5L 3s: Difference between revisions

Latest revision as of 13:59, 5 May 2025

↖ 4L 2s	↑ 5L 2s	6L 2s ↗
← 4L 3s	5L 3s	6L 3s →
↙ 4L 4s	↓ 5L 4s	6L 4s ↘

┌╥╥┬╥╥┬╥┬┐
│║║│║║│║││
││││││││││
└┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLsLLsLs
sLsLLsLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

3\8 to 2\5 (450.0 ¢ to 480.0 ¢)

Dark

3\5 to 5\8 (720.0 ¢ to 750.0 ¢)

TAMNAMS information

Name

oneirotonic

Prefix

oneiro-

Abbrev.

onei

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

3\8 (450.0 ¢)

Supersoft (L:s = 4:3)

11\29 (455.2 ¢)

8\21 (457.1 ¢)

13\34 (458.8 ¢)

5\13 (461.5 ¢)

12\31 (464.5 ¢)

7\18 (466.7 ¢)

Superhard (L:s = 4:1)

9\23 (469.6 ¢)

Collapsed (L:s = 1:0)

2\5 (480.0 ¢)

For the tritave-equivalent MOS structure with the same step pattern, see 5L 3s (3/1-equivalent).

5L 3s, named oneirotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 450 ¢ to 480 ¢, or from 720 ¢ to 750 ¢. 5L 3s can be seen as a warped diatonic scale, because it has one extra small step compared to diatonic (5L 2s).

Name

TAMNAMS suggests the temperament-agnostic name oneirotonic as the name of 5L 3s. The name was originally used as a name for the 5L 3s scale in 13edo. 'Oneiro' is sometimes used as a shortened form.

'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as father is technically an abstract regular temperament (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate 3L 2s.

Scale properties

Intervals

Intervals of 5L 3s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-oneirostep	Perfect 0-oneirostep	P0oneis	0	0.0 ¢
1-oneirostep	Minor 1-oneirostep	m1oneis	s	0.0 ¢ to 150.0 ¢
1-oneirostep	Major 1-oneirostep	M1oneis	L	150.0 ¢ to 240.0 ¢
2-oneirostep	Minor 2-oneirostep	m2oneis	L + s	240.0 ¢ to 300.0 ¢
2-oneirostep	Major 2-oneirostep	M2oneis	2L	300.0 ¢ to 480.0 ¢
3-oneirostep	Diminished 3-oneirostep	d3oneis	L + 2s	240.0 ¢ to 450.0 ¢
3-oneirostep	Perfect 3-oneirostep	P3oneis	2L + s	450.0 ¢ to 480.0 ¢
4-oneirostep	Minor 4-oneirostep	m4oneis	2L + 2s	480.0 ¢ to 600.0 ¢
4-oneirostep	Major 4-oneirostep	M4oneis	3L + s	600.0 ¢ to 720.0 ¢
5-oneirostep	Perfect 5-oneirostep	P5oneis	3L + 2s	720.0 ¢ to 750.0 ¢
5-oneirostep	Augmented 5-oneirostep	A5oneis	4L + s	750.0 ¢ to 960.0 ¢
6-oneirostep	Minor 6-oneirostep	m6oneis	3L + 3s	720.0 ¢ to 900.0 ¢
6-oneirostep	Major 6-oneirostep	M6oneis	4L + 2s	900.0 ¢ to 960.0 ¢
7-oneirostep	Minor 7-oneirostep	m7oneis	4L + 3s	960.0 ¢ to 1050.0 ¢
7-oneirostep	Major 7-oneirostep	M7oneis	5L + 2s	1050.0 ¢ to 1200.0 ¢
8-oneirostep	Perfect 8-oneirostep	P8oneis	5L + 3s	1200.0 ¢

Generator chain

Generator chain of 5L 3s
Bright gens	Scale degree	Abbrev.
12	Augmented 4-oneirodegree	A4oneid
11	Augmented 1-oneirodegree	A1oneid
10	Augmented 6-oneirodegree	A6oneid
9	Augmented 3-oneirodegree	A3oneid
8	Augmented 0-oneirodegree	A0oneid
7	Augmented 5-oneirodegree	A5oneid
6	Major 2-oneirodegree	M2oneid
5	Major 7-oneirodegree	M7oneid
4	Major 4-oneirodegree	M4oneid
3	Major 1-oneirodegree	M1oneid
2	Major 6-oneirodegree	M6oneid
1	Perfect 3-oneirodegree	P3oneid
0	Perfect 0-oneirodegree Perfect 8-oneirodegree	P0oneid P8oneid
−1	Perfect 5-oneirodegree	P5oneid
−2	Minor 2-oneirodegree	m2oneid
−3	Minor 7-oneirodegree	m7oneid
−4	Minor 4-oneirodegree	m4oneid
−5	Minor 1-oneirodegree	m1oneid
−6	Minor 6-oneirodegree	m6oneid
−7	Diminished 3-oneirodegree	d3oneid
−8	Diminished 8-oneirodegree	d8oneid
−9	Diminished 5-oneirodegree	d5oneid
−10	Diminished 2-oneirodegree	d2oneid
−11	Diminished 7-oneirodegree	d7oneid
−12	Diminished 4-oneirodegree	d4oneid

Modes

Scale degrees of the modes of 5L 3s
UDP	Cyclic order	Step pattern	Scale degree (oneirodegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8
7\|0	1	LLsLLsLs	Perf.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Perf.
6\|1	4	LLsLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.
5\|2	7	LsLLsLLs	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.
4\|3	2	LsLLsLsL	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Perf.
3\|4	5	LsLsLLsL	Perf.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.
2\|5	8	sLLsLLsL	Perf.	Min.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.
1\|6	3	sLLsLsLL	Perf.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Perf.
0\|7	6	sLsLLsLL	Perf.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Perf.

Proposed mode names

The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands.

Modes of 5L 3s
UDP	Cyclic order	Step pattern	Mode names
7\|0	1	LLsLLsLs	Dylathian
6\|1	4	LLsLsLLs	Ilarnekian
5\|2	7	LsLLsLLs	Celephaïsian
4\|3	2	LsLLsLsL	Ultharian
3\|4	5	LsLsLLsL	Mnarian
2\|5	8	sLLsLLsL	Kadathian
1\|6	3	sLLsLsLL	Hlanithian
0\|7	6	sLsLLsLL	Sarnathian

Tunings

Simple tunings

The simplest tuning for 5L 3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively.

Simple Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 18edo		Soft (3:2) 21edo
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\18	0.0	0\21	0.0
Minor 1-oneirodegree	m1oneid	1\13	92.3	1\18	66.7	2\21	114.3
Major 1-oneirodegree	M1oneid	2\13	184.6	3\18	200.0	3\21	171.4
Minor 2-oneirodegree	m2oneid	3\13	276.9	4\18	266.7	5\21	285.7
Major 2-oneirodegree	M2oneid	4\13	369.2	6\18	400.0	6\21	342.9
Diminished 3-oneirodegree	d3oneid	4\13	369.2	5\18	333.3	7\21	400.0
Perfect 3-oneirodegree	P3oneid	5\13	461.5	7\18	466.7	8\21	457.1
Minor 4-oneirodegree	m4oneid	6\13	553.8	8\18	533.3	10\21	571.4
Major 4-oneirodegree	M4oneid	7\13	646.2	10\18	666.7	11\21	628.6
Perfect 5-oneirodegree	P5oneid	8\13	738.5	11\18	733.3	13\21	742.9
Augmented 5-oneirodegree	A5oneid	9\13	830.8	13\18	866.7	14\21	800.0
Minor 6-oneirodegree	m6oneid	9\13	830.8	12\18	800.0	15\21	857.1
Major 6-oneirodegree	M6oneid	10\13	923.1	14\18	933.3	16\21	914.3
Minor 7-oneirodegree	m7oneid	11\13	1015.4	15\18	1000.0	18\21	1028.6
Major 7-oneirodegree	M7oneid	12\13	1107.7	17\18	1133.3	19\21	1085.7
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	18\18	1200.0	21\21	1200.0

Hypohard tunings

Hypohard oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with meantone diatonic tunings:

The large step is a "meantone", around the range of 10/9 to 9/8.
The major 2-mosstep is a meantone- to flattone-sized major third, thus is a stand-in for the classical diatonic major third.

With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to 7/6.

EDOs that are in the hypohard range include 13edo, 18edo, and 31edo, and are associated with A-Team temperament.

13edo has characteristically small 1-mossteps of about 185 ¢. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best 11/8 out of all hypohard tunings.
18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3 ¢, a perfect 5-mosstep) and falling fifths (666.7 ¢, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
31edo can be used to make the major 2-mosstep a near-just 5/4.
44edo (generator 17\44 = 463.64 ¢), 57edo (generator 22\57 = 463.16 ¢), and 70edo (generator 27\70 = 462.857 ¢}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8.

Hypohard Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Semihard (5:2) 31edo		Hard (3:1) 18edo
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\31	0.0	0\18	0.0
Minor 1-oneirodegree	m1oneid	1\13	92.3	2\31	77.4	1\18	66.7
Major 1-oneirodegree	M1oneid	2\13	184.6	5\31	193.5	3\18	200.0
Minor 2-oneirodegree	m2oneid	3\13	276.9	7\31	271.0	4\18	266.7
Major 2-oneirodegree	M2oneid	4\13	369.2	10\31	387.1	6\18	400.0
Diminished 3-oneirodegree	d3oneid	4\13	369.2	9\31	348.4	5\18	333.3
Perfect 3-oneirodegree	P3oneid	5\13	461.5	12\31	464.5	7\18	466.7
Minor 4-oneirodegree	m4oneid	6\13	553.8	14\31	541.9	8\18	533.3
Major 4-oneirodegree	M4oneid	7\13	646.2	17\31	658.1	10\18	666.7
Perfect 5-oneirodegree	P5oneid	8\13	738.5	19\31	735.5	11\18	733.3
Augmented 5-oneirodegree	A5oneid	9\13	830.8	22\31	851.6	13\18	866.7
Minor 6-oneirodegree	m6oneid	9\13	830.8	21\31	812.9	12\18	800.0
Major 6-oneirodegree	M6oneid	10\13	923.1	24\31	929.0	14\18	933.3
Minor 7-oneirodegree	m7oneid	11\13	1015.4	26\31	1006.5	15\18	1000.0
Major 7-oneirodegree	M7oneid	12\13	1107.7	29\31	1122.6	17\18	1133.3
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	31\31	1200.0	18\18	1200.0

Hyposoft tunings

Hyposoft oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings,

The large step of oneirotonic tends to be intermediate in size between 10/9 and 11/10; the small step size is a semitone close to 17/16, about 92 ¢ to 114 ¢.
The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342 ¢) to 4\13 (369 ¢).

21edo's P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71 ¢) and Baroque diatonic semitones (114.29 ¢, close to quarter-comma meantone's 117.11 ¢).
34edo's 9:10:11:13 is even better.

This set of JI identifications is associated with petrtri temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" petrtri temperament is.)

Hyposoft Tunings of 5L 3s
Scale degree	Abbrev.	Soft (3:2) 21edo		Semisoft (5:3) 34edo		Basic (2:1) 13edo
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\21	0.0	0\34	0.0	0\13	0.0
Minor 1-oneirodegree	m1oneid	2\21	114.3	3\34	105.9	1\13	92.3
Major 1-oneirodegree	M1oneid	3\21	171.4	5\34	176.5	2\13	184.6
Minor 2-oneirodegree	m2oneid	5\21	285.7	8\34	282.4	3\13	276.9
Major 2-oneirodegree	M2oneid	6\21	342.9	10\34	352.9	4\13	369.2
Diminished 3-oneirodegree	d3oneid	7\21	400.0	11\34	388.2	4\13	369.2
Perfect 3-oneirodegree	P3oneid	8\21	457.1	13\34	458.8	5\13	461.5
Minor 4-oneirodegree	m4oneid	10\21	571.4	16\34	564.7	6\13	553.8
Major 4-oneirodegree	M4oneid	11\21	628.6	18\34	635.3	7\13	646.2
Perfect 5-oneirodegree	P5oneid	13\21	742.9	21\34	741.2	8\13	738.5
Augmented 5-oneirodegree	A5oneid	14\21	800.0	23\34	811.8	9\13	830.8
Minor 6-oneirodegree	m6oneid	15\21	857.1	24\34	847.1	9\13	830.8
Major 6-oneirodegree	M6oneid	16\21	914.3	26\34	917.6	10\13	923.1
Minor 7-oneirodegree	m7oneid	18\21	1028.6	29\34	1023.5	11\13	1015.4
Major 7-oneirodegree	M7oneid	19\21	1085.7	31\34	1094.1	12\13	1107.7
Perfect 8-oneirodegree	P8oneid	21\21	1200.0	34\34	1200.0	13\13	1200.0

Parasoft and ultrasoft tunings

The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to porcupine temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a porcupine generator. The chord 10:11:13 is very well approximated in 29edo.

Soft Tunings of 5L 3s
Scale degree	Abbrev.	6:5 45edo		Supersoft (4:3) 29edo		Soft (3:2) 21edo
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\45	0.0	0\29	0.0	0\21	0.0
Minor 1-oneirodegree	m1oneid	5\45	133.3	3\29	124.1	2\21	114.3
Major 1-oneirodegree	M1oneid	6\45	160.0	4\29	165.5	3\21	171.4
Minor 2-oneirodegree	m2oneid	11\45	293.3	7\29	289.7	5\21	285.7
Major 2-oneirodegree	M2oneid	12\45	320.0	8\29	331.0	6\21	342.9
Diminished 3-oneirodegree	d3oneid	16\45	426.7	10\29	413.8	7\21	400.0
Perfect 3-oneirodegree	P3oneid	17\45	453.3	11\29	455.2	8\21	457.1
Minor 4-oneirodegree	m4oneid	22\45	586.7	14\29	579.3	10\21	571.4
Major 4-oneirodegree	M4oneid	23\45	613.3	15\29	620.7	11\21	628.6
Perfect 5-oneirodegree	P5oneid	28\45	746.7	18\29	744.8	13\21	742.9
Augmented 5-oneirodegree	A5oneid	29\45	773.3	19\29	786.2	14\21	800.0
Minor 6-oneirodegree	m6oneid	33\45	880.0	21\29	869.0	15\21	857.1
Major 6-oneirodegree	M6oneid	34\45	906.7	22\29	910.3	16\21	914.3
Minor 7-oneirodegree	m7oneid	39\45	1040.0	25\29	1034.5	18\21	1028.6
Major 7-oneirodegree	M7oneid	40\45	1066.7	26\29	1075.9	19\21	1085.7
Perfect 8-oneirodegree	P8oneid	45\45	1200.0	29\29	1200.0	21\21	1200.0

Parahard tunings

23edo oneiro combines the sound of neogothic tunings like 46edo and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as 46edo's neogothic major second, and is both a warped 22edo superpyth diatonic and a warped 24edo semaphore semiquartal (and both nearby scales are superhard MOSes).

Superhard Tuning of 5L 3s
Scale degree	Abbrev.	Superhard (4:1) 23edo
Scale degree	Abbrev.	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\23	0.0
Minor 1-oneirodegree	m1oneid	1\23	52.2
Major 1-oneirodegree	M1oneid	4\23	208.7
Minor 2-oneirodegree	m2oneid	5\23	260.9
Major 2-oneirodegree	M2oneid	8\23	417.4
Diminished 3-oneirodegree	d3oneid	6\23	313.0
Perfect 3-oneirodegree	P3oneid	9\23	469.6
Minor 4-oneirodegree	m4oneid	10\23	521.7
Major 4-oneirodegree	M4oneid	13\23	678.3
Perfect 5-oneirodegree	P5oneid	14\23	730.4
Augmented 5-oneirodegree	A5oneid	17\23	887.0
Minor 6-oneirodegree	m6oneid	15\23	782.6
Major 6-oneirodegree	M6oneid	18\23	939.1
Minor 7-oneirodegree	m7oneid	19\23	991.3
Major 7-oneirodegree	M7oneid	22\23	1147.8
Perfect 8-oneirodegree	P8oneid	23\23	1200.0

Ultrahard tunings

Main article: 5L 3s/Temperaments § Buzzard

Buzzard is a rank-2 temperament in the pseudocollapsed range. It represents the only harmonic entropy minimum of the oneirotonic spectrum.

In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. 23edo, 28edo and 33edo can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. 38edo & 43edo are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but 48edo is where it really comes into its own in terms of harmonies, providing not only an excellent 3/2, but also 7/4 and archipelago harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.

Beyond that, it's a question of which intervals you want to favor. 53edo has an essentially perfect 3/2, 58edo gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while 63edo does the same for the basic 4:6:7 triad. You could in theory go up to 83edo if you want to favor the 7/4 above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.

Ultrahard Tunings of 5L 3s
Scale degree	Abbrev.	7:1 38edo		10:1 53edo		12:1 63edo
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-oneirodegree	P0oneid	0\38	0.0	0\53	0.0	0\63	0.0
Minor 1-oneirodegree	m1oneid	1\38	31.6	1\53	22.6	1\63	19.0
Major 1-oneirodegree	M1oneid	7\38	221.1	10\53	226.4	12\63	228.6
Minor 2-oneirodegree	m2oneid	8\38	252.6	11\53	249.1	13\63	247.6
Major 2-oneirodegree	M2oneid	14\38	442.1	20\53	452.8	24\63	457.1
Diminished 3-oneirodegree	d3oneid	9\38	284.2	12\53	271.7	14\63	266.7
Perfect 3-oneirodegree	P3oneid	15\38	473.7	21\53	475.5	25\63	476.2
Minor 4-oneirodegree	m4oneid	16\38	505.3	22\53	498.1	26\63	495.2
Major 4-oneirodegree	M4oneid	22\38	694.7	31\53	701.9	37\63	704.8
Perfect 5-oneirodegree	P5oneid	23\38	726.3	32\53	724.5	38\63	723.8
Augmented 5-oneirodegree	A5oneid	29\38	915.8	41\53	928.3	49\63	933.3
Minor 6-oneirodegree	m6oneid	24\38	757.9	33\53	747.2	39\63	742.9
Major 6-oneirodegree	M6oneid	30\38	947.4	42\53	950.9	50\63	952.4
Minor 7-oneirodegree	m7oneid	31\38	978.9	43\53	973.6	51\63	971.4
Major 7-oneirodegree	M7oneid	37\38	1168.4	52\53	1177.4	62\63	1181.0
Perfect 8-oneirodegree	P8oneid	38\38	1200.0	53\53	1200.0	63\63	1200.0

Approaches

5L 3s/Temperaments

Samples

The Angels' Library by Inthar in the Sarnathian (23233233) mode of 21edo oneirotonic (score)

WT13C Prelude II (J Oneirominor) (score) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little.

(13edo, first 30 seconds is in J Celephaïsian)

(13edo, L Ilarnekian)

(by Igliashon Jones, 13edo, J Celephaïsian)

13edo Oneirotonic Modal Studies

Scale tree

Scale tree and tuning spectrum of 5L 3s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
3\8						450.000	750.000	1:1	1.000	Equalized 5L 3s
					17\45	453.333	746.667	6:5	1.200
				14\37		454.054	745.946	5:4	1.250
					25\66	454.545	745.455	9:7	1.286
			11\29			455.172	744.828	4:3	1.333	Supersoft 5L 3s
					30\79	455.696	744.304	11:8	1.375
				19\50		456.000	744.000	7:5	1.400
					27\71	456.338	743.662	10:7	1.429
		8\21				457.143	742.857	3:2	1.500	Soft 5L 3s
					29\76	457.895	742.105	11:7	1.571
				21\55		458.182	741.818	8:5	1.600
					34\89	458.427	741.573	13:8	1.625	Golden oneirotonic (458.3592 ¢)
			13\34			458.824	741.176	5:3	1.667	Semisoft 5L 3s
					31\81	459.259	740.741	12:7	1.714
				18\47		459.574	740.426	7:4	1.750
					23\60	460.000	740.000	9:5	1.800
	5\13					461.538	738.462	2:1	2.000	Basic 5L 3s Scales with tunings softer than this are proper
					22\57	463.158	736.842	9:4	2.250
				17\44		463.636	736.364	7:3	2.333
					29\75	464.000	736.000	12:5	2.400
			12\31			464.516	735.484	5:2	2.500	Semihard 5L 3s
					31\80	465.000	735.000	13:5	2.600	Golden A-Team (465.0841 ¢)
				19\49		465.306	734.694	8:3	2.667
					26\67	465.672	734.328	11:4	2.750
		7\18				466.667	733.333	3:1	3.000	Hard 5L 3s
					23\59	467.797	732.203	10:3	3.333
				16\41		468.293	731.707	7:2	3.500
					25\64	468.750	731.250	11:3	3.667
			9\23			469.565	730.435	4:1	4.000	Superhard 5L 3s
					20\51	470.588	729.412	9:2	4.500
				11\28		471.429	728.571	5:1	5.000
					13\33	472.727	727.273	6:1	6.000
2\5						480.000	720.000	1:0	→ ∞	Collapsed 5L 3s

5L 3s: Difference between revisions

Latest revision as of 13:59, 5 May 2025

Contents

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