I learned long ago that no one approach is 'the only logical' one that's easiest for everyone to comprehend. The semitone sequence intervals treatment above is one approach to modality in hexatonic and pentatonic tunes. A different one, which may be more appealing to many, with many examples from Scottish tunes, is at: http://www.purr.demon.co.uk/jack/Music/Modes.abc. This is in ABC so you can copy it then display and play the examples. Jack Campin's modes and scalesNote: The graphical form in SFMODE.GIF, following, is much easier to use than the two tables below.
Modes:
Key Signatures and Scales. b = flat, # = sharp, (m = minor) Major = Ionian [1st and last cols. same, just dif. notation] Key signatures, no m following it means major. 4#-Lyd 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 6# X 7b-Mxld X 6b 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# Maj/Ion 6b 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 6# key Gb Db Ab Eb Bb F C G D A E B F# ---------------------------------------------------------------- 1 Gb Db Ab Eb Bb F C G D A E B F# G D A E B Gb C#/Db G# D# A# F C G 2 Ab Eb Bb F C G D A E B F# C# G# A E B Gb Db Ab D#/Eb A# F C G D A 3 Bb F C G D A E B F# C# G# D# A# 4 Cb Gb Db Ab Eb Bb F C G D A E B Lyd 4# C G D A E B F#/Gb C# G# D# A# E# B# 5 Db Ab Eb Bb F C G D A E B F# C# D A E B Gb Db G#/Ab D# A# F C G D 6 Eb Bb F C G D A E B F# C# G# D# Mxl 7b E Cb Gb Db Ab Eb A#/Bb F C G D A E 7 F C G D A E B F# C# G# D# A# E# Minor = Aeolian Key signatures, all followed by m (no space) for minor, e.g., Ebm 2b,5b Lc X X 6b 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 2b-Phry X 6b 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 6# 6#-Drn 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 6# X X Min/Aeol 6b 5b 4b 3b 2b 1b 0 1# 2# 3# 4# 5# 6# X key Eb Bb F C G D A E B F# C# G# D# A# ----------------------------------------------------------------- (1) 1 Eb Bb F C G D A E B F# C# G# D# A# P/L 2b E/Fb B/Cb Gb Db Ab Eb Bb/A# F C G D A E B (2) 2 F C G D A E B F# C# G# D# A# E# C 3 Gb Db Ab Eb Bb F C G D A E B F# C# (3) G D A E B Gb Db/C# G# D# A# F C G D (4) 4 Ab Eb Bb F C G D A E B F# C# G# D# Lc 5b A E B/Cb Gb Db Ab Eb/D# A# F C G D A E (5) 5 Bb F C G D A E B F# C# G# D# A# E# 6 Cb Gb Db Ab Eb Bb F C G D A E B F# (6)Dr6# C G D A E B Gb/F# C# G# D# A# E# C G 7 Db Ab Eb Bb F C G D A E B F# C# G# (7) D A E B Gb Db Ab/G# D# A# F C G D A * Dorian: Note from the table that it is flatted 6th of the minor scale that is sharpened. Keys with flats in signature simply lose the last flat. Add next sharp for the others. For 'theme coding,' by Breathnach/ Gore system, reference scale is always based on the major intervals, so all minor mode tunes are written as having flats for 3rd, 6th and 7th of their (major) scale. The major scale for reference is at left. ['theme coding' here is actually a poor misnomer. We simply code the beginning of a tune in by standard time sequence that is independent of key.] Ref. Charles Gore, 'The Scottish Fiddle Music Index', 1994. Scales for heptatonic, hexatonic and pentatonic modes; Semitone sequences: For hexatonic modes add semitones in parentheses of 7-note 'Greek' mode semitone sequences, (1 2) for the hexatonic above, and (2 1) for that below, and both for the pentatonic modes, pi1 through pi5 (Bertrand Bronson's numbering, 'The Ballad as Song', p. 80, 1969.) Mode -- semitone sequence -- keynote for no sharps or flats lyd 2 2 (2 1) 2 2 1 F lyd/ion 2 2 3 2 2 1 F, C ion/ (pi1) 2 2 (1 2) 2 (2 1) C (pi1- C, F, G) ion/mix 2 2 1 2 2 3 C, G mix/ (pi2) 2 (2 1) 2 2 (1 2) G (pi2- G, C, D) mix/dor 2 3 2 2 1 2 G, D dor/ (pi3) 2 (1 2) 2 (2 1) 2 D (pi3- D, G, A) dor/ael 2 1 2 2 3 2 D, A ael/ (pi4) (2 1) 2 2 (1 2) 2 A (pi4- A, D, E) ael/phy 3 2 2 1 2 2 A, E phy/ (pi5) (1 2) 2 (2 1) 2 2 E (pi5- E, A, B) phy/loc 1 2 2 3 2 2 E, B loc 1 2 2 (1 2) 2 2 B Two other 7 note (non-'Greek') scales, rarely encountered, are: melodic minor 2 1 2 2 2 2 1 dorian with 7th natural or ascending D E F G A B C# D or major with 3rd flatted melodic minor A B C D E F# G# A (examples) C D Eb F G A B C descending 2 2 1 2 2 1 2 this is just aeolian/ melodic minor A G F E D C B A minor (descending) harmonic minor 2 1 2 2 1 3 1 aeolian with 7th natural (example) A B C D E F G# A C D Eb F G Ab B C
Anne Geddes Gilchrist in 'Notes on the Modal System of Gaelic Tunes', JFSS IV, p. 150-3 (1911), derived and numbered the pentatonic modes differently. Her system was followed by Sharp and Karpeles in the introduction to 'English Folk Songs from the Southern Appalachians'. Bronson's seems to be much more logical.
Bronson's # Gilchrist's Semitone pentatonic pentatonic sequence mode mode # pi1 3 2 2 3 2 3 pi2 1 2 3 2 2 3 pi3 4 2 3 2 3 2 pi4 2 3 2 2 3 2 pi5 5 3 2 3 2 2