Why the Lydian flat-7 mode is so cool

April 15, 2007

Composer William Kraft (Bill) and I were having lunch one day at the UCLA Faculty Center. Half way through a bite of his sandwich (teachers and composers ALWAYS talk with their mouths full) he bolted and said “Roger, I have a new mode I’ve been working with. It’s terrific, it has so many great qualities. Kinda tonal, kinda not.” I responded “May I guess what the mode is?” He looked confused and skeptical. How could anyone know what mode I’ve been using? He’s just a young whippersnapper from Harvard. “Ok, sure try to guess.” I enumerated the notes of the mode: “C D E F# G A Bb.” He was shocked. “Damn, how did you know? That’s the spookiest thing I’ve experienced all day!”

As human brains evolved their ability to perceive vibrations in the atmosphere as sound, and then as pitch, they evolved the ability to hear timbre, or musical color. The timbre is the element that differentiates one voice from another, whether it be another human, or a musical instrument. One of the quantifiable ways that our minds perceive timbre is by the sonic “aura” that hovers above every pitch made by an orchestral instrument (This is not true for metallophones, bells, gongs, cymbals etc.). This gorgeous aura sounds in varying intensities, depending on the sound source. This aura is commonly called the overtone series, or harmonics, or partials, or Nature’s scale, or formants.

Overtone series example © Robert J Frank

[Illustration © David J. Frank]

(The notes in parenthesis mean that they do not correspond exactly with our commonly used tuning system.) If you take the fundamental and the first 13 partials you roughly have a dominant 7th chord with a sharp 11th. In the example below you’ll see, from left to right, the Lydian flat-7 mode, a secondal cluster made from that scale, a much loved C13th chord spelled tertially, and Alexander Scriabin’s famous “Mystic chord.”

lydb7.jpg

Rufus Wainwright’s early song “Damned Ladies” has a magical chord progression that is so exotic I am shocked at its simplicity: a deceptive resolution from V7/IV to V7, and not just V7, a lydian flat-7 infused V7. (Below is an audio clip, a piano-vocal transcription, and the modal and chordal underpinnings of the passage.)

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gilda.jpg

(The text here is “Or is it Gilda’s waiting passion to be stabbed and killed again:”)
damned-ladies.jpg

Another melody beloved by many baby boomers and one that uses lydian flat-7 in a melody is Left Banke’s “Pretty Ballerina.”

ballerina.jpg

Here is an audio clip of that opening melody. You hear the mode quite prominently here.

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The lydian flat-7mode is also used by Stravinsky, Ravel, Debussy, and me. The mode has been “in the air” for a while, so my guess at Bill’s “new mode” wasn’t so hard. In that it’s in the overtone scale, perhaps it’s hard-wired into our brains.

{ 13 comments… read them below or add one }

Brad Wood April 15, 2007 at 11:16 am

I’m skimming through Daniel Levitin’s book, This Is Your Brain on Music. I say skimming because much of the material is familiar, but I’m hoping that I’m getting to the new stuff soon.

Apparently a central thesis is that music is far more central and important than many assert, “perhaps even more fundamental to our species than language” (from the dustjacket). Levitin certainly appears to endorse the “brains hardwired for music” hypothesis.

He does make one observation about how maddening is the convention of numbering overtones as above, which is discrepant (being one less than) the integer multiplier of the fundamental frequency. Thus our first octave is twice the fundamental frequency, the second overtone three times, etc. I think the numerology works a lot better when the multiplier integer and not the overtone number is used, but then I may not have given the latter much of a chance. I wonder how Scriabin thought of it.

Roger Bourland April 15, 2007 at 11:33 am

Yeah, I know what you mean. I usually number them 1,2,3,4… and not FUNDAMENTAL, 1,2,3…. I guess the illustration above differentiates the difference in sound between the fundamental and an overtone. ARE they truly different?

Do overtones have overtones?

Brad Wood April 15, 2007 at 1:14 pm

Here is Levitin, with my bracketed additions:

“The overtones are often referred to by numbers: The first overtone is the first vibration frequency above the fundamental, the second overtone is the second vibration frequency…etc. Because physicists like to make the world confusing for the rest of us, there is a parallel system of terminology called harmonics, and I think it was designed to make undergraduates go crazy. In the lingo of harmonics the first harmonic is the fundamental frequency, the second harmonic is equal to the first overtone, and so on. Not all instruments vibrate in modes that are so neatly defined. Sometimes, as with the piano (because it is a percussive instrument), the overtones can be close, but not exact, [integer] multiples of the fundamental frequency, and this contributes to their characteristic sound. Percussions instruments, chimes, and other objects—depending on [physical material] composition and shape—often have overtones that are clearly not integer multiples of the fundamental, and these are called partials or inharmonic overtones… (Levitin, op. cit., pg. 42)

arezeeman April 15, 2007 at 11:42 pm

I love this scale, too, but I internalized it in a different form, and think about it in somewhat different (but complimentary) terms. Take the mode starting on the 4th note of your Lydian flat-7 and you have what my jazz improvisation teacher called an “augmented scale,” which fits perfectly with a number of altered dominant chords, especially #9 (which, to jazz musicians, usually implies either a raised or lowered 5th). The mode starting on the 5th note is the (ascending) melodic minor scale.

The excerpt from “Pretty Ballerina” (a song I’m sorry to say I don’t know) could be interpreted as purely octotonic. But in my mind that’s how this note collection works–depending on how you approach it, it can be almost whole-tone or almost octotonic. My entirely subjective feeling is that its coolness comes more from that aspect than from the way it projects the overtone series. And trying to talk, in fundamental terms, about how or why a scale “works” is such an exercise in subjectivity–not a bad one, at all, but one that ends up saying more about individual ways of hearing and understanding than about physics and acoustics.

I appreciated reading your thoughts, though. I often find myself struggling, especially when I’m teaching, to verbalize my impressions of the distinct personalities of certain scales and modes. Ultimately there may not be much point to it–they’ll hear it, or not, and in their own way–though my hope is always to get them listening more closely.

Roger Bourland April 16, 2007 at 7:04 am

Thanks for your comments Robert. I never considered trying the “modes” of that mode. I knew about the melodic minor mode on the 5th scale degree, but never looked at the one starting on 4.

I don’t hear Ballerina as octatonic, or “implied” octatonic as Peter Van Den Toorn calls it. I really DO hear Lydian flat-7.

I think every mode has its own taste or flavor or mood, but I think you’re probably right that it is always subjective, and what a student hears is likely not the same as what I hear. We are using the Marvin Clenndining theory text book. They break up the modes into tetrachords to get the students to hear them better. My TAs had good luck with their technique of learning the modes.

PK April 16, 2007 at 9:34 am

Just for sake of argument, considering how high up the series the raised 4th shows up (and my old ears ain’t what they once were), might part of its interest come from the implied harmonic ambiguity created by the leading tone to the dominant? Kind of like the frisson of the major/minor shift in the Theme from Exodus (you wrote about a few posts back), the veil dance of what is dominant to what, implied by this scale, might make for a richness.

Brad Wood April 16, 2007 at 10:30 am

Also not acquainted with Ballerina, when I looked at the example I heard it (with my “jazz” ears) as a descending incomplete diminished scale (alternating whole tones and semitones)—that is, if the fragment had only shown the first eleven eighth notes, I would have guessed the next four might be D#-C#-D#-C#.

arezeeman April 16, 2007 at 7:29 pm

Yep. I suspect that, like me, Brad may have spent hours and hours (and hours) practicing diminished scale patterns (“diminished scale” is jazz-speak for octotonic). After a while you only have to hear a few notes and your ear reflexively fill in the rest. Your quote from “Pretty Ballerina” has just one gap–fill it in one way (with a D) and you have the Lydian flat-5, fill it in the way Brad suggests, and you have pure octotonic (and you also have jazz cliche). It’s a very useful ambiguity.

There are a few recordings of the song on iTunes (none by Left Banke). One of them (from Chinese Puzzle) starts with an instrumental variation of the line you quoted that fills in the gap and is unambigously Lydian flat-7. The one by Alice Cooper has a guitar riff that uses the octotonic part only in a fairly pungent way. Guess I’ll have to find this song somewhere or another and hear the whole thing.

Brad Wood April 17, 2007 at 1:17 pm

Thanks for the terminological clue-in Robert. A little wikipedia entry informs me that “…(there are other possible eight-tone scales, but the diminished is by far the most common). The latter term (‘octatonic pitch collection’) was first introduced by Arthur Berger in 1963 (van den Toorn 1983). …”

I see also that Rimsky-Koraskov claimed to have invented it, although the entry mentions its formulation by Arab musicians in the 7th century, and cites Liszt’s use in No. 5 of the Transcendental Etudes.

Roger Bourland April 17, 2007 at 2:10 pm

Stravinsky referred to the octatonic scale as “the Rimskii scale.” You’ll hear it in Sadko as major-minor 7th chords (dominant 7th chords) descending in minor 3rds. You’ll hear it also pop up in young Igor’s “Fireworks” as well.

nocal_composer July 7, 2007 at 7:26 am

Forgetting the functional references for a minute, here is a catalog of Forte analysis which shows some of the interesting subsets and their interval vectors. I didn’t look at supersets

3-6 (0,2,4)
3-6 (0,2,4)
3-2 (0,1,3) [0,2,3]
3-2 (0,1,3) [0,2,3]
3-2 (0,1,3) [0,2,3]
Interval Vector Total:

4-21 (0,2,4,6)
4-11 (0,1,3,5) [0,2,4,5]
4-10 (0,2,3,5)
4-3 (0,1,3,4)
Interval Vector Total:

5-24 (0,1,3,5,7) [0,2,4,6,7]
5-23 (0,2,3,5,7) [0,2,4,5,7]
5-10 (0,1,3,4,6) [0,2,3,5,6]
Interval Vector Total:

6-33 (0,2,3,5,7,9) [0,2,4,6,7,9]) {dom11}
6-Z24 (0,1,3,4,6,8) [0,2,4,5,7,8]
Interval Vector Total:

7-34 (0,1,3,4,6,8,10)

Interval Vector Total:

What does this tell us? well, for one – its the closest 7 note set to it’s neighbor 7-35 – the diatonic – only one 1/2 step moved.

[What makes the diatonic interesting boys and girls? Well, the alchemist think its the only set that has a completely uneven number of intervals (e.g. no two intervals have the same number) which may make it more distinct to our hearing? Personally, I think its the placement / seperation of the minor seconds which have the least number of intervals in the collection outside of the Tritone.]

Hmmm I wonder, what other sets are closely related to 7-35 by only 1/2 step difference?

(24) 7-29: (0,1,2,4,6,7,9) [0,2,3,5,7,8,9]
(24) 7-30: (0,1,2,4,6,8,9) [0,1,3,5,7,8,9]
(24) 7-32: (0,1,3,4,6,8,9) {harm-min} [0,1,3,5,6,8,9]

I’ll have to hear what these sound like. I’m sure there are other closely related family members that might be interesting to look at outside of the obvious WholeTone and Octatonic collections

And then there are the lovely subsets and partitions which might have some fun melodic play and pattern in them when working together in those 7-34 scaly modes.

Anyway, the chain of discovery and analysis can go on in many ways based on the toys in the composers west coast sandbox…Overtones of overtones; Tartani tones bring it on…

nocal_composer July 7, 2007 at 7:32 am

ps html parsing stripped the interval vectors above. Here are the most important of em…I also missed out 7-27 so I expect some east coast theorist to get all huffy

[344451] (24) 7-27: (0,1,2,4,5,7,9) [0,2,4,5,7,8,9]
[336333] (24) 7-31: (0,1,3,4,6,7,9) [0,2,3,5,6,8,9]
[335442] (24) 7-32: (0,1,3,4,6,8,9) {harm-min} [0,1,3,5,6,8,9]
[262623] (12) 7-33: (0,1,2,4,6,8,A)
[254442] (12) 7-34: (0,1,3,4,6,8,A)
[254361] (12) 7-35: (0,1,3,5,6,8,A) {diatonic}

Roger Bourland July 7, 2007 at 7:39 am

I think I know what all this adds up to: Lydian flat 7 is a very rich collection to use. It can conjure many, many moods.

Thanks for your very generous and smart post nocal!

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