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theory-lesson2Note: This post requires a basic knowledge of intervals, which you can acquire by checking out my post Keith’s Crash Course On Intervals for Self-Taught Musicians. If you are not familiar with solfege syllables (do re mi fa sol), also read our Solfege Syllables To Intervals Translation chart.


 


 


 


This article comes as a response to a user question left in a comment on my article on modes. The question is:


Why (supposedly) can’t we hear Locrian mode?


Of all the seven modes derived from the major scale, Locrian is the only one considered to be a “theoretical mode”–one that our ears cannot actually hear. While there are supposed examples of Locrian mode, naysayers can argue that while these songs appear to be Locrian on paper, we hear them as a combination of chords borrowed from different parallel modes (“modal interchange”) or as being in a relative key.*


First, let’s explore what makes this particular tonality so interesting. Locrian is the only mode with a tritone interval and no perfect fifth (relative to the root note, not between the other notes of the key–in other words there is fi but no sol [see solfege chart]). This means that the root chord of a Locrian song is a diminished triad, which is comprised of the root, a minor third, and a tritone (the tritone would be called a diminished fifth in this context). It is this tritone that makes a diminished triad inherently unstable. While root chords are supposed to sound like a point of resolution or finality, tritones are so unstable that some say our ears can usually only hear them as going somewhere; we cannot hear a I diminished triad as ‘home.’


The most common place to find a tritone is in a V7 chord (V dominant 7), one of only a few seventh chords regularly used in classical music, and a chord which almost always resolves to I. The reason is because of its tritone. In my Intervals post, I explained that only intervals between the root and other notes are considered essential to a chord, not the relationships between the other notes. Tritones are the exception. This interval is so dissonant that it stands out in any context. The V7 has a tritone interval between its major 3rd and minor 7th. The major 3rd of a V7 chord will always be the leading tone (major 7th of the key or solfege syllable ti) and the minor 7th on the V7 chord will always be fa. When we listen to a V7 chord, our ears hear a strong pull from the leading tone up to solfege syllable do (root of the key) and from fa down to mi (major third of the key). Put do and mi together and you’ve got the I major chord.

Example: in the key of C major, a V7 chord is GBDF. B is both the major 3rd in this G7 chord and the leading tone of C major. F is the minor 7th and fa.

Technically speaking, there are several characteristics that are unique to a tritone. For one, it is the only interval which inverts to itself. For example, if you take the tritone interval from G to Db and flip it you get Db to G–another tritone. Secondly, it is the only interval which is not considered major, minor, or perfect. (It just is, man.) The tritone is in a league of its own.


Each of the 13 possible intervals are considered more stable (“consonant”) or less stable (“dissonant”). The tritone is one of the most dissonant. Played alone, a minor 2nd is more dissonant and jarring. This interval, like a tritone, is in neither the major (Ionian) nor minor (Aeolian) scales. In the context of a chord, however, a minor 2nd can sound quite pretty. In a major 7 chord, for example, the distance from the major 7th up to the root is a minor 2nd. But since we hear the major 7th interval going in the opposite direction, it sounds dissonant in a colorful way. Tritones always sound a little jarring to me (and yes, I’m including dominant chords). In the case of both intervals, our ear wants to hear perfect intervals (a unison and a perfect fifth, respectively), but they fall slightly short.


The latest pop song to come anywhere close to Locrian lately is Ciara’s “Like A Surgeon,” which features fi as the second bass note during the chorus (G in the key of C# minor). You could call this a borrowed chord (bVmaj7 from C# Lydian), but perhaps another brief flirtation with polytonality a la “Single Ladies” (both songs feature the writing and production of The-Dream and Christopher “Tricky” Stewart) because she sings minor 2nd (called a b9 tension in this context) over it, which is not considered an available tension on major 7 chords.



Most common examples of Locrian are riffs (short melodies which are repeated), not songs. The reasons why our ears tend to drift astray when hearing Locrian only apply to chords and harmony. Riffs are not like chords. They are more flexible. Because the notes are not occurring simultaneously (in the case of many rock riffs), our ear does not hear all of the same tendencies that intervals might suggest. All this being said, it’s hard not to hear YYZ as Locrian with the lead riff constantly reinforcing the root.


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9 Responses to “Tritones & Why Locrian Mode “Doesn’t Exist””

  1. Erlend says:

    That was a throughout answer! Can’t wait for more sonic destruction, though!

  2. B.BarNavi says:

    I completely disagree. Though to Western ears, there’s that deadly unresolvable tritone, Locrian mode actually figures in many North African and Middle Eastern (linear, not vertical) harmonies. Such an example is the Casablanca version of the classic Sabbath eve Jewish prayer “Magen Avot”.

    http://www.tht.co.il/voice10.asp

    In the second clip from the bottom (http://yeshiva.kivun.org.il/voice/j-005.mp3), the cantor begins in major (Ionian), before shifting the tonic down exactly one semitone in order to enter Locrian mode. Far from being riff-like, this mode has a dominant (on the third). This is the primary mode of prayer for Moroccan Jews, as has been attested by A.Z. Idelsohn, and other communities use it as well.
    One could also analyze it as Mixolydian ending on the major third. For some ears, it is certainly that way. After all, the dominant third of this particular Locrian mode is also the dominant fifth on Mixolydian. Even so, the prayer is firmly locked on Locrian as the tonic.

  3. FixYourMix says:

    @B.BarNavi-

    Excellent response. I agree that Locrian mode exists, although I’m not hearing it i your example. Maybe I’m missing the semitone shift you’re talking about, but I just hear Ionian with te (b7) added near the very end (parallel Mixo). It also makes sense that non-Westerners might be more able to hear something as Locrian. I read somewhere that some Eastern cultures reported hearing minor scales as happy and major scales as sad, so it wouldn’t surprise me.

  4. Phil says:

    @B.BarNavi-

    Great comments. It should be noted that this blog is primarily concerned with the western pop idiom which in itself is not necessarily a wholly classical interpretation of harmony but is decidedly not Eastern or ethnic.

    Perhaps the title is misleading or sensationalizing in that it suggests (in quotes) that locrian doesn’t exist when clearly it does from an academic perspective and to non-Western classically-rooted ears.

    However, it’d be a bit like correcting a pop producer for saying a singer is flat by saying “Well, in India they have microtonality, so technically he’s not flat, he’s just singing a non-Western note.”

    Another comment I wanted to make about this post is that since it only takes two notes to establish a chord (the first and third) locrian mode could exist with just a minor chord on the root, omitting the fifth.

    You could argue that it doesn’t exist because when you go to the V there is no tendency tone to lead you back to i, but then that is also the case in a true aeolian mode as well, which I think we all agree exists in all idioms.

  5. c sahar says:

    Just a little history about Locrian. In medieval music the equivalent scale in its interval make up (on the white keys of the piano B – b)was Hypophrygian. However, the tonic and dominants were different – E for the tonic and A for the Dominant.

    The classification of Locrian came much later – interestingly when the dominant 7 chord became more acceptable in Western music (in Rennaissance music you rarely find dominant 7the as the dissonance of the tritone and 7th was very jarring to Medieval and early Renaissance ears, usually diminished chords were more allowable)

    Note in relation BarNavi’s response, using the third degree of the scale as a dominant for some modes was common to avoid either the tritone or avoid B as a dominant area.

    Finally, when I wrote my own short choral piece in Locrian I realize months afterwards I gravitated to the 4th and 7th degrees of the Locrian scale I used – thereby unconsciously writing at times in Hypophyrgian.

  6. Harlan Carpenter says:

    I completely agree with all the comments about why it is impossible to resolve into a locrian mode, or end on a diminished 7 or diminished triad. However, without diminished 7 chords or diminished triads, I wouldn’t be able to play guitar at all… Example: When playing Duke Ellington’s classic “Caravan”, on the first part (before the E7, A7, D7, G7 boogie patterns) I use a completely chromatic bass line–pre-recorded on a classic Digitech JamMan unit. I play the entire first part melody of the song with twelve bars of this chromatic bass line, and perform the entire melody with diminished triads enhancing the lead. Contrary to popular belief, it is impossible to play a long vamp of E minor chord through this whole first part. The entire background should be ALL diminished, except a short ending on each line.

    Of course then, you can kick into the long E7,A7,D7,G7 boogie, which everyone is smart enough to pick up on.

    I developed this version some time ago, and it is pretty explosive. I have left several wise-ass experts scratching their heads, and wondering not only how I play it–but also how the hell I figured out how to do it in the first place… I also put it on a 68 minute CD which I developed, arranged and recorded, just to tweak a few noses…!

    Harlan Carpenter

  7. Harlan Carpenter says:

    Try this (for guitarists): Finger B, G# and D notes in 4th position on 3rd, 4th, and 5th strings respectively. Now strum all six strings, leaving 1st, 2nd, and 6th stings open… Voila–E dominant 7 chord, with a doubled 5th (B).

    Move the same fingering up two frets and repeat the process, again leaving 1st, 2nd and 6th strings open… Oops…what’s that…? E, E(octave), Bb(b5), C#(6th–or if you prefer 13th), B, and E. Wow…!

    Do the same thing one fret higher… Uh-oh…! I think we just discovered something…! E, F (b9), B, D, B (doubled again), and E.

    Now back down a fret, then two frets; then repeat the process; up and back…up and back… Listen carefully as you strum each chord–all six strings…

    Guitar magic…!

    Harlan Carpenter

  8. Harlan Carpenter says:

    Naming modes C ionian, D dorian, E phrygian, F lydian, etc., is clumsy, at least… Why not simply say: C major scale, C to C; or D to D; E to E; etc.

    This would also eliminate confusion about chord nomenclature. For example, music students often get confused about why the F note of G7 chord is called a minor seventh. Their first introduction to the chord is its diatonic function as the V7 of the key of C major. They often count upward (in C major scale) from G to F, and discover that there are seven intervals, and the F is natural, not flat–relative to C major.

    The confusion results from the fact that G7 is actually based on its relationship to the G major scale, not C major. So F note IS actually a minor form of F#–from the G7 chord’s real place of origin–the G major scale.

    It is a natural tendency for a new student to count intervals upward from G to F in C major scale–which is actually the myxolydian mode of C major scale.

    I happen to have been one of those students who was confused that way at one point…

    So I have developed a method of teaching modes which identifies each as a component of the scale in which it is being played. It’s all right to know the names of modes, but to have to identify each as A aeolian, or B locrian, etc., is ridiculous and time wasting…!

    This also might help dispel the myth that “locrian mode is imaginary”…

    Harlan Carpenter

  9. Harlan Carpenter says:

    At the risk of having poor old Django Reinhardt turn over in his grave, if anyone would like to learn more about what I’ve hinted at in the above entries, contact me at harlancarpenter@yahoo.com. What I’ve hinted at so far doesn’t scratch the surface…!

    Harlan Carpenter

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