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Tritones & Why Locrian Mode “Doesn’t Exist”

Posted by Keith Freund On June - 27 - 20099 COMMENTS

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.

Over the past two weeks we have been discussing items pertaining to the audio spectrum at large.  In this article we’ll begin breaking down the audio spectrum into its component parts.  Though we disagree a bit on our subdivisions, Jay’s primer has excellent listening examples to hear each section individually.

 

Generally speaking, sounds can be lumped into three basic segments of the audio spectrum:  Bass, Mid, and Treble. 

 

The associated ranges would be approximately:

 

Bass 25 to 300 Hz.

Mids 300 to 2.4k Hz

Treble 2.4 to 20 kHz

 

Additionally, they can further be broken down in numerous ways depending on how people want to define sections:

 

Sub 25 to 45 Hz

Bass 45 to 300 Hz

Low-Mid 300 to 600 Hz

Mid 600  to 1.2k Hz

High-Mid  1.2 to 2.4 kHz

Treble 2.4 to 15 kHz

Super Treble 15 kHz to ~ 100 kHz

 

This Interactive Frequency Chart, much like the Carnegie Chart in the earlier article will help you understand how the frequency ranges match up with practical instrumentation.

 

For practical purposes, Sub-Bass should be anything that sounds below the lowest fundamental note of your song.  This can include percussion and any sub-harmonics, resonations, formants, and room tones.  These are frequencies that would really only be reproduced by sub-woofers and large format PA/sound reinforcement systems.  Some of this is undesirable—if you’ve ever watched an NFL game on windy day with a system that has a sub, pretty much everything is a big bass wash because of low-frequency wind noise.  We’ll go more in depth on that next week.

 

Bass should be reserved for the fundamental notes of the changes.  That is, the lowest sounding note of each chord progression.  This typically would include all the notes that would normally be played by a bass (Victor Wooten excluded).  This would also include bass playing synths and the left hand of the piano in many instances.

 

The Low-Mids and Mids include fundamental notes for melodic instruments as well as the first few orders of harmonics.  Harmonics help us distinguish sounds from each other and play a very important role in presence and clarity.  More on this when I examine the mid frequencies in two weeks.

 

The High-Mids deserve their own category because these frequencies contain sudden transient content.  For percussion, this would be the sound of sticks or mallets hitting the drum heads and cymbals.  For guitarists, this would be the sound of picks striking strings.  For vocalists, this would be the sound of hard consonance and sibilance.  All of these can be problematic, but also contribute greatly to impression of presence.

 

The treble portion of the audio spectrum contains almost nothing but upper harmonics of treble instruments and room tone.  This helps lead instruments and vocals sound present and full, but also adds brightness and clarity to a mix.

 

Over the next few weeks I’ll go into greater detail on problems with each part of the frequency spectrum.

More from Phil’s Audible Spectrum series:

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