Negri: Difference between revisions

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* Four of them make a tempered [[4/3]].

It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out [[49/48]], [[65/64]] and [[91/90]]. This is called '''negra''', and it is realized consistently in [[19edo]] and [[~~29 edo~~]]. Other tunings which may be usable as a negri or negra temperament include [[9edo]], [[10edo]], [[28edo]], [[47edo]], and [[48edo]], all of which are consistent through (at least) the 5 limit.

It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out [[49/48]], [[65/64]] and [[91/90]]. This is called '''negra''', and it is realized consistently in [[19edo]] and [[29edo]]. Other tunings which may be usable as a negri or negra temperament include [[9edo]], [[10edo]], [[28edo]], [[47edo]], and [[48edo]], all of which are consistent through (at least) the 5 limit.

Negri is generated by a large "semitone" of around 125 cents and forms 9-note and 10-note MOS's, Negri-9 and Negri-10, at [[1L 8S]] and [[9L 1s]] respectively. In [[19edo]], the Negri generator is the "diatonic half step" of 2\19, which allows these MOS's to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the [[tetrachord]]s of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E Double Harmonic Major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri-9 and Negri-10 contain at least one mode of the double harmonic scale as a subset.

Negri is generated by a large "semitone" of around 125 cents and forms 9-note and 10-note MOS's, Negri-9 and Negri-10, at [[1L 8s]] and [[9L 1s]] respectively. In [[19edo]], the Negri generator is the "diatonic half step" of 2\19, which allows these MOS's to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the [[tetrachord]]s of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E Double Harmonic Major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri-9 and Negri-10 contain at least one mode of the double harmonic scale as a subset.

Another useful mode of Negri-9 is Lssssssss, which in 19edo would be A B C Db D# E F Gb G# A. This has a minor triad (A C E) for a tonic chord, which can be extended to a 7-limit utonal tetrad (A C E D#), as well as 7-limit otonal tetrads on E and F that can function as, respectively, a dominant seventh chord and a German Augmented Sixth chord. This scale also contains the popular Hungarian Minor mode of the Double Harmonic scale, A B C D# E F G# A.

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 * Four of them make a tempered [[4/3]].
-It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out [[49/48]], [[65/64]] and [[91/90]]. This is called '''negra''', and it is realized consistently in [[19edo]] and [[29 edo]]. Other tunings which may be usable as a negri or negra temperament include [[9edo]], [[10edo]], [[28edo]], [[47edo]], and [[48edo]], all of which are consistent through (at least) the 5 limit.
+It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out [[49/48]], [[65/64]] and [[91/90]]. This is called '''negra''', and it is realized consistently in [[19edo]] and [[29edo]]. Other tunings which may be usable as a negri or negra temperament include [[9edo]], [[10edo]], [[28edo]], [[47edo]], and [[48edo]], all of which are consistent through (at least) the 5 limit.
-Negri is generated by a large "semitone" of around 125 cents and forms 9-note and 10-note MOS's, Negri-9 and Negri-10, at [[1L 8S]] and [[9L 1s]] respectively. In [[19edo]], the Negri generator is the "diatonic half step" of 2\19, which allows these MOS's to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the [[tetrachord]]s of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E Double Harmonic Major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri-9 and Negri-10 contain at least one mode of the double harmonic scale as a subset.
+Negri is generated by a large "semitone" of around 125 cents and forms 9-note and 10-note MOS's, Negri-9 and Negri-10, at [[1L 8s]] and [[9L 1s]] respectively. In [[19edo]], the Negri generator is the "diatonic half step" of 2\19, which allows these MOS's to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the [[tetrachord]]s of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E Double Harmonic Major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri-9 and Negri-10 contain at least one mode of the double harmonic scale as a subset.
 Another useful mode of Negri-9 is Lssssssss, which in 19edo would be A B C Db D# E F Gb G# A. This has a minor triad (A C E) for a tonic chord, which can be extended to a 7-limit utonal tetrad (A C E D#), as well as 7-limit otonal tetrads on E and F that can function as, respectively, a dominant seventh chord and a German Augmented Sixth chord. This scale also contains the popular Hungarian Minor mode of the Double Harmonic scale, A B C D# E F G# A.