Xenharmonic Wiki

Generator ranges of MOS: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 333143716 - Original comment: **
 
Frostburn (talk | contribs)
autopatrolled, emailconfirmed
322 edits
m →8-tone: Denote 2L 6s as consisting of 2 periods.
 
(58 intermediate revisions by 10 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below are ranges of generators for various L-s patterns of [[MOS scale]]s, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of bright generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma. We have normalized to the formula for the step size where the leading term is positive.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-10 13:51:08 UTC</tt>.<br>
: The original revision id was <tt>333143716</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside.


=2=
== 2, 3, and 4-tone ==
'''Note 1: These sets are given for the sake of completeness as they are not really scales'''
|| 1L1s || 1\2 &lt;  g  &lt; 1  || 1\2 &lt;  g  &lt; 2\3 ||
 
'''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does not apply to them'''
=3=
 
{| class="wikitable"
||  1L2s  || 2\3 &lt;  g  &lt; 1  || 2\3 &lt;  g  &lt; 3\4  ||
|-
||  2L1s  || 1\3 &lt;  g  &lt; 1\2  || 1\3 &lt;  g  &lt; 2\5 ||
! | L-s pattern
! | Generator range
=4=
! | Boundaries of best, better, good behavior
! | Large step-Small step
||  1L3s  || 3\4 &lt;  g  &lt; 1  || 3\4 &lt;  g  &lt; 4\5  ||
|-
||  2L2s  || 1\4 &lt;  g  &lt; 1\2  || 1\4 &lt;  g  &lt; 1\3 ||
| | [[1L 1s|''1L 1s'']]
||  3L1s  || 1\4 &lt;  g  &lt; 1\3  || 1\4 &lt;  g  &lt; 2\7 ||
| | ''1\2 &lt; g &lt; 1''
| | ''g = 2\3, 3\4, 4\5-5\6''
=5=
| | ''g-(1-g) = 2g-1''
|-
||  1L4s  || 4\5 &lt;  g  &lt; 1  || 4\5 &lt;  g  &lt; 5\6  ||
| | [[1L 2s]]
||  2L3s  || 2\5 &lt;  g  &lt; 1\2  || 2\5 &lt;  g  &lt; 3\7 ||
| | 2\3 &lt; g &lt; 1
||  3L2s  || 3\5 &lt;  g  &lt; 2\3  || 3\5 &lt;  g  &lt; 5\8 ||
| | g = 3\4, 4\5, 5\6-6\7
||  4L1s  || 1\5 &lt;  g  &lt; 1\4  || 1\5 &lt;  g  &lt; 2\9 ||
| | 2g-1-(1-g) = 3g-2
|-
=6=
| | [[2L 1s|''2L 1s'']]
| | ''1\3 &lt; g &lt; 1\2''
||  1L5s  || 5\6 &lt;  g  &lt; 1  || 5\6 &lt;  g  &lt; 6\7  ||
| | ''g = 2\5, 3\7, 4\9-5\11''
||  2L4s  || 1\3 &lt;  g  &lt; 1\2  || 1\3 &lt;  g  &lt; 2\5 ||
| | ''g-(1-2g)= 3g-1''
||  3L3s  || 1\6 &lt;  g  &lt; 1\3  || 1\6 &lt;  g  &lt; 2\9 ||
|-
||  4L2s
| | [[1L 3s]]
| | 3\4 &lt; g &lt; 1
| | g = 4\5, 5\6, 6\7-7\8
| | 3g-2-(1-g) = 4g-3
|-
| | [[2L 2s|''2L 2s'']] ''= 1L 1s (2)''
| | ''1\4 &lt; g &lt; 1\2''
| | ''g = 2\6, 3\8, 4\10-5\12''
| | ''g-(1\2-g) = 2g-1\2''
|-
| | [[3L 1s|''3L 1s'']]
| | ''1\4 &lt; g &lt; 1\3''
| | ''g = 2\7, 3\10, 4\13-5\16''
| | ''g-(1-3g) = 4g-1''
|}
 
== 5-tone ==
'''Note: italicized generators from here below generate scales which are weakly tonal'''
{| class="wikitable"
|-
! | L-s pattern
! | Generator range
! | Boundaries of best, better, good behavior
! | Large step-Small step
|-
| | [[1L 4s]]
| | 4\5 &lt; g &lt; 1
| | g = 5\6, 6\7, 7\8-8\9
| | 4g-3-(1-g) = 5g-4
|-
| | [[2L 3s]]
| | 2\5 &lt; g &lt; 1\2
| | g = 3\7, 4\9, 5\11-6\13
| | 3g-1-(1-2g) = 5g-2
|-
| | [[3L 2s]]
| | 3\5 &lt; g &lt; 2\3
| | g = 5\8, 7\11, 9\14-11\17
| | 2g-1-(2-3g) = 5g-3
|-
| | [[4L 1s|''4L 1s'']]
| | ''1\5 &lt; g &lt; 1\4''
| | ''g = 2\9, 3\13, 4\17-5\21''
| | ''g-(1-4g) = 5g-1''
|}
 
== 6-tone ==
{| class="wikitable"
|-
! | L-s pattern
! | Generator range
! | Boundaries of best, better, good behavior
! | Large step-Small step
|-
| | [[1L 5s]]
| | 5\6 &lt; g &lt; 1
| | g = ''6\7'', 7\8, 8\9-9\10
| | 5g-4-(1-g) = 6g-5
|-
| | [[2L 4s]]
| | 2\6 &lt; g &lt; 1\2
| | g = 3\8, 4\10, 5\12-6\14
| | 2g-1\2-(1\2-g) = 3g-1
|-
| | [[3L 3s|''3L 3s'']] ''= 1L 1s (3)''
| | ''1\6 &lt; g &lt; 1\3''
| | ''g = 2\9, 3\12, 4\15-5\18''
| | ''g-(1\3-g) = 2g-1\3''
|-
| | [[4L 2s|''4L 2s'']] ''= 2L 1s (2)''
| | ''1\6 &lt; g &lt; 1\4''
| | ''g = 2\10, 3\14, 4\18-5\22''
| | ''g-(1\2-2g) = 3g-1\2''
|-
| | [[5L 1s|''5L 1s'']]
| | ''1\6 &lt; g &lt; 1\5''
| | ''g = 2\11, 3\16, 4\21-5\26''
| | ''g-(1-5g) = 6g-1''
|}
 
== 7-tone ==
{| class="wikitable"
|-
! | L-s pattern
! | Generator range
! | Boundaries of best, better, good behavior
! | Large step-Small step
|-
| | [[1L 6s]]
| | 6\7 &lt; g &lt; 1
| | g = ''7\8'', 8\9, 9\10-10\11
| | 6g-5-(1-g) = 7g-6
|-
| | [[2L 5s]]
| | 3\7 &lt; g &lt; 1\2
| | g = 4\9, 5\11, 6\13-7\15
| | 5g-2-(1-2g) = 7g-3
|-
| | [[3L 4s]]
| | 2\7 &lt; g &lt; 1\3
| | g = 3\10, 4\13, 5\16-6\19
| | 4g-1-(1-3g) = 7g-2
|-
| | [[4L 3s]]
| | 5\7 &lt; g &lt; 3\4
| | g = 8\11, 11\15, 14\19-17\23
| | 3g-2-(3-4g) = 7g-5
|-
| | [[5L 2s]]
| | 4\7 &lt; g &lt; 3\5
| | g = 7\12, 10\17, 13\22-16\27
| | 2g-1-(3-5g) = 7g-4
|-
| | [[6L 1s|''6L 1s'']]
| | ''1\7 &lt; g &lt; 1\6''
| | ''g = 2\13, 3\19, 4\25-5\31''
| | ''g-(1-6g) = 7g-1''
|}
 
== 8-tone ==
{| class="wikitable"
|-
! | L-s pattern
! | Generator range
! | Boundaries of best, better, good behavior
! | Large step-Small step
|-
| | [[1L 7s]]
| | 7\8 &lt; g &lt; 1
| | g = ''8\9, 9\10'', 10\11-11\12
| | 7g-6-(1-g) = 8g-7
|-
| | [[2L 6s|''2L 6s'']] ''= 1L 3s (2)''
| | 3\8 &lt; g &lt; 1\2
| | g = ''4\10'', 5\12, 6\14-7\16
| | 3g-1-(1\2-g) = 4g-3\2
|-
| | [[3L 5s]]
| | 5\8 &lt; g &lt; 2\3
| | g = 7\11, 9\14, 11\17-13\20
| | 5g-3-(2-3g) = 8g-5
|-
| | [[4L 4s|''4L 4s'']] ''= 1L 1s (4)''
| | ''1\8 &lt; g &lt; 1\4''
| | ''g = 2\12, 3\16, 4\20-5\24''
| | ''g-(1\4-g) = 2g-1\4''
|-
| | [[5L 3s]]
| | 3\8 &lt; g &lt; 2\5
| | g = 5\13, 7\18, 9\23-11\28
| | 3g-1-(2-5g) = 8g-3
|-
| | [[6L 2s|
Retrieved from "https://en.xen.wiki/w/Generator_ranges_of_MOS"