Intervals of Negri-9

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This is one possible naming system, suggested by Ray Perlner, for intervals of negri temperament based on the negri[9] scale. The names of intervals are chosen to give intuition for those used to diatonic interval naming conventions, even when this results in a slight abuse of notation. For example, 3 step intervals are called "ditones", not because the true ditone of 81/64 would be rendered as such (this system would refer to the interval mapping to 81/64 as a doubly augmented semifourth), but because the "ditones" which appear naturally in the negri[9] MOS scale are either a little larger (major) or a little smaller (minor) than a true ditone. 3-limit intervals, and intervals that divide 3-limit intervals exactly in half are referred to as "perfect" regardless of how commonly they occur in the MOS scale.

Name Size* Ratio No. of Negri Generators(~125.6¢) Comments
Unisons
Perfect unison (P1) 0 1/1 0
Augmented unison (A1) 69.9 36/35~21/20~27/26 -9
Seconds
Diminished second (d2) 55.7 25/24~28/27~50/49~64/63 10 "Negri[10] Chroma"
Minor second (m2) 125.6 16/15~15/14~14/13~13/12 1
Major second (M2) 195.5 9/8 -8 Also "major wholetone"
Semifourths
Diminished semifourth (d2.5) 181.2 10/9 11 Also "minor wholetone"
Perfect semifourth (P2.5) 251.1 8/7~7/6~15/13 2
Augmented semifourth (A2.5) 321.0 6/5 -7 Also "minor third"
Ditones
Minor ditone (m3.3) 376.7 5/4~16/13 3 Also "major third"
Major ditone (M3.3) 446.6 9/7~13/10 -6 Also "supermajor third"
Fourths
Perfect fourth (P4) 502.3 4/3 4
Augmented fourth (A4) 572.2 7/5~18/13 -5
Fifths
Diminished fifth (d5) 628.8 10/7~13/9 5 Also "supermajor fourth"
Perfect fifth (P5) 697.7 3/2 -4
Tetratones
Minor tetratone (m5.7) 753.4 14/9~20/13 6 Also "subminor sixth"
Major tetratone (M5.7) 813.5 8/5 -3 Also "minor sixth"
Semitwelfths
diminished semitwelfth (d6.5) 879.0 5/3 7 Also "major sixth"
Perfect semitwelfth (P6.5) 948.9 7/4~12/7~26/15 -2 Also "supermajor sixth"
Augmented semitwelfth (A6.5) 1017.8 9/5 -11 Also "just minor seventh"
Sevenths
Minor seventh (m7) 1004.5 16/9 8 Also "Pythagorean minor 7th"
Major seventh (M7) 1074.4 15/8~13/7~28/15~24/13 -1
Augmented seventh (A7) 1144.3 48/25~27/14~49/25~63/32 -10
Octaves
Diminished octave (d8) 1130.1 35/18~40/21~52/27 9
Perfect octave (P8) 1200 2/1 0
Augmented octave (A8) 1269.9 72/35~21/10~27/13 -9
  • In POTE 11-limit porcupine