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(18 dazwischenliegende Versionen desselben Benutzers werden nicht angezeigt)
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Eine mögliche Definition für die '''diatonische''' Skala ist als der durch das Übereinanderschichten von "Quinten" (bzw. "Quarten") erzeugte [[MOS|MOS-Skalentyp]] namens '''5L 2s''', also mit 5 großen Schritten und 2 kleinen Schritten. Das entsprechende Schrittmuster lautet LLLsLLs (wenn man die verschiedene Modi ignoriert).
Eine mögliche Definition für die '''diatonische''' Skala ist als der durch das Übereinanderschichten von "Quinten" (bzw. "Quarten") erzeugte [[MOS|MOS-Skalentyp]] namens '''5L2s''', also mit 5 großen Schritten und 2 kleinen Schritten. Das entsprechende Schrittmuster lautet LLLsLLs (wenn man die verschiedenen Modi ignoriert).
 
== Generatorbereiche ==
 
== Modi ==
== Modi ==
Die diatonischen Modi haben bekannte Namen aus der klassischen westlichen Musiktheorie:  
Die diatonischen Modi haben bekannte Namen aus der klassischen westlichen Musiktheorie:  
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|}
|}
== Skalenbaum ==
== Skalenbaum ==
Wenn man das Intervall 4\7 (vier Schritte von [[7-EDO]]) auf ein Ende setzt und 3\5 (drei Schritte von [[5-EDO]]) auf das andere, liegen alle andere möglichen 5L 2s-Skalen in einem Kontinuum zwischen den zweien Enden. Man kann dieses Kontinuum unterteilen, indem man die Zähler der beiden Endbrüche addiert und dann die Nenner addiert (diese Operation heißt die [[Mediant]]-Operation oder die Farey-Summe). Zwischen 4\7 und 3\5 entsteht also (4+3)\(7+5) = 7\12, also sieben Schritte von 12-EDO:
Wenn man das Intervall 4\7 (vier Schritte von [[7-EDO]]) auf ein Ende setzt und 3\5 (drei Schritte von [[5-EDO]]) auf das andere, liegen alle andere möglichen 5L2s-Skalen in einem Kontinuum zwischen den beiden Enden. Man kann dieses Kontinuum unterteilen, indem man die Zähler der beiden Endbrüche addiert und dann die Nenner addiert (diese Operation heißt die [[Mediant]]en-Operation oder die Farey-Summe). Zwischen 4\7 und 3\5 entsteht also (4+3)\(7+5) = 7\12, also sieben Schritte von 12-EDO:


{| class="wikitable"
{| class="wikitable"
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|}


Wenn man diese Mediant-Operation weiter ausführt, tauchen im Kontinuum größere EDOs auf. Also ist das diatonische [[Skalenbaum]] wie folgendes:
Wenn man diese Medianten-Operation weiter ausführt, tauchen im Kontinuum größere EDOs auf. Also ist der resultierende diatonische [[Skalenbaum]] (bis zur Tiefe 6) wie folgt:


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" | Generator
! colspan="7" | Generatorintervall
! Cents
! Cent-Größe
! L
! L
! s
! s
! L/s
! L/s
! Comments
! Hinweis
|-
|-
| 4\7 || || || || || || || 685.714 || 1 || 1 || 1.000 ||
| 4\7 || || || || || || || 685,714 || 1 || 1 || 1,000 ||
|-
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
| || || || || || || 27\47 || 689,362 || 7 || 6 || 1,167 ||
|-
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
| || || || || || 23\40 || || 690,000 || 6 || 5 || 1,200 ||
|-
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
| || || || || || || 42\73 || 690,411 || 11 || 9 || 1,222 ||
|-
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
| || || || || 19\33 || || || 690,909 || 5 || 4 || 1,250 ||
|-
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
| || || || || || || 53\92 || 691,304 || 14 || 11 || 1,273 ||
|-
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
| || || || || || 34\59 || || 691,525 || 9 || 7 || 1,286 ||
|-
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
| || || || || || || 49\85 || 691,765 || 13 || 10 || 1,300 ||
|-
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
| || || || 15\26 || || || || 692,308 || 4 || 3 || 1,333 ||
|-
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
| || || || || || || 56\97 || 692,784 || 15 || 11 || 1,364 ||
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
| || || || || || 41\71 || || 692,958 || 11 || 8 || 1,375 ||
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| || || || || || || 67\116 || 693,103 || 18 || 13 || 1,385 ||
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| || || || || 26\45 || || || 693,333 || 7 || 5 || 1,400 ||
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
| || || || || || || 63\109 || 693,578 || 17 || 12 || 1,417 ||
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| || || || || || 37\64 || || 693,750 || 10 || 7 || 1,429 ||
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| || || || || || || 48\83 || 693,976 || 13 || 9 || 1,444 ||
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| || || 11\19 || || || || || 694,737 || 3 || 2 || 1,500 || L/s = 3/2
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| || || || || || || 51\88 || 695,455 || 14 || 9 || 1,556 ||
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| || || || || || 40\69 || || 695,652 || 11 || 7 || 1,571 ||
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| || || || || || || 69\119 || 695,798 || 19 || 12 || 1,583 ||
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| || || || || 29\50 || || || 696,000 || 8 || 5 || 1,600 ||
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Goldene mitteltönige Stimmung
| || || || || || || 66\131 || 696,183 || 21 || |13 || 1,615 || Goldene mitteltönige Stimmung
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| || || || || || 47\81 || || 696,296 || 13 || 8 || 1,625 ||
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||  
| || || || || || || 65\112 || 696,429 || 18 || 11 || 1,636 ||  
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Mitteltönige Stimmungen sind in diesem Generatorbereich
| || || || 18\31 || || || || 696,774 || 5 || 3 || 1,667 || Mitteltönige Stimmungen sind in diesem Generatorbereich
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| || || || || || || 61\105 || 697,143 || 17 || 10 || 1,700 ||
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| || || || || || 43\74 || || 697,297 || 12 || 7 || 1,714 ||
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| || || || || || || 68\117 || 697,436 || 19 || 11 || 1,727 ||
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
| || || || || 25\43 || || || 697,674 || 7 || 4 || 1,750 ||
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| || || || || || || 57\98 || 697,959 || 16 || 9 || 1,778 ||
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| || || || || ||32\55 || || 698,182 || 9 || 5 || 1,800 ||
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| || || || || || || 39\67 || 698,507 || 11 || 6 || 1,833 ||
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || <!--Basic diatonic<br>(Generators smaller than this are proper)-->
| || 7\12 || || || || || || 700,000 || 2 || 1 || 2,000 || <!--Basic diatonic<br>(Generators smaller than this are proper)-->
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| || || || || || || 38\65 || 701,539 || 11 || 5 || 2,200 ||
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 || Das EDO-Generatorintervall, das unter EDOs <= 200 zum reinen [[3/2]] am nächsten ist
| || || || || || 31\53 || || 701,887 || 9 || 4 || 2,250 || Das EDO-Generatorintervall, das unter EDOs <= 200 zum reinen [[3/2]] am nächsten ist
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| || || || || || || 55\94 || 702,128 || 16 || 7 || 2,286 ||
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| || || || || 24\41 || || || 702,409 || 7 || 3 || 2,333 ||
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| || || || || || || 65\111 || 702,703 || 19 || 8 || 2,375 ||
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| || || || || || 41\70 || || 702,857 || 12 || 5 || 2,400 ||
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| || || || || || || 58\99 || 703,030 || 17 || 7 || 2,428 ||
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| || || || 17\29 || || || || 703,448 || 5 || 2 || 2,500 ||
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| || || || || || || 61\104 || 703,846 || 18 || 7 || 2,571 ||
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| || || || || || 44\75 || || 704,000 || 13 || 5 || 2,600 ||
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Goldene "Neogotisch"-Stimmung
| || || || || || || 71\121 || 704,132 || 21 || 8 || 2,625 || Goldene "Neogotisch"-Stimmung
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 || "Neogotisch"-Generatorbereich
| || || || || 27\46 || || || 704,348 || 8 || 3 || 2,667 || "Neogotisch"-Generatorbereich
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| || || || || || || 64\109 || 704,587 || 19 || 7 || 2,714 ||
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| || || || || || 37\63 || || 704,762 || 11 || 4 || 2,750 ||
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| || || || || || || 47\80 || 705,000 || 14 || 5 || 2,800 ||
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| || || 10\17 || || || || || 705,882 || 3 || 1 || 3,000 || L/s = 3/1
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| || || || || || || 43\73 || 706,849 || 13 || 4 || 3,250 ||
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
| || || || || || 33\56 || || 707,143 || 10 || 3 || 3,333 ||
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
| || || || || || || 56\95 || 707,368 || 17 || 5 || 3,400 ||
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
| || || || || 23\39 || || || 707,692 || 7 || 2 || 3,500 ||
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
| || || || || || || 59\100 || 708,000 || 18 || 5 || 3,600 ||
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
| || || || || || 36\61 || || 708,197 || 11 || 3 || 3,667 ||
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
| || || || || || || 49\83 || 708,434 || 15 || 4 || 3,750 ||
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || [[Archy]]-Generatorbereich
| || || || 13\22 || || || || 709,091 || 4 || 1 || 4,000 || [[Archy]]-Generatorbereich
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
| || || || || || || 42\71 || 709,859 || 13 || 3 || 4,333 ||
|-
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
| || || || || || 29\49 || || 710,204 || 9 || 2 || 4,500 ||
|-
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
| || || || || || || 45\76 || 710,526 || 14 || 3 || 4,667 ||
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
| || || || || 16\27 || || || 711,111 || 5 || 1 || 5,000 ||
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
| || || || || || || 35\59 || 711,864 || 11 || 2 || 5,500 ||
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
| || || || || || 19\32 || || 712,500 || 6 || 1 || 6,000 ||
|-
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
| || || || || || || 22\37 || 713,514 || 7 || 1 || 7,000 ||
|-
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
| 3\5 || || || || || || || 720,000 || 1 || 0 || → ∞ ||
|}
|}
<!--
Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.
Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.


[[File:5L2s.jpg|alt=5L2s.jpg|5L2s.jpg]]
== Temperaturen ==


5L 2s contains the pentatonic MOS [[2L_3s|2L 3s]] and (with the sole exception of the 5L 2s of 12EDO) is itself contained in a dodecaphonic MOS: either [[7L_5s|7L 5s]] or [[5L_7s|5L 7s]], depending on whether the fifth is flatter than or sharper than 7\12 (700c).-->
[[Kategorie:MOS]]
Abgerufen von „https://de.xen.wiki/w/5L2s“