Ekmelic System (72-EDO)

Subdivisions of the whole tone, from A thru A double sharp and from A thru A double flat.

• Semitone degrees
• Third tone degrees
• Quarter tone degrees
• Sixth tone degrees
• Twelfth tone degrees

Ekmelic Series

See also Ekmelic Series for an explanation and to create arbitrary series.

• Sequence 1 on 1 (partial-tone series) with 8 degrees
• Sequence 3 on 2 with 8 degrees
• Sequence 5 on 1 with 7 degrees
• Sequence 5 on 2 with 7 degrees
• Sequence 5 on 3 with 8 degrees

Naturetone System

• 2nd thru 16th partial tone (110 - 880 Hz)
• Four harmonic tones, partial tones 4 - 8
• Eight melodic (melody and harmony forming) tones, partial tones 8 - 16
• 16 chromatic tones, partial tones 16 - 32

Other Systems

• Diatonic Just Intonation scale 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 (c d e f g a b c)
• Chromatic Just Intonation scale 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 16/9 15/8 2/1 (c d-flat d e-flat e f f-sharp g a-flat a b-flat b c)
• “Hagia” scale (Plagal II) of the Byzantine church music, with the degrees νή πά βου γα δί κε ζω νή (c d e f g a b c)

Tetrachords

Special intervals defined as subdivisions into four tones in the form A + B + C = fourth and classified into the modes “enharmonic”, “chromatic”, and “diatonic” (rendered here with the root d'.)

Tetrachords after Archytas of Tarent (428–347 B.C.)

• Enharmonic 28/27 36/35 5/4, with perfect major third
• Chromatic 28/27 15/14 6/5, with perfect minor third
• Diatonic 28/27 9/8 8/7, with seventh whole tone

Tetrachords after Aristoxenos (370–300 B.C.)

• Enharmonion: quarter tone + quarter tone + 2 tone
• Chroma malakon: third tone + third tone + 11/6 tone
• Chroma hemiolon: 3/8 tone + 3/8 tone + 7/4 tone
• Chroma toniaion: semitone + semitone + 3/2 tone
• Diatonon malakon: semitone + 3/4 tone + 5/4 tone
• Diatonon syntonon: semitone + tone + tone

Tetrachords after Didymos Chalkénteros (63 B.C.–10 A.D.)

• Enharmonic 32/31 31/30 5/4, with perfect major third
• Chromatic 16/15 25/24 6/5, with perfect minor third
• Diatonic 16/15 10/9 9/8, with major and minor whole tone

Further Tetrachords

• “European” 9/8 10/9 16/15, corresponds to major with perfect third
• “Oriental” 10/9 11/10 12/11, corresponds to Rast with neutral (Arabic) third
• Tempered: whole tone + whole tone + semitone