Scales and Musical Modes in Celtic, Anglo-American and English Folk Songs

Authentic and Plagal Scales

There is quite a complicated literature on authentic and plagal scales in the context of Gregorian chant. This includes a consideration of "subfinal" and "subtonal" notes and other intricacies.* [*See https://en.wikipedia.org/wiki/Mode_(music).]

With regard to English folk tunes (and the same is true of Celtic and Anglo-American folk melodies) Julia Bishop has a more straightforward explanation:

Tunes can be divided into two categories according to where the ‘tonal centre’ – often the final note of the tune – lies in relation to the other notes. In tunes with a so-called ‘authentic’ range, the tonal centre lies at the extremes of the range, with the rest of the notes used in the tune being located in between. By contrast, in tunes with a plagal range the tonal centre lies more or less halfway between the lowest notes of the tune and the highest ones. [Roud, Steve and Bishop, Julia (2012) The New Penguin Book of English Folk Songs, pp. lii-liv.]

The concepts of authentic and plagal scales, however, have no effect on which notes comprise a scale or mode and can therefore be discounted in the following discussion.


Full Scales and Gapped Scales

When analysing a folk melody we need to ascertain the number of notes in the scale. A full scale is heptatonic, or, in plain English, it has seven notes. A gapped scale has fewer than seven notes. If the scale is hexatonic it has six notes. If the scale is pentatonic it has five notes.

Full Heptatonic Scales

Heptatonic scales can be defined in accordance with the classification system of Glarean, who refers to them as modes.

Heinrich Glarean (in Latin Henricus Glareanus) was born in 1488 and died in 1563. His most famous work, the Dodecachordon, was published in Basle, Switzerland, in 1547 and it established him as a famous and influential musical theorist.[*] [* The Dodecachordon (in Latin) and other works by Glarean are available from the International Music Score Library Project at http://imslp.org/wiki/Category:Glareanus,_Henricus ] The following is partly based on Glarean’s ideas.

In an octave of music there are twelve notes, separated by semitone intervals. These, marked off by commas, are:

A, A# (or Bb), B, C, C# (or Db), D, D# (or Eb), E, F, F# (or Gb), G, G# (or Ab).

Some avant-garde composers in the twentieth century, notably the Austro-American Arnold Schoenberg (1874-1951) developed a so-called chromatic scale that included all 12 of these notes. Most composers, however, employ scales of 8 notes, although they may sometimes modulate to a different key without changing the key signature, or add accidental sharps, flats and naturals to give a pleasing or interesting sound or dissonance. In classical music there are three main scales: the major, the melodic minor and the harmonic minor. In Celtic, Anglo-American and English folk melodies the melodic and harmonic minors are not usually used, but the major, as will be seen, is common.

It was Heinrich Glarean who gave to the seven heptatonic scales the names of Ionian, Aeolian, Mixolydian, Dorian, Phrygian, Lydian and Locrian modes. He believed that this was what they were called in the ancient world. He was quite wrong in this belief, but his nomenclature has nevertheless been retained.
The four modes or scales most usually encountered in Celtic, Anglo-American and English folk song are as follows:


1. Ionian/Major Heptatonic Scale

The Ionian mode, which is identical to the Major scale, was, according to Glarean, the one most frequently used by composers in his day. It has also been the most common scale among classical composers. In his analysis in "English Folk Songs from the Southern Appalachians", Cecil Sharp characterises this scale as Mode 1a+b Heptatonic.

The notes of the C Ionian or C Major scale are C, D, E, F, G, A, B, C’ and you get them by playing upwards from C to C’ on the white notes of a piano, or if, in tonic solfa, you sing the familiar scale of “do, re, mi, fa, so, la, ti, do”. Note the distribution of tone and semitone intervals in this scale:

C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C’

The above is known as the C Ionian mode because the starting note is C. However, the critical point about any mode is that it always has its semitone intervals in the same place. Indeed, every mode is defined by the position of its semitone intervals. So if, for example, we want to sing the Ionian mode but start on the note of G, we still sing "do re mi..." as before, but start on the G note. However, when we play just up the white keys of a piano we get:

G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G’

...and of course that is wrong, as can be seen by comparison with the previous example, because the second semitone is now in the wrong place. To fix this, we have to use F# (a black key on the piano) instead of F, which gives us the desired result:

G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(TONE)-F#-(SEMITONE)-G’

This is called the G Ionian mode, or G Major scale. In fact, we can sing the Ionian mode (or indeed any mode) starting on any note we like. Our starting note is called the key, or tonic. The system of singing "do, re, mi.." is called solfa, thus the system of singing a consistent "do, re, mi..." starting on any tonic is called tonic solfa. It is not the same as the alternative fixed-do system called solfège, which does not concern us here. Tonic solfa is very useful when considering modes, and since the positions of the two semitone intervals are critical to identifying the mode, it is worth noting that they always (and only) occur after the -i words, shown emphasised here: "do, re, mi, fa, so, la, ti, do".


2. Aeolian/Minor Heptatonic Scale

The Aeolian mode is similar to the modern minor scales in their melodic and harmonic forms but without the accidentals that sharpen, naturalise or flatten some of the notes of those scales. Sharp characterises this scale as Mode 5a+b Heptatonic. The notes of the Aeolian mode in tonic solfa are sung as “la, ti, do, re, mi, fa, so, la”. The A Aeolian notes are A, B, C, D, E, F, G, A’, and you get this scale on a piano when you play upwards from A to A’ on the white keys. Note the distribution of the tone and semitone intervals in this scale:

A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A’


3. Mixolydian Heptatonic Scale

Sharp characterises the Mixolydian mode as Mode 4a+b Heptatonic. The notes of the Mixolydian mode in tonic solfa are sung as “so, la, ti, do, re, mi, fa, so”. The G Mixolydian notes are G, A, B, C, D, E, F, G’, and you get this scale on a piano when you play upwards from G to G’ on the white keys. Again, note the distribution of the tone and semitone intervals in this scale:

G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G’

The Mixolydian mode differs in but one note from the Ionian: the seventh note is flattened to make the final interval of the scale a tone instead of a semitone, and the one before it a semitone instead of a tone.


4. Dorian Heptatonic Scale

Sharp characterises the Dorian mode as Mode 2a+b Heptatonic. The notes of the Dorian mode in tonic solfa are sung as “re, mi, fa, so, la, ti, do, re”. The D Dorian notes are D, E, F, G, A, B, C, D’ and you get this scale on a piano when you play upwards from D to D’ on the white keys. Once more, note the distribution of the tone and semitone intervals in this scale:

D-(TONE)-E-(SEMI-TONE)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMI-TONE)-C-(TONE)-D’


Other Scales

There are three other modal scales. One is the Phrygian mode. Sharp characterises this scale as Mode 5a+b Heptatonic. Its notes in tonic solfa are “mi, fa, so, la, ti, do, re, mi”. The E Phrygian notes are E, F, G, A, B, C, D, E’ and you get this scale on a piano when you play upwards from E to E’ on the white keys. Here is the distribution of the tone and semitone intervals:

E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E'

Another is the Lydian mode. Sharp characterises this scale as Mode 3a+b Heptatonic. Its notes in tonic solfa are “fa, so, la, ti, do, re, mi, fa”. The F Lydian notes are F, G, A, B, C, D, E, F’ and you get this scale on a piano when you play upwards from F to F’ on the white keys. Here is the distribution of the tone and semitone intervals:

F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F'

Finally there is the Locrian mode. Its notes in tonic solfa are “ti, do, re, mi, fa, so, la, ti”. The B Locrian notes are B, C, D, E, F, G, A, B’ and you get this scale on a piano when you play upwards from B to B’ on the white keys. Here is the distribution of the tone and semitone intervals:

B-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B'

The Phrygian mode is rarely encountered in Celtic, Anglo-American and English folk song (though common in Iberian folk music, for example), however, and the full Lydian and Locrian modes scarcely appear at all.

Gapped Hexatonic and Pentatonic Scales

In 1911 the Folk Song Journal published a collection of Celtic folk melodies. Anne G. Gilchrist assigned each tune to its respective scale or mode and wrote a note to explain how and why she had done this.* [*Gilchrist, Annie G., "Note on the Modal System of Gaelic Tunes," Journal of the Folk-Song Society, Vol. 4, No. 16 (Dec., 1911), pp. 150-153.] Immediately after this note was a gloss from Lucy Broadwood.* [*Broadwood, Lucy E., "Additional Note on the Gaelic Scale System," Journal of the Folk-Song Society, Vol. 4, No. 16 (Dec., 1911), pp. 154-156.] Both Gilchrist's note and Broadwood's gloss dealt with the question of gapped scales.

Cecil Sharp dedicated two chapters of English Folk Song: Some Conclusions (1907) to a study of the various scales in which English folk songs have come down to us. These are Chapter 5, “The Modes,” and Chapter 6, “English Folk-Scales,” and the topic is also treated elsewhere in that book. Then, in his Introduction to English Folk Songs from the Southern Appalachians (1917) Sharp includes a section entitled “Scales and Modes.”* [*Campbell, Olive Dame and Sharp, Cecil J. (1917) English Folk Songs from the Southern Appalachians, pp. xv-xviii.] This begins:

Very nearly all these Appalachian tunes are cast in “gapped” scales, that is to say, scales containing only five, or sometimes six, notes to the octave, instead of the seven with which we are familiar, a “hiatus” or “gap” occurring where a note is omitted.

Sharp then goes on to discuss the prevalence of pentatonic and hexatonic scales in Appalachian music at that time, drawing parallels with Scottish and Irish tunes, and invoking the aid of Gilchrist’s “very clear exposition of this matter” in her note of 1911. He also, most helpfully for later scholars, categorises the musical scale of every tune in the book in accordance with his modified version of Gilchrist’s criteria, as Pentatonic (5 note), Hexatonic (6 note), and Heptatonic (7 note).

It is a useful heuristic and analytical exercise to do as Sharp does. Firstly, to simplify and clarify his analysis he assumes that tunes have been transposed to eliminate the sharps and flats from their key signatures. Secondly, he links gapped scales to their corresponding full scales. If we follow Sharp's method, therefore, we should not consider hexatonic and pentatonic tunes to be in separate hexatonic and pentatonic scales. Instead we should look at them as modal melodies--Ionian/Major, Aeolian, Dorian, Mixolydian, Lydian (a mode included by Sharp despite its rarity as a full scale) and (very occasionally occurring) Phrygian--in which the singers and performers have eschewed one or two of the notes that were theoretically available to them. This then poses the problematic question as to which notes the singers would have sung if they had used the full seven note scale. Sometimes, as will be seen, this can be deduced, but sometimes it cannot. In some cases we have to make guesses as to what the missing notes would have been. Sometimes we can never definitively know, and this uncertainty, as will be seen, leads to a number of conclusions.

Gapped hexatonic scales in Celtic, Anglo-American and English folk song are all hemitonic or, in other words, they contain a semitone. All gapped pentatonic scales, however, are anhemitonic--i.e. they contain no semitones.


1. Ionian/Major Hexatonic and Pentatonic Scales

1.1 Ionian Hexatonic Scale (Type 1a). This is the Ionian/Major Heptatonic scale with the 3rd (E) note missing. Sharp characterises this scale as 1a Hexatonic.

C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C’

Thus the notes of the scale are:

C-(TONE)-D-(1.5 TONES)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C’

If a tune transposes to what seems to be C Ionian/C Major but is hexatonic and has no Es there is only one possibility. If the Es were natural, the tune would be C Ionian/C Major. If the Es were flattened the scale would be unviable. The tune must therefore be C Ionian/C Major with a missing 3rd.

1.2 Ionian Hexatonic Scale (Type 1b). This is the Ionian/Major Heptatonic scale with the 7th (B) note missing. Sharp characterises this scale as 1b Hexatonic.

C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C’

Thus the notes of the scale are:

C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(1.5 TONES)-C'

If a tune transposes to what seems to be C Ionian/C Major but is hexatonic and has no Bs in it there are two possibilities. If the Bs were natural, the scale would be C Ionian/C Major. If the Bs were flattened the scale would be C Mixolydian. The tune must therefore be either C Ionian/C Major or C Mixolydian with a missing 7th.

1.3 Ionian Pentatonic Scale. This is the Ionian/Major Heptatonic scale with the 3rd (E) and 7th (B) notes missing. Sharp characterises this scale as 1 Pentatonic.

C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C’

Thus the notes of the scale are:

C-(TONE)-D-(1.5 TONES)-F-(TONE)-G-(TONE)-A-(1.5 TONES)-C’

If a tune transposes to what seems to be C Ionian/C Major but is pentatonic and has no Bs and also no Es in it there are three possibilities. Firstly, if they had been there, the B and the E might both have been natural to produce a C Ionian/C Major scale. Secondly, the B might have been flattened to produce a C Mixolydian tune. Thirdly, both the B and the E might have been flattened to produce a C Dorian tune.


2. Aeolian/Minor Hexatonic and Pentatonic Scales

2.1 Aeolian Hexatonic Scale (Type 5b).

This is the Aeolian/Minor Heptatonic scale with the 5th (E) note missing. Sharp characterises this scale as 5b Hexatonic.

A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A'

Thus the notes of the scale are:

A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(1.5 TONES)-F-(TONE)-G-(TONE)-A

If a tune transposes to what seems to be A Aeolian/A Minor but has no Es in it there is only one possibility. If the Es were natural the scale would be A Aeolian/A Minor. If the Es were flattened the scale would not be viable. This hexatonic scale can thus be accurately categorised as an A Aeolian/Minor scale with the fifth (E) notes missing.

2.2 Aeolian Hexatonic Scale (Type 5a).

This is the Aeolian/Minor Heptatonic scale with the 2nd (B) note missing. Sharp characterises this scale as 5a Hexatonic.

A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A

Thus the notes of the scale are:

A-(1.5 TONES)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A

If a tune transposes to what seems to be A Aeolian/A Minor but has no Bs there are two possibilities. If the Bs were natural the scale would have been A Aeolian/A Minor. If the Bs were flattened the scale would have been A Phrygian.

2.3 Aeolian Pentatonic Scale (Type 5).

This is the Aeolian/Minor Heptatonic scale with the 2nd (B) and 5th (E) notes missing. Sharp characterises this scale as 5 Pentatonic.

A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A’

Thus the notes of the scale are:

A-(1.5 TONES)-C-(TONE)-D-(1.5 TONES)-F-(TONE)-G-(TONE)-A’

If a tune transposes to what seems to be A Aeolian/A Minor but has no Bs and Es in it there are three possibilities. If the Es and the Bs were both natural the scale would be A Aeolian/A Minor. If the Bs were flattened and the Es were natural the scale would be A Phrygian. If both the Bs and the Es were flattened the scale would be A Locrian.


3. Mixolydian Hexatonic and Pentatonic Scales

3.1 Mixolydian Hexatonic Scale (Type 4b).

This is the Mixolydian Heptatonic scale with the 6th (E) notes missing. Sharp characterises this scale as Mode 4b.

G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G’

Thus the notes of the scale are:
G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(1.5 TONES)-(SEMITONE)-F-(TONE)-G’

If a tune transposes to what seems to be G Mixolydian but has no Es in it, there is only one possibility. If the Es were natural the scale would be G Mixolydian. If the Es were flattened the scale would not be viable. This hexatonic scale can thus be accurately categorised as a G Mixolydian scale with the sixth (E) note missing.

3.2 Mixolydian Hexatonic Scale (Type 4a).

This is the Mixolydian Heptatonic scale with the 3rd (B) notes missing. Sharp characterises this scale as Mode 4a.

G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G’

Thus the notes of the scale are:

G-(TONE)-A-(!.5 TONES)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F-(TONE)-G’

If a tune transposes to what seems to be G Mixolydian but has no Bs in it there are two possibilities. If the Bs were natural the scale would be G Mixolydian. If the Bs were flattened the scale would be G Dorian.

3.3 Mixolydian Pentatonic Scale (Type 4).

This is the Mixolydian Heptatonic scale with the 3rd (B) and 6th (E) notes missing. Sharp characterises this scale as Mode 4.

G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D-(TONE)-E [missing]-(SEMI-TONE)-F-(TONE)-G’

Thus the notes of the scale are:

G-(TONE)-A-(1.5 TONES)-C-(TONE)-D-(1.5 TONES)-F-(TONE)-G’

If a tune transposes to what seems to be G Mixolydian but has no Bs and no Es in it there are three possibilities.. If the Bs and the Es were both natural the scale would be G Mixolydian. If the Bs were flattened and the Es were natural the scale would be G Dorian. If both the Bs ad the Es were flattened the scale would be G Aeolian.


4. Dorian Hexatonic and Pentatonic Scales

4.1 Dorian Hexatonic Scale (Type 2a).

This is the Dorian Heptatonic scale with the 2nd (E) notes missing. Sharp characterises this scale as Mode 2a.

D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D’

Thus the notes of the scale are:

D-(1.5 TONES)-F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D’

If a tune transposes to what seems to be D Dorian, but has no Es in it there is only one possibility. If the Es were natural the scale would be D Dorian. If the Es were flattened the scale would not be viable. This hexatonic scale can thus be accurately categorised as a D Dorian scale with the sixth (E) notes missing.

4.2 Dorian Hexatonic Scale (Type 2b).

This is the Dorian Heptatonic scale with the 6th (B) notes missing. Sharp characterises this scale as Mode 2b.

D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D’

Thus the notes of the scale are:

D-(TONE)-E-(SEMITONE)-F-(TONE)-G-(TONE)-A-(1.5 TONES)-C-(TONE)-D’

If a tune transposes to what seems to be D Dorian, but has no Bs in it there are two possibilities. If the Bs were natural the scale would be D Dorian. If the Bs were flattened the scale would be D Aeolian.

4.3 Dorian Pentatonic Scale (Type 2).

This is the Dorian Heptatonic scale with the 2nd (E) and 6th (B) notes missing. Sharp characterises this scale as Mode 2.

D-(TONE)-E [missing]-(SEMITONE)-F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D’

Thus the notes of the scale are:

D-(1.5 TONES)-F-(TONE)-G-(TONE)-A-(1.5 TONES)-C-(TONE)-D’

If a tune transposes to what seems to be D Dorian, but has no Es and no Bs in it there are three possibilities. If the Es and the Bs were both natural the scale would be D Dorian. If the Es were natural and the Bs were flattened the scale would be D Aeolian. If both the Es ad the Bs were flattened the scale would have been D Phrygian.


5. Lydian Hexatonic and Pentatonic Scales

Despite the rarity of Lydian heptatonic scales in Celtic, Anglo-American and English folk melodies, Sharp includes the Lydian heptatonic scale, together with the hexatonic and pentatonic scales that are derived from it, in his listing of tune scales found in Appalachian music, designating them as "Mode 3."

5.1 Lydian Hexatonic Scale (Type 3b).

This is the Lydian Heptatonic scale with the 7th (E) notes missing. Sharp characterises this scale as Mode 3b.

F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F'

Thus the notes of the scale are:

F-(TONE)-G-(TONE)-A-(TONE)-B-(SEMITONE)-C-(TONE)-D-(1.5 TONES)-F'

Note that this scale contains a semitone, or, in other words, it is hemitonic.

If a tune transposes to what seems to be F Lydian but has no Es in it there is only one possibility. If the Es were natural the scale would be F Lydian. If the Es were flattened the scale would be unviable. This hexatonic scale can thus be accurately categorised as an F Lydian scale with the 7th (E) notes missing.

5.2 Lydian Hexatonic Scale (Type 3a).

This is the Lydian Heptatonic scale with the 4th (B) notes missing. Sharp characterises this scale as Mode 3a.

F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F'

Thus the notes of the scale are:

F-(TONE)-G-(TONE)-A-(1.5 TONES)-C-(TONE)-D-(TONE)-E-(SEMITONE)-F'

If a tune transposes to what seems to be F Lydian but has no Bs in it there are two possibilities. If the Bs were natural the scale would be F Lydian. If the Bs were flattened the scale would be F Ionian/F Major.

5.3 Lydian Pentatonic Scale (Type 3).

This is the Lydian Heptatonic scale with the 4th (B) and the 7th (E) notes missing. Sharp characterises this scale as Mode 3.

F-(TONE)-G-(TONE)-A-(TONE)-B [missing]-(SEMITONE) C-(TONE)-D-(TONE)-E [missing]-(SEMITONE)-F'

Thus the notes of the scale are:

F-(TONE)-G-(TONE)-A-(1.5 TONES)-C-(TONE)-D-(1.5 TONES)-F'

If a tune transposes to what seems to be F Lydian, but has no Bs and no Es in it there are three possibilities. If the Bs and the Es were both natural the scale would be F Lydian. If the Bs were flattened and the Es were natural the scale would be F Ionian/F Major. If both the Bs and the Es were flattened the scale would be F Mixolydian.


6. Phrygian and Locrian Gapped Scales

Sharp makes little or no mention of these, presumably since he did not encounter them in the Appalachians, but also perhaps because they do not fit neatly into his system. Certainly Phrygian and Locrian heptatonic scales are very rare in Celtic, Anglo-American and English folk melody. However, for the sake of completeness, and since the classification of pentatonic tunes in particular is problematic, clarification is needed. Essentially, the difficulty is caused by the elimination of semitone intervals. We can see this most clearly by looking again at the gapped scales, but this time in tonic solfa. Sharp's system essentially takes out mi or ti for the hexatonic forms, and mi and ti for the pentatonic forms, as shown below:

Ionian full: do re mi fa so la ti do
Ionian hexatonic: do re -- fa so la ti do or do re mi fa so la -- do
Ionian pentatonic: do re -- fa so la -- do

Aeolian full: la ti do re mi fa so la
Aeolian hexatonic: la -- do re mi fa so la or la ti do re -- fa so la
Aeolian pentatonic: la -- do re -- fa so la

Mixolydian full: so la ti do re mi fa so
Mixolydian hexatonic: so la -- do re mi fa so or so la ti do re -- fa so
Mixolydian pentatonic: so la -- do re -- fa so

Dorian full: re mi fa so la ti do re
Dorian hexatonic: re -- fa so la ti do re or re mi fa so la -- do re
Dorian pentatonic: re -- fa so la -- do re

Lydian full: fa so la ti do re mi fa
Lydian hexatonic: fa so la -- do re mi fa or fa so la ti do re -- fa
Lydian pentatonic: fa so la -- do re -- fa

That is all well and good, but what happens when the mode starts with mi, as it does with Phrygian, or ti, as it does with Locrian? Clearly, we cannot take out the tonic notes! Instead, to get rid of the semitone intervals we have to remove fa in the case of Phrygian and do in the case of Locrian. That means that we potentially now have two pentatonic forms for each of these modes, whereas there is only one such form for the other modes. Here are the gapped scales for these two modes.

Phrygian full: mi fa so la ti do re mi
Phrygian hexatonic: mi -- so la ti do re mi or mi fa so la -- do re mi
Phrygian pentatonic: mi -- so la -- do re mi [or mi -- so la ti -- re mi]

In practice, the second form of the pentatonic Phrygian would not be used because it lacks do, the note that underpins the entire tonal system, thus there is really only one form.

Locrian full: ti do re mi fa so la ti
Locrian hexatonic: ti -- re mi fa so la ti or ti do re -- fa so la ti
Locrian pentatonic: [ti -- re -- fa so la ti or] ti -- re mi -- so la ti

With Locrian, however, there is no choice; do has to go, which is the reason why Locrian sounds so strange to our ears, because we have lost that underpinning note, thus the scale seems unstable. In the first pentatonic form, though, the gaps are really too close for comfort, being separated by only one note (re), so in practice the second pentatonic form would be used.

As pointed out earlier, when considering the other modes, there are alternative interpretations of the pentatonic forms if we insert sharpened or flattened notes in the gaps. For completeness, we need to consider both pentatonic forms in each of the Phrygian and Locrian too.

In the Phrygian first form, if we restore the fa and sharpen it (fi) and restore the ti, we get a transposed form of the Aeolian: mi fi so la ti do re mi, which we can see from the positions of the semitone intervals marked by the notes in bold. (Please refer to the full list above, and remember that it is the relative positions of the semitones that determine the mode). The same thing happens in the second form if we restore the fa and sharpen it (fi) and restore the do.
Alternatively, if in the first form we restore the fa without sharpening it and restore the ti and flatten it (ta), we get a transposed version of the Locrian: mi fa so la ta do re mi.
Additionally, for the Phrygian second form, if we restore the fa and sharpen it (fi) and restore the do and sharpen it (di), we get a transposed form of the Dorian: mi fi so la ti di re mi, again revealed by the semitone positions.

In the Locrian second pentatonic form, if we restore the do and then restore the fa and sharpen it (fi), we get a transposed form of the Phrygian: ti do re mi fi so la ti.
Alternatively, if we restore the do and sharpen it (di) and restore the fa and sharpen it (fi), we get a transposed version of the Aeolian: ti di re mi fi so la ti.

The above ambiguities mean that it can be extremely difficult if not impossible to establish exactly what the mode of a gapped scale is.

Summary and Conclusions

It is useful heuristically and analytically to follow the practice of Cecil Sharp and link gapped (hexatonic and pentatonic) scales to the full (heptatonic) scales with which they are associated.

If gapped scales in Celtic, Anglo-American and English folk melodies are transposed to remove the sharps and flats from their key signatures the following is true.

1. All hexatonic scales contain a semitone and are thus hemitonic.

2. No pentatonic scales contain a semitone and are thus all anhemitonic.

3. The hexatonic scales that can be linked to the Ionian/Major, Aeolian/Minor, Mixolydian, Dorian and Lydian heptatonic scales lack either their B notes or their E notes and the pentatonic scales lack both their B notes and their E notes.

4. Hexatonic scales that can be linked to the Ionian/Major, Aeolian/Minor, Mixolydian, Dorian and Lydian heptatonic scales and that lack their E notes can be characterised as being in one possible mode; this is the same mode as the heptatonic scale created if an E natural is added to the existing six notes.

5. Hexatonic scales that can be linked to the Ionian/Major, Aeolian/Minor, Mixolydian, Dorian and Lydian heptatonic scales and that lack their B notes can be characterised as being in two possible modes. This is either the same mode as the heptatonic scale created if a B natural is added to the existing six notes; or it is the same mode as the heptatonic scale created if a B flat is added to the existing six notes.

6. Pentatonic scales that can be linked to the Ionian/Major, Aeolian/Minor, Mixolydian, Dorian and Lydian heptatonic scales and that lack both their B notes and their E notes can be characterised as being in three possible modes. This is either the same mode as the heptatonic scale created if a B natural and an E natural are added to the existing five notes; or it is the same mode as the heptatonic scale created if a B flat and an E natural are added to the existing five notes; or it is the same mode as the heptatonic scale created if both a B flat and an E flat are added to the existing 5 notes.

7. Given the rarity of the Phrygian heptatonic scale in Celtic, Anglo-American and English folk melody it is probably appropriate to classify gapped scales that could theoretically be linked to the Phrygian heptatonic scale as linked instead to the Aeolian/Minor or Dorian heptatonic scales.

8, Given the rarity of the Locrian and Phrygian heptatonic scales in Celtic, Anglo-American and English folk melody it is probably appropriate to classify gapped scales that could theoretically be linked to the Locrian heptatonic scale as linked instead to the Aeolian/Minor heptatonic scale.

Thus gapped scales can be linked to all of the full heptatonic scales identified by Glarean, namely Ionian/Major, Aeolian/Minor, Mixolydian, Dorian, Phrygian, Lydian and Locrian. Moreover, every pentatonic scale can be theoretically linked to 3 different heptatonic scales.