Undecimal primodality - Revision history

BudjarnLambeth: Link

2025-06-07T07:59:58Z

Link

← Older revision		Revision as of 07:59, 7 June 2025
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	When the 11th harmonic is selected as a numerary nexus to relate other harmonics against, the resultant collection of pitches together forms the '''undecimal primodality'''. The undecimal [[primodality]] is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.		When the 11th harmonic is selected as a [[numerary nexus]] to relate other harmonics against, the resultant collection of pitches together forms the '''undecimal primodality'''. The undecimal [[primodality]] is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.

	== Examining undecimal ==		== Examining undecimal ==

Inthar: /* Second octave */ cap

2023-06-27T16:02:03Z

Second octave: cap

← Older revision		Revision as of 16:02, 27 June 2023
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	Undecimal also grants "opposite" color intervals in the form of second octave intervals that go flat relative to key interval areas rather than uniformly sharp like the majority of Undecimal. These "relatively flatter" intervals can be seen in 41/22 at 1077.7 cents as a relatively darker maj7, 29/22 at 478 cents as a subfourth relative to the 417 cent 14/11. These can be combined with the "prime fifths" from the first octave to generate startling combinations which push, pull, and subvert expectation like 22:28:34:41:52:58.		Undecimal also grants "opposite" color intervals in the form of second octave intervals that go flat relative to key interval areas rather than uniformly sharp like the majority of Undecimal. These "relatively flatter" intervals can be seen in 41/22 at 1077.7 cents as a relatively darker maj7, 29/22 at 478 cents as a subfourth relative to the 417 cent 14/11. These can be combined with the "prime fifths" from the first octave to generate startling combinations which push, pull, and subvert expectation like 22:28:34:41:52:58.

	Lastly, ~~The~~ gorgeous Zalzalian neutral third, 27/22 at ~354.5 cents, shows up in the second octave. This can be combined with the rich diversity of neutrals from the first octave to form a strong neutral base.		Lastly, the gorgeous Zalzalian neutral third, 27/22 at ~354.5 cents, shows up in the second octave. This can be combined with the rich diversity of neutrals from the first octave to form a strong neutral base.

	== Basic triads ==		== Basic triads ==

Inthar at 16:01, 27 June 2023

2023-06-27T16:01:48Z

← Older revision		Revision as of 16:01, 27 June 2023
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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~~/13th~~ apart.		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.

Inthar: Inthar moved page Undecimal Primodality to Undecimal primodality: WP:TITLE

2023-06-27T14:25:27Z

Inthar moved page Undecimal Primodality to Undecimal primodality: WP:TITLE

← Older revision	Revision as of 14:25, 27 June 2023
(No difference)

Inthar: +cat

2021-06-20T02:44:45Z

+cat

← Older revision		Revision as of 02:44, 20 June 2021
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	22:32:33 Undecimal 5 Falling Comma Triad		22:32:33 Undecimal 5 Falling Comma Triad

			[[Category:Primodality]]

Inthar: bold lemma, + link

2021-06-20T02:37:07Z

bold lemma, + link

← Older revision		Revision as of 02:37, 20 June 2021
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	When the 11th harmonic is selected as a numerary nexus to relate other harmonics against, the resultant collection of pitches together forms the undecimal primodality. The undecimal primodality is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.		When the 11th harmonic is selected as a numerary nexus to relate other harmonics against, the resultant collection of pitches together forms the '''undecimal primodality'''. The undecimal [[primodality]] is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.

	== Examining undecimal ==		== Examining undecimal ==

Inthar: /* Basic triads */cap convention

2021-06-20T02:36:13Z

Basic triads: cap convention

← Older revision		Revision as of 02:36, 20 June 2021
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	Lastly, The gorgeous Zalzalian neutral third, 27/22 at ~354.5 cents, shows up in the second octave. This can be combined with the rich diversity of neutrals from the first octave to form a strong neutral base.		Lastly, The gorgeous Zalzalian neutral third, 27/22 at ~354.5 cents, shows up in the second octave. This can be combined with the rich diversity of neutrals from the first octave to form a strong neutral base.

	== Basic ~~Triads~~ ==		== Basic triads ==

	22:23:33 Undecimal Phrgyian Triad		22:23:33 Undecimal Phrgyian Triad

Inthar: /* Examining undecimal */

2021-06-20T02:35:35Z

Examining undecimal

← Older revision		Revision as of 02:35, 20 June 2021
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	Undecimal has quality super and neutral intervals. The 11:15 at 536.9c is a remarkable superfourth. It's a highly active, interval which has a tendency to bridge almost all the intervals in the family together. The 11:15 superfourth is very tunable by ear and has it's own distinct identity rather than sounding like a flatter version of 8:11. Additionally, it forms a parallel relationship with the 11:20 superminor seventh at 1034.9c. Between the two, a 3:4 relationship exists similar to the familiar perfect fourth relationship between 4 and b7 in 12edo. However, in this family the relationship is shifted much higher to super fourth and superminor seventh. Between this brighter super 4-b7 relationship and the sharper 3-7 relationship, tertian or 12edo-esque structures rendered in Undecimal tend to sound brighter than /13, /17, and /19 color variants. Neutral intervals appear in the first octave as 11:12 and 11:18, 150.6c neutral second and an 852c neutral sixth from 11:18. The 11:19 at 948 cents contributes a unique middle-augmented sixth which tends to sound more like a hypermajor sixth when surrounded by the sharper Undecimal intervals.		Undecimal has quality super and neutral intervals. The 11:15 at 536.9c is a remarkable superfourth. It's a highly active, interval which has a tendency to bridge almost all the intervals in the family together. The 11:15 superfourth is very tunable by ear and has it's own distinct identity rather than sounding like a flatter version of 8:11. Additionally, it forms a parallel relationship with the 11:20 superminor seventh at 1034.9c. Between the two, a 3:4 relationship exists similar to the familiar perfect fourth relationship between 4 and b7 in 12edo. However, in this family the relationship is shifted much higher to super fourth and superminor seventh. Between this brighter super 4-b7 relationship and the sharper 3-7 relationship, tertian or 12edo-esque structures rendered in Undecimal tend to sound brighter than /13, /17, and /19 color variants. Neutral intervals appear in the first octave as 11:12 and 11:18, 150.6c neutral second and an 852c neutral sixth from 11:18. The 11:19 at 948 cents contributes a unique middle-augmented sixth which tends to sound more like a hypermajor sixth when surrounded by the sharper Undecimal intervals.


	=== Second octave ===		=== Second octave ===
	22:44 (2p:4p)		22:44 (2p:4p)

Inthar: /* Examining undecimal */

2021-06-20T02:33:56Z

Examining undecimal

← Older revision		Revision as of 02:33, 20 June 2021
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	== Examining undecimal ==		== Examining undecimal ==
			Throughout the course of this writing, we will examine the first 2 octaves of the undecimal primodality.
	=== First octave ===		=== First octave ===
	11:22 (1p:2p)		11:22 (1p:2p)

Inthar at 02:33, 20 June 2021

2021-06-20T02:33:47Z

← Older revision		Revision as of 02:33, 20 June 2021
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	When the 11th harmonic is selected as a numerary nexus to relate other harmonics against, the resultant collection of pitches together forms the undecimal primodality. The undecimal primodality is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.		When the 11th harmonic is selected as a numerary nexus to relate other harmonics against, the resultant collection of pitches together forms the undecimal primodality. The undecimal primodality is a gorgeous and flexible family of intervals. It contains possibility of bright diatonic gestures, a rich diversity of neutrals, color opposite qualities, and key super intervals. It's initial genesis step size is 150.6 cents.

	~~Throughout the course of this writing, we will examine the first 2 octaves of the undecimal primodality:~~


	== Examining undecimal ==		== Examining undecimal ==