Modes of Negri-9

Todo: intro, cleanup

Features of Negri[9]

The nine note MOS of the Negri temperament is an excellent framework for both melody and harmony. In particular, this 9 note scale contains two 4:5:6:7 tetrads, and two 1/7:1/6:1/5:1/4 tetrads, and with a suitably tuned generator is the smallest proper MOS with 9 or fewer notes where these tetrads are as well in tune. The 13th harmonic is also easily accessible, with the octave reduced 13th harmonic (13/8) being tuned the same as 8/5.

The Modes

Ray Perlner coined names for the 9 modes of Negri[9], mostly based on the fact that, in 19EDO, a 7-note subset of Negri-9 is equivalent to the well-known double harmonic scale. e.g. Mode 1, "Austro-Hungarian Minor" is spelled A B C Db D# E F Gb G# A' and contains the Hungarian Minor scale, A B C D# E F G# A' as a subset. These are denoted "Ray's name."

More systematic names based on UDP notation are also given. For Negri[9], the chroma-aligned generator is 15/8 (alternatively 28/15, 13/7, or 24/13). All generators below refer to this generator.

The table below also gives step patterns and example spellings in ups and downs notation for 19EDO and 29EDO.

Mode Number	Ray's Name	UDP Name	19 edo Step Pattern	19 EDO Spelling	29 edo Step Pattern	29 EDO Spelling	Interval Qualities	Other Notes
1	Austro-Hungarian Minor	8|0	322222222	A B C Db D# E F Gb G# A'	533333333	A B C^ C#^ D#v E F^ F#^ G#v A'	M2 A2.5 M3.3 A4 P5 M5.7 P6.5 M7
2	Reoriented	0|8	222222223	B C Db D# E F Gb G# A B'	333333335	B C^ C#^ D#v E F^ F#^ G#v A B'	m2 p2.5 m3.3 p4 d5 m5.7 d6.5 m7
3	Negri Augmented Major	1|7	222222232	C Db D# E F Gb G# A B C'	333333353	C^ C#^ D#v E F^ F#^ G#v A B C^'	m2 p2.5 m3.3 p4 d5 m5.7 d6.5 M7
4	Faceless	2|6	222222322	Db D# E F Gb G# A B C Db'	333333533	C#^ D#v E F^ F#^ G#v A B C^ C#^'	m2 p2.5 m3.3 p4 d5 m5.7 P6.5 M7
5	Amended	3|5	222223222	D# E F Gb G# A B C Db D#'	333335333	D#v E F^ F#^ G#v A B C^ C#^ D#v'	m2 p2.5 m3.3 p4 d5 M5.7 P6.5 M7
6	Symmetric Negri Major	4|4	222232222	E F Gb G# A B C Db D# E'	333353333	E F^ F#^ G#v A B C^ C#^ D#v E'	m2 p2.5 m3.3 p4 P5 M5.7 P6.5 M7
7	Carolingian	5|3	222322222	F Gb G# A B C Db D# E F'	333533333	F^ F#^ G#v A B C^ C#^ D#v E F^'	m2 p2.5 m3.3 A4 P5 M5.7 P6.5 M7
8	Estranged	6|2	223222222	Gb G# A B C Db D# E F Gb'	335333333	F#^ G#v A B C^ C#^ D#v E F^ F#^'	m2 p2.5 M3.3 A4 P5 M5.7 P6.5 M7
9	Ultra-Hittite	7|1	232222222	G# A B C Db D# E F Gb G#'	353333333	G#v A B C^ C#^ D#v E F^ F#^ G#v'	m2 A2.5 M3.3 A4 P5 M5.7 P6.5 M7