|
|
| (78 intermediate revisions by 22 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | |en=2L 3s |
| : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-05 19:22:12 UTC</tt>.<br>
| | |es= |
| : The original revision id was <tt>217505066</tt>.<br>
| | |de= |
| : The revision comment was: <tt></tt><br>
| | |ja=2L 3s |
| 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>
| | {{Infobox MOS |
| <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">"Classic" pentatonic. Perhaps the most common scale in the world.
| | | Name = pentic |
| | | Periods = 1 |
| | | nLargeSteps = 2 |
| | | nSmallSteps = 3 |
| | | Equalized = 2 |
| | | Collapsed = 1 |
| | | Pattern = LsLss |
| | }} |
|
| |
|
| ||||||||||~ Generator || ||~ Cents ||~ Scale steps ||~ Comments ||
| | : ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].'' |
| || 2\5 || || || || || || 480 || 1 1 1 1 1 ||= ||
| |
| || || || || || || 11\27 || 488.89 || 6 5 5 6 5 ||= Slendro (insofar as it resembles a MOS)
| |
| would be in this region ||
| |
| || || || || || 9\22 || || 490.91 || 5 4 4 5 4 || ||
| |
| || || || || 7\17 || || || 494.12 || 4 3 3 4 3 || ||
| |
| || || || || || 12\29 || || 496.55 || 7 5 5 7 5 || ||
| |
| || || || || || || 17\41 || 497.56 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here ||
| |
| || || || 5\12 || || || || 500 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic ||
| |
| || || || || || 13\31 || || 503.23 || 8 5 5 8 5 ||= Optimal meantone pentatonic
| |
| is around here ||
| |
| || || || || 8\19 || || || 505.26 || 5 3 3 5 3 || ||
| |
| || || 3\7 || || || || || 514.29 || 2 1 1 2 1 || ||
| |
| || || || || 7\16 || || || 525 || 5 2 2 5 2 ||= Pelog (insofar as it resembles a MOS)
| |
| would be in this region ||
| |
| || || || 4\9 || || || || 533.33 || 3 1 1 3 1 || ||
| |
| || || || || 5\11 || || || 545.45 || 4 1 1 4 1 || ||
| |
| || 1\2 || || || || || || 600 || 1 0 0 1 0 || ||
| |
|
| |
|
| From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.
| | {{MOS intro}} This scale is the "classic" pentatonic scale, which is perhaps the most common scale in the world. |
|
| |
|
| From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are [[meantone]] and [[mavila]].
| | The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest [[harmonic entropy]] of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]]. |
|
| |
|
| There is also the interesting 2.3.7 temperament that tempers out 64/63 ("no-fives [[dominant]]").</pre></div>
| | == Names == |
| <h4>Original HTML content:</h4>
| | The [[TAMNAMS]] system suggests the name '''pentic''', derived from an [[Wiktionary: pent #Etymology 2|informal clipping of "pentatonic"]] that is sometimes used to refer to this scale. |
| <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>2L 3s</title></head><body>&quot;Classic&quot; pentatonic. Perhaps the most common scale in the world.<br />
| |
| <br />
| |
|
| |
|
| | == Scale properties == |
| | {{TAMNAMS use}} |
|
| |
|
| <table class="wiki_table">
| | === Intervals === |
| <tr>
| | {{MOS intervals}} |
| <th colspan="5">Generator<br />
| |
| </th>
| |
| <td><br />
| |
| </td>
| |
| <th>Cents<br />
| |
| </th>
| |
| <th>Scale steps<br />
| |
| </th>
| |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>2\5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>480<br />
| |
| </td>
| |
| <td>1 1 1 1 1<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11\27<br />
| |
| </td>
| |
| <td>488.89<br />
| |
| </td>
| |
| <td>6 5 5 6 5<br />
| |
| </td>
| |
| <td style="text-align: center;">Slendro (insofar as it resembles a MOS)<br />
| |
| would be in this region<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9\22<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>490.91<br />
| |
| </td>
| |
| <td>5 4 4 5 4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\17<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>494.12<br />
| |
| </td>
| |
| <td>4 3 3 4 3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>12\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>496.55<br />
| |
| </td>
| |
| <td>7 5 5 7 5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>17\41<br />
| |
| </td>
| |
| <td>497.56<br />
| |
| </td>
| |
| <td>10 7 7 10 7<br />
| |
| </td>
| |
| <td style="text-align: center;">Pythagorean pentatonic is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>500<br />
| |
| </td>
| |
| <td>3 2 2 3 2<br />
| |
| </td>
| |
| <td style="text-align: center;">Familiar 12-equal pentatonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>503.23<br />
| |
| </td>
| |
| <td>8 5 5 8 5<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimal meantone pentatonic<br />
| |
| is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>505.26<br />
| |
| </td>
| |
| <td>5 3 3 5 3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3\7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>514.29<br />
| |
| </td>
| |
| <td>2 1 1 2 1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\16<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>525<br />
| |
| </td>
| |
| <td>5 2 2 5 2<br />
| |
| </td>
| |
| <td style="text-align: center;">Pelog (insofar as it resembles a MOS)<br />
| |
| would be in this region<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4\9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>533.33<br />
| |
| </td>
| |
| <td>3 1 1 3 1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>545.45<br />
| |
| </td>
| |
| <td>4 1 1 4 1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>600<br />
| |
| </td>
| |
| <td>1 0 0 1 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | === Generator chain === |
| From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.<br /> | | {{MOS genchain}} |
| <br />
| | |
| From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/mavila">mavila</a>.<br /> | | === Modes === |
| <br />
| | {{MOS mode degrees}} |
| There is also the interesting 2.3.7 temperament that tempers out 64/63 (&quot;no-fives <a class="wiki_link" href="/dominant">dominant</a>&quot;).</body></html></pre></div> | | |
| | === Mode names === |
| | There are three sets of mode names: descriptive, modal (5 of the 7 heptatonic modes), and traditional Chinese. |
| | {{MOS modes |
| | | Table Headers= |
| | Descriptive $ |
| | Modal $ |
| | Chinese $ |
| | | Table Entries= |
| | Fifthless $ |
| | Phrygian $ |
| | Jué (角) $ |
| | Minor $ |
| | Aeolian $ |
| | Yǔ (羽) $ |
| | Thirdless Minor* $ |
| | Dorian $ |
| | Shāng (商) $ |
| | Thirdless Major* $ |
| | Mixolydian $ |
| | Zhǐ (徵) $ |
| | Major $ |
| | Ionian $ |
| | Gōng (宫) $ |
| | }} |
| | <nowiki />* Thirdless Minor/Major is also known as Suspended Minor/Major |
| | |
| | == Scales == |
| | === Scale list === |
| | * [[Archy5]] – 49edo tuning |
| | * [[Edson5]] – 29edo tuning |
| | * [[Pythagorean5]] – Pythagorean tuning |
| | * [[Meantone5]] – 31edo tuning |
| | |
| | === Scale tree === |
| | {{MOS tuning spectrum |
| | | Depth = 6 |
| | | 6/5 = Slendro (insofar as it resembles a MOS) would<br />be in this region |
| | | 9/7 = No-5s [[superpyth]]/dominant is around here |
| | | 13/9 = Pythagorean pentatonic is around here |
| | | 3/2 = Familiar [[12edo|12-equal]] pentatonic |
| | | 8/5 = Optimal meantone pentatonic is around here |
| | | 5/2 = Five-note subset of [[pelog]] (insofar as it<br />resembles a MOS) would be in this region |
| | }} |
| | |
| | From a [[3-limit]] perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic. |
| | |
| | From a [[5-limit]] perspective, the most interesting temperaments with this kind of pentatonic scale are [[meantone]] and [[mavila]]. |
| | |
| | There is also the 2.3.7 temperament that tempers out [[64/63]] ([[archy]], "no-fives [[Meantone family#Dominant|dominant]]"). |
| | |
| | [[Category:Pentic]] |
| | [[Category:5-tone scales]] |