1L 7s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
ArrowHead294 (talk | contribs)
15,213 edits
m Update link, scale tree [MOS tuning spectrum] template, and comments
 
Line 27: Line 27:
== Scale tree ==
== Scale tree ==
Generator ranges:
Generator ranges:
* Chroma-positive generator: 1050 cents (7\8) to 1200 cents (1\1)
* Chroma-positive generator: 1050{{c}} (7\8) to 1200{{c}} (1\1)
* Chroma-negative generator: 0 cents (0\1) to 150 cents (1\8)
* Chroma-negative generator: 0{{c}} (0\1) to 150{{c}} (1\8)


{| class="wikitable center-all"
{{MOS tuning spectrum
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
| 6/5 = [[Bohpier]]
! Cents
| 11/7 = [[Bleu]]
! L
| 8/5 = [[Jerome]]/bleu
! s
| 13/8 = Golden jerome (139.2429{{c}})
! L/s
| 9/5 = [[Twothirdtonic]]
! Comments
| 5/2 = [[Negri]]
|-
| 13/5 = Golden negri (124.7656{{c}})
| 1\8 || || || || || || 150.000 || 1 || 1 || 1.000 ||
| 10/3 = [[Miracle]]
|-
| 5/1 = [[Passion]], [[ripple]]
| || || || || || 5\41 || 146.341 || 6 || 5 || 1.200 || [[Bohpier]]
}}
|-
| || || || || 4\33 || || 145.455 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\58 || 144.828 || 9 || 7 || 1.286 ||
|-
| || || || 3\25 || || || 144.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\67 || 143.284 || 11 || 8 || 1.375 ||
|-
| || || || || 5\42 || || 142.857 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\59 || 142.373 || 10 || 7 || 1.429 ||
|-
| || || 2\17 || || || || 141.176 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\60 || 140.000 || 11 || 7 || 1.571 || [[Bleu]]
|-
| || || || || 5\43 || || 139.535 || 8 || 5 || 1.600 || [[Jerome]]/bleu
|-
| || || || || || 8\69 || 139.130 || 13 || 8 || 1.625 || Golden jerome (139.2429¢)
|-
| || || || 3\26 || || || 138.462 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\61 || 137.705 || 12 || 7 || 1.714 ||
|-
| || || || || 4\35 || || 137.143 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\44 || 136.364 || 9 || 5 || 1.800 || [[Twothirdtonic]]
|-
| || 1\9 || || || || || 133.333 || 2 || 1 || 2.000 || Basic 1L 7s <br>(small steps larger than this are proper)
|-
| || || || || || 4\37 || 129.730 || 9 || 4 || 2.250 ||
|-
| || || || || 3\28 || || 128.571 || 7 || 3 || 2.333 ||
|-
| || || || || || 5\47 || 127.660 || 12 || 5 || 2.400 ||
|-
| || || || 2\19 || || || 126.316 || 5 || 2 || 2.500 || [[Negri]]
|-
| || || || || || 5\48 || 125.000 || 13 || 5 || 2.600 || Golden negri (124.7656¢)
|-
| || || || || 3\29 || || 124.138 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\39 || 123.077 || 11 || 4 || 2.750 ||
|-
| || || 1\10 || || || || 120.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\31 || 116.129 || 10 || 3 || 3.333 || [[Miracle]]
|-
| || || || || 2\21 || || 114.286 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\32 || 112.500 || 11 || 3 || 3.667 ||
|-
| || || || 1\11 || || || 109.091 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\23 || 104.348 || 9 || 2 || 4.500 ||
|-
| || || || || 1\12 || || 100.000 || 5 || 1 || 5.000 || [[Passion]], [[ripple]]
|-
| || || || || || 1\13 || 92.308 || 6 || 1 || 6.000 ||
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}


== Trivia ==
== Trivia ==
This scale is a leap year pattern of the tabular Iranian calendar, where the leap year is inserted 7 times once in 4 years, with 1 gap of 5 years. Curiously enough, one short step of this scale is close to the one step of [[Bohlen-Pierce]].
This scale is a leap year pattern of the tabular Iranian calendar, where the leap year is inserted 7 times once in 4 years, with 1 gap of 5 years. Curiously enough, one short step of this scale is close to the one step of the [[Bohlen–Pierce scale]].
 
[[Category:8-tone scales]]
[[Category:8-tone scales]]

Latest revision as of 18:23, 13 March 2025

↑ 1L 6s 2L 6s ↗
1L 7s 2L 7s →
↓ 1L 8s 2L 8s ↘
Scale structure
Step pattern Lsssssss
sssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\8 to 1\1 (1050.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\8 (0.0 ¢ to 150.0 ¢)
TAMNAMS information
Name antipine
Prefix apine-
Abbrev. ap
Related MOS scales
Parent 1L 6s
Sister 7L 1s
Daughters 8L 1s, 1L 8s
Neutralized 2L 6s
2-Flought 9L 7s, 1L 15s
Equal tunings
Equalized (L:s = 1:1) 7\8 (1050.0 ¢)
Supersoft (L:s = 4:3) 22\25 (1056.0 ¢)
Soft (L:s = 3:2) 15\17 (1058.8 ¢)
Semisoft (L:s = 5:3) 23\26 (1061.5 ¢)
Basic (L:s = 2:1) 8\9 (1066.7 ¢)
Semihard (L:s = 5:2) 17\19 (1073.7 ¢)
Hard (L:s = 3:1) 9\10 (1080.0 ¢)
Superhard (L:s = 4:1) 10\11 (1090.9 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
View • Talk • Edit

1L 7s, named antipine in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 7 small steps, repeating every octave. Generators that produce this scale range from 1050 ¢ to 1200 ¢, or from 0 ¢ to 150 ¢. This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, bleu. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.

Name

TAMNAMS suggests the temperament-agnostic name antipine as the name of 1L 7s. The name is based on being the opposite pattern of 7L 1s (pine).

Scale properties

Intervals

Intervals of 1L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-apinestep Perfect 0-apinestep P0aps 0 0.0 ¢
1-apinestep Perfect 1-apinestep P1aps s 0.0 ¢ to 150.0 ¢
Augmented 1-apinestep A1aps L 150.0 ¢ to 1200.0 ¢
2-apinestep Minor 2-apinestep m2aps 2s 0.0 ¢ to 300.0 ¢
Major 2-apinestep M2aps L + s 300.0 ¢ to 1200.0 ¢
3-apinestep Minor 3-apinestep m3aps 3s 0.0 ¢ to 450.0 ¢
Major 3-apinestep M3aps L + 2s 450.0 ¢ to 1200.0 ¢
4-apinestep Minor 4-apinestep m4aps 4s 0.0 ¢ to 600.0 ¢
Major 4-apinestep M4aps L + 3s 600.0 ¢ to 1200.0 ¢
5-apinestep Minor 5-apinestep m5aps 5s 0.0 ¢ to 750.0 ¢
Major 5-apinestep M5aps L + 4s 750.0 ¢ to 1200.0 ¢
6-apinestep Minor 6-apinestep m6aps 6s 0.0 ¢ to 900.0 ¢
Major 6-apinestep M6aps L + 5s 900.0 ¢ to 1200.0 ¢
7-apinestep Diminished 7-apinestep d7aps 7s 0.0 ¢ to 1050.0 ¢
Perfect 7-apinestep P7aps L + 6s 1050.0 ¢ to 1200.0 ¢
8-apinestep Perfect 8-apinestep P8aps L + 7s 1200.0 ¢

Generator chain

Generator chain of 1L 7s
Bright gens Scale degree Abbrev.
8 Augmented 0-apinedegree A0apd
7 Augmented 1-apinedegree A1apd
6 Major 2-apinedegree M2apd
5 Major 3-apinedegree M3apd
4 Major 4-apinedegree M4apd
3 Major 5-apinedegree M5apd
2 Major 6-apinedegree M6apd
1 Perfect 7-apinedegree P7apd
0 Perfect 0-apinedegree
Perfect 8-apinedegree		 P0apd
P8apd
−1 Perfect 1-apinedegree P1apd
−2 Minor 2-apinedegree m2apd
−3 Minor 3-apinedegree m3apd
−4 Minor 4-apinedegree m4apd
−5 Minor 5-apinedegree m5apd
−6 Minor 6-apinedegree m6apd
−7 Diminished 7-apinedegree d7apd
−8 Diminished 8-apinedegree d8apd

Modes

Scale degrees of the modes of 1L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (apinedegree)
0 1 2 3 4 5 6 7 8
7|0 1 Lsssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|1 8 sLssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|2 7 ssLsssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|3 6 sssLssss Perf. Perf. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|4 5 ssssLsss Perf. Perf. Min. Min. Min. Maj. Maj. Perf. Perf.
2|5 4 sssssLss Perf. Perf. Min. Min. Min. Min. Maj. Perf. Perf.
1|6 3 ssssssLs Perf. Perf. Min. Min. Min. Min. Min. Perf. Perf.
0|7 2 sssssssL Perf. Perf. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 1050 ¢ (7\8) to 1200 ¢ (1\1)
  • Chroma-negative generator: 0 ¢ (0\1) to 150 ¢ (1\8)


Scale tree and tuning spectrum of 1L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\8 1050.000 150.000 1:1 1.000 Equalized 1L 7s
36\41 1053.659 146.341 6:5 1.200 Bohpier
29\33 1054.545 145.455 5:4 1.250
51\58 1055.172 144.828 9:7 1.286
22\25 1056.000 144.000 4:3 1.333 Supersoft 1L 7s
59\67 1056.716 143.284 11:8 1.375
37\42 1057.143 142.857 7:5 1.400
52\59 1057.627 142.373 10:7 1.429
15\17 1058.824 141.176 3:2 1.500 Soft 1L 7s
53\60 1060.000 140.000 11:7 1.571 Bleu
38\43 1060.465 139.535 8:5 1.600 Jerome/bleu
61\69 1060.870 139.130 13:8 1.625 Golden jerome (139.2429 ¢)
23\26 1061.538 138.462 5:3 1.667 Semisoft 1L 7s
54\61 1062.295 137.705 12:7 1.714
31\35 1062.857 137.143 7:4 1.750
39\44 1063.636 136.364 9:5 1.800 Twothirdtonic
8\9 1066.667 133.333 2:1 2.000 Basic 1L 7s
Scales with tunings softer than this are proper
33\37 1070.270 129.730 9:4 2.250
25\28 1071.429 128.571 7:3 2.333
42\47 1072.340 127.660 12:5 2.400
17\19 1073.684 126.316 5:2 2.500 Semihard 1L 7s
Negri
43\48 1075.000 125.000 13:5 2.600 Golden negri (124.7656 ¢)
26\29 1075.862 124.138 8:3 2.667
35\39 1076.923 123.077 11:4 2.750
9\10 1080.000 120.000 3:1 3.000 Hard 1L 7s
28\31 1083.871 116.129 10:3 3.333 Miracle
19\21 1085.714 114.286 7:2 3.500
29\32 1087.500 112.500 11:3 3.667
10\11 1090.909 109.091 4:1 4.000 Superhard 1L 7s
21\23 1095.652 104.348 9:2 4.500
11\12 1100.000 100.000 5:1 5.000 Passion, ripple
12\13 1107.692 92.308 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 7s

Trivia

This scale is a leap year pattern of the tabular Iranian calendar, where the leap year is inserted 7 times once in 4 years, with 1 gap of 5 years. Curiously enough, one short step of this scale is close to the one step of the Bohlen–Pierce scale.

Retrieved from "https://en.xen.wiki/index.php?title=1L_7s&oldid=185729"