Forte 3-10

The Whole Tone Scale, 1 2 3 #4 #5 b7, has quite a few interesting subsets, including the well-known augmented triad and the dominant chords 7b5 and 7#5. Today we'll look at the "triad" 1-3-#4 and its inversion, 1-3-b7. These are known by the Forte number 3-10.

These have no obvious tonal application but are found in many common heptatonic scales, including Melodic Minor, its inverse Harmonic Major and also Neapolitan, all of which are close relatives of Whole Tone.

Here are full-fretboard diagrams of the two inversions of Forte 3-10 -- up top is 1-3-#4 and below is 1-3-b7:

I'm particularly interested here is not-too-crazy heptatonics that can be covered by three copies of 1-3-#4 or 1-3-b7 at various transpositions. For clarity I'll call 1-3-#4 "majb5" and 1-3-b7 "7¬5", but I don't really want to think about these as fragments of more familiar dominant chords. I found three interesting groups, which I'll describe from most to least promising.

A mode of Shadvidamargini(1,b2,b3,#4,5,6,b7) is obtained from majb5 at 1, b3 and b5. Playing it a minor third higher at b3, b5 and bb7 produces Ramapriya (1,b2,3,#4,5,6,b7), is obtained from 7¬5 at the 1, b5 and 6.

The fact that the roots form a diminished triad makes these a bit easier to learn. If we combine the two scales we get the octatonic 1,b2,b3,3,#4,5,6,b7, which is the Half-Whole diminished scale. Something magical happens here: this is covered by majb5 at the 1, b3, b5 and 6 (i.e. the notes of a dim7 chord) or by the 7¬5 at the same notes. So you can freely mix the two inversions built on those notes and get this scale. Then avoiding the 3 recovers Shadvidamargini, while avoiding the b3 gets you back to Ramapriya. This provides a very interesting perspective on on old friend, and suggests some ways to play the diminished scale you may not have thought of before.

Playing majb5 at the 1, #4 and 5 produces Vishwambari (1,b2,3,#4,5,#6,7). The inverse of this scale is Hatakambari (1,b2,3,4,5,#6,7), which can be obtained by playing 7¬5 at the 1, b2 or 5. Here the roots follow a sus #4 and a sus b2 triad, respectively.

Again, playing either of the inversions of 3-10 at all these positions -- 1, b2, #4 and 5 -- produces the same scale. This time it has ten notes so it's close to the total chromatic: 1 b2 2 3 4 b5 5 b6 b7 7. Its coscale is the tritone b3, 6. This suggests quite a different approach from the first one, but also suggests that the other possible combinations of the inversion of 3-10 at those four transpositions might be interesting.

However, many of them produce the symmetrical octatonic 1 b2 3 4 b5 5 b7 7, which I call Double Chromatic. Its coscale is 3-10, i.e. another copy of 1, b2, #4 and 5, this time built on the 2. There are some combinations that add one or two notes, so this might deserve a more thorough look in the future.

Playing majb5 instead at the 1, 4 and b5 produces a mode of Jhalavarali (1,b2,bb3,#4,5,b6,7). Jhalavarali itself is majb5 played at the 2, 7 and 8; its inverse is Salagam (1,b2,bb3,#4,5,b6,bb7), which is 7¬5 played at the 2, 8 and 9. In this case the patterns of roots seem less useful for memorization, since they follow an unusual three-note pattern (Forte 3-5).

Playing majb5 at the 2, 7, 8 and 9 produces the nine-note scale 1 b2 2 b3 b5 5 b6 6 7; playing 7¬5 at the same transpositions gives us the very similar (but different) 1 b2 2 4 b5 5 b6 6 7. I'm not sure at this point what to make of these, or whether this approach is likely to bear much fruit here.