MJ Smith has said most of it...

> So this is the analogue computer for the I-VIII modal system. What
> might they have done with the ficta?

I would rather call the keyboard 'digital' - in every way. Nothing to
do with electronic of course - remember Jacquard and the punched
cards.

If the sole purpose of 'ficta' is to provide leading notes, their
tuning is most effectively made by pure thirds above the respective
dominants, or pure sixths above the supertonic (to use modern
terminology). With the Medieval base of Pythagorean tuning this was
achieved by tuning every 'ficta' note by descending pure fifths as if
it were a flat. Then the fifth B-F# (tuned as B-Gb) is bad. The Urbino
clavichord picture shows this tuning painstakingly transcribed by the
intarsia maker.

Then C-C# (tuned as C-Db by pure fifths) is a Pythagorean comma
smaller than C#-D, giving rise to the common notion of a small
chromatic semitone: 'semitonium minus', which is a comma smaller than
the large diatonic semitone 'secunda minor'. This notion of the
comma's difference between two types of semitone survived as a
theoretician's saw until about 1800, although it ceased to have any
accurate relation to musical reality when meantone came along, where
the difference is much larger. (The same goes for 'nine-comma
theory'...)

Ugolino discusses in "Tractatus monochordi" two different dispositions
of the ficta:

"Istorum autem fictorum semitoniorum duplex est divisio, una qua
minora praecedunt maiora semitonia, altera qua maiora antecedunt
minora."

i.e. in the first, the small semitones precede the large (as described
above), and vice versa in the second (where all ficta are tuned by
pure fifths as sharps). Since the monochord divisions are explicitly
described, we know that 'precede' means from left to right or bottom
to top.

Then

"Prima igitur monochordi ficta divisio ad perfectionem est imperfecta
et ad colorationem
perfecta. Haec autem secunda ad perfectionem perfecta, sed ad
colorationem redditur imperfecta."

The first monochord division is imperfect with regard to its
perfection (presumably the bad fifth B-F#), but perfect with regard to
its coloration (apparently the pure thirds or sixths made by the
leading notes F#,C#,G#,D#). The other way round for the second
division: its perfection (ascending fifths up to D#?) is perfect, but
its coloration imperfect (ficta leading notes make dissonant thirds or
sixths).

'Coloration' is of course the Latinized precursor of 'chromaticism'.

"Ex his igitur duabus monochordi divisionibus sic unitis, quoniam et
maiora sunt ibi semitonia atque minora quibus et imperfecta
perficiuntur et perfecta colorantur, ipsum monochordum vere dicitur
esse perfectum. Nam potest intelligens organista maiore uti semitonio
atque minore, altero quidem ad perfectionem, altero vero ad
colorationem."

Ugolino thinks it would be absolutely perfect if one had both types of
semitone available (in between the tones F-G-A-B and C-D-E): the
intelligent organist would use one for perfection and the other for
coloration.

http://www.chmtl.indiana.edu/tml/15th/UGOTRAM_06GF.gif

However, both E-F and B-C would remain *small* semitones - so even the
idealized 17-note keyboard doesn't make C-E into a consonant interval!

~~~T~~~