BudjarnLambeth: Removed from lists because it’s already in lists of scales

2023-04-24T00:33:05Z

Removed from lists because it’s already in lists of scales

← Older revision		Revision as of 00:33, 24 April 2023
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	Impossible tones: none		Impossible tones: none
	[[Category:88cet]]		[[Category:88cet]]
	~~[[Category:Lists]]~~
	[[Category:MOS scales]]		[[Category:MOS scales]]
	[[Category:nonoctave]]		[[Category:nonoctave]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:todo:link]]		[[Category:todo:link]]

Fredg999 category edits: Moving from Category:List to Category:Lists using Cat-a-lot

2022-02-26T04:55:23Z

Moving from Category:List to Category:Lists using Cat-a-lot

← Older revision		Revision as of 04:55, 26 February 2022
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	Impossible tones: none		Impossible tones: none
	[[Category:88cet]]		[[Category:88cet]]
	[[Category:~~list~~]]		[[Category:Lists]]
	[[Category:MOS scales]]		[[Category:MOS scales]]
	[[Category:nonoctave]]		[[Category:nonoctave]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:todo:link]]		[[Category:todo:link]]

Fredg999 category edits: Moving from Category:Scales to Category:Lists of scales using Cat-a-lot

2022-02-26T03:10:25Z

Moving from Category:Scales to Category:Lists of scales using Cat-a-lot

← Older revision		Revision as of 03:10, 26 February 2022
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	[[Category:MOS scales]]		[[Category:MOS scales]]
	[[Category:nonoctave]]		[[Category:nonoctave]]
	[[Category:scales]]		[[Category:Lists of scales]]
	[[Category:todo:link]]		[[Category:todo:link]]

Keenan Pepper: Clean up categories

2021-04-24T19:37:29Z

Clean up categories

← Older revision		Revision as of 19:37, 24 April 2021
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	[[Category:88cet]]		[[Category:88cet]]
	[[Category:list]]		[[Category:list]]
	[[Category:~~mos~~]]		[[Category:MOS scales]]
	[[Category:nonoctave]]		[[Category:nonoctave]]
	[[Category:scales]]		[[Category:scales]]
	[[Category:todo:link]]		[[Category:todo:link]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>Andrew_Heathwaite: Imported revision 236864320 - Original comment:

2011-06-15T12:38:40Z

**Imported revision 236864320 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-06-15 12:38:40 UTC</tt>.<br>
: The original revision id was <tt>236864320</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">Within the frame of [[88cET]], taking a pattern such as 3+1 produces a scale which is a subset of the chromatic 88cET. This particular example could be considered a moment of symmetry scale with a period of 4 and a generator of 3 or 1 (which are inversions in modulo 4). This page attempts to list many of the simplest scales that can be derived in this manner.

=1=

Period: 1
Degrees (also Ubiquitous tones): 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Impossible tones: none

Note: If 1 degree is taken as the period, then the full chromatic 88cET gamut is arrived at. Having only one step size, this is not an MOS. It is somewhat arbitrary to stop counting at 41, but that is the convention here.

=2=

Period: 2
Degrees (also Ubiquitous tones): 0 2 4 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Impossible tones: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

Note: If 2 degrees is taken as the period, we arrive at 176cET (nearly the 4th root of 3/2). Having only one step size, this is not an MOS. Half the intervals of 88cET are available all the time (we use the phrase "Ubiquitous tones" for this); the other half is available never ("Impossible tones"). Andrew Heathwaite has nicknamed this scale "Stride."

=3=

Period: 3
Degrees (also Ubiquitous tones): 0 3 6 9 12 15 18 21 24 27 30 33 36 39
Impossible tones: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 34 35 37 38 40 41

Note: One third of the intervals of 88cET are available all the time; the remaining two thirds are available never.

=2+1 / 1+2=

Period: 3
Generator: 1 or 2
Degrees Mode 1 (2+1): 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41
Degrees Mode 2 (1+2): 0 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 24 25 27 28 30 31 33 34 36 37 39 40
Ubiquitous tones: 0 3 6 12 15 18 21 24 27 30 33 36 39
Common tones: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 34 35 37 38 40 41
Impossible tones: none

Note: Here, the set of "Ubiquitous tones" refers to the intervals available in all modes. The set of "Common tones" refers to intervals that are available in this scale, but not in every mode. (For instance, Mode 1 contains degree 1 and no degree 2, and Mode 2 contains degree 2 and no degree 1 -- so degrees 1 and 2 are Common tones but not Ubiquitous tones.) There are no "Impossible tones" in this scale.

=4=

Period: 4
Degrees (also Ubiquitous tones): 0 4 8 12 16 20 24 28 32 36 40
Impossible tones: 1 2 3 5 6 7 9 10 11 13 14 15 17 18 19 21 22 23 25 26 27 29 30 31 33 34 35 37 38 39 41

=3+1 / 1+3=

Period: 4
Generator: 1 or 3
Degrees Mode 1 (3+1): 0 3 4 7 8 11 12 15 16 19 20 23 24 27 28 31 32 35 36 39 40
Degrees Mode 2 (1+3): 0 1 4 5 8 9 12 13 16 17 20 21 24 25 28 29 32 33 36 37 40 41
Ubiquitous tones: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
Common tones: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Impossible tones: 2 6 10 14 18 22 26 30 34 38

Note: Andrew Heathwaite has nicknamed this scale "Snake".

=5=

Period: 5
Degrees (also Ubiquitous tones): 0 5 10 15 20 25 30 35 40
Impossible tones: 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 39 41

=4+1 / 1+4=

Period: 5
Generator: 1 or 4
Degrees Mode 1 (4+1): 0 4 5 9 10 14 15 19 20 24 25 29 30 34 35 39 40
Degrees Mode 2 (1+4): 0 1 5 6 10 11 15 16 20 21 25 26 30 31 35 36 40 41
Ubiquitous tones: 0 5 10 15 20 25 30 35 40
Common tones: 1 4 6 9 11 14 16 19 21 24 26 29 31 34 36 39 41
Impossible tones: 2 3 7 8 12 13 17 18 22 23 27 28 32 33 37 38

=3+2 / 2+3=

Period: 5
Generator: 2 or 3
Degrees Mode 1 (3+2): 0 3 5 8 10 13 15 18 20 23 25 28 30 33 35 38 40
Degrees Mode 2 (2+3): 0 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40
Ubiquitous tones: 0 5 10 15 20 25 30 35 40
Common tones: 2 3 7 8 12 13 17 18 22 23 27 28 32 22 37 38
Impossible tones: 1 4 6 9 11 14 16 19 21 24 26 29 31 34 36 39 41

Note: The Impossible tones and Common tones for the past two scale families are switched, while the Ubiquitous tones stay the same.

=2+2+1 / 2+1+2 / 1+2+2=

Period: 5
Generator: 2 or 3
Degrees Mode 1 (2+2+1): 0 2 4 5 7 9 10 12 14 15 17 19 20 22 24 25 27 29 30 32 34 35 37 39 40
Degrees Mode 2 (2+1+2): 0 2 3 5 7 8 10 12 13 15 17 18 20 22 23 25 27 28 30 32 33 35 37 38 40
Degrees Mode 3 (1+2+2): 0 1 3 5 6 8 10 11 13 15 16 18 20 21 23 25 26 28 30 31 33 35 36 38 40 41
Ubiquitous tones: 0 5 10 15 20 25 30 35 40
Common tones: 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 39 4
Impossible tones: none</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>symmetrical scales of 88cET</title></head><body>Within the frame of <a class="wiki_link" href="/88cET">88cET</a>, taking a pattern such as 3+1 produces a scale which is a subset of the chromatic 88cET. This particular example could be considered a moment of symmetry scale with a period of 4 and a generator of 3 or 1 (which are inversions in modulo 4). This page attempts to list many of the simplest scales that can be derived in this manner.<br />
<br />
<h1 id="toc0"><a name="x1"></a>1</h1>
<br />
Period: 1<br />
Degrees (also Ubiquitous tones): 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41<br />
Impossible tones: none<br />
<br />
Note: If 1 degree is taken as the period, then the full chromatic 88cET gamut is arrived at. Having only one step size, this is not an MOS. It is somewhat arbitrary to stop counting at 41, but that is the convention here.<br />
<br />
<h1 id="toc1"><a name="x2"></a>2</h1>
<br />
Period: 2<br />
Degrees (also Ubiquitous tones): 0 2 4 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40<br />
Impossible tones: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41<br />
<br />
Note: If 2 degrees is taken as the period, we arrive at 176cET (nearly the 4th root of 3/2). Having only one step size, this is not an MOS. Half the intervals of 88cET are available all the time (we use the phrase &quot;Ubiquitous tones&quot; for this); the other half is available never (&quot;Impossible tones&quot;). Andrew Heathwaite has nicknamed this scale &quot;Stride.&quot;<br />
<br />
<h1 id="toc2"><a name="x3"></a>3</h1>
<br />
Period: 3<br />
Degrees (also Ubiquitous tones): 0 3 6 9 12 15 18 21 24 27 30 33 36 39<br />
Impossible tones: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 34 35 37 38 40 41<br />
<br />
Note: One third of the intervals of 88cET are available all the time; the remaining two thirds are available never.<br />
<br />
<h1 id="toc3"><a name="x2+1 / 1+2"></a>2+1 / 1+2</h1>
<br />
Period: 3<br />
Generator: 1 or 2<br />
Degrees Mode 1 (2+1): 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41<br />
Degrees Mode 2 (1+2): 0 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 24 25 27 28 30 31 33 34 36 37 39 40<br />
Ubiquitous tones: 0 3 6 12 15 18 21 24 27 30 33 36 39<br />
Common tones: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 34 35 37 38 40 41<br />
Impossible tones: none<br />
<br />
Note: Here, the set of &quot;Ubiquitous tones&quot; refers to the intervals available in all modes. The set of &quot;Common tones&quot; refers to intervals that are available in this scale, but not in every mode. (For instance, Mode 1 contains degree 1 and no degree 2, and Mode 2 contains degree 2 and no degree 1 -- so degrees 1 and 2 are Common tones but not Ubiquitous tones.) There are no &quot;Impossible tones&quot; in this scale.<br />
<br />
<h1 id="toc4"><a name="x4"></a>4</h1>
<br />
Period: 4<br />
Degrees (also Ubiquitous tones): 0 4 8 12 16 20 24 28 32 36 40<br />
Impossible tones: 1 2 3 5 6 7 9 10 11 13 14 15 17 18 19 21 22 23 25 26 27 29 30 31 33 34 35 37 38 39 41<br />
<br />
<h1 id="toc5"><a name="x3+1 / 1+3"></a>3+1 / 1+3</h1>
<br />
Period: 4<br />
Generator: 1 or 3<br />
Degrees Mode 1 (3+1): 0 3 4 7 8 11 12 15 16 19 20 23 24 27 28 31 32 35 36 39 40<br />
Degrees Mode 2 (1+3): 0 1 4 5 8 9 12 13 16 17 20 21 24 25 28 29 32 33 36 37 40 41<br />
Ubiquitous tones: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40<br />
Common tones: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39<br />
Impossible tones: 2 6 10 14 18 22 26 30 34 38<br />
<br />
Note: Andrew Heathwaite has nicknamed this scale &quot;Snake&quot;.<br />
<br />
<h1 id="toc6"><a name="x5"></a>5</h1>
<br />
Period: 5<br />
Degrees (also Ubiquitous tones): 0 5 10 15 20 25 30 35 40<br />
Impossible tones: 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 39 41<br />
<br />
<h1 id="toc7"><a name="x4+1 / 1+4"></a>4+1 / 1+4</h1>
<br />
Period: 5<br />
Generator: 1 or 4<br />
Degrees Mode 1 (4+1): 0 4 5 9 10 14 15 19 20 24 25 29 30 34 35 39 40<br />
Degrees Mode 2 (1+4): 0 1 5 6 10 11 15 16 20 21 25 26 30 31 35 36 40 41<br />
Ubiquitous tones: 0 5 10 15 20 25 30 35 40<br />
Common tones: 1 4 6 9 11 14 16 19 21 24 26 29 31 34 36 39 41<br />
Impossible tones: 2 3 7 8 12 13 17 18 22 23 27 28 32 33 37 38<br />
<br />
<h1 id="toc8"><a name="x3+2 / 2+3"></a>3+2 / 2+3</h1>
<br />
Period: 5<br />
Generator: 2 or 3<br />
Degrees Mode 1 (3+2): 0 3 5 8 10 13 15 18 20 23 25 28 30 33 35 38 40<br />
Degrees Mode 2 (2+3): 0 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40<br />
Ubiquitous tones: 0 5 10 15 20 25 30 35 40<br />
Common tones: 2 3 7 8 12 13 17 18 22 23 27 28 32 22 37 38<br />
Impossible tones: 1 4 6 9 11 14 16 19 21 24 26 29 31 34 36 39 41<br />
<br />
Note: The Impossible tones and Common tones for the past two scale families are switched, while the Ubiquitous tones stay the same.<br />
<br />
<h1 id="toc9"><a name="x2+2+1 / 2+1+2 / 1+2+2"></a>2+2+1 / 2+1+2 / 1+2+2</h1>
<br />
Period: 5<br />
Generator: 2 or 3<br />
Degrees Mode 1 (2+2+1): 0 2 4 5 7 9 10 12 14 15 17 19 20 22 24 25 27 29 30 32 34 35 37 39 40<br />
Degrees Mode 2 (2+1+2): 0 2 3 5 7 8 10 12 13 15 17 18 20 22 23 25 27 28 30 32 33 35 37 38 40<br />
Degrees Mode 3 (1+2+2): 0 1 3 5 6 8 10 11 13 15 16 18 20 21 23 25 26 28 30 31 33 35 36 38 40 41<br />
Ubiquitous tones: 0 5 10 15 20 25 30 35 40<br />
Common tones: 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 39 4<br />
Impossible tones: none</body></html></pre></div>