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As far as I am aware, there are two ways to construct the five modes of the pentatonic scale.

The first is to go to the major diatonic, remove the fourth and seventh scale degrees (as these are a tritone apart) and call this the major pentatonic. Then just permute the formula. (Example: major pentatonic is {2,2,3,2,3}, next mode is {2,3,2,3,2}, next is {3,2,3,2,2}, etc.

But the second, and I believe the most fundamental, way to do it is to visit all 7 diatonic modes and remove whatever scale degrees create a tritone between them. For example, C Dorian contains [C D Eb F G A Bb], and the distance between Eb and A is a tritone. Thus the Dorian mode of the pentatonic scale (in key of C) is [C D F G Bb], which in terms of the semitone formulas is {2,3,2,3,2}, which is of course the first permutation of the major pentatonic formula.

When you repeat this analysis for Lydian and Locrian modes of the diatonic scale the pattern breaks.

My question: How do we interpret this?

For example consider C Locrian, which has [C Db Eb F Gb Ab Bb]. Remove the tritone between C and Gb, so we're left with Locrian pentatonic of [Db Eb F Ab Bb]. This obviously doesn't contain the tonic (which makes it unwieldy to use). But in terms of the interval formula this is {2,2,3,2,3}, which is the major pentatonic!

(Similarly for Lydian, you end up with the same formula as Mixolydian pentatonic, but with no tonic).

As there is no intervalic difference between Locrian pentatonic and major pentatonic, does that mean Locrian pentatonic doesn't exist?

  • Your method of removing the tritone doesn't match up with Google results for these scales: R 2 3 #4 6 and R b3 4 b5 b7 where the point seems to be include the tritone above the root (should be called tonic, roots belong to chords.) – Michael Curtis Jan 30 at 18:15
  • Thanks for your response. I see now that guitarists tend to use these pentatonic scales. But it still begs the question of how they are constructed. In the formula you gave for Lydian (R 2 3 #4 6 R), the 5 and 7 are removed. Could we choose any arbitrary pair of notes to remove and call the result Lydian pentatonic? And, if so, why do we typically choose the tritone-forming note pairs in the other five diatonic modes? – Alan Jan 31 at 10:54
  • @Alan I don't think it begs the question ...but to answer it instead: it's widely proposed that pentatonic scales are constructed as minimal Pythagorean scales. That has nothing to do with set theory but moving in the circle of fifths, and it doesn't work for those Lydian / Locrian scales. – leftaroundabout Jan 31 at 19:54
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Your method of removing the tritone doesn't match up with Google results for these scales: R 2 3 #4 6 and R b3 4 b5 b7 where the point seems to be include the tritone above the root (should be called tonic, roots belong to chords.)

The sources listing these scales are - if not entirely - mostly guitar sites. Personally, I'm skeptical when reading them. Anyone can take a collection of tones and put a name to them, but that doesn't necessarily mean the thing is a bona fide cultural thing.

That theoretical versus cultural distinction has implications for the origin of these scales. Consider the common pentatonic scale. It is often described as derived from a diatonic scale with two tones removed. But in reality no one knows the origin of the pentatonic scale. It's origin is prehistoric. It's a cultural thing passed on through generations with no definitive origin.

...Could we choose any arbitrary pair of notes to remove and call the result Lydian pentatonic?

I can't find any other references to explain the origin. Actually, I never heard of Lydian pentatonic before your question.

...we typically choose the tritone-forming note pairs in the other five diatonic modes?

The modern view of modes in pop, rock, and jazz is different that the Medieval modal system. The modern view looks for characteristic tones and intervals that distinguish seven modes.

Probably the most straight forward way to look at it is tonal tones and modal tones.

All modes have the same tonal tones: tonic, subdominant a perfect fourth above the tonic, and a dominant a perfect fifth above the tonic, except:

  • Lydian where the subdominant is an augmented fourth above the tonic
  • Locrian where the dominant is a diminished fifth above the tonic

Just from that you can see the raised subdominant is very characteristic of Lydian only, and the lowered dominant is very characteristic of Locrian only. Those intervals above the tonic are not found in any of the other diatonic modes. Both are the tritones appearing in these two scales - Lydian pentatonic and Locrian pentatonic.

As the A4 and d5 are enharmonically equal - both 6 half steps, or both named tritone - a tonic with tritone above is ambiguous. You need either the exact interval spelled out or at least one more tone to know if the mode is Lydian of Locrian. The mediant seems a good one to use, because it will clarify things into general major/minor groups.

The modal tones are the mediant and submediant, and I suppose also the supertonic and seventh degree can be grouped with modal degrees. The qualities of these degrees determine the other modes, but I won't elaborate, because they don't immediately distinguish Lydian and Locrian like the tonal degrees.

Do Lydian and Locrian Pentantonic Scales Exist?

Well, they "exist" on those guitar tutorial pages.

Whether they are bona fide cultural things is doubtful IMO. They seem pretty theoretical.

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    It has been said that the pentatonic is actually the precursor to the major 7 note scale. I wouldn't trust half of what's said on a lot of guitar sites... – Tim Jan 31 at 17:15

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