2L 7s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = balzano
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 21:18:08 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>385896390</tt>.<br>
| nLargeSteps = 2
: The revision comment was: <tt></tt><br>
| nSmallSteps = 7
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 4
<h4>Original Wikitext content:</h4>
| Collapsed = 1
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=2L+7s=  
| Pattern = LsssLssss
}}


Generators range from 600 cents ([[2edo]]) to 533.33 cents ([[9edo]]).
{{MOS intro}}
== Names ==
This scale is called '''balzano''' in [[TAMNAMS]] nomenclature.


|| 4\9 ||  ||  ||  ||  || 533.33 ||  || 133.33 ||  ||
== Scale properties ==
||  ||  || 9\20 ||  ||  || 540 || 180 || 120 ||  ||
{{TAMNAMS use}}
||  ||  ||  ||  || 23\51 || 541.18 || 188.235 || 117.65 ||  ||
||  ||  ||  || 14\31 ||  || 541.935 || 193.55 || 116.13 || Casablanca is around here. ||
||  || 5\11 ||  ||  ||  || 545.45 || 218.18 || 109.09 ||  ||
||  ||  || 6\13 ||  ||  || 553.85 || 276.92 || 92.31 || generators smaller than this may be considered "impractical" ||
||  ||  ||  ||  || 13\28 || 557.14 || 300 || 85.14 || Thuja is around here. ||
||  ||  ||  || 7\15 ||  || 560 || 320 || 80 || generators smaller than this are "impractical" ||
|| 1\2 ||  ||  ||  ||  || 600 || 600 || 0 ||  ||


Around L=300c. s=85 cents, thuja appears, which is a complex temperament whose generator represents 11/8.</pre></div>
=== Intervals ===
<h4>Original HTML content:</h4>
{{MOS intervals}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;2L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2L+7s&lt;/h1&gt;
&lt;br /&gt;
Generators range from 600 cents (&lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;) to 533.33 cents (&lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;).&lt;br /&gt;
&lt;br /&gt;


=== Generator chain ===
{{MOS genchain}}


&lt;table class="wiki_table"&gt;
=== Modes ===
    &lt;tr&gt;
{{MOS mode degrees}}
        &lt;td&gt;4\9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;180&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23\51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;541.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188.235&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;541.935&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;193.55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Casablanca is around here.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;553.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;276.92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92.31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;generators smaller than this may be considered &amp;quot;impractical&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13\28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;557.14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;85.14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thuja is around here.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;generators smaller than this are &amp;quot;impractical&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Scale tree ==
Around L=300c. s=85 cents, thuja appears, which is a complex temperament whose generator represents 11/8.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{MOS tuning spectrum
| 11/3 = [[Thuja]]
| 5/3 = [[Casablanca]]
}}
 
[[Category:9-tone scales]]
[[Category:Balzano| ]]

Latest revision as of 18:56, 3 March 2025

↖ 1L 6s ↑ 2L 6s 3L 6s ↗
← 1L 7s 2L 7s 3L 7s →
↙ 1L 8s ↓ 2L 8s 3L 8s ↘ 
┌╥┬┬┬╥┬┬┬┬┐
│║│││║│││││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssss
ssssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\9 to 1\2 (533.3 ¢ to 600.0 ¢)
Dark 1\2 to 5\9 (600.0 ¢ to 666.7 ¢)
TAMNAMS information
Name balzano
Prefix bal-
Abbrev. bz
Related MOS scales
Parent 2L 5s
Sister 7L 2s
Daughters 9L 2s, 2L 9s
Neutralized 4L 5s
2-Flought 11L 7s, 2L 16s
Equal tunings
Equalized (L:s = 1:1) 4\9 (533.3 ¢)
Supersoft (L:s = 4:3) 13\29 (537.9 ¢)
Soft (L:s = 3:2) 9\20 (540.0 ¢)
Semisoft (L:s = 5:3) 14\31 (541.9 ¢)
Basic (L:s = 2:1) 5\11 (545.5 ¢)
Semihard (L:s = 5:2) 11\24 (550.0 ¢)
Hard (L:s = 3:1) 6\13 (553.8 ¢)
Superhard (L:s = 4:1) 7\15 (560.0 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 7s, named balzano in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 7 small steps, repeating every octave. Generators that produce this scale range from 533.3 ¢ to 600 ¢, or from 600 ¢ to 666.7 ¢.

Names

This scale is called balzano in TAMNAMS nomenclature.

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.

Intervals

Intervals of 2L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-balstep Perfect 0-balstep P0bzs 0 0.0 ¢
1-balstep Minor 1-balstep m1bzs s 0.0 ¢ to 133.3 ¢
Major 1-balstep M1bzs L 133.3 ¢ to 600.0 ¢
2-balstep Minor 2-balstep m2bzs 2s 0.0 ¢ to 266.7 ¢
Major 2-balstep M2bzs L + s 266.7 ¢ to 600.0 ¢
3-balstep Minor 3-balstep m3bzs 3s 0.0 ¢ to 400.0 ¢
Major 3-balstep M3bzs L + 2s 400.0 ¢ to 600.0 ¢
4-balstep Diminished 4-balstep d4bzs 4s 0.0 ¢ to 533.3 ¢
Perfect 4-balstep P4bzs L + 3s 533.3 ¢ to 600.0 ¢
5-balstep Perfect 5-balstep P5bzs L + 4s 600.0 ¢ to 666.7 ¢
Augmented 5-balstep A5bzs 2L + 3s 666.7 ¢ to 1200.0 ¢
6-balstep Minor 6-balstep m6bzs L + 5s 600.0 ¢ to 800.0 ¢
Major 6-balstep M6bzs 2L + 4s 800.0 ¢ to 1200.0 ¢
7-balstep Minor 7-balstep m7bzs L + 6s 600.0 ¢ to 933.3 ¢
Major 7-balstep M7bzs 2L + 5s 933.3 ¢ to 1200.0 ¢
8-balstep Minor 8-balstep m8bzs L + 7s 600.0 ¢ to 1066.7 ¢
Major 8-balstep M8bzs 2L + 6s 1066.7 ¢ to 1200.0 ¢
9-balstep Perfect 9-balstep P9bzs 2L + 7s 1200.0 ¢

Generator chain

Generator chain of 2L 7s
Bright gens Scale degree Abbrev.
10 Augmented 4-baldegree A4bzd
9 Augmented 0-baldegree A0bzd
8 Augmented 5-baldegree A5bzd
7 Major 1-baldegree M1bzd
6 Major 6-baldegree M6bzd
5 Major 2-baldegree M2bzd
4 Major 7-baldegree M7bzd
3 Major 3-baldegree M3bzd
2 Major 8-baldegree M8bzd
1 Perfect 4-baldegree P4bzd
0 Perfect 0-baldegree
Perfect 9-baldegree		 P0bzd
P9bzd
−1 Perfect 5-baldegree P5bzd
−2 Minor 1-baldegree m1bzd
−3 Minor 6-baldegree m6bzd
−4 Minor 2-baldegree m2bzd
−5 Minor 7-baldegree m7bzd
−6 Minor 3-baldegree m3bzd
−7 Minor 8-baldegree m8bzd
−8 Diminished 4-baldegree d4bzd
−9 Diminished 9-baldegree d9bzd
−10 Diminished 5-baldegree d5bzd

Modes

Scale degrees of the modes of 2L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (baldegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LsssLssss Perf. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Perf.
7|1 5 LssssLsss Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
6|2 9 sLsssLsss Perf. Min. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
5|3 4 sLssssLss Perf. Min. Maj. Maj. Perf. Perf. Min. Maj. Maj. Perf.
4|4 8 ssLsssLss Perf. Min. Min. Maj. Perf. Perf. Min. Maj. Maj. Perf.
3|5 3 ssLssssLs Perf. Min. Min. Maj. Perf. Perf. Min. Min. Maj. Perf.
2|6 7 sssLsssLs Perf. Min. Min. Min. Perf. Perf. Min. Min. Maj. Perf.
1|7 2 sssLssssL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|8 6 ssssLsssL Perf. Min. Min. Min. Dim. Perf. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\9 533.333 666.667 1:1 1.000 Equalized 2L 7s
21\47 536.170 663.830 6:5 1.200
17\38 536.842 663.158 5:4 1.250
30\67 537.313 662.687 9:7 1.286
13\29 537.931 662.069 4:3 1.333 Supersoft 2L 7s
35\78 538.462 661.538 11:8 1.375
22\49 538.776 661.224 7:5 1.400
31\69 539.130 660.870 10:7 1.429
9\20 540.000 660.000 3:2 1.500 Soft 2L 7s
32\71 540.845 659.155 11:7 1.571
23\51 541.176 658.824 8:5 1.600
37\82 541.463 658.537 13:8 1.625
14\31 541.935 658.065 5:3 1.667 Semisoft 2L 7s
Casablanca
33\73 542.466 657.534 12:7 1.714
19\42 542.857 657.143 7:4 1.750
24\53 543.396 656.604 9:5 1.800
5\11 545.455 654.545 2:1 2.000 Basic 2L 7s
Scales with tunings softer than this are proper
21\46 547.826 652.174 9:4 2.250
16\35 548.571 651.429 7:3 2.333
27\59 549.153 650.847 12:5 2.400
11\24 550.000 650.000 5:2 2.500 Semihard 2L 7s
28\61 550.820 649.180 13:5 2.600
17\37 551.351 648.649 8:3 2.667
23\50 552.000 648.000 11:4 2.750
6\13 553.846 646.154 3:1 3.000 Hard 2L 7s
19\41 556.098 643.902 10:3 3.333
13\28 557.143 642.857 7:2 3.500
20\43 558.140 641.860 11:3 3.667 Thuja
7\15 560.000 640.000 4:1 4.000 Superhard 2L 7s
15\32 562.500 637.500 9:2 4.500
8\17 564.706 635.294 5:1 5.000
9\19 568.421 631.579 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 7s
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