E perfect-4th
503.4 C:F perfect-4th
503.4 D:G perfect-4th
503.4 D#:G# perfect-4th
503.4 Eb:Ab perfect-4th
503.4 E:A perfect-4th
503.4 F:Bb perfect-4th
503.4 F#:B perfect-4th

462.4 Bb:D# augmented-3rd
462.4 Db:F# augmented-3rd
462.4 F:A# augmented-3rd
462.4 Ab:C# augmented-3rd
462.4 Eb:G# augmented-3rd

427.4 G#:C diminished-4th
427.4 A:Db diminished-4th
427.4 A#:D diminished-4th
427.4 B:Eb diminished-4th
427.4 C#:F diminished-4th
427.4 D#:G diminished-4th
427.4 E:Ab diminished-4th
427.4 F#:Bb diminished-4th

386.3 Bb:D major-3rd
386.3 Ab:C major-3rd
386.3 A:C# major-3rd
386.3 B:D# major-3rd
386.3 C:E major-3rd
386.3 Db:F major-3rd
386.3 D:F# major-3rd
386.3 Eb:G major-3rd
386.3 E:G# major-3rd
386.3 F:A major-3rd
386.3 F#:A# major-3rd
386.3 G:B major-3rd

351.3 A#:Db double-diminished-4th

310.3 A:C minor-3rd
310.3 Bb:Db minor-3rd
310.3 B:D minor-3rd
310.3 C:Eb minor-3rd
310.3 C#:E minor-3rd
310.3 D#:F# minor-3rd
310.3 E:G minor-3rd
310.3 F:Ab minor-3rd
310.3 G#:B minor-3rd
310.3 A#:C# minor-3rd
310.3 D:F minor-3rd
310.3 F#:A minor-3rd
310.3 G:Bb minor-3rd

269.2 Bb:C# augmented-2nd
269.2 C:D# augmented-2nd
269.2 Db:E augmented-2nd
269.2 Eb:F# augmented-2nd
269.2 F:G# augmented-2nd
269.2 G:A# augmented-2nd
269.2 Ab:B augmented-2nd

234.2 C#:Eb diminished-3rd
234.2 A#:C diminished-3rd
234.2 B:Db diminished-3rd
234.2 D#:F diminished-3rd
234.2 F#:Ab diminished-3rd
234.2 G#:Bb diminished-3rd

193.2 Bb:C major-2nd (whole-tone)
193.2 C:D major-2nd (whole-tone)
193.2 C#:D# major-2nd (whole-tone)
193.2 Db:Eb major-2nd (whole-tone)
193.2 E:F# major-2nd (whole-tone)
193.2 F:G major-2nd (whole-tone)
193.2 G#:A# major-2nd (whole-tone)
193.2 A:B major-2nd (whole-tone)
193.2 B:C# major-2nd (whole-tone)
193.2 D:E major-2nd (whole-tone)
193.2 Eb:F major-2nd (whole-tone)
193.2 F#:G# major-2nd (whole-tone)
193.2 G:A major-2nd (whole-tone)
193.2 Ab:Bb major-2nd (whole-tone)

152.1 Db:D# double-augmented-prime
152.1 Ab:A# double-augmented-prime

117.1 C#:D minor-2nd (diatonic-semitone)
117.1 B:C minor-2nd (diatonic-semitone)
117.1 C:Db minor-2nd (diatonic-semitone)
117.1 D:Eb minor-2nd (diatonic-semitone)
117.1 D#:E minor-2nd (diatonic-semitone)
117.1 E:F minor-2nd (diatonic-semitone)
117.1 F#:G minor-2nd (diatonic-semitone)
117.1 G:Ab minor-2nd (diatonic-semitone)
117.1 G#:A minor-2nd (diatonic-semitone)
117.1 A:Bb minor-2nd (diatonic-semitone)
117.1 A#:B minor-2nd (diatonic-semitone)

76.0 Bb:B augmented-prime (chromatic-semitone)
76.0 Db:D augmented-prime (chromatic-semitone)
76.0 F:F# augmented-prime (chromatic-semitone)
76.0 A:A# augmented-prime (chromatic-semitone)
76.0 C:C# augmented-prime (chromatic-semitone)
76.0 D:D# augmented-prime (chromatic-semitone)
76.0 Eb:E augmented-prime (chromatic-semitone)
76.0 G:G# augmented-prime (chromatic-semitone)
76.0 Ab:A augmented-prime (chromatic-semitone)

41.1 C#:Db diminished-2nd
41.1 D#:Eb diminished-2nd
41.1 G#:Ab diminished-2nd
41.1 A#:Bb diminished-2nd

0.0 C:C perfect-prime (unison)
0.0 C#:C# perfect-prime (unison)
0.0 Db:Db perfect-prime (unison)
0.0 D:D perfect-prime (unison)
0.0 D#:D# perfect-prime (unison)
0.0 Eb:Eb perfect-prime (unison)
0.0 E:E perfect-prime (unison)
0.0 F:F perfect-prime (unison)
0.0 F#:F# perfect-prime (unison)
0.0 G:G perfect-prime (unison)
0.0 G#:G# perfect-prime (unison)
0.0 Ab:Ab perfect-prime (unison)
0.0 A:A perfect-prime (unison)
0.0 A#:A# perfect-prime (unison)
0.0 Bb:Bb perfect-prime (unison)
0.0 B:B perfect-prime (unison)

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

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > ...Partch's description of Handel's 16-tone extended-meantone
> > organ keyboard...

http://www.music.ed.ac.uk/russell/conference/Gwynnonparker.html

Dr. Burney, in his 'Sketch of the Life of Handel,'...1785, says, 'The
organ in the chapel of this [i.e.the Foundling] hospital was a present
from Handel' But how are we to reconcile this statement with the
following, [European Magazine, Feb. 1799] 'Handel did not give the
organ to the Foundling Hospital. It was built at the expense of the
charity, under the direction of Dr. Smith, the learned Master of
Trinity College, Cambridge, who added demitones, &c., and some
niceties not occurring on other organs.'" (Edward F. Rimbault, Notes
and Queries, April 17, 1852)

Dr. Burney, in his account of the 1784 Commemoration of Handel, when
recording his impressions upon The Messiah performance remarks,
"The favorite bass song, The Trumpet shall sound, was very well
performed by Signor Tasca and Mr. Sarjant. Some passages however in
the trumpet part have always a bad effect from the natural
imperfection of the instrument, The fourth and sixth of a key on
trumpets and French horns are naturally so much out of tune that no
player can make them perfect. These sounds should never be used but in
short passing notes, to which no bass is given that can discover their
false intonation. Mr. Sarjant's tone is extremely sweet and clear, but
every time he was obliged to dwell upon G, the fourth of D (the key
sound) displeasure appeared in every countenance, for which I was
extremely concerned, knowing how inevitable such an effect must be
from such a cause. In the Halleluha Chorus G, the fourth of the key,
is sustained during two entire bars. In the Dettingen Te Deum, and in
many other places, this false concord or interval perpetually deforms
the fair face of harmony, and indeed the face of almost any one that
hears it, with an expression of pain."
So wrote Dr. Burney. Now for the truth. The trumpet is a perfect
instrument in respect to all sounds generated from its key sound or
unit. All its harmonics are exquisitely in tune. Hark ! at the seventh
where it comes -- the ratio of 7 to 8 -- how pure and noble it is!
This seventh we never hear on the piano, and only in one or two places
in the old-fashioned organ. From its own innate perfection the trumpet
refuses all unnatural, that is imperfect, sounds or ratios. They are
obtained with great difficulty and heard with disgust. No trumpet can
geenerate the fourth of its key. But the flat fifth is a pure primary
harmonic, and this is the sound trumpet players have to coax or
torture into a fourth. The instrument is not the unnatural wretch Dr.
Burney imagines; it is the instrumentalist who is the evil doer. The
case with the D trumpet stands thus. F sharp, its third, is its 1/5,
5X2=10. A flat is its flat fifth or 1/11. Twice 10 is 20, twice 11,
22. Between comes in 21, which is G natural, not the fourth of D, but
the pure seventh of A. Carry up these ratios once more. Twice 20 is
40, twice 22, 44. Now F sharp is 40, and A flat is 44, so that 41, 42,
and 43 lie between the two sounds. 1/41 of D os a very sharp major
third, a primary harmonic. 42 is the 21 or 7th of A. But G, the root
of D, or rather its octave, stands between 42 and 43. Thus the player
has to coax 44 into 42 1/2 or thereabouts.
(Henry John Gauntlett, Notes and Queries, Sept. 19, 1857)

Clark

Handel's 16-tone meantone organ (was: 7:5 tritone in Common Practice JI ...)

🔗monz <monz@tonalsoft.com>

🔗Tom Dent <stringph@gmail.com>

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