Hi Peter,

Sorry, there does not (yet) exist a complete version of the theory outside the alto forum.

It is true that the theory has mainly evolved from a series of WORD documents. But it has undergone some filing directly in the forum, and probably still will. Luckily the forum software supports repeated editing of messages already posted, which allows reworking and extending the 'paper'.

Anyhow, maybe this will help you:
The surface of the alto forum offers two modes of presenting the messages:
<Threaded view> and <Flat view>.
Perhaps you have been only using <Threaded view> up to now.

If you're in <Threaded view>, just click on menu item <Flat view>, to switch over to <Flat view>.
And, vice versa, if you're in <Flat view>, just click on menu item <Threaded view>, to switch over to <Threaded view>.

<Flat view> integrates several adjacent messages of a thread into one 'page'.
So it takes just 4 successive 'pages', to read the whole theory.
Proceeding to the next page is triggered by clicking on <Next> at the bottom of a page.

PS: I'm glad you like the theory.

§9, Digression 2
has been replaced by the new
§12.4 TRANSPOSING DOWNWARDS WITHOUT EXCEEDING BASS RANGES

James,

I've been thinking about your idea to examine the advantages and disadvantages of several guitar types in order to complement an alto guitar as a flat key friendly instrument type by a sharp key friendly instrument type, in the context of playing baroque music.

The longer I've been pondering on this topic, the more it gained in attractivity.

But let's try to proceed systematically:
In order to have a common base for further examination, we might start with specifying precisely
.. what flat/sharp key friendliness means
.. which are the guitar types to examine.


FLAT/SHARP KEY FRIENDLINESS OF A GUITAR TYPE

Here is a proposal for a definition:

A guitar type is (baroque) flat / sharp key friendly, if the arrangement of a baroque lute piece originally composed in a flat / sharp key, in such a way that the sound (in terms of primary tone frequencies) of the piece is preserved, usually produces scores in a convenient key signature. In this context, key signature blank is considered belonging to the flat keys.

Remark 1:
This definition is restricted to baroque lute music because the discussion of the topic depends on the instrument type the original music is composed for.

Remark 2:
It is presupposed that preserving tone frequencies applies to the second string of a lute course, if the strings of this course are tuned in octave.

Remark 3:
It is assumed that the following key signatures are convenient key signatures for guitar arrangements: 5#, 4#, 3#, 2#, 1#, blank, 1b.

Remark 4:
It is presupposed that the synchronization of notes (on sound level) with tone frequencies is the same for all instrument types involved (i.e. also for the underlying baroque lute). This guarantees, that the arrangement key signature for a given baroque piece on a given instrument type is not ambiguous.

This will be made more transparent by the following examples.

Example 1:
Let us assume that we have a piece in G, played on a Baroque lute tuned with 440 Hz for a1. A sound preserving arrangement of this piece for an alto also tuned with 440 Hz for a1 is produced by transposing three semitones down, which results in an arranging key of E, i.e. key signature 4#. 4# is a convenient arranging key signature.

Example 2:
The sound for the same piece is also preserved by the same arrangement if both instruments are tuned with 415.305 Hz (or any other frequency) for a1.

Example 3:
However, if the pitch of the lute is one semitone below the pitch of the alto (for example with 415.305 Hz for a1 on the lute and 440 Hz for a1 on the alto), a sound preserving arrangement is achieved by transposing 4 semitones down, which results in an arranging key of Eb, i.e. key signature 3b. This is not a convenient arranging key signature for guitars.


NUMBER OF STRINGS

In order to achieve comparability, the guitar types examined should allow to produce sound preserving arrangements of the same pieces.

Producing a sound preserving arrangement implies, that the bass range of the respective guitar type is not exceeded. One might demand, that the number of strings be sufficient to produce a sound preserving arrangement of any lute piece written for a 13 course lute (with course 13 being used). This makes sense, as this is the most common type of music in Weiss's oeuvre.


DESCRIBING GUITAR TYPES

In order have the same level of description, one might describe a guitar type by

.. Determining whether it's a transposing or non-transposing guitar type

.. Specifying its number of strings

.. Identifying the variably tuned strings

.. Specifying its natural tunings. The tuning for the convenient key signature 1# on score level will be taken as a representative of these tunings.


GUITAR TYPES

The alto guitar will also be described according to the pattern defined above (see Guitar type 1).


Guitar type 1

A transposing guitar type with 12 strings.
Variably tuned strings: 6 to 12.

Natural tunings for strings 6 to 12: see <A Theory of Scordatura for Music by S.L. Weiss>, §10.2.

Tuning for key signature 1# on score level:
e1..b...f#..d..A..E..D..C..B1..A1..G1...F1#
Resulting tuning on sound level:
g1..d1..a...f..c..G..F..Eb..D..C...B1b..A1


Guitar type 2

A transposing guitar type with 13 strings.
Variably tuned strings: 7 to 13.

Natural tunings for strings 7 to 13 on score level: Similar to natural tunings for strings 7 to 13 for a 13 string alto on score level (see <A Theory of Scordatura for Music by S.L. Weiss>, §10.2.) .

Tuning for key signature 1# on score level:
e1..b...f#..d..A..E..D..C...B1..A1..G1..F1#..E1
Resulting tuning on sound level:
a1..e1..b...g..d..A..G..F....E...D....C...B1....A1


Guitar type 3

A non-transposing guitar type with 10 strings.
Variably tuned strings: 6 to 10.

Natural tunings for strings 6 to 10 on score and sound level: Similar to natural tunings for strings 6 to 12 for guitar type 1 on score level.

Tuning for key signature 1# on score level:
e1..b..f#..d..A..E..D..C..B1..A1
Resulting tuning on sound level:
e1..b..f#..d..A..E..D..C..B1..A1

This guitar type is easy to implement by using a 10-string guitar with baroque tuning.


Guitar type 4

A non-transposing guitar type with 12 strings.
Variably tuned strings: 6 to 12.

Natural tunings for strings 8 to 12 on score and sound level: Similar to natural tunings for strings 6 to 10 for guitar type 1. Natural tunings for string 6 on score level: G#, G or Gb depending on key signature. Natural tunings for string 7 on score level: F# or F, depending on key signature.

Tuning for key signature 1# on score level:
e1..b..f#..d..A..G..F#..E..D..C..B1..A1
Resulting tuning on sound level:
e1..b..f#..d..A..G..F#..E..D..C..B1..A1


Guitar type 5

A non-transposing guitar type with 12 strings.
Variably tuned strings: 6 to 12.

Natural tunings for strings 6 to 12 on score and sound level: Similar to natural tunings for strings 8, 9, 10, 11, 12, 6, 7 of guitar type 4.

Tuning for key signature 1# on score level:
e1..b..f#..d..A..E..D..C..B1..A1..G...F#
Resulting tuning on sound level:
e1..b..f#..d..A..E..D..C..B1..A1..G...F#


(DRAFT OF) A ROAD MAP FOR FURTHER EXAMINATION

E1. Verifying flat/sharp key friendliness of the guitar types

E2. Comparing the guitar types with respect to criteria, which can be examined independently of concrete pieces:

E2.1 Number of variably tuned strings

In order not to increase the risk of creating unfrettable constellations on a guitar type, it is fortunate, if the number of variably tuned strings is equal to the number of variably tuned courses of the underlying baroque lute, i.e. = 7.

E2.2 Correspondences of adjacent lute courses with fixed tuning and adjacent guitar strings with fixed tuning

It is fortunate if frettings or parts of frettings of lute courses with fixed tuning can be preserved. The probability of achieving this increases with the number of adjacent strings of the respective guitar type with the same fixed tuning (on sound level) as adjacent lute courses.

E2.3 Identical transformation note -> fretting position for the pair of guitar types

The aim of the examination is to complement an alto guitar as a flat key friendly instrument type by a sharp key friendly instrument type. With respect to sight-reading it is fortunate, if the same fretting positions on the two instrument types correspond to the same notes on score level. So one can switch back and forth between the two instrument types without having to observe a change of the rules for locating the notes on the respective instrument type.

E3. Comparing the guitar types with respect to criteria, which can only be examined with concrete pieces as a basis

E3.1 Playability of the music
The only difference between the tunings of the 13 string alto and the tunings of guitar type 2 on score level is, that the 6th string of the 13 string alto is variably tuned, whereas the 6th string of guitar type 2 has fixed tuning. A closer inspection reveals, that for the key signatures we focus on in this treatise, namely the convenient key signatures, there is no difference in tuning.

So we can test the playability of arrangements for guitar type 2 on a 13 string alto, using a transposition of 5 semitones down.

Similarly the playability of arrangements for guitar type 3 can be simulated on an 11- or 13-string alto, using original scores (i.e. scores for the lute, without transposition).

The test of the playability of the music on guitar types 4 and 5 requires the availability of an appropriate instrument, using original scores.

E3.2 Actual sound

This requires the availability of appropriate instruments.

Silvanig,
A very thoughtful analysis. Just a few comments on the problem of playing baroque lute music on a guitar with typical guitar tuning, i.e., fourths and one third in the first six strings.
1) There are two problems in trying to play baroque lute music on a multi-string guitar in E: a) the open 6th and 7th courses on a baroque lute, viz., G and F, which can be sharpened, offer a supporting bass that cannot always be reproduced or reproduced easily by fretting the 6th string;
2) the different tuning of a baroque lute(f', d', a, f, d, A, etc.), means in many cases that a lutenist plays notes in the treble across the strings, that a guitarist plays along the string; played in the way a guitarist plays, although all the notes are reproduced, the campanella effect inherent in performance on a baroque lute is lost. Further, certain chords, slurs and ornaments are not playable on a guitar, i.e., a chord may have a note missing, etc.. I have noted in transcribing baroque pieces that a composer can deliberately choose alternative fingerings to exploit the campanella effect.
Both points are important. While a piece by Weiss played on guitar may still sound impressive, it would be enhanced by the natural campanella effect of performance on a baroque lute, and, of course, on a lute, all chords and slurs can be played accurately. In my experience, problems with slurs, ornaments and chords can be more or less important in a given piece, one can be lucky. Accuracy of performance on a guitar-like instrument is possible if one adopts the "Dresden" guitar developed by Michael Thames. It has thirteen strings, and is tuned like a baroque lute, but without any octave strings in the bass as could occur on some baroque lutes. Being tuned like a baroque lute, one can play from tablature, and/or, learn a new fret board. While this may sound like a lot to learn, if one's major interest is baroque lute music, the effort must be worthwhile.
If one is prepared to live with the inaccuracies caused by guitar tuning, performance of baroque pieces in open or sharp keys can have point 1), and a number of arrangements of other music, greatly helped by a 12s guitar in E with tuning along the lines you have indicated, e', b, g, d, A, G, F, E, D, C, B', A'. The additional G and F can be placed below the A'. This tuning was proposed by the Russian guitarist, Nikolai Pavlistcheff, sometime in the 1840's, I believe, when he went to live in Poland.
James.

James,

I have added the instrument type proposed by Pavlistcheff as guitar type 5 to the list of guitar types to be examined.

ANALYSIS CONTINUED:

E1. VERIFYING FLAT / SHARP KEY FRIENDLINESS OF GUITAR TYPES 1 TO 5


Inspection of guitar type 1

Lute key signature............................:6#...5#...4#....3#....2#...1#.....bl....1b...2b....3b...4b...5b...6b
Guitar key signature (scores)...........:3b...4b...5b....6#....5#...4#....3#....2#...1#....bl....1b...2b...3b
Convenient key signature (scores)..:..-......-......-......-....OK..OK..OK..OK..OK..OK..OK....-......-

Hints:

.. Guitar key signature 6b, which would be an alternative counterpart to lute key signature 3#, has been omitted, assuming that 6# is a better key signature than 6b.

.. OK/- indicates a convenient/inconvenient arranging key signature

Verifying the thesis, that guitar type 1 is flat key friendly:

Lute key signatures blank, 1b, 2b, 3b and 4b lead to convenient key signatures on score level, but not 5b and 6b. The definition of flat key friendliness requires that a sound preserving arrangement usually produces scores in a convenient key signature. As 5b and 6b are rarely used (from where we stand, there are just 2 pieces in the whole Weiss oeuvre composed with these key signatures), the definition of flat key friendliness is fulfilled.


Inspection of guitar type 2

Lute key signature............................:6#...5#...4#....3#....2#...1#....bl....1b...2b...3b...4b...5b...6b
Guitar key signature (scores)...........:5b...6#...5#....4#....3#...2#....1#....bl...1b...2b...3b...4b...5b
Convenient key signature (scores)..:..-......-...OK..OK..OK..OK..OK..OK..OK....-......-.....-....-

Verifying the thesis, that guitar type 2 is sharp key friendly:

Lute key signatures 1#, 2#, 3# and 4# lead to convenient key signatures on score level, but not 5# and 6#. But as 5# and 6# are rarely used (from where we stand, there is no piece in the whole Weiss oeuvre composed with these key signatures), the definition of sharp key friendliness is fulfilled.


Inspection of guitar type 3

As this instrument type is a non-transposing one, there is no difference between scores and sound.

Formally applying the same scheme as above, we have:
Lute key signature............................:6#...5#...4#...3#....2#....1#....bl....1b...2b...3b...4b...5b...6b
Guitar key signature (scores)...........:6#...5#...4#...3#....2#....1#....bl....1b...2b...3b...4b...5b...6b
Convenient key signature (scores)..:..-...OK..OK..OK..OK..OK..OK..OK....-......-......-..... -.....-

Verifying the thesis, that guitar type 3 is sharp key friendly:

Key signatures 1#, 2#, 3#, 4# and 5# are convenient key signatures, but not 6#. But as 6# is rarely used (from where we stand, there is no piece in the whole Weiss oeuvre composed in this key signature), the definition of sharp key friendliness is fulfilled.


Inspection of guitar types 4 and 5

Like guitar type 3.