And I partly understand. It's one of the most difficult common scales to put in harmony. It just doesn't work with classic notions of chord and cadence. And that's probably related to the way traditions that prefer this scale tend not to be big on chords. Though I haven't done any sort of objective analysis, it seems that in monophonic, multitimbral traditions (one note at a time but multiple, possibly different instruments or singers sharing that note), it's often preferred. It makes for exciting melodies. If you want polyphonic harmony, in other words chords that move, you'll probably have to break out of the scale often.
But I think if you look around the world, there are 3 most common scales: major, pentatonic‡, and the Byzantine/Jewish/Arabian/etc one I'm lavishing with attention today. Cultures have discovered and rediscovered these scales ad infinitum because there are fundamental reasons the ear is drawn to them most.
‡ (The major pentatonic most of all for pentatonics, pentatonic meaning 5 notes in the scale, but I think there are reasons to emphasize the set of notes as one united scale even more than it is five modes, given that you basically can't play anything that sounds bad or off—try it! Sit at a piano and play the black keys, and tell me if you can really go wrong. It doesn't matter where your bass note is. Plonk on the black keys, and it'll sound good. This is the most universal core of music around the world. Major pentatonic, minor pentatonic, mixolydian position pentatonic, etc, whichever note in the pattern you start on, people around the world love it.)
What I've just realized about the Byzantine scale (in Western music it's called the Double Harmonic Major scale, but who cares, that makes it sound so specialized when it isn't at all) is that it's not only symmetric (I did know that before), the only perfectly symmetric scale in 7 notes (hm, I should check this claim for its conditions), but it's actually symmetric within its two halves. It's the most fractal-looking scale I've ever seen.
You can see what I mean... if 1 means the note is on, and 0 means it's off, here is the pattern of every regular Major key:
101011 101011
(If we're in C Major, this means there's a C in our scale, there isn't a C#, there is a D, there isn't a D#, there is an E, etc.)
(If we're in C Major, this means there's a C in our scale, there isn't a C#, there is a D, there isn't a D#, there is an E, etc.)
You can see it's got a nice sort of symmetry, not a mirror, but repetition.
101011 <-> 101011
101011 <-> 101011
Here's Phrygian, ¶the¶ Flamenco scale:
110101 110101
¶ (Not exactly true. Flamenco music uses other scales also. But I think Phrygian most immediately harkens to what's different about Flamenco and Spanish music overall, for most people, in the lowered second note. It's a convenient and practical jumping-off point for Minor, Phrygian Dominant, Double Harmonic Major, and from there even the latter's popular mode Double Harmonic Minor. Also, I'm not concerned about whether we call Phrygian a scale or a mode, for sticklers out there, as we're comparing chromatic patterns with fixed beginnings and endings.)
¶ (Not exactly true. Flamenco music uses other scales also. But I think Phrygian most immediately harkens to what's different about Flamenco and Spanish music overall, for most people, in the lowered second note. It's a convenient and practical jumping-off point for Minor, Phrygian Dominant, Double Harmonic Major, and from there even the latter's popular mode Double Harmonic Minor. Also, I'm not concerned about whether we call Phrygian a scale or a mode, for sticklers out there, as we're comparing chromatic patterns with fixed beginnings and endings.)
It's the Major scale, flipped. Neato, right?
101011 101011 Major
110101 110101 Phrygian
Major sounds like it wants to rise and keep rising. Phrygian sounds like it wants to fall and stop. They're perfect opposites.
-
If you're unfamiliar with scales and modes, these 2 patterns live in a family of 7 connected musical patterns called the modes of the diatonic scale (diatonic meaning 7 notes). They are also called the Church modes, because they go back past Renaissance music to Gregorian chant. And even earlier than that: they go beyond the first musical notation, so we don't know when they started. (If familiar with modes, you can skip to the next section.) What I'm calling a "family" of modes (such a family is called a scale, and this 7-note/diatonic scale is the most standard scale around the world, at that), is kind of like a large piece of fabric, and the modes are like sections of it. Maybe we can pick on wallpaper—imagine some kind of tartan wallpaper in a big roll, if you like. This big piece of tissue, the common musical scale, is based on the idea of harmonics, which are whole-number multiples of a core frequency. It isn't critical here, but harmonics are essentially multipliers for sounds. Anyway to make a very long story short, this scale, this big "fabric" or "tartan wallpaper roll" is just the white keys on a piano.
In your mind, picture a rectangle of that striped wallpaper, and focus on the edges, which will look different depending on where you cut. If a scale is a big roll of wallpaper, a mode is a specific section cut from it, the stripes in the pattern situated wherever they are as a result of the cut at the beginning and the cut at the end of the section. Actually, the cut at the end occurs at the same point in the pattern as the cut at the beginning, the first time the pattern begins to repeat. That's always true with modes. And to go back and use my other metaphor, if the scale is a landscape, its 7 modes are like 7 big, overlapping photos of that landscape, or better still, 7 full panoramas with different center points. All this is most easily understood with your ears, by just playing the regular letter notes on a piano (white keys) or any other instrument: A, B, C, D, E, F, G. Hey, no sharps or flats yet! Now for the exciting bit. Starting on each letter and playing notes around it, you'll get a slightly different vibe. Actually, these vibes can feel very different from each other. There are 7 of those modes, one centered on each letter. They're like 7 windows looking out of the same castle on the same heathery, windswept valley, but focused on different parts of it with different emotions coming in through each window. There's the A window, the B window, the C window...
Major is the vibe you get when you start on C and play the white keys up or down to the next C. To be candid, just play anywhere, but always return to a C as the central station, the "home base" sound. Keep hitting C a lot, and also explore and play anything else, but just the white keys for now. So, whether it sounds lovely or excruciating, that's Major (C Major in particular, but I'll get to that). Phrygian, meanwhile, is the vibe you get from starting on E and playing the white keys up or down to the next E. And just like before, play all around, but only the white keys for now and keep returning to E as "home." Wherever you go every day, you start at home and end up at home, right? Travel the same way with music. If you don't return home, you'll feel lost or strange. Music uses that trick also, but most of the time, most of us return home at the end of the day, and the same is true in music. (Also, I know "only white keys" really sounds like some kind of racism, ha, and I'm sorry about that. There are pianos available that reverse the colors... though they tend to be more expensive because they look super rad and are in demand. Whichever palette your keyboard uses, interesting music tends to break out of this "only white keys" or "only black keys" thing.) Now, so far our keyboard strolling has demonstrated 2 of the 7 modes. The other 5 modes come from starting on F (Lydian), G (Mixolydian), A (Minor), B (Locrian), and D (Dorian).
There's much more, though, and this is just the tip of the iceberg of scale patterns. You can slide any pattern to start on any key of a piano, or on any frequency in the whole sound spectrum, including frequencies too high or low for a piano, or else drifting somewhere between the keys of a piano. For all starting points other than the mode's home letter on a piano, maintaining that mode's pattern or vibe will require black keys; or if we're between keys on the piano, we'll need more between-keys; if we're dealing with a musical staff and written notes, it'll require some sharps or flats. While C Major is all the white keys from C to C, F Major is almost all the letter notes from F to F, except not quite, because there will be no B key, but instead the B flat key to the left of it. And while E Phrygian is all the white keys from E to E, C Phrygian will have 4 black keys and only 3 white keys. The same goes for starting any of the modes on another letter. We break out of the white keys somewhere (or the black keys if the piano has reversed colors).
Note this is an artifact of piano design, not of sound itself. If you learn to sing and never look at a piano, there's no difference between E Phrygian and C Phrygian except where your voice is. The audio spectrum does not "think" or "feel" in terms of black keys or white keys, sharps or flats. Those are human constructs. On a guitar, sharp notes, flat notes, and natural notes look identical, because they are. A note is a frequency. Two notes are a pair of frequencies. Whether that pair sounds sharp, flat, or in tune depends on what you're used to hearing and what you're expecting, not actually on the frequencies themselves, not in any way that systematically matches the whole "sharps and flats" thing. Which isn't to say there's no reason for it, but sometimes we need to step back and look at ground truth.
One more point about naming. Often modes themselves are just called "scales," which is confusing. Basically all these patterns are scales, but "mode" is a special meaning of "scale" that refers to the (sibling) patterns you get from starting at different points in the same (parent) pattern. Let's pretend for a second, for illustration, that music is just numbers, not notes, not even sound. You could say the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2 ... are a scale, because, as you'll notice, it's a repeating pattern. If you started say on 4, that would create a different mode of the same scale: 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7 ... But since it's also a repeating pattern, it's also correct to call it a scale. It's just a scale that we're thinking of as a mode of another scale.
Minor mode (also called Aeolian):
A, B, C, D, E, F, G, A
Major mode (also called Ionian):
C, D, E, F, G, A, B, C
Phrygian mode:
E, F, G, A, B, C, D, E
And so on, for all 7 letters. The letters are shared, so it's all the same larger scale.
The spacing between the letters is not the same, so these modes have different sounds, feelings, atmospheres.
-
Back to the relationship between these two modes I was showing you, now that we've got a little background.
101011 101011 Major
110101 110101 Phrygian
Major is the second-brightest of the 7 diatonic modes (just below Lydian, the pattern starting on F). Phrygian is the second-darkest of them (just above Locrian, the pattern starting on B). You can see there's a kind of mirror of symmetry in between them, I hope. If so, that isn't your imagination. That isn't just a human construct. That's a real symmetry.
101011 101011 Major
110101 110101 Phrygian
Major sounds like it wants to rise and keep rising. Phrygian sounds like it wants to fall and stop. They're perfect opposites.
-
If you're unfamiliar with scales and modes, these 2 patterns live in a family of 7 connected musical patterns called the modes of the diatonic scale (diatonic meaning 7 notes). They are also called the Church modes, because they go back past Renaissance music to Gregorian chant. And even earlier than that: they go beyond the first musical notation, so we don't know when they started. (If familiar with modes, you can skip to the next section.) What I'm calling a "family" of modes (such a family is called a scale, and this 7-note/diatonic scale is the most standard scale around the world, at that), is kind of like a large piece of fabric, and the modes are like sections of it. Maybe we can pick on wallpaper—imagine some kind of tartan wallpaper in a big roll, if you like. This big piece of tissue, the common musical scale, is based on the idea of harmonics, which are whole-number multiples of a core frequency. It isn't critical here, but harmonics are essentially multipliers for sounds. Anyway to make a very long story short, this scale, this big "fabric" or "tartan wallpaper roll" is just the white keys on a piano.
In your mind, picture a rectangle of that striped wallpaper, and focus on the edges, which will look different depending on where you cut. If a scale is a big roll of wallpaper, a mode is a specific section cut from it, the stripes in the pattern situated wherever they are as a result of the cut at the beginning and the cut at the end of the section. Actually, the cut at the end occurs at the same point in the pattern as the cut at the beginning, the first time the pattern begins to repeat. That's always true with modes. And to go back and use my other metaphor, if the scale is a landscape, its 7 modes are like 7 big, overlapping photos of that landscape, or better still, 7 full panoramas with different center points. All this is most easily understood with your ears, by just playing the regular letter notes on a piano (white keys) or any other instrument: A, B, C, D, E, F, G. Hey, no sharps or flats yet! Now for the exciting bit. Starting on each letter and playing notes around it, you'll get a slightly different vibe. Actually, these vibes can feel very different from each other. There are 7 of those modes, one centered on each letter. They're like 7 windows looking out of the same castle on the same heathery, windswept valley, but focused on different parts of it with different emotions coming in through each window. There's the A window, the B window, the C window...
Major is the vibe you get when you start on C and play the white keys up or down to the next C. To be candid, just play anywhere, but always return to a C as the central station, the "home base" sound. Keep hitting C a lot, and also explore and play anything else, but just the white keys for now. So, whether it sounds lovely or excruciating, that's Major (C Major in particular, but I'll get to that). Phrygian, meanwhile, is the vibe you get from starting on E and playing the white keys up or down to the next E. And just like before, play all around, but only the white keys for now and keep returning to E as "home." Wherever you go every day, you start at home and end up at home, right? Travel the same way with music. If you don't return home, you'll feel lost or strange. Music uses that trick also, but most of the time, most of us return home at the end of the day, and the same is true in music. (Also, I know "only white keys" really sounds like some kind of racism, ha, and I'm sorry about that. There are pianos available that reverse the colors... though they tend to be more expensive because they look super rad and are in demand. Whichever palette your keyboard uses, interesting music tends to break out of this "only white keys" or "only black keys" thing.) Now, so far our keyboard strolling has demonstrated 2 of the 7 modes. The other 5 modes come from starting on F (Lydian), G (Mixolydian), A (Minor), B (Locrian), and D (Dorian).
There's much more, though, and this is just the tip of the iceberg of scale patterns. You can slide any pattern to start on any key of a piano, or on any frequency in the whole sound spectrum, including frequencies too high or low for a piano, or else drifting somewhere between the keys of a piano. For all starting points other than the mode's home letter on a piano, maintaining that mode's pattern or vibe will require black keys; or if we're between keys on the piano, we'll need more between-keys; if we're dealing with a musical staff and written notes, it'll require some sharps or flats. While C Major is all the white keys from C to C, F Major is almost all the letter notes from F to F, except not quite, because there will be no B key, but instead the B flat key to the left of it. And while E Phrygian is all the white keys from E to E, C Phrygian will have 4 black keys and only 3 white keys. The same goes for starting any of the modes on another letter. We break out of the white keys somewhere (or the black keys if the piano has reversed colors).
Note this is an artifact of piano design, not of sound itself. If you learn to sing and never look at a piano, there's no difference between E Phrygian and C Phrygian except where your voice is. The audio spectrum does not "think" or "feel" in terms of black keys or white keys, sharps or flats. Those are human constructs. On a guitar, sharp notes, flat notes, and natural notes look identical, because they are. A note is a frequency. Two notes are a pair of frequencies. Whether that pair sounds sharp, flat, or in tune depends on what you're used to hearing and what you're expecting, not actually on the frequencies themselves, not in any way that systematically matches the whole "sharps and flats" thing. Which isn't to say there's no reason for it, but sometimes we need to step back and look at ground truth.
One more point about naming. Often modes themselves are just called "scales," which is confusing. Basically all these patterns are scales, but "mode" is a special meaning of "scale" that refers to the (sibling) patterns you get from starting at different points in the same (parent) pattern. Let's pretend for a second, for illustration, that music is just numbers, not notes, not even sound. You could say the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2 ... are a scale, because, as you'll notice, it's a repeating pattern. If you started say on 4, that would create a different mode of the same scale: 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7 ... But since it's also a repeating pattern, it's also correct to call it a scale. It's just a scale that we're thinking of as a mode of another scale.
Minor mode (also called Aeolian):
A, B, C, D, E, F, G, A
Major mode (also called Ionian):
C, D, E, F, G, A, B, C
Phrygian mode:
E, F, G, A, B, C, D, E
And so on, for all 7 letters. The letters are shared, so it's all the same larger scale.
The spacing between the letters is not the same, so these modes have different sounds, feelings, atmospheres.
-
Back to the relationship between these two modes I was showing you, now that we've got a little background.
101011 101011 Major
110101 110101 Phrygian
Major is the second-brightest of the 7 diatonic modes (just below Lydian, the pattern starting on F). Phrygian is the second-darkest of them (just above Locrian, the pattern starting on B). You can see there's a kind of mirror of symmetry in between them, I hope. If so, that isn't your imagination. That isn't just a human construct. That's a real symmetry.
But here's the Byzantine scale:
110011 110011
It's symmetric, then it's symmetric inside each half. That's got to be related to why it's so goddamn compelling.
You can't get Byzantine by playing only white keys on a piano, unlike the others I've been talking about.
Also notice that you can get to it in two steps from the previous scale above it, Phrygian, and those two steps are actually the same step reflected in each half of the scale:
110101 110101
110011 110101
110011 110011
Traditional Spanish music just loves to navigate these three scales. They are called the Phrygian mode of the diatonic scale, the Phrygian dominant scale, and the Double Harmonic major scale, respectively, if we want to be "correct" (whatever that really means) and use the conventional names in English, down to which letters are capitalized. Personally, I call them Phrygian, Spanish Phrygian, and Byzantine. Works for me.
110101 110101 (Phrygian mode of the diatonic scale / Phrygian)
110011 110101 (Phrygian dominant / Spanish Phrygian)
110011 110011 (Double Harmonic major / Byzantine)
The last one is most recognizable as Middle Eastern or Gypsy or just downright foreign and exotic (though, believe me, there are much more foreign sounds out there).
Just in case you didn't believe anything eldritch was going on, let's visit the Hirajōshi scale, a family of pentatonic modes played on the koto, the zither-like national instrument of Japan. This classic Japanese sound is what you get by removing those two notes instead of moving them.
110001 110001 (Hirajōshi scale's corresponding mode, showing the alignment of patterns)
You can't get Byzantine by playing only white keys on a piano, unlike the others I've been talking about.
Also notice that you can get to it in two steps from the previous scale above it, Phrygian, and those two steps are actually the same step reflected in each half of the scale:
110101 110101
110011 110101
110011 110011
Traditional Spanish music just loves to navigate these three scales. They are called the Phrygian mode of the diatonic scale, the Phrygian dominant scale, and the Double Harmonic major scale, respectively, if we want to be "correct" (whatever that really means) and use the conventional names in English, down to which letters are capitalized. Personally, I call them Phrygian, Spanish Phrygian, and Byzantine. Works for me.
110101 110101 (Phrygian mode of the diatonic scale / Phrygian)
110011 110101 (Phrygian dominant / Spanish Phrygian)
110011 110011 (Double Harmonic major / Byzantine)
The last one is most recognizable as Middle Eastern or Gypsy or just downright foreign and exotic (though, believe me, there are much more foreign sounds out there).
Just in case you didn't believe anything eldritch was going on, let's visit the Hirajōshi scale, a family of pentatonic modes played on the koto, the zither-like national instrument of Japan. This classic Japanese sound is what you get by removing those two notes instead of moving them.
110001 110001 (Hirajōshi scale's corresponding mode, showing the alignment of patterns)
Detail: between the two halves in all the scales above, there's a note that isn't on. I'm using a tradition going back to ancient Greece of dividing scales into two "tetrachords," two groups of four notes, stacked one on the other. For most scales we use, there's one note missing between the two tetrachords. Hence the gap above. As the ancients would see it, we play a tetrachord, a little jump, and then another tetrachord. The jumped-over note is the same note an ambulance siren plays. It doesn't sound nice in many circumstances. (It's often left out in various ways, even though it's actually critical to the push and pull of melodic and harmonic development as for example in the Tristan chord, but that's another story.)
So the Byzantine scale actually looks like this:
1100110110011
And the first 1 and the last 1 are the same letter, the last being exactly one octave higher. For example, if we're in the key of E Byzantine, then the notes will be:
E F G# A B C D# E
By the way, the note skipped over in the middle of E Byzantine is an A#. It isn't part of the scale, but as I said, we shouldn't entirely ignore these notes, which are called tritones. A#, the tritone, is the line of symmetry for this octave. It's the harsh center. Blues loves tritones! And going back some centuries, baroque composers figured out they could use them to change keys seamlessly. (Remember C Major versus F Major? Or E Phrygian versus C Phrygian? That's changing key. It makes an immediately audible difference, and if you aren't careful, it can sound totally wrong and incompetent, an obvious mistake. Then again, are mistakes necessarily bad? Anyway, crafty use of these ignored, underdog, siren-ugly tritones makes this a moot point, because with them you can change to any other key and have it sound right and pretty amazing.) You can grimace at the tritone, you can pretend the tritone doesn't exist, but it's still right there in the middle, and it still has soul.
By the way, the note skipped over in the middle of E Byzantine is an A#. It isn't part of the scale, but as I said, we shouldn't entirely ignore these notes, which are called tritones. A#, the tritone, is the line of symmetry for this octave. It's the harsh center. Blues loves tritones! And going back some centuries, baroque composers figured out they could use them to change keys seamlessly. (Remember C Major versus F Major? Or E Phrygian versus C Phrygian? That's changing key. It makes an immediately audible difference, and if you aren't careful, it can sound totally wrong and incompetent, an obvious mistake. Then again, are mistakes necessarily bad? Anyway, crafty use of these ignored, underdog, siren-ugly tritones makes this a moot point, because with them you can change to any other key and have it sound right and pretty amazing.) You can grimace at the tritone, you can pretend the tritone doesn't exist, but it's still right there in the middle, and it still has soul.
There's an Indian tradition called Carnatic, which is probably the most complex, nuanced scale system in popular use. It has about 22 notes available (give or take depending on the particular area or tuning approach) instead of 12. Singers work within that system with hundreds of different scales, literally, and they know how to work them accurately.
The first song that's usually learned in the Carnatic tradition uses the Byzantine scale. Of all the hundreds! That strongly suggests it's one of the most compelling scales to the ear. And that's obvious. It just is. But it's maybe the most "scientific" test a culture has done, given that Carnatic has such a high-resolution tuning system, and they could have picked a zillion other places to start.
I would say maybe it's the visual symmetry appealing to new Carnatic practitioners as a mnemonic device, but I doubt that applies when singing, very much. Maybe? Maybe the scale is only so popular around the world because it's somehow easier to remember. But I can also say I've always been very drawn to this scale, and I didn't know about the symmetry for years. And the symmetry within the symmetry, the fractal quality? I didn't know that at all, yet I suspect my ears did all along.
