7L 5s: Difference between revisions

Revision as of 14:08, 3 March 2025

↖ 6L 4s	↑ 7L 4s	8L 4s ↗
← 6L 5s	7L 5s	8L 5s →
↙ 6L 6s	↓ 7L 6s	8L 6s ↘

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└┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLsLsLLsLsLs
sLsLsLLsLsLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

5\12 to 3\7 (500.0 ¢ to 514.3 ¢)

Dark

4\7 to 7\12 (685.7 ¢ to 700.0 ¢)

TAMNAMS information

Related to

5L 2s (diatonic)

With tunings

1:1 to 2:1 (soft-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

5\12 (500.0 ¢)

Supersoft (L:s = 4:3)

18\43 (502.3 ¢)

13\31 (503.2 ¢)

21\50 (504.0 ¢)

8\19 (505.3 ¢)

19\45 (506.7 ¢)

11\26 (507.7 ¢)

Superhard (L:s = 4:1)

14\33 (509.1 ¢)

Collapsed (L:s = 1:0)

3\7 (514.3 ¢)

7L 5s, also called m-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500 ¢ to 514.3 ¢, or from 685.7 ¢ to 700 ¢.

7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.

Meantone is the only notable harmonic entropy minimum.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Proposed Names

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.

Modes of 7L 5s
UDP	Cyclic order	Step pattern	Mode names (by Eliora)	Mode names (by Ganaram)
11\|0	1	LLsLsLLsLsLs	July	Martian
10\|1	6	LLsLsLsLLsLs	December	Aprilian
9\|2	11	LsLLsLsLLsLs	May	Maian
8\|3	4	LsLLsLsLsLLs	October	Junian
7\|4	9	LsLsLLsLsLLs	March	Quintillian Julian
6\|5	2	LsLsLLsLsLsL	August	Sextilian Augustan
5\|6	7	LsLsLsLLsLsL	January	Septembian
4\|7	12	sLLsLsLLsLsL	June	Octobian
3\|8	5	sLLsLsLsLLsL	November	Novembian
2\|9	10	sLsLLsLsLLsL	April	Decembian
1\|10	3	sLsLLsLsLsLL	September	Janian
0\|11	8	sLsLsLLsLsLL	February	Februan

Scales

Meaneb471a – an equal beating tuning of meantone
Meantone12 – 31edo tuning
Ratwolf – 20/13 wolf fifth tuning of meantone
Meaneb471 – the other equal beating tuning of meantone
Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Scale tree and tuning spectrum of 7L 5s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
5\12						500.000	700.000	1:1	1.000	Equalized 7L 5s
					28\67	501.493	698.507	6:5	1.200
				23\55		501.818	698.182	5:4	1.250
					41\98	502.041	697.959	9:7	1.286
			18\43			502.326	697.674	4:3	1.333	Supersoft 7L 5s Meantone / meridetone
					49\117	502.564	697.436	11:8	1.375
				31\74		502.703	697.297	7:5	1.400	Meantone / huygens / grosstone
					44\105	502.857	697.143	10:7	1.429
		13\31				503.226	696.774	3:2	1.500	Soft 7L 5s
					47\112	503.571	696.429	11:7	1.571
				34\81		503.704	696.296	8:5	1.600	Meantone
					55\131	503.817	696.183	13:8	1.625	Golden meantone (503.7855 ¢)
			21\50			504.000	696.000	5:3	1.667	Semisoft 7L 5s Meantone / meanpop
					50\119	504.202	695.798	12:7	1.714
				29\69		504.348	695.652	7:4	1.750
					37\88	504.545	695.455	9:5	1.800
	8\19					505.263	694.737	2:1	2.000	Basic 7L 5s Scales with tunings softer than this are proper
					35\83	506.024	693.976	9:4	2.250
				27\64		506.250	693.750	7:3	2.333
					46\109	506.422	693.578	12:5	2.400
			19\45			506.667	693.333	5:2	2.500	Semihard 7L 5s ↕&nbspFlattone;
					49\116	506.897	693.103	13:5	2.600	Golden flattone (506.9365 ¢)
				30\71		507.042	692.958	8:3	2.667
					41\97	507.216	692.784	11:4	2.750
		11\26				507.692	692.308	3:1	3.000	Hard 7L 5s
					36\85	508.235	691.765	10:3	3.333
				25\59		508.475	691.525	7:2	3.500
					39\92	508.696	691.304	11:3	3.667
			14\33			509.091	690.909	4:1	4.000	Superhard 7L 5s
					31\73	509.589	690.411	9:2	4.500
				17\40		510.000	690.000	5:1	5.000
					20\47	510.638	689.362	6:1	6.000
3\7						514.286	685.714	1:0	→ ∞	Collapsed 7L 5s

@@ Line 2: / Line 2: @@
 {{MOS intro|Other Names=m-chromatic}}
-L 5s represents the chromatic scale of [[meantone]], or meantone chromatic scale. Such scales are characterized by having a small step ([[diatonic semitone]]) that is larger than the [[chroma]] ([[chromatic semitone]]), the reverse of [[5L 7s]].
+L&nbsp;5s represents the chromatic scale of [[meantone]], or meantone chromatic scale. Such scales are characterized by having a small step ([[diatonic semitone]]) that is larger than the [[chroma]] ([[chromatic semitone]]), the reverse of [[5L&nbsp;7s]].
 Meantone is the only notable harmonic entropy minimum.
-==Intervals==
-{{MOS intervals}}
+== Scale properties ==
-== Modes ==
+{{TAMNAMS use}}
-{{MOS mode degrees}}
+{{MOS data}}
 === Proposed Names ===
 Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.
-{{MOS modes|Table Headers=Mode names<br>(by [[User:Eliora|Eliora]]); Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]])|Table Entries=July; Martian; December; Aprilian; May; Maian; October; Junian; March; Quintillian <br>Julian; August; Sextilian <br>Augustan; January; Septembian; June; Octobian; November; Novembian; April; Decembian; September; Janian; February; Februan}}
+{{MOS modes
+| Table Headers=
+Mode names<br />(by [[User:Eliora|Eliora]]) $
+Mode names<br />(by [[User:Ganaram inukshuk|Ganaram]])
+| Table Entries=
+July $
+Martian $
+December $
+Aprilian $
+May $
+Maian $
+October $
+Junian $
+March $
+Quintillian <br>Julian $
+August $
+Sextilian <br>Augustan $
+January $
+Septembian $
+June $
+Octobian $
+November $
+Novembian $
+April $
+Decembian $
+September $
+Janian $
+February $
+Februan $
+}}
 == Scales ==
@@ Line 21: / Line 51: @@
 == Scale tree ==
-{{Scale tree|Comments=4/3: Meantone / [[meridetone]];
+{{MOS tuning spectrum
-/5: Meantone / [[huygens]] / [[grosstone]];
+| 4/3 = Meantone / [[meridetone]]
-/8: [[Golden meantone]] (503.7855¢);
+| 7/5 = Meantone / [[huygens]] / [[grosstone]]
-/5: [[Meantone]];
+| 13/8 = [[Golden meantone]] (503.7855{{c}})
-/3: Meantone / [[meanpop]];
+| 8/5 = [[Meantone]]
-/2: ↕ [[Flattone]];
+| 5/3 = Meantone / [[meanpop]]
-/5: Golden flattone (506.9365¢)}}
+| 5/2 = ↕&nbsp[[Flattone]];
+| 13/5 = Golden flattone (506.9365{{c}})
+}}
 [[Category:12-tone scales]]
 [[Category:M-chromatic| ]]<!-- main article -->
 [[Category:Chromatic scales]]

7L 5s: Difference between revisions

Revision as of 14:08, 3 March 2025

Contents

Scale properties

Proposed Names

Scales

Scale tree

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7L 5s: Difference between revisions

Revision as of 14:08, 3 March 2025

Scale properties

Proposed Names

Scales

Scale tree

Navigation menu

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