§6.3 UNIFORMITY OF THE O-NOTATION FOR VARIABLY TUNED COURSES

The set of pairs (key signature, corresponding natural tuning) for the 11 string baroque lute has a property, which is important for sight-reading:

Given an arbitrary variably tuned course, the empty strings of this course are represented by the same note symbol in the scores, whatever natural tuning is used. This representation is called the standard representation of this course (in O-notation).

Example:
Course 10 is represented by a note symbol, which is divided in the middle by the 4th ledger line below the five line stave.
Using key signature 4#, the 10th course is tuned to (d#D#), and, the key signature containing a # for d, the 10th course is represented within the scores by this note symbol, without modification.
Using key signature 2#, the 10th course is tuned to (dD), and, the key signature containing no # for d, the 10th course is represented within the scores by the same note symbol, without modification.
Using key signature 4b, the 10th course is tuned to (dbDb), and, the key signature containing a b for d, the 10th course is represented within the scores by the same note symbol, without modification.

Hint:
There are examples of Weiss pieces, the tuning of which is the natural tuning for some key signature, but the key signature of the piece differs from this key signature. In this case the representation of a variably tuned course is not necessarily identical with the standard representation of this course (in O-notation).

§7 NATURAL TUNINGS OF A 13 COURSE BAROQUE LUTE

§7.1 ALGORITHM

The natural tuning of the variably tuned strings of a 13 course baroque lute for a key is determinded as follows:

Step 1:
Determine the start note in O-Notation as follows:
= G#, if the key signature consists of 3#, 4#, 5#, 6#
= Gb, if the key signature consists of 5b or 6b
= G, else

Step 2:
Determine the key-specific descending note sequence n1 n2 n3 n4 n5 n6 n7 for the key and the start note

Step 3:
Determine the natural tuning of the variably tuned strings as
(o1 n1) (o2 n2) (o3 n3) (o4 n4) (o5 n5) (o6 n6) (o7 n7)
Where o1 = n1 + one octave, o2 = n2 + one octave and so on.

§7.2 COMPLETE LIST OF NATURAL TUNINGS OF A 13 COURSE BAROQUE LUTE

I) TUNING OF VARIABLY TUNED STRINGS (in O-Notation):

Tuning for key signature =6#: (g#G#) (f#F#) (e#E#) (d#D#) (c#C#) (BB1) (A#A1#)
Tuning for key signature =5#: (g#G#) (f#F#) (eE) (d#D#) (c#C#) (BB1) (A#A1#)
Tuning for key signature =4#: (g#G#) (f#F#) (eE) (d#D#) (c#C#) (BB1) (AA1)
Tuning for key signature =3#: (g#G#) (f#F#) (eE) (dD) (c#C#) (BB1) (AA1)
Tuning for key signature =2#: (gG) (f#F#) (eE) (dD) (c#C#) (BB1) (AA1)
Tuning for key signature =1#: (gG) (f#F#) (eE) (dD) (cC) (BB1) (AA1)
Tuning for key signature = : (gG) (fF) (eE) (dD) (cC) (BB1) (AA1)
Tuning for key signature =1b: (gG) (fF) (eE) (dD) (cC) (BbB1b) (AA1)
Tuning for key signature =2b: (gG) (fF) (ebEb) (dD) (cC) (BbB1b) (AA1)
Tuning for key signature =3b: (gG) (fF) (ebEb) (dD) (cC) (BbB1b) (AbA1b)
Tuning for key signature =4b: (gG) (fF) (ebEb) (dbDb) (cC) (BbB1b) (AbA1b)
Tuning for key signature =5b: (gbGb) (fF) (ebEb) (dbDb) (cC) (BbB1b) (AbA1b)
Tuning for key signature =6b: (gbGb) (fF) (ebEb) (dbDb) (cbCb) (BbB1b) (AbA1b)

So the tuning for key signature 2b is identical with standard tuning.

II) RETUNING BASED ON STANDARD TUNING:

Retuning for key signature =6#: Sharpen courses 7, 8, 9(twice), 10, 11, 12, 13
Retuning for key signature =5#: Sharpen courses 7, 8, 9, 10, 11, 12, 13
Retuning for key signature =4#: Sharpen courses 7, 8, 9, 10, 11, 12
Retuning for key signature =3#: Sharpen courses 7, 8, 9, 11, 12
Retuning for key signature =2#: Sharpen courses 8, 9, 11, 12
Retuning for key signature =1#: Sharpen courses 8, 9, 12
Retuning for key signature = : Sharpen courses 9, 12
Retuning for key signature =1b: Sharpen course 9,
Retuning for key signature =2b:
Retuning for key signature =3b: Flatten course 13
Retuning for key signature =4b: Flatten courses 10, 13
Retuning for key signature =5b: Flatten courses 7, 10, 13
Retuning for key signature =6b: Flatten courses 7, 10, 11, 13

§7.3 UNIFORMITY OF THE O-NOTATION FOR VARIABLY TUNED COURSES

This property is also valid for the 13 course baroque lute (for details see §6.3).

§8 TUNINGS IN THE DRESDEN AND LONDON WEISS MANUSCRIPTS

The following analysis is based on the details about tunings provided by Jean-Daniel Forget.

The scope of the analysis are all pieces in the Dresden and London Weiss Manuscripts, with the exception of the duos of the Dresden Manuscript and the concerts of the London Manuscript.

§8.1 CLASSIFICATION OF THE SCORES

The scores are assigned to three classes:

Suite:
A set of connected pieces which is originally called a suite, a suonata or a partie.

Sequence of pieces:
A set of connected pieces which is no suite.

Single piece:
A piece of music which is not connected to another piece.

The Dresden MS consists of 34 suites.
The London MS consists of 27 suites, 3 sequences of pieces and 34 single pieces.

§8.2 KEY-CONFORM AND INDIVIDUAL TUNING

The following definitions will be used in the analysis of Weiss scores.

Definition:
A piece of music has key-conform tuning on an instrument, if the tuning for the piece is identical with the natural tuning for the key of the piece on this instrument.

Definition:
A suite / sequence of pieces has key-conform tuning, if all pieces of the suite / sequence have key-conform tuning.

Definition:
A piece of music / suite / sequence of pieces has individual tuning, if it hasn't key-conform tuning.

Conclusion for 13 course baroque lutes:
If a suite / sequence of pieces has key-conform tuning, and all pieces in the suite / sequence of pieces have the same tuning, then all these pieces have the same key signature.
Proof:
Let us assume that this conclusion is not true. Then there exists a suite with the same tuning for all pieces, but at least two pieces having different key signatures. From the list of natural tunings on a 13 course baroque lute follows, that two different key signatures also have different tunings. This is a contradiction to the assumption.
Comment:
The same conclusion is not valid in context with 11 course baroque lutes, as key signatures blank and 1b have the same tunings (likewise 2b and 3b).

§8.3 LEVEL OF ASSIGNMENT OF A TUNING

For every suite / sequence of pieces / single piece in the two manuscripts, the level of assignment of a tuning is the same suite / sequence of pieces / single piece.

In other words: A tuning is never changed within a suite or sequence of pieces.

§8.4 WEISS MUSIC FOR AN 11 COURSE BAROQUE LUTE

Key signature 3#:

Suites in the Dresden MS with key-conform tuning:
No 17 (A)

Key signature 2#:

Single pieces in the London MS with key-conform tuning:
No 6 (D)

Key signature 1b :

Suites in the London MS with key-conform tuning:
No XIV (F) : Jean-Daniel Forget assigns a 13 course lute, but in fact an 11 course lute is sufficient

Single pieces in the London MS with key-conform tuning:
No 3 (F), 4 (F), 25 (d), 39 (d), 40 (d)

Key signature 2b :

Single pieces in the London MS with key-conform tuning (standard tuning):
No 8 (Bb), 9 (Bb), 10 (Bb), 28 (Bb)

Key signature 3b :

Single pieces in the London MS with key-conform tuning (standard tuning):
No 27 (c)

Mixed key signatures:

Sequence of pieces in the London MS with individual tuning:
No 57 (G and g): Used tuning: Natural tuning for key G.

§8.5 WEISS MUSIC FOR A 13 COURSE BAROQUE LUTE

§8.5.1 WEISS MUSIC FOR A 13 COURSE BAROQUE LUTE, WITHOUT COURSE 13 BEING USED

Key signature 2#:

Suites in the London MS with key-conform tuning:
No II (D)

Single pieces in the London MS with key-conform tuning:
No 67 (D)

Key signature 1#:

Suites in the London MS with key-conform tuning:
No IV (G)

Key signature :

Single pieces in the London MS with key-conform tuning:
No 61 (C), 62 (C)

Key signature 1b:

Suites in the Dresden MS with key-conform tuning:
No 3 (F, Sarabande in d )

Single pieces in the London MS with key-conform tuning:
No 59 (F), 16 (d)

Key signature 2b:

Suites in the London MS with key-conform tuning (standard tuning):
No III (g, Menuet ii in Bb)

Key signature 3b:

Jean-Daniel Forget only provides tunings for courses 1 to 12.
It is assumed, that the unused course 13 is tuned to (AA1) in O-notation, which is identical to the typical tuning for key signature 3b in context with course 13 being used.

Suites in the Dresden MS:
No 31 (c).
Used tuning: Natural tuning for Bb/g (standard tuning) => individual tuning

Suites in the London MS:
No VI (Eb), V (c).
Used tuning: Natural tuning for Bb/g (standard tuning) => individual tuning

Mixed key signatures:

Suites in the Dresden MS with individual tuning:
No 9 (C and c): Used tuning: Natural tuning for key C


§8.5.2 WEISS MUSIC FOR A 13 COURSE BAROQUE LUTE, WITH COURSE 13 BEING USED

Key signature 3#:

Suites in the Dresden MS with key-conform tuning:
No 18 (A), 19 (A), 20 (A, Sarabande in f#), 21 (A, Sarabande in f#), 22 (A), 23 (f#, Sarabande in A)

Suites in the London MS with key-conform tuning:
No VIII (A, Sarabande in f#), XI (A)

Key signature 2#:

Suites in the London MS with key-conform tuning:
No XIII (D) , XX (D)

Sequences of pieces in the London MS with key-conform tuning:
No 66 (D)

Single pieces in the London MS with key-conform tuning:
No 65 (D)

Key signature 1#:

Suites in the London MS with key-conform tuning:
No XVI (G, Sarabande in e)

Single pieces in the London MS with key-conform tuning:
No 11 (G), 13 (G), 18 (G)

Key signature :

Suites in the Dresden MS with key-conform tuning:
No 10 (C, Sarabande in a), 11 (C), 12 (C, Sarabande in a), 13 (a, Rigaudon in C), 14 (a, Sarabande in C), 15 (a), 16 (a, Sarabande in C)

Suites in the London MS with key-conform tuning:
No XII (C) , XXIII (a)

Single pieces in the London MS with key-conform tuning:
No 23 (C), 35 (C), 36 (C), 63 (C), 64 (C), 26 (a)

Key signature 1b :

Suites in the Dresden MS with key-conform tuning:
No 1 (F), 2 (F, Sarabande in d), 4 (F, Sarabande in d), 5 (d), 6 (d), 7 (d, Sarabande in F), 8 (d, Sarabande in F)

Suites in the London MS with key-conform tuning:
No I (F, Sarabande in d) , XXII (F, Sarabande in d), XXV (F, Menuet 2do in d), XXVI (F, Sarabande in d), VII (d), IX (d), Suite en duo (d, Menuet in F)

Single pieces in the London MS with key-conform tuning:
No 2 (F), 48 (F), 22 (d)

Key signature 2b :

Suites in the Dresden MS with key-conform tuning (standard tuning):
No 24 (Bb, Sarabande in g), 25 (Bb), 26 (Bb), 27 (Bb, Sarabande in g), 29 (g, Sarabande in Bb), 30 (g, Polonoise in Bb)

Suites in the London MS with key-conform tuning (standard tuning):
No X (Bb) , XVII (Bb), XIX (g)

Sequences of pieces in the London MS with key-conform tuning (standard tuning):
No 24, Duette (g): Jean-Daniel Forget assigns a tuning for 12 courses, but in fact 13 are needed.

Single pieces in the London MS with key-conform tuning (standard tuning):
No 12 (Bb), 29 (Bb)

Key signature 3b :

Suites in the Dresden MS with individual tuning:
No 34 (Eb), 32 (c, Sarabande and Angloise in Eb), 33 (c, Siciliana in Eb )
Used tuning: Natural tuning for Bb/g (standard tuning)

Suites in the London MS with individual tuning:
No XXIV (Eb) , XXI (c, Sarabande and La belle Tiroloise in Eb)
Used tuning: Natural tuning for Bb/g (standard tuning)

Single piece in the London MS with individual tuning:
No 56 (Eb)
Used tuning: Natural tuning for Bb (standard tuning)

Key signature 4b :

Suites in the Dresden MS with individual tuning:
No 28 (f)
Used tuning: Natural tuning for g (standard tuning)

Suites in the London MS with individual tuning:
No XV (f)
Used tuning: Natural tuning for g (standard tuning)

Key signature 5b :

Single pieces in the London MS with individual tuning:
No 60 (bb)
Used tuning: (gG) (fF) (ebEb) (dbDb) (cC) (BbB1b) (AA1)
This is not a natural tuning of any key.

Key signature 6b :

Single pieces in the London MS with individual tuning:
No 34 (eb)
Used tuning: (gG) (fF) (ebEb) (dbDb) (cbCb) (BbB1b) (AbA1b).
This, too, is not a natural tuning of any key.

Mixed key signatures:

Suites in the London MS with individual tuning:
No XVIII (C and c): Used tuning: Natural tuning for key C