tetrachords ii

So here's a little more concerning tetrachords. So far we've accrued 3 different tetrachords (with notes starting on C for analysis):

major tetrachord (C D E F)
minor tetrachord (C D Eb F)
phrygian tetrachord (C Db Eb F)

And we've been able to put those together as a pair to form a scale/mode in 9 different ways:

Major Scale (maj tet + maj tet)
Mixolydian (maj tet + min tet)
Dorian (min tet + min tet)
Phrygian (phryg tet + phryg tet)
Aeolian (min tet + phryg tet)
Melodic Minor (min tet + maj tet)
Neapolitan Major (phryg tet + maj tet)
Dorian b2 (phryg tet + min tet)
Mixolydian b6 (maj tet + phryg tet)

If we add just one more tetrachord we'll be able to up our total to 16 different scales. So let's add one which we'll call the harmonic tetrachord. It's the upper tetrachord of the harmonic minor scale, and looks like this taken out of a C harmonic minor context:
So with this tetrachord we can add the following scales to our syllabus:

Harmonic Minor (min tet + harm tet)
Harmonic Major (maj tet + harm tet)
Double Harmonic (harm tet + harm tet)
Neapolitan Minor (phryg tet + harm tet)
Ionian b2 (harm tet + maj tet)^FN1
Mixolydian b2 (harm tet + min tet) [mode v of harmonic major]
Phrygian Dominant (harm tet + phryg tet) [mode v of harmonic minor]


Next time? One more tetrachord...

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1. This is a very rare mode and I haven't yet been able to locate it in a scale syllabus -- in fact the Ionian b2 name is just one I gave it as it is purely descriptive.