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 are found in many common heptatonic scales, including Major, Melodic Minor, its inverse Harmonic Major and also Neapolitan, all of which are close relatives of Whole Tone. From a tonal perspective 1-3-b7 looks like an incomplete dominant chord, and in a more obscure way so does 1-3-#4. But we'd like to think of them as their own things.

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.