Undecimal primodality: Difference between revisions
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First, let's examine the second octave's relationship to 12edo major and minor since most ears reading this have their senses rooted in that system. The 37/22 acts identically to 12edos major sixth as it's less than .02 cents away at 900 cents. 35/22 also sits within 4 cents of the 12edo minor sixth. These intervals often come into play when rendering tertian harmony in /11. These can be used to evoke fresh but familiar sensations in average listeners such as demonstrated in [https://youtu.be/3iWRlf3wrPs Spiritualistica] and [https://youtu.be/PIhFupdwv3M Timelessness]. 31/22 as 593.7 cents offers a lush tritone with it's own attractive quality which can operate as a tritone parallel for Maj#11 or 7#11 sounds. | First, let's examine the second octave's relationship to 12edo major and minor since most ears reading this have their senses rooted in that system. The 37/22 acts identically to 12edos major sixth as it's less than .02 cents away at 900 cents. 35/22 also sits within 4 cents of the 12edo minor sixth. These intervals often come into play when rendering tertian harmony in /11. These can be used to evoke fresh but familiar sensations in average listeners such as demonstrated in [https://youtu.be/3iWRlf3wrPs Spiritualistica] and [https://youtu.be/PIhFupdwv3M Timelessness]. 31/22 as 593.7 cents offers a lush tritone with it's own attractive quality which can operate as a tritone parallel for Maj#11 or 7#11 sounds. | ||
The 13/11 minor third provided by the first octave finds its fifth in 39/22. With the root added, these form 22:26:39, the Undecimal min7 chord. Since the root has also gained a perfect fifth, we can now create a full, 4 note minor seventh chord 22:26:33:39 representing R-b3-5-b7 with two 2:3s an 11 | The 13/11 minor third provided by the first octave finds its fifth in 39/22. With the root added, these form 22:26:39, the Undecimal min7 chord. Since the root has also gained a perfect fifth, we can now create a full, 4 note minor seventh chord 22:26:33:39 representing R-b3-5-b7 with two 2:3s an 11:13 apart. | ||
The second octave grants us an acute major second, 25/22 at 221.3 cents and a lower minor second with 23/22 at 76.9 cents. The 25/22 major second runs sharp along with the 417, 537, and 1119 "diatonic" major intervals. As a result when joined by those intervals, the system begins to sound uniformly sharp but regular (if all are sharp, none are sharp). By contrast, the first octave only gives the neutral second from 12/11 which tends to act more xen relative to the "diatonic" intervals. These colors can be interplayed to form a wide variety of possibilities across an axis of familiarity or novelty relative to your ear. | The second octave grants us an acute major second, 25/22 at 221.3 cents and a lower minor second with 23/22 at 76.9 cents. The 25/22 major second runs sharp along with the 417, 537, and 1119 "diatonic" major intervals. As a result when joined by those intervals, the system begins to sound uniformly sharp but regular (if all are sharp, none are sharp). By contrast, the first octave only gives the neutral second from 12/11 which tends to act more xen relative to the "diatonic" intervals. These colors can be interplayed to form a wide variety of possibilities across an axis of familiarity or novelty relative to your ear. | ||