4L 7s: Difference between revisions

Revision as of 09:40, 24 August 2021

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Scale structure

Step pattern

LsLssLssLss
ssLssLssLsL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

8\11 to 3\4 (872.7 ¢ to 900.0 ¢)

Dark

1\4 to 3\11 (300.0 ¢ to 327.3 ¢)

TAMNAMS information

Related to

4L 3s (smitonic)

With tunings

2:1 to 1:0 (hard-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

8\11 (872.7 ¢)

Supersoft (L:s = 4:3)

27\37 (875.7 ¢)

19\26 (876.9 ¢)

30\41 (878.0 ¢)

11\15 (880.0 ¢)

25\34 (882.4 ¢)

14\19 (884.2 ¢)

Superhard (L:s = 4:1)

17\23 (887.0 ¢)

Collapsed (L:s = 1:0)

3\4 (900.0 ¢)

4L 7s refers to the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 3\11edo (three degrees of 11edo, 327.27¢), representing approximate diatonic minor thirds (6/5). One of the harmonic entropy minimums in this range is Kleismic/Hanson.

4L 7s has a heptatonic subset, which is the hard end of the spectrum of the smitonic scale (4L 3s).

A proposed name for this scale is kleistonic, based on an extension of TAMNAMS to bigger MOS scales.

Notation

The notation used in this article is LssLsLssLss = АВГДЕЅЗИѲІѦА, based on old Cyrillic numerals 1-10, and the addition of the small yus (Ѧ) for 11 (old "ya" symbolically representing І҃А҃=11). A titlo can be optionally used as a numeric sign (А҃), depending on font rendering, clarity, and style. Chromas are represented by regular sharps and flats.

Thus the 15edo gamut is as follows: А А#/Вb В Г Д Д#/Еb Е Ѕ Ѕ#/Зb З И Ѳ Ѳ#/Іb І Ѧ А

Letter names

The letters can be named in English as such: Az, Vede, Glagol, Dobro, Yest, Dzelo, Zemlya, Izhe, Thita, I (Ee), Yas. They can also be named as numbers 1-11.

Intervals

Generators	Notation (1/1 = А҃)	Interval category name	Generators	Notation of 2/1 inverse	Interval category name
The 11-note MOS has the following intervals (from some root):
0	А	perfect unison	0	А	dodecave (same as octave)
1	Д	perfect kleifourth (minor third)	-1	Ѳ	perfect kleininth (major sixth)
2	Зb	minor kleiseventh	-2	Ѕ	major kleisixth
3	Іb	minor kleitenth	-3	Г	major kleithird
4	Вb	minor kleisecond	-4	Ѧ	major kleieleventh
5	Еb	minor kleififth	-5	И	major kleieighth
6	Иb	minor kleieighth	-6	Е	major kleififth
7	Ѧb	minor kleieleventh	-7	В	major kleisecond
8	Гb	minor kleithird	-8	І	major kleitenth
9	Ѕb	minor kleisixth	-9	З	major kleiseventh
10	Ѳb	diminished kleininth	-10	Д#	augmented kleithird
The chromatic 15-note MOS (either 4L 11s, 11L 4s, or 15edo) also has the following intervals (from some root):
11	Аb	diminished dodecave	-11	А#	augmented unison (chroma)
12	Дb	diminished kleifourth	-12	Ѳ#	augmented kleininth
13	Зbb	diminished kleiseventh	-13	Ѕ#	augmented kleisixth
14	Іbb	diminished kleitenth	-14	Г#	augmented kleithird

Genchain

The generator chain for this scale is as follows:

Дb	Аb	Ѳb	Ѕb	Гb	Ѧb	Иb	Еb	Вb	Іb	Зb	Д	А	Ѳ	Ѕ	Г	Ѧ	И	Е	В	І	З	Д#	А#	Ѳ#	Ѕ#	Г#	Ѧ#	И#	Е#	В#	І#	З#
d4	d12	d9	m6	m3	m11	m8	m5	m2	m10	m7	P4	P1	P9	M6	M3	M11	M8	M5	M2	M10	M7	A4	A1	A9	A6	A3	A11	A8	A5	A2	A10	A7

Tuning ranges

Soft range

The soft range for tunings of kleistonic encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than 4\15 = 320¢.

This is the range associated with extensions of Orgone[7]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.

Soft kleistonic edos include 15edo and 26edo. The sizes of the generator, large step and small step of kleistonic are as follows in various soft kleistonic tunings:

	15edo (basic)	26edo (soft)	Some JI approximations
generator (g)	4\15, 320.00	7\26, 323.08	77/64, 6/5
L (octave - 3g)	2\15, 160.00	3\26, 138.46	12/11, 13/12
s (4g - octave)	1\15, 80.00	2\19, 92.31	21/20, 22/21, 20/19

Hypohard

Hypohard tunings of kleistonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢.

This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth (3/2), an octave above. This is the range associated with the eponymous Kleismic (aka Hanson) temperament and its extensions.

Hypohard kleistonic edos include 15edo, 19edo, and 34edo. The sizes of the generator, large step and small step of kleistonic are as follows in various hypohard kleistonic tunings:

	15edo (basic)	19edo (hard)	34edo (semihard)	Some JI approximations
generator (g)	4\15, 320.00	5\19, 315.79	9\34, 317.65	6/5
L (octave - 3g)	2\15, 160.00	3\19, 189.47	5\34, 176.47	10/9, 11/10 (in 15edo)
s (4g - octave)	1\15, 80.00	1\19, 63.16	2\34, 70.59	25/24, 26/25 (in better kleismic tunings)

Parahard

Parahard tunings of kleistonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢.

The minor third is at its purest here, but the resulting scales tend to approximate intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone.

Parahard kleistonic edos include 19edo, 23edo, and 42edo. The sizes of the generator, large step and small step of kleistonic are as follows in various parahard kleistonic tunings:

	19edo (hard)	23edo (superhard)	42edo (parahard)	Some JI approximations
generator (g)	5\19, 315.79	6\23, 313.04	11\42, 314.29	6/5
L (octave - 3g)	3\19, 189.47	4\23, 208.70	7\42, 200.00	10/9, 9/8
s (4g - octave)	1\19, 63.16	1\23, 52.17	2\42, 57.14	28/27, 33/32

Hyperhard

Hyperhard tunings of kleistonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢.

The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity, where the small step is generally flat of a quarter tone.

Hyperhard kleistonic edos include 23edo, 31edo, and 27edo. The sizes of the generator, large step and small step of kleistonic are as follows in various hyperhard kleistonic tunings:

	23edo (superhard)	31edo (extrahard)	27edo (pentahard)	Some JI approximations
generator (g)	6\23, 313.04	8\31, 309.68	7\27, 311.11	6/5
L (octave - 3g)	4\23, 208.70	6\31, 232.26	5\27, 222.22	8/7, 9/8
s (4g - octave)	1\23, 52.17	1\31, 38.71	1\27, 44.44	36/35, 45/44

Modes

The names are based on smitonic modes, modified with the "super-" prefix, with thematic additions, as there are an extra 4 modes available.

Mode	UDP	Name
LsLssLssLss	10\|0	Supernerevarine
LssLsLssLss	9\|1	Supervivecan
LssLssLsLss	8\|2	Superbaardauan
LssLssLssLs	7\|3	Superlorkhanic
sLsLssLssLs	6\|4	Supervvardenic
sLssLsLssLs	5\|5	Supersothic
sLssLssLsLs	4\|6	Supernumidian
sLssLssLssL	3\|7	Superkagrenacan
ssLsLssLssL	2\|8	Supernecromic
ssLssLsLssL	1\|9	Superalmalexian
ssLssLssLsL	0\|10	Superdagothic

Temperaments

Scales

Scale tree

The spectrum looks like this:

Generator						Cents		L	s	L/s	Comments
Generator						Chroma-positive	Chroma-negative	L	s	L/s	Comments
8\11						872.727	327.273	1	1	1.000
					43\59	874.576	325.424	6	5	1.200	Oregon
				35\48		875.000	325.000	5	4	1.250
					62\85	875.294	324.706	9	7	1.286
			27\37			875.676	324.324	4	3	1.333
					73\100	876.000	324.000	11	8	1.375
				46\63		876.190	323.810	7	5	1.400
					65\89	876.404	323.596	10	7	1.428	Orgone
		19\26				876.923	323.077	3	2	1.500	L/s = 3/2
					68\93	877.419	322.581	11	7	1.571	Magicaltet
				49\67		877.612	322.388	8	5	1.600
					79\108	877.778	322.222	13	8	1.625	Golden superkleismic
			30\41			878.049	321.951	5	3	1.667	Superkleismic
					71\97	878.351	321.649	12	7	1.714
				41\56		878.571	321.429	7	4	1.750
					52\71	878.873	321.127	9	5	1.800
	11\15					880.000	320.000	2	1	2.000	Basic kleistonic (Generators smaller than this are proper)
					47\64	881.250	318.750	9	4	2.250
				36\49		881.633	318.367	7	3	2.333	Catalan
					61\83	881.928	318.072	12	5	2.400
			25\34			882.353	317.647	5	2	2.500
					64\87	882.759	317.241	13	5	2.600	Countercata
				39\53		883.019	316.981	8	3	2.667	Hanson/cata
					53\72	883.333	316.667	11	4	2.750	Catakleismic
		14\19				884.211	315.789	3	1	3.000	L/s = 3/1
					45\61	885.246	314.754	10	3	3.333	Parakleismic
				31\42		885.714	314.286	7	2	3.500
					48\65	886.154	313.846	11	3	3.667
			17\23			886.957	313.043	4	1	4.000
					37\50	888.000	312.000	9	2	4.500	Oolong
				20\27		888.889	311.111	5	1	5.000	Starlingtet
					23\31	890.323	309.677	6	1	6.000	Myna
3\4						900.000	300.000	1	0	→ inf

@@ Line 405: / Line 405: @@
 == Temperaments ==
+== Scales ==
+* [[Oregon11]]
+* [[Orgone11]]
+* [[Magicaltet11]]
+* [[Cata11]]
+* [[Starlingtet11]]
+* [[Myna11]]
 == Scale tree ==

4L 7s: Difference between revisions

Revision as of 09:40, 24 August 2021

Contents

Notation

Letter names

Intervals

Genchain

Tuning ranges

Soft range

Hypohard

Parahard

Hyperhard

Modes

Temperaments

Scales

Scale tree

Navigation menu

Дb	Аb	Ѳb	Ѕb	Гb	Ѧb	Иb	Еb	Вb	Іb	Зb	Д	А	Ѳ	Ѕ	Г	Ѧ	И	Е	В	І	З	Д#	А#	Ѳ#	Ѕ#	Г#	Ѧ#	И#	Е#	В#	І#	З#
d4	d12	d9	m6	m3	m11	m8	m5	m2	m10	m7	P4	P1	P9	M6	M3	M11	M8	M5	M2	M10	M7	A4	A1	A9	A6	A3	A11	A8	A5	A2	A10	A7

Дb	Аb	Ѳb	Ѕb	Гb	Ѧb	Иb	Еb	Вb	Іb	Зb	Д	А	Ѳ	Ѕ	Г	Ѧ	И	Е	В	І	З	Д#	А#	Ѳ#	Ѕ#	Г#	Ѧ#	И#	Е#	В#	І#	З#
d4	d12	d9	m6	m3	m11	m8	m5	m2	m10	m7	P4	P1	P9	M6	M3	M11	M8	M5	M2	M10	M7	A4	A1	A9	A6	A3	A11	A8	A5	A2	A10	A7

4L 7s: Difference between revisions

Revision as of 09:40, 24 August 2021

Notation

Letter names

Intervals

Genchain

Tuning ranges

Soft range

Hypohard

Parahard

Hyperhard

Modes

Temperaments

Scales

Scale tree

Navigation menu

Search

Дb	Аb	Ѳb	Ѕb	Гb	Ѧb	Иb	Еb	Вb	Іb	Зb	Д	А	Ѳ	Ѕ	Г	Ѧ	И	Е	В	І	З	Д#	А#	Ѳ#	Ѕ#	Г#	Ѧ#	И#	Е#	В#	І#	З#
d4	d12	d9	m6	m3	m11	m8	m5	m2	m10	m7	P4	P1	P9	M6	M3	M11	M8	M5	M2	M10	M7	A4	A1	A9	A6	A3	A11	A8	A5	A2	A10	A7