The major scale is constructed as a stack of perfect fifths, so it contains the maximum number of them of any seven-note scale: six, in fact, because of that pesky diminished fifth between the 5 and 7 of the scale. I wondered which other scales (in 12EDO) contain lots of fifths.

Intuitively, I guessed that the more perfect fifths a scale has, the more familiar, consonant and Major-scale-ish it might sound. I expected, therefore, to find the scales in common tonal use -- the usual suspects like Harmonic and Melodic Minor -- near the top of any list of fifths-ful scales. But I was wrong.

The Fifths-Ful Heptatonics

Here I think is a list of all the heptatonic scale groups containing five perfect fifths, the most you can have if you're not the Major scale:

• Pavani (1 b2 bb3 #4 5 6 7)
• Jhalavarali (1 b2 bb3 #4 5 b6 7)
• Salagam (1 b2 bb3 #4 5 b6 bb7)
• Kamavardhani (1 b2 3 #4 5 b6 7)
• Bhavapriya (1 b2 b3 #4 5 b6 b7)
• Varunapriya (1 2 b3 4 5 #6 7)
• Vanaspati (1 b2 bb3 4 5 6 b7)
• Ratnangi (1 b2 bb3 4 5 b6 b7)
• Chalanata (1 #2 3 4 5 #6 7)
• Apeliotean (1 3 4 #4 5 6 7)
• Lipsean (1 b3 4 5 b6 6 b7)
• Ethian (1 2 b3 b4 4 5 6)

You can pretty easily search for these scales in the Encyclopedia to find more normal spellings, harmonization suggestions, guitar boxes and all their modes.

The first nine (Pavani to Varunapriya) are melakatas, and I'd have guessed they'd make a strong showing since you're guaranteed a perfect fifth by construction. The melakata system, as far as I know, doesn't make any more promises than that but from my initial search it looks like three is the fewest fifths a melakata can have, with Ramapriya and Sucharitra being examples.

The last three are weirdos, though. Apeliotean and Lipsean are two of the scales I call the eight winds; the other one is one that didn't fit into the general criteria for the Encyclopedia or for any of the exceptions I made. But all three are very far away from a major scale and I'm very surprised to see them on this list. By the way, "Ethian" is Justin Pecot's name that I got from Ian Ring's website -- it's convenient to have something to call this scale but the name doesn't have any actual currency, it's just made up (so are all names, though).

Fifths and Tonal Gravity

Harmonic and Melodic Minor have four perfect fifths each, so all these are more fifths-ful than those. What does that mean in practice? Every note in a scale can be a centre of tonal gravity -- not in the sense of tonal harmony but just a simpler sense of a tone towards which the music might tend to be pulled. A piece of music can have multiple centres of tonal gravity pulling in different directions with different strengths all at once.

If a note is going to exert a gravitational pull, it helps for it to be supported by other notes. Doubling it at the octave is one way, since that reinforces its vibrations. Doubling at a perfect fifth -- the next harmonic up -- is also good, and it's musically richer because that's a different note, not just the same note at a different pitch.

Now, this kind of appeal to overtones is all very well but it only sort-of works in 12EDO, where the fifths are imperfect and get out of phase very quickly, completely negating the alleged reinforcement effect. So we have to be cautious about dressing up our musical preferences as if they were natural and scientific. Still, most musical cultures recognise something like fifths as functional consonances and that's what I'm trying to exploit here.

The claim then would be that, when working in any scale or tuning, a pitch that has a perfect fifth above or below it will tend to have more "tonal gravity" than one that doesn't. Think of the Major scale modes, for example: the one everyone struggles the most with is Locrian, which is surely in part because we're trying to tonicise a note in a scale that doesn't provide it with a fifth for stabilisation. Playing music in Locrian is like trying to waltz on the moon.

The listed scales therefore offer the most options for tonal gravity reinforced by fifths. I think that makes them interesting, especially when none of them is used in Western music and a few are more or less unheard-of. I think these are also promising candidates for the basis of shimmer tunings and similar ideas.