I think I made at least one critical error in my analysis of the scale above. Specifically, I think the F# should be a G. This changes how things come out a lot and it makes more sense with data I have seen in the literature regarding frequency of various modes in Breton tunes.
So, here is another try. Hopefully with a few less errors. Still a work in progress though.
I think the notes on this flute, from bottom to top, are F, G, G#, Bb, C, C#, Eb.
These are the same notes as the G# major scale, so we could say that G# is the parent major scale.
G# A# B# C# D# E# G
G# Bb C C# Eb F G
1-2-3-4-5-6-7
The notes are not laid out on the flute in the normal way though. Instead, they are rotated so that the 6th degree of the major scale (F) is the flute’s bell note.
This gives the following intervals, which is the aeolian mode.
T S T T S T T == aeolian mode
So if you use the flute’s bell note as the tonic then you can play tunes in F aeolian mode. According to some papers I read, these tunes exist in Breton music, but are not especially common.
F G G# Bb C C# Eb F
T S T T S T T
1 2 3 4 5 6 7 1
But here is where it gets more convincing. If you use Bb as the tonic then you can play Bb dorian tunes, and, more importantly, Bb hypodorian tunes, which range from the F below, which is the 5th of the Bb dorian scale and the flute’s bell note.
Bb C C# Eb F G G# Bb
T S T T T S T
1 2 3 4 5 6 7 1
Hypodorien tunes are extremely common in Breton music (~30%), and hypodorien mode is the most common of all modes in Vannetais tunes (~33%).
So I think this is the strong motivation for this flute design! It also seems consistent with the names Sylvain Barou gave to the tuning.
The flute also gives you access to the following other modes
G# Ionian (common in Breton music) with a range of a couple of extra steps below the tonic.
G# Bb C C# Eb F G G#
1 2 3 4 5 6 7 1
Bb Dorian (already discussed above)
C Phrygian and C hypophrygian (ranging from G, which is the 5th of the C phrygian scale, below). Both are both quite common modes in Breton tunes and even more common in Vennetais tunes.
C C# Eb F G G# Bb C
1 2 3 4 5 6 7 1
C# Lydian
Eb Mixolydian
F Aeolian (already discussed above)
G Locrian … supposedly quite common in Breton tunes (7%) and Vennetaises (13%)
So, this seems more promising to me, but I’m still keen to hear from anyone with real experience in this area.