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| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <h2>IMPORTED REVISION FROM WIKISPACES</h2> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-13 11:17:52 UTC</tt>.<br> | | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 21:38:42 UTC</tt>.<br> |
| : The original revision id was <tt>589280430</tt>.<br> | | : The original revision id was <tt>590309760</tt>.<br> |
| : The revision comment was: <tt></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> | | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> |
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| <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">[[toc]] | | <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">[[toc]] |
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| An (incomplete) list of [[Omnitetrachordality|omnitetrachordal]] (OTC) scale patterns. | | An (incomplete) list of [[Omnitetrachordality|omnitetrachordal]] (OTC) scales. |
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| | ---- |
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| =Scales with two step sizes= | | =Scales with two step sizes= |
| (not necessarily [[MOS]] or [[Distributional Evenness|DE]]) | | (not necessarily [[MOS]] or [[Distributional Evenness|DE]]) |
| [[Omnitetrachordal scale|Omnitetrachordal scales]] are mostly tempered (irrational) scales. In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit [[Just intonation|JI]]) version is possible.
| | These are mostly tempered (irrational) scales. For a few patterns (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit [[Just intonation|JI]]) version with only two step sizes is possible. |
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| ==5 tones (2+1+2)==
| | In some cases, multiple OTC patterns with the same number of large and small steps exist. |
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| ===[[2L 3s|2L+3s]]===
| | Follow the links for more detailed info on each scale! //(Some links may not be working yet...)// |
| The familiar classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings. Is [[MOS]]. [[{$page}#ref1|(1)]]
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| [[image:TN_05_02_03_sL_s_sL.png link="file:05_02_03_sL_s_sL.png"]] | | ==3 tones== |
| | [[OTC 2L ns|2L+s]] (the simplest possible OTC scale; s=9/8, L=4/3) |
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| Pythagorean (3-limit JI): L=[[32_27|32/27]], s=9/8
| | ==4 tones== |
| generator = L+s (480.0 to 600.0 cents)
| | (no OTC scales possible) |
| [[{$page}#perfect|P]] = 1.4424745962
| |
| notable [[EDO]]s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31
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| modes:
| | ==5 tones== |
| || || {{ sL s sL }} || || | | [[OTC 2L 3s|2L+3s]] - sLsLs (MOS) |
| || || {{ Ls s Ls }} || || | | [[OTC 3L 2s|3L+2s]] - LsLsL (MOS) |
| || {{ s sL sL }} || || ||
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| || {{ s Ls Ls }} || || {{ sL sL s }} ||
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| || || || {{ Ls Ls s }} ||
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| | ==6 tones== |
| | [[OTC 2L ns|2L+4s]] - LsssLs |
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| ===[[3L 2s|3L+2s]]=== | | ==7 tones== |
| Father? MOS; [[{$page}#perfect|imperfect]]; [[{$page}#ref1|(1)]]
| | [[OTC 2L 5s|2L+5s]] - sLsssLs (MOS) |
| | [[OTC 5L 2s|5L+2s]] - LsLLLsL (MOS) |
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| [[image:TN_05_03_02_Ls_L_Ls.png link="file:05_03_02_Ls_L_Ls.png"]] | | ==8 tones== |
| | [[OTC 2L ns|2L+6s]] - LssssLss |
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| generator = L+s (400.0 to 480.0 cents)
| | ==9 tones== |
| notable EDOs: 8, 11b, 13, 18, 23b
| | [[OTC 2L ns|2L+7s]] - LsssssLss |
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| modes:
| | ==10 tones== |
| || || {{ Ls L Ls }} || || | | [[OTC 2L 8s|2L+8s]] - LsssssLsss |
| || || {{ sL L sL }} || || | | [[OTC 3L 7s|3L+7s]] - LsssLsLsss |
| || {{ L Ls Ls }} || || || | | [[OTC 5L 5s|5L+5s]] - LsLsLsLsLs (MOS) |
| || {{ L sL sL }} || || {{ Ls Ls L }} || | | [[OTC 7L 3s|7L+3s]] - sLLLsLLLsL |
| || || || {{ sL sL L }} || | | [[OTC 8L 2s|8L+2s]] - LLsLLLsLLL |
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| | ==11 tones== |
| | [[OTC 2L ns|2L+9s]] - LssssssLsss |
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| ==7 tones (3+1+3)== | | ==12 tones== |
| | [[OTC 2L 10s|2L+10s]] - LsssLsssssss (4+4+4), sssLssssLsss (5+2+5) |
| | [[OTC 5L 7s|5L+7s]] - ssLsLssLsLsL (MOS) |
| | [[OTC 7L 5s|7L+5s]] - LLsLsLLsLsLs (MOS) |
| | [[OTC 10L 2s|10L+2s]] - LLLsLLLLsLLL |
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| ===[[2L 5s|2L+5s]]=== | | ==13 tones== |
| [[Mavila Temperament Modal Harmony|Mavila]] diatonic MOS. [[{$page}#perfect|Imperfect]]. [[{$page}#ref1|(1)]] | | [[OTC 2L ns|2L+11s]] - LsssssssLssss |
| | [[OTC 7L 6s|7L+6s]] - sLLLssLssLLLs |
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| [[image:TN_07_02_05_sLs_s_sLs.png link="file:07_02_05_sLs_s_sLs.png"]] | | ==14 tones== |
| | [[OTC 2L ns|2L+12s]] - LssssssssLssss |
| | [[OTC 5L 9s|5L+9s]] - sssLsLsssLsLsL |
| | [[OTC 7L 7s|7L+7s]] - LsLsLsLsLsLsLs (MOS) |
| | [[OTC 12L 2s|12L+2s]] - LLLLLLLsLLLLLs |
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| generator = L+2s (514.3 to 600.0 cents)
| | ==15 tones== |
| notable EDOs: 9, 11, 16, 23
| | [[OTC 2L ns|2L+13s]] - LssssssssLsssss |
| | [[OTC 7L 8s|7L+8s]] - LsLLssLsLLssLss, LssLLsLssLLsLss |
| | [[OTC 12L 3s|12L+3s]] - LsLLLLLsLLLLLsL |
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| modes:
| | ==16 tones== |
| || || {{ sLs s sLs }} || || | | [[OTC 2L ns|2L+14s]] - LsssssssssLsssss |
| || || {{ Lss s Lss }} || ||
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| || {{ s ssL ssL }} || || ||
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| || {{ s sLs sLs }} || || {{ ssL ssL s }} ||
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| || {{ s Lss Lss }} || || {{ sLs sLs s }} ||
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| || || || {{ Lss Lss s }} ||
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| || || {{ ssL s ssL }} || ||
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| | ==17 tones== |
| | [[OTC 2L ns|2L+15s]] - LsssssssssLssssss (7+3+7), LssssssssssLsssss (6+5+6) |
| | [[OTC 5L 12s|5L+12s]] - sLsssLssLssLsssLs (MOS) |
| | [[OTC 7L 10s|7L+10s]] - sLsLsLssLssLsLsLs, sLssLLssLssLLssLs |
| | [[OTC 10L 7s|10L+7s]] - LsLsLsLLsLLsLsLsL, LsLLssLLsLLssLLsL |
| | [[OTC 12L 5s|12L+5s]] - LsLLLsLLsLLsLLLsL (MOS) |
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| ===[[5L 2s|5L+2s]]=== | | ==18 tones== |
| Classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]); MOS. [[{$page}#ref1|(1)]]
| | [[OTC 2L ns|2L+16s]] - LssssssssssLssssss |
| | [[OTC 7L 11s|7L+11s]] - LLsssLsLLsssLsssLs, LsssLLsLsssLLsLsss |
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| [[image:TN_07_05_02_LsL_L_Ls.png link="file:07_05_02_LsL_L_Ls.png"]] | | ==19 tones== |
| | [[OTC 2L ns|2L+17s]] - LsssssssssssLssssss |
| | [[OTC 5L 14s|5L+14s]] - sLssssLssLssLssssLs |
| | [[OTC 7L 12s|7L+12s]] - sLssLsLssLssLsLssLs (MOS) |
| | [[OTC 10L 9s|10L+9s]] - LsLLsssLLsLLsssLLsL |
| | [[OTC 12L 7s|12L+7s]] - LsLLsLsLLsLLsLsLLsL (MOS) |
| | [[OTC 14L 5s|14L+5s]] - LLLLsLLsLLLLsLLsLLs |
| | [[OTC 17L 2s|17L+2s]] - LLLLLsLLLLLLLsLLLLL |
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| Pythagorean (3-limit JI): L=9/8, s=[[256_243|256/243]]
| | ==20 tones== |
| P = 2.2600167527
| | [[OTC 2L ns|2L+18s]] - LsssssssssssLsssssss |
| generator = 2L+s (480.0 to 514.3 cents)
| | [[OTC 7L 13s|7L+13s]] - sssLsssLssLLsssLssLL, sssLsssLsLsLsssLsLsL, sssLsssLLssLsssLLssL |
| notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.
| | [[OTC 12L 8s|12L+8s]] - sLLssLLsLLLssLLsLLLs, sLLssLLLsLLssLLLsLLs, sLsLsLLLsLsLsLLLsLsL |
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| modes:
| | ==21 tones== |
| || || {{ LLs L LLs }} || || Ionian || | | [[OTC 2L ns|2L+19s]] - LssssssssssssLsssssss |
| || || {{ LsL L LsL }} || || Dorian ||
| | [[OTC 5L 16s|5L+16s]] - sLsssssLssLssLsssssLs |
| || || {{ sLL L sLL }} || || Phrygian || | | [[OTC 7L 14s|7L+14s]] - ssssLssssLsLLssssLsLL, ssssLssssLLsLssssLLsL |
| || {{ L LLs LLs }} || || || Lydian || | |
| || {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||
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| || {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||
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| || || || {{ sLL sLL L }} || Locrian ||
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| | ==22 tones== |
| | [[OTC 2L ns|2L+20s]] - LssssssssssssLssssssss (9+4+9), LsssssssssssssLsssssss (8+6+8) |
| | [[OTC 5L 17s|5L+17s]] - ssssLsssLssssLsssLsssL (MOS) |
| | [[OTC 7L 15s|7L+15s]] - LssLsLsssLssLsLsssLsss, LsssLsLssLsssLsLssLsss, LsssLLsssLsssLLsssLsss |
| | [[OTC 10L 12s|10L+12s]] - LsLsLsLsLsLssLsLsLsLss |
| | [[OTC 12L 10s|12L+10s]] - sLsLsLsLsLsLLsLsLsLsLL, sLLsLsLLssLLssLLsLsLLs, sLLssLLLssLLssLLLssLLs |
| | [[OTC 15L 7s|15L+7s]] - sLLLssLLLsLLLssLLLsLLL |
| | [[OTC 17L 5s|17L+5s]] - sLLLsLLLsLLLLsLLLsLLLL (MOS) |
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| ==10 tones (4+2+4)== | | ==23 tones== |
| | [[OTC 2L ns|2L+21s]] - LsssssssssssssLssssssss |
| | [[OTC 7L 16s|7L+16s]] - ssssLssssLssLLssssLssLL, ssLsLsLssssLssssLsLsLss, ssssLssssLLssLssssLLssL |
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| ===[[5L 5s|5L+5s]]=== | | ==24 tones== |
| Blackwood MOS. This omnitetrachordal scale has some unusual properties:
| | [[OTC 2L ns|2L+22s]] - LssssssssssssssLssssssss |
| * it has only two modes
| | [[OTC 5L 19s|5L+19s]] - sssssLsssLsssssLsssLsssL |
| * either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
| | [[OTC 7L 17s|7L+17s]] - sssLsssLssLssLsssLssLssL, sssLsssLsssLsLsssLsssLsL |
| * it is its own dual (changing all L to s, and vice versa, gives the same scale)
| | [[OTC 10L 14s|10L+14s]] - LssLLssssLLssLLssssLLssL, sssLsLsLsLsssLsLsLsLsLsL |
| * the (imperfect) tuning of 3/2 is independent of L/s ratio (fixed at exactly 720 cents)
| | [[OTC 12L 12s|12L+12s]] - LsLsLsLsLsLsLsLsLsLsLsLs (MOS), ssLsLLssLLssLsLLssLLssLL, ssLLsLssLLssLLsLssLLssLL |
| | [[OTC 14L 10s|14L+10s]] - LssLLLLssLLssLLssLLLLssL, LLsLsLsLsLsLsLLLsLsLsLsL |
| | [[OTC 15L 9s|15L+9s]] - LLsssLLLsLLLsLLLsssLLLsL |
| | [[OTC 17L 7s|17L+7s]] - LLLsLLsLLsLLLsLLsLLsLLLs, LLLsLsLLLsLLLsLLLsLsLLLs |
| | [[OTC 19L 5s|19L+5s]] - LLLsLLLLLsLLLsLLLLLsLLLs |
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| [[image:TN_10_05_05_LsLs_Ls_LsLs.png link="file:10_05_05_LsLs_Ls_LsLs.png"]] | | ==>24 tones== |
| | Many larger OTC L+s scales are believed to exist, but due to exponentially increasing computation time, these have not yet been studied in detail. Scales of the form [[OTC 2L ns|2L+ns]] are known to exist up to size 53, and assumed to exist for any larger size. |
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| generator = s (0 to 120 cents)
| | ==L/s matrix== |
| [[periods and generators|period]] = 1/5 octave | | ||= ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||= **6** ||= **7** ||= **8** ||= **9** ||= **10** ||= **11** ||= **12** ||= **13** ||= **14** ||= **15** ||= **16** ||= **17** ||= **18** ||= **19** ||= **20** ||= **21** ||= **22** ||= **23** ||= **24** ||= **L** || |
| notable EDOs: 15, 20, 25
| | ||= **1** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **2** ||= ||= ||= [[OTC 2L 3s|x]] ||= ||= [[OTC 2L 5s|x]] ||= ||= ||= [[OTC 2L 8s|x]] ||= ||= [[OTC 2L 10s|x]] ||= ||= [[OTC 2L 12s|x]] ||= ||= ||= ||= ||= [[OTC 2L 17s|x]] ||= ||= ||= ||= ||= [[OTC 2L 22s|x]] ||= ||= ||= || |
| | ||= **3** ||= ||= [[OTC 2L 3s|x]] ||= ||= ||= ||= ||= [[OTC 7L 3s|x]] ||= ||= ||= ||= ||= [[OTC 12L 3s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **4** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **5** ||= ||= [[OTC 2L 5s|x]] ||= ||= ||= [[OTC 5L 5s|x]] ||= ||= [[OTC 7L 5s|x]] ||= ||= ||= ||= ||= [[OTC 12L 5s|x]] ||= ||= [[OTC 14L 5s|x]] ||= ||= ||= [[OTC 17L 5s|x]] ||= ||= [[OTC 19L 5s|x]] ||= ||= ||= ||= ||= ||= || |
| | ||= **6** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= [[OTC 7L 6s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **7** ||= ||= [[OTC 2L ns|x]] ||= [[OTC 3L 7s|x]] ||= ||= [[OTC 5L 7s|x]] ||= ||= [[OTC 7L 7s|x]] ||= ||= ||= [[OTC 10L 7s|x]] ||= ||= [[OTC 12L 7s|x]] ||= ||= ||= [[OTC 15L 7s|x]] ||= ||= [[OTC 17L 7s|x]] ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **8** ||= ||= [[OTC 2L 8s|x]] ||= ||= ||= ||= ||= [[OTC 7L 8s|x]] ||= ||= ||= ||= ||= [[OTC 12L 8s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **9** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 9s|x]] ||= ||= ||= ||= ||= [[OTC 10L 9s|x]] ||= ||= ||= ||= ||= [[OTC 15L 9s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **10** ||= ||= [[OTC 2L 10s|x]] ||= ||= ||= ||= ||= [[OTC 7L 10s|x]] ||= ||= ||= ||= ||= [[OTC 12L 10s|x]] ||= ||= [[OTC 14L 10s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **11** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= [[OTC 7L 11s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **12** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 12s|x]] ||= ||= [[OTC 7L 12s|x]] ||= ||= ||= [[OTC 10L 12s|x]] ||= ||= [[OTC 12L 12s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **13** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= [[OTC 7L 13s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **14** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 14s|x]] ||= ||= [[OTC 7L 14s|x]] ||= ||= ||= [[OTC 10L 14s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **15** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= [[OTC 7L 15s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **16** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 16s|x]] ||= ||= [[OTC 7L 16s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **17** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 17s|x]] ||= ||= [[OTC 7L 17s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **18** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **19** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= [[OTC 5L 19s|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **20** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **21** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **22** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **23** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **24** ||= ||= [[OTC 2L ns|x]] ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || |
| | ||= **s** ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} ||= {{ }} || |
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| modes:
| | ---- |
| || {{ Ls LsLs LsLs }} || {{ LsLs Ls LsLs }} || {{ LsLs LsLs Ls }} ||
| |
| || {{ sL sLsL sLsL }} || {{ sLsL sL sLsL }} || {{ sLsL sLsL sL }} ||
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| | =Scales with 3 step sizes= |
| | * [[OTC 22 sruti|22-tone Indian 'sruti' scale]] |
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| ===[[7L 3s|7L+3s]]===
| | ---- |
| [[Mohajira]] / [[Neutral third scales|neutral-thirds]] [[MODMOS]]
| |
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| [[image:TN_10_07_03_sLLL_sL_sLLL.png link="file:10_07_03_sLLL_sL_sLLL.png"]]
| | =Definitions and formulas= |
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| |
|
| P = 2.5872804832
| | [[#dual]]**"Dual"** refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, {{ sLssL }} and {{ LsLLs }} are duals. If a scale is OTC, its dual is often OTC as well, but not always! |
| generator = 2L+s (342.9 to 360.0 cents)
| |
| notable EDOs: 17, 24, 27, 31, 41
| |
|
| |
|
| {{ sLLsLLsLLL }} (MOS)
| | [[#perfect]]**"Perfect"** means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo subgroup]].) |
| {{ || }}
| |
| {{ sLLLsLsLLL }} (OTC MODMOS)
| |
|
| |
|
| modes:
| | In this case the value **P** is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> ``=`` L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> ``=`` s/L ``=`` 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ). |
| || || {{ LsLL Ls LsLL }} || ||
| |
| || || {{ sLLL sL sLLL }} || ||
| |
| || || {{ LLLs Ls LLLs }} || ||
| |
| || || {{ LLsL sL LLsL }} || ||
| |
| || {{ Ls LsLL LsLL }} || || ||
| |
| || {{ sL sLLL sLLL }} || || ||
| |
| || {{ Ls LLLs LLLs }} || || {{ LsLL LsLL Ls }} ||
| |
| || {{ sL LLsL LLsL }} || || {{ sLLL sLLL sL }} ||
| |
| || || || {{ LLLs LLLs Ls }} ||
| |
| || || || {{ LLsL LLsL sL }} ||
| |
|
| |
|
| | In some cases, P may be less than zero. I'm not yet sure what this means :) |
|
| |
|
| ===[[3L 7s|3L+7s]]===
| | The value of P is calculated as follows: |
| The [[{$page}#dual|dual]] of 7L+3s, this scale pattern barely qualifies as omnitetrachordal. | |
|
| |
|
| [[image:TN_10_03_07_Lsss_Ls_Lsss.png link="file:10_03_07_Lsss_Ls_Lsss.png"]]
| | a ``=`` the number of L steps per 2/1 |
| | b ``=`` the number of s steps per 2/1 |
| | c ``=`` the number of L steps per 4/3 |
| | d ``=`` the number of s steps per 4/3 |
| | x ``=`` log<span style="vertical-align: sub;">2</span>(4/3) ``=`` ~0.41504 octaves ``=`` ~498.045 cents |
|
| |
|
| notable EDOs: 13, 16b
| | aL+bs ``=`` log<span style="vertical-align: sub;">2</span>(2/1) = 1 |
| | cL+ds ``=`` x |
|
| |
|
| modes: LsssLsLsss, etc.
| | s ``=`` (c-ax)/(bc-ad) |
| | L ``=`` (x-ds)/c |
| | P ``=`` L/s |
|
| |
|
| | Note that the same procedure could be used to calculate the L/s ratio necessary to give any other just interval, such as 5/4, 11/8, etc. |
|
| |
|
| ===[[2L 8s|2L+8s]]===
| | [[#Q]]**Q** is calculated similarly to P, but indicates a limit of sorts -- a point on the L/s continuum beyond which the omnitetrachordality of the scale can be considered to 'break down' in some way. |
| [[Pajara]] MODMOS. Best at lower ratios of L/s. [[{$page}#ref1|(1)]]
| |
|
| |
|
| [[image:TN_10_02_08_sLss_ss_sLss.png link="file:10_02_08_sLss_ss_sLss.png"]]
| | Consider for example the 2L+8s pajara MODMOS, LsssssLsss -- at P ``=`` L/s ``=`` 1.885, L+3s forms a just 4/3. As L/s increases, L gets larger and s smaller; at Q ``=`` L/s ``=`` 4.827, a just 4/3 is not L+3s, but L+2.5s. Past this point, L+2s will therefore be closer to a just 4/3 than L+3s: |
|
| |
|
| P = 1.8849491924
| | [[image:P_Q_C_LsssssLsss.png]] |
| generator = s (0 to 120 cents)
| |
| [[periods and generators|period]] = 1/2 octave | |
| notable EDOs: 12, 14, 16, 22, 26
| |
|
| |
|
| {{ LssssLssss }} (MOS)
| | For some scales, Q will not exist. For others, a second Q may exist that is less than P, placing a lower bound on the L/s ratio as well as an upper one. |
| {{ || }}
| |
| {{ LsssssLsss }} (OTC MODMOS)
| |
|
| |
|
| modes:
| | We can also consider a point C, where the number of steps "crosses" the just 4/3 entirely - in the example above, this corresponds to 4/3 ``=`` L+2s. Q is then halfway between P and C, i.e. |
| || || {{ sssL ss sssL }} || || Standard Pentachordal Minor ||
| | C ``=`` 2Q-P |
| || || {{ ssLs ss ssLs }} || || - ||
| | Q ``=`` (C+P)/2 |
| || || {{ sLss ss sLss }} || || Alternate Pentachordal Major ||
| | P ``=`` 2Q-C |
| || || {{ Lsss ss Lsss }} || || - ||
| |
| || {{ ss sssL sssL }} || || || - ||
| |
| || {{ ss ssLs ssLs }} || || || Alternate Pentachordal Minor ||
| |
| || {{ ss sLss sLss }} || || {{ sssL sssL ss }} || - ||
| |
| || {{ ss Lsss Lsss }} || || {{ ssLs ssLs ss }} || Standard Pentachordal Major ||
| |
| || || || {{ sLss sLss ss }} || - ||
| |
| || || || {{ Lsss Lsss ss }} || - ||
| |
| (The names of the modes are Paul Erlich's - see [[http://lumma.org/tuning/erlich/erlich-decatonic.pdf]].)
| |
|
| |
|
| | ...which leads to the curious result that, although P is undefined when calculated by the normal method (due to division by zero) for a scale such as blackwood[10] (LsLsLsLsLs), C and Q can be calculated, and thus a value of P ``=`` -1 can be found anyway, even though it seems not to be of any use :) |
|
| |
|
| ===[[8L 2s|8L+2s]]=== | | **"L/s range"**: For any L+s scale pattern, the ratio L/s may range from 1 (L``=``s, in which case the scale is (L+s)edo ) to ~infinity (s``=``0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended. |
| The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.
| | </pre></div> |
| | | <h4>Original HTML content:</h4> |
| [[image:TN_10_08_02_LsLL_LL_LsLL.png link="file:10_08_02_LsLL_LL_LsLL.png"]]
| | <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>Gallery of omnitetrachordal scales</title></head><body><!-- ws:start:WikiTextTocRule:80:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 1em;"><a href="#Scales with two step sizes">Scales with two step sizes</a></div> |
| | | <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-3 tones">3 tones</a></div> |
| notable EDOs: 18, 26b
| | <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-4 tones">4 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-5 tones">5 tones</a></div> |
| modes: LsLLLLLsLL, etc.
| | <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-6 tones">6 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-7 tones">7 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-8 tones">8 tones</a></div> |
| ==12 tones (5-2-5)== | | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-9 tones">9 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-10 tones">10 tones</a></div> |
| ===[[5L 7s|5L+7s]]=== | | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-11 tones">11 tones</a></div> |
| 12-tone MOS of the helmholtz / garibaldi / [[Schismatic family|schismatic]] and [[superpyth]] temperaments (slightly sharp 3/2). Very usable at any L/s ratio. Many modes may be pentachordally split in two ways. | | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-12 tones">12 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-13 tones">13 tones</a></div> |
| [[image:TN_12_05_07_sLssL_sL_sLssL.png link="file:12_05_07_sLssL_sL_sLssL.png"]]
| | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-14 tones">14 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-15 tones">15 tones</a></div> |
| Pythagorean (3-limit JI): L=2187/2048, s=256/243
| | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-16 tones">16 tones</a></div> |
| P = 1.2600167527
| | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-17 tones">17 tones</a></div> |
| generator = 2L+3s (480.0 to 500.0 cents)
| | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-18 tones">18 tones</a></div> |
| notable EDOs: 17, 22, 27, 29, 41, 53, etc.
| | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-19 tones">19 tones</a></div> |
| | | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-20 tones">20 tones</a></div> |
| modes:
| | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-21 tones">21 tones</a></div> |
| || || {{ sLsLs sL sLsLs }} || {{ sLsLs sLsLs Ls }} ||
| | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-22 tones">22 tones</a></div> |
| || || {{ LsLss Ls LsLss }} || ||
| | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-23 tones">23 tones</a></div> |
| || || {{ sLssL sL sLssL }} || ||
| | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-24 tones">24 tones</a></div> |
| || || {{ LssLs Ls LssLs }} || ||
| | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-&gt;24 tones">&gt;24 tones</a></div> |
| || || {{ ssLsL sL ssLsL }} || ||
| | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-L/s matrix">L/s matrix</a></div> |
| || {{ sL sLsLs sLsLs }} || {{ sLsLs Ls sLsLs }} || ||
| | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 1em;"><a href="#Scales with 3 step sizes">Scales with 3 step sizes</a></div> |
| || {{ Ls LsLss LsLss }} || || ||
| | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 1em;"><a href="#Definitions and formulas">Definitions and formulas</a></div> |
| || {{ sL sLssL sLssL }} || || {{ sLsLs sLsLs sL }} ||
| | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --></div> |
| || {{ Ls LssLs LssLs }} || || {{ LsLss LsLss Ls }} ||
| | <!-- ws:end:WikiTextTocRule:108 --><br /> |
| || {{ sL ssLsL ssLsL }} || {{ sLssL sL ssLsL }} || ||
| | An (incomplete) list of <a class="wiki_link" href="/Omnitetrachordality">omnitetrachordal</a> (OTC) scales.<br /> |
| || {{ Ls sLsLs sLsLs }} || || {{ LssLs LssLs Ls }} ||
| | <br /> |
| || || || {{ ssLsL ssLsL sL }} ||
| | <hr /> |
| | | <br /> |
| | | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc0"><a name="Scales with two step sizes"></a><!-- ws:end:WikiTextHeadingRule:26 -->Scales with two step sizes</h1> |
| ===[[7L 5s|7L+5s]]=== | | (not necessarily <a class="wiki_link" href="/MOS">MOS</a> or <a class="wiki_link" href="/Distributional%20Evenness">DE</a>)<br /> |
| 12-tone MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2). [[{$page}#perfect|Imperfect]], but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.
| | These are mostly tempered (irrational) scales. For a few patterns (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit <a class="wiki_link" href="/Just%20intonation">JI</a>) version with only two step sizes is possible.<br /> |
| | <br /> |
| | In some cases, multiple OTC patterns with the same number of large and small steps exist. <br /> |
| | <br /> |
| | Follow the links for more detailed info on each scale! <em>(Some links may not be working yet...)</em><br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc1"><a name="Scales with two step sizes-3 tones"></a><!-- ws:end:WikiTextHeadingRule:28 -->3 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+s</a> (the simplest possible OTC scale; s=9/8, L=4/3)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc2"><a name="Scales with two step sizes-4 tones"></a><!-- ws:end:WikiTextHeadingRule:30 -->4 tones</h2> |
| | (no OTC scales possible)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc3"><a name="Scales with two step sizes-5 tones"></a><!-- ws:end:WikiTextHeadingRule:32 -->5 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%203s">2L+3s</a> - sLsLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%203L%202s">3L+2s</a> - LsLsL (MOS)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc4"><a name="Scales with two step sizes-6 tones"></a><!-- ws:end:WikiTextHeadingRule:34 -->6 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+4s</a> - LsssLs<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc5"><a name="Scales with two step sizes-7 tones"></a><!-- ws:end:WikiTextHeadingRule:36 -->7 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%205s">2L+5s</a> - sLsssLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%205L%202s">5L+2s</a> - LsLLLsL (MOS)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc6"><a name="Scales with two step sizes-8 tones"></a><!-- ws:end:WikiTextHeadingRule:38 -->8 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+6s</a> - LssssLss<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc7"><a name="Scales with two step sizes-9 tones"></a><!-- ws:end:WikiTextHeadingRule:40 -->9 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+7s</a> - LsssssLss<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc8"><a name="Scales with two step sizes-10 tones"></a><!-- ws:end:WikiTextHeadingRule:42 -->10 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%208s">2L+8s</a> - LsssssLsss<br /> |
| | <a class="wiki_link" href="/OTC%203L%207s">3L+7s</a> - LsssLsLsss<br /> |
| | <a class="wiki_link" href="/OTC%205L%205s">5L+5s</a> - LsLsLsLsLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%207L%203s">7L+3s</a> - sLLLsLLLsL<br /> |
| | <a class="wiki_link" href="/OTC%208L%202s">8L+2s</a> - LLsLLLsLLL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc9"><a name="Scales with two step sizes-11 tones"></a><!-- ws:end:WikiTextHeadingRule:44 -->11 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+9s</a> - LssssssLsss<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc10"><a name="Scales with two step sizes-12 tones"></a><!-- ws:end:WikiTextHeadingRule:46 -->12 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%2010s">2L+10s</a> - LsssLsssssss (4+4+4), sssLssssLsss (5+2+5)<br /> |
| | <a class="wiki_link" href="/OTC%205L%207s">5L+7s</a> - ssLsLssLsLsL (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%207L%205s">7L+5s</a> - LLsLsLLsLsLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%2010L%202s">10L+2s</a> - LLLsLLLLsLLL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc11"><a name="Scales with two step sizes-13 tones"></a><!-- ws:end:WikiTextHeadingRule:48 -->13 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+11s</a> - LsssssssLssss<br /> |
| | <a class="wiki_link" href="/OTC%207L%206s">7L+6s</a> - sLLLssLssLLLs<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc12"><a name="Scales with two step sizes-14 tones"></a><!-- ws:end:WikiTextHeadingRule:50 -->14 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+12s</a> - LssssssssLssss<br /> |
| | <a class="wiki_link" href="/OTC%205L%209s">5L+9s</a> - sssLsLsssLsLsL<br /> |
| | <a class="wiki_link" href="/OTC%207L%207s">7L+7s</a> - LsLsLsLsLsLsLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%2012L%202s">12L+2s</a> - LLLLLLLsLLLLLs<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc13"><a name="Scales with two step sizes-15 tones"></a><!-- ws:end:WikiTextHeadingRule:52 -->15 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+13s</a> - LssssssssLsssss<br /> |
| | <a class="wiki_link" href="/OTC%207L%208s">7L+8s</a> - LsLLssLsLLssLss, LssLLsLssLLsLss<br /> |
| | <a class="wiki_link" href="/OTC%2012L%203s">12L+3s</a> - LsLLLLLsLLLLLsL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc14"><a name="Scales with two step sizes-16 tones"></a><!-- ws:end:WikiTextHeadingRule:54 -->16 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+14s</a> - LsssssssssLsssss<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc15"><a name="Scales with two step sizes-17 tones"></a><!-- ws:end:WikiTextHeadingRule:56 -->17 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+15s</a> - LsssssssssLssssss (7+3+7), LssssssssssLsssss (6+5+6)<br /> |
| | <a class="wiki_link" href="/OTC%205L%2012s">5L+12s</a> - sLsssLssLssLsssLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%207L%2010s">7L+10s</a> - sLsLsLssLssLsLsLs, sLssLLssLssLLssLs<br /> |
| | <a class="wiki_link" href="/OTC%2010L%207s">10L+7s</a> - LsLsLsLLsLLsLsLsL, LsLLssLLsLLssLLsL<br /> |
| | <a class="wiki_link" href="/OTC%2012L%205s">12L+5s</a> - LsLLLsLLsLLsLLLsL (MOS)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc16"><a name="Scales with two step sizes-18 tones"></a><!-- ws:end:WikiTextHeadingRule:58 -->18 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+16s</a> - LssssssssssLssssss<br /> |
| | <a class="wiki_link" href="/OTC%207L%2011s">7L+11s</a> - LLsssLsLLsssLsssLs, LsssLLsLsssLLsLsss<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc17"><a name="Scales with two step sizes-19 tones"></a><!-- ws:end:WikiTextHeadingRule:60 -->19 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+17s</a> - LsssssssssssLssssss<br /> |
| | <a class="wiki_link" href="/OTC%205L%2014s">5L+14s</a> - sLssssLssLssLssssLs<br /> |
| | <a class="wiki_link" href="/OTC%207L%2012s">7L+12s</a> - sLssLsLssLssLsLssLs (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%2010L%209s">10L+9s</a> - LsLLsssLLsLLsssLLsL<br /> |
| | <a class="wiki_link" href="/OTC%2012L%207s">12L+7s</a> - LsLLsLsLLsLLsLsLLsL (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%2014L%205s">14L+5s</a> - LLLLsLLsLLLLsLLsLLs<br /> |
| | <a class="wiki_link" href="/OTC%2017L%202s">17L+2s</a> - LLLLLsLLLLLLLsLLLLL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc18"><a name="Scales with two step sizes-20 tones"></a><!-- ws:end:WikiTextHeadingRule:62 -->20 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+18s</a> - LsssssssssssLsssssss<br /> |
| | <a class="wiki_link" href="/OTC%207L%2013s">7L+13s</a> - sssLsssLssLLsssLssLL, sssLsssLsLsLsssLsLsL, sssLsssLLssLsssLLssL<br /> |
| | <a class="wiki_link" href="/OTC%2012L%208s">12L+8s</a> - sLLssLLsLLLssLLsLLLs, sLLssLLLsLLssLLLsLLs, sLsLsLLLsLsLsLLLsLsL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc19"><a name="Scales with two step sizes-21 tones"></a><!-- ws:end:WikiTextHeadingRule:64 -->21 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+19s</a> - LssssssssssssLsssssss<br /> |
| | <a class="wiki_link" href="/OTC%205L%2016s">5L+16s</a> - sLsssssLssLssLsssssLs<br /> |
| | <a class="wiki_link" href="/OTC%207L%2014s">7L+14s</a> - ssssLssssLsLLssssLsLL, ssssLssssLLsLssssLLsL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc20"><a name="Scales with two step sizes-22 tones"></a><!-- ws:end:WikiTextHeadingRule:66 -->22 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+20s</a> - LssssssssssssLssssssss (9+4+9), LsssssssssssssLsssssss (8+6+8)<br /> |
| | <a class="wiki_link" href="/OTC%205L%2017s">5L+17s</a> - ssssLsssLssssLsssLsssL (MOS)<br /> |
| | <a class="wiki_link" href="/OTC%207L%2015s">7L+15s</a> - LssLsLsssLssLsLsssLsss, LsssLsLssLsssLsLssLsss, LsssLLsssLsssLLsssLsss<br /> |
| | <a class="wiki_link" href="/OTC%2010L%2012s">10L+12s</a> - LsLsLsLsLsLssLsLsLsLss<br /> |
| | <a class="wiki_link" href="/OTC%2012L%2010s">12L+10s</a> - sLsLsLsLsLsLLsLsLsLsLL, sLLsLsLLssLLssLLsLsLLs, sLLssLLLssLLssLLLssLLs<br /> |
| | <a class="wiki_link" href="/OTC%2015L%207s">15L+7s</a> - sLLLssLLLsLLLssLLLsLLL<br /> |
| | <a class="wiki_link" href="/OTC%2017L%205s">17L+5s</a> - sLLLsLLLsLLLLsLLLsLLLL (MOS)<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc21"><a name="Scales with two step sizes-23 tones"></a><!-- ws:end:WikiTextHeadingRule:68 -->23 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+21s</a> - LsssssssssssssLssssssss<br /> |
| | <a class="wiki_link" href="/OTC%207L%2016s">7L+16s</a> - ssssLssssLssLLssssLssLL, ssLsLsLssssLssssLsLsLss, ssssLssssLLssLssssLLssL<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc22"><a name="Scales with two step sizes-24 tones"></a><!-- ws:end:WikiTextHeadingRule:70 -->24 tones</h2> |
| | <a class="wiki_link" href="/OTC%202L%20ns">2L+22s</a> - LssssssssssssssLssssssss<br /> |
| | <a class="wiki_link" href="/OTC%205L%2019s">5L+19s</a> - sssssLsssLsssssLsssLsssL<br /> |
| | <a class="wiki_link" href="/OTC%207L%2017s">7L+17s</a> - sssLsssLssLssLsssLssLssL, sssLsssLsssLsLsssLsssLsL<br /> |
| | <a class="wiki_link" href="/OTC%2010L%2014s">10L+14s</a> - LssLLssssLLssLLssssLLssL, sssLsLsLsLsssLsLsLsLsLsL<br /> |
| | <a class="wiki_link" href="/OTC%2012L%2012s">12L+12s</a> - LsLsLsLsLsLsLsLsLsLsLsLs (MOS), ssLsLLssLLssLsLLssLLssLL, ssLLsLssLLssLLsLssLLssLL<br /> |
| | <a class="wiki_link" href="/OTC%2014L%2010s">14L+10s</a> - LssLLLLssLLssLLssLLLLssL, LLsLsLsLsLsLsLLLsLsLsLsL<br /> |
| | <a class="wiki_link" href="/OTC%2015L%209s">15L+9s</a> - LLsssLLLsLLLsLLLsssLLLsL<br /> |
| | <a class="wiki_link" href="/OTC%2017L%207s">17L+7s</a> - LLLsLLsLLsLLLsLLsLLsLLLs, LLLsLsLLLsLLLsLLLsLsLLLs<br /> |
| | <a class="wiki_link" href="/OTC%2019L%205s">19L+5s</a> - LLLsLLLLLsLLLsLLLLLsLLLs<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc23"><a name="Scales with two step sizes-&gt;24 tones"></a><!-- ws:end:WikiTextHeadingRule:72 -->&gt;24 tones</h2> |
| | Many larger OTC L+s scales are believed to exist, but due to exponentially increasing computation time, these have not yet been studied in detail. Scales of the form <a class="wiki_link" href="/OTC%202L%20ns">2L+ns</a> are known to exist up to size 53, and assumed to exist for any larger size.<br /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc24"><a name="Scales with two step sizes-L/s matrix"></a><!-- ws:end:WikiTextHeadingRule:74 -->L/s matrix</h2> |
|
| |
|
| [[image:TN_12_07_05_LsLLs_Ls_LsLLs.png link="file:12_07_05_LsLLs_Ls_LsLLs.png"]]
| |
|
| |
|
| generator = 3L+2s (500.0 to 514.3 cents)
| | <table class="wiki_table"> |
| notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.
| | <tr> |
| | | <td style="text-align: center;"><br /> |
| modes:
| | </td> |
| || || {{ LsLLs Ls LsLLs }} || ||
| | <td style="text-align: center;"><strong>1</strong><br /> |
| || || {{ sLLsL sL sLLsL }} || ||
| | </td> |
| || || {{ LLsLs Ls LLsLs }} || ||
| | <td style="text-align: center;"><strong>2</strong><br /> |
| || {{ Ls LsLsL LsLsL }} || {{ LsLsL sL LsLsL }} || ||
| | </td> |
| || {{ sL sLsLL sLsLL }} || || ||
| | <td style="text-align: center;"><strong>3</strong><br /> |
| || {{ Ls LsLLs LsLLs }} || || {{ LsLsL LsLsL Ls }} ||
| | </td> |
| || {{ sL sLLsL sLLsL }} || || {{ sLsLL sLsLL sL }} ||
| | <td style="text-align: center;"><strong>4</strong><br /> |
| || {{ Ls LLsLs LLsLs }} || || {{ LsLLs LsLLs Ls }} ||
| | </td> |
| || {{ sL LsLsL LsLsL }} || || {{ sLLsL sLLsL sL }} ||
| | <td style="text-align: center;"><strong>5</strong><br /> |
| || || || {{ LLsLs LLsLs Ls }} ||
| | </td> |
| || || {{ LsLsL Ls LsLsL }} || {{ LsLsL LsLsL sL }} ||
| | <td style="text-align: center;"><strong>6</strong><br /> |
| || || {{ sLsLL sL sLsLL }} ||
| | </td> |
| | | <td style="text-align: center;"><strong>7</strong><br /> |
| | | </td> |
| ===[[10L 2s|10L+2s]]===
| | <td style="text-align: center;"><strong>8</strong><br /> |
| [[Pajara]] MODMOS. Good for most any ratio of L to s.
| | </td> |
| | | <td style="text-align: center;"><strong>9</strong><br /> |
| [[image:TN_12_10_02_LLsLL_LL_LLsLL.png link="file:12_10_02_LLsLL_LL_LLsLL.png"]]
| | </td> |
| | | <td style="text-align: center;"><strong>10</strong><br /> |
| P = 1.1300083763
| | </td> |
| generator = L (100.0 to 120.0 cents)
| | <td style="text-align: center;"><strong>11</strong><br /> |
| [[periods and generators|period]] = 1/2 octave
| | </td> |
| notable EDOs: 22, 32, 34, 46
| | <td style="text-align: center;"><strong>12</strong><br /> |
| | | </td> |
| {{ LLLLLsLLLLLs }} (MOS)
| | <td style="text-align: center;"><strong>13</strong><br /> |
| {{ || }}
| | </td> |
| {{ LLLLLLsLLLLs }} (OTC MODMOS)
| | <td style="text-align: center;"><strong>14</strong><br /> |
| | | </td> |
| modes:
| | <td style="text-align: center;"><strong>15</strong><br /> |
| || {{ LL LLLLs LLLLs }} || || ||
| | </td> |
| || {{ LL LLLsL LLLsL }} || || ||
| | <td style="text-align: center;"><strong>16</strong><br /> |
| || {{ LL LLsLL LLsLL }} || || {{ LLLLs LLLLs LL }} ||
| | </td> |
| || {{ LL LsLLL LsLLL }} || || {{ LLLsL LLLsL LL }} ||
| | <td style="text-align: center;"><strong>17</strong><br /> |
| || {{ LL sLLLL sLLLL }} || || {{ LLsLL LLsLL LL }} ||
| | </td> |
| || || || {{ LsLLL LsLLL LL }} ||
| | <td style="text-align: center;"><strong>18</strong><br /> |
| || || || {{ sLLLL sLLLL LL }} ||
| | </td> |
| || || {{ LLLLs LL LLLLs }} || ||
| | <td style="text-align: center;"><strong>19</strong><br /> |
| || || {{ LLLsL LL LLLsL }} || ||
| | </td> |
| || || {{ LLsLL LL LLsLL }} || ||
| | <td style="text-align: center;"><strong>20</strong><br /> |
| || || {{ LsLLL LL LsLLL }} || ||
| | </td> |
| || || {{ sLLLL LL sLLLL }} || ||
| | <td style="text-align: center;"><strong>21</strong><br /> |
| | | </td> |
| | | <td style="text-align: center;"><strong>22</strong><br /> |
| ===[[2L 10s|2L+10s]]=== | | </td> |
| [[{$page}#dual|Dual]] of 10L+2s. Probably only useful for small values of L/s.
| | <td style="text-align: center;"><strong>23</strong><br /> |
| | | </td> |
| [[image:TN_12_02_10_ssLss_ss_ssLss.png link="file:12_02_10_ssLss_ss_ssLss.png"]]
| | <td style="text-align: center;"><strong>24</strong><br /> |
| | | </td> |
| notable EDOs: 14, 16
| | <td style="text-align: center;"><strong>L</strong><br /> |
| | | </td> |
| modes: ssLssssssLss, etc.
| | </tr> |
| | | <tr> |
| | | <td style="text-align: center;"><strong>1</strong><br /> |
| ==13 tones (5+3+5)== | | </td> |
| | | <td style="text-align: center;"><br /> |
| ===[[7L 6s|7L+6s]]===
| | </td> |
| [[Tetracot family|Tetracot]] MODMOS. Best tuned at high values of L/s.
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| | | </td> |
| [[image:TN_13_07_06_ssLLL_ssL_ssLLL.png link="file:13_07_06_ssLLL_ssL_ssLLL.png"]]
| | <td style="text-align: center;"><br /> |
| | | </td> |
| P = 5.1745609664
| | <td style="text-align: center;"><br /> |
| generator = L+s (171.4 to 184.6 cents)
| | </td> |
| notable EDOs: 20, 27, 34, 41
| | <td style="text-align: center;"><br /> |
| | | </td> |
| {{ sLsLsLsLsLsLL }} (MOS)
| | <td style="text-align: center;"><br /> |
| {{ || || || }}
| | </td> |
| {{ ssLLLssLssLLL }} (OTC MODMOS)
| | <td style="text-align: center;"><br /> |
| | | </td> |
| modes:
| | <td style="text-align: center;"><br /> |
| || {{ Lss LssLL LssLL }} || || ||
| | </td> |
| || {{ ssL ssLLL ssLLL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ sLs sLLLs sLLLs }} || || ||
| | </td> |
| || {{ Lss LLLss LLLss }} || || {{ LssLL LssLL Lss }} ||
| | <td style="text-align: center;"><br /> |
| || {{ ssL LLssL LLssL }} || || {{ ssLLL ssLLL ssL }} ||
| | </td> |
| || || || {{ sLLLs sLLLs sLs }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ LLLss LLLss Lss }} ||
| | </td> |
| || || || {{ LLssL LLssL ssL }} ||
| | <td style="text-align: center;"><br /> |
| || || {{ LssLL Lss LssLL }} || ||
| | </td> |
| || || {{ ssLLL ssL ssLLL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ sLLLs sLs sLLLs }} || ||
| | </td> |
| || || {{ LLLss Lss LLLss }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LLssL ssL LLssL }} || ||
| | </td> |
| | | <td style="text-align: center;"><br /> |
| | | </td> |
| | | <td style="text-align: center;"><br /> |
| ==14 tones (6+2+6)==
| | </td> |
| | | <td style="text-align: center;"><br /> |
| ===[[5L 9s|5L+9s]]===
| | </td> |
| [[Semaphore and Godzilla|Semaphore / godzilla]] MODMOS. Usable at any L/s ratio.
| | <td style="text-align: center;"><br /> |
| | | </td> |
| [[image:TN_14_05_09_LsssLs_Ls_LsssLs.png link="file:14_05_09_LsssLs_Ls_LsssLs.png"]]
| | <td style="text-align: center;"><br /> |
| | | </td> |
| P = 3.5200335053
| | <td style="text-align: center;"><br /> |
| generator = L+2s (240.0 to 257.1 cents)
| | </td> |
| notable EDOs: 19, 24, 29, 33, 34, 53
| | <td style="text-align: center;"><br /> |
| | | </td> |
| {{ ssLssLssLssLsL }} ([[MOS]])
| | <td style="text-align: center;"><br /> |
| {{ || || }}
| | </td> |
| {{ sssLsLsssLsLsL }} (OTC [[MODMOS]])
| | <td style="text-align: center;"><br /> |
| | | </td> |
| modes:
| | <td style="text-align: center;"><br /> |
| || {{ sL sLsLss sLsLss }} || || ||
| | </td> |
| || {{ Ls LsLsss LsLsss }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ sL sLsssL sLsssL }} || || {{ sLsLss sLsLss sL }} ||
| | </td> |
| || {{ Ls LsssLs LsssLs }} || || {{ LsLsss LsLsss Ls }} ||
| | </tr> |
| || {{ sL sssLsL sssLsL }} || || {{ sLsssL sLsssL sL }} ||
| | <tr> |
| || {{ Ls ssLsLs ssLsLs }} || || {{ LsssLs LsssLs Ls }} ||
| | <td style="text-align: center;"><strong>2</strong><br /> |
| || || || {{ sssLsL sssLsL sL }} ||
| | </td> |
| || || || {{ ssLsLs ssLsLs Ls }} ||
| | <td style="text-align: center;"><br /> |
| || || {{ sLsLss sL sLsLss }} || ||
| | </td> |
| || || {{ LsLsss Ls LsLsss }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ sLsssL sL sLsssL }} || ||
| | </td> |
| || || {{ LsssLs Ls LsssLs }} || ||
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%203s">x</a><br /> |
| || || {{ sssLsL sL sssLsL }} || ||
| | </td> |
| || || {{ ssLsLs Ls ssLsLs }} || ||
| | <td style="text-align: center;"><br /> |
| | | </td> |
| | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%205s">x</a><br /> |
| | | </td> |
| ===[[12L 2s|12L+2s]]===
| | <td style="text-align: center;"><br /> |
| [[Injera]] MODMOS. Imperfect (P<0); best for L/s >= 1.5 [[{$page}#ref1|(1)]]
| | </td> |
| | | <td style="text-align: center;"><br /> |
| [[image:TN_14_12_02_sLLLLL_LL_sLLLLL.png link="file:14_12_02_sLLLLL_LL_sLLLLL.png"]]
| | </td> |
| | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%208s">x</a><br /> |
| generator = L (85.7 to 100.0 cents)
| | </td> |
| [[periods and generators|period]] = 1/2 octave
| | <td style="text-align: center;"><br /> |
| notable EDOs: 26, 38, 40, 50
| | </td> |
| | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">x</a><br /> |
| {{ LLLLLLsLLLLLLs }} (MOS)
| | </td> |
| {{ || }}
| | <td style="text-align: center;"><br /> |
| {{ LLLLLLLsLLLLLs }} (OTC MODMOS)
| | </td> |
| | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2012s">x</a><br /> |
| modes:
| | </td> |
| || {{ LL LLLLLs LLLLLs }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ LL LLLLsL LLLLsL }} || || ||
| | </td> |
| || {{ LL LLLsLL LLLsLL }} || || {{ LLLLLs LLLLLs LL }} ||
| | <td style="text-align: center;"><br /> |
| || {{ LL LLsLLL LLsLLL }} || || {{ LLLLsL LLLLsL LL }} ||
| | </td> |
| || {{ LL LsLLLL LsLLLL }} || || {{ LLLsLL LLLsLL LL }} ||
| | <td style="text-align: center;"><br /> |
| || {{ LL sLLLLL sLLLLL }} || || {{ LLsLLL LLsLLL LL }} ||
| | </td> |
| || || || {{ LsLLLL LsLLLL LL }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ sLLLLL sLLLLL LL }} ||
| | </td> |
| || || {{ LLLLLs LL LLLLLs }} || ||
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2017s">x</a><br /> |
| || || {{ LLLLsL LL LLLLsL }} || ||
| | </td> |
| || || {{ LLLsLL LL LLLsLL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LLsLLL LL LLsLLL }} || ||
| | </td> |
| || || {{ LsLLLL LL LsLLLL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ sLLLLL LL sLLLLL }} || ||
| | </td> |
| | | <td style="text-align: center;"><br /> |
| | | </td> |
| ==15 tones (6+3+6)== | | <td style="text-align: center;"><br /> |
| | | </td> |
| ===[[7L 8s|7L+8s]]===
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2022s">x</a><br /> |
| [[Porcupine]] MODMOS
| | </td> |
| | | <td style="text-align: center;"><br /> |
| [[image:TN_15_07_08_ssLsLL_ssL_ssLsLL.png link="file:15_07_08_ssLsLL_ssL_ssLsLL.png"]]
| | </td> |
| | | <td style="text-align: center;"><br /> |
| [[{$page}#perfect|P]] = 3.3809207248
| | </td> |
| generator = L+s (160.0 to 171.4 cents)
| | <td style="text-align: center;"><br /> |
| notable EDOs: 22, 29, 36, 37, 43, 65
| | </td> |
| | | </tr> |
| {{ LsLsLsLsLsLsLss }} (MOS)
| | <tr> |
| {{ || || }}
| | <td style="text-align: center;"><strong>3</strong><br /> |
| {{ LsLLssLsLLssLss }} (OTC MODMOS)
| | </td> |
| | | <td style="text-align: center;"><br /> |
| modes:
| | </td> |
| || || {{ LssLsL Lss LssLsL }} || ||
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%203s">x</a><br /> |
| || || {{ ssLsLL ssL ssLsLL }} || ||
| | </td> |
| || || {{ sLsLLs sLs sLsLLs }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LsLLss Lss LsLLss }} || ||
| | </td> |
| || || {{ sLLssL ssL sLLssL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LLssLs sLs LLssLs }} || ||
| | </td> |
| || {{ Lss LssLsL LssLsL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ ssL ssLsLL ssLsLL }} || || ||
| | </td> |
| || {{ sLs sLsLLs sLsLLs }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ Lss LsLLss LsLLss }} || || {{ LssLsL LssLsL Lss }} ||
| | </td> |
| || {{ ssL sLLssL sLLssL }} || || {{ ssLsLL ssLsLL ssL }} ||
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%203s">x</a><br /> |
| || {{ sLs LLssLs LLssLs }} || || {{ sLsLLs sLsLLs sLs }} ||
| | </td> |
| || || || {{ LsLLss LsLLss Lss }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ sLLssL sLLssL ssL }} ||
| | </td> |
| || || || {{ LLssLs LLssLs sLs }} ||
| | <td style="text-align: center;"><br /> |
| | | </td> |
| | | <td style="text-align: center;"><br /> |
| ===[[12L 3s|12L+3s]]===
| | </td> |
| [[Augmented]] MODMOS. Best at higher L/s ratios.
| | <td style="text-align: center;"><br /> |
| | | </td> |
| [[image:TN_15_12_03_LLLLLs_LLs_LLLLLs.png link="file:15_12_03_LLLLLs_LLs_LLLLLs.png"]]
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%203s">x</a><br /> |
| | | </td> |
| P = 12.5377181246
| | <td style="text-align: center;"><br /> |
| generator = L (80.0 to 100.0 cents)
| | </td> |
| period = 1/3 octave
| | <td style="text-align: center;"><br /> |
| notable EDOs: 27, 39, 51
| | </td> |
| | | <td style="text-align: center;"><br /> |
| {{ LLLLsLLLLsLLLLs }} (MOS)
| | </td> |
| {{ || || }}
| | <td style="text-align: center;"><br /> |
| {{ LLLLLsLLsLLLLLs }} (OTC MODMOS)
| | </td> |
| | | <td style="text-align: center;"><br /> |
| modes:
| | </td> |
| || || {{ LLsLLL LLs LLsLLL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LsLLLL LsL LsLLLL }} || ||
| | </td> |
| || || {{ sLLLLL sLL sLLLLL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LLLLLs LLs LLLLLs }} || ||
| | </td> |
| || || {{ LLLLsL LsL LLLLsL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ LLLsLL sLL LLLsLL }} || ||
| | </td> |
| || {{ LLs LLsLLL LLsLLL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ LsL LsLLLL LsLLLL }} || || ||
| | </td> |
| || {{ sLL sLLLLL sLLLLL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ LLs LLLLLs LLLLLs }} || || ||
| | </td> |
| || {{ LsL LLLLsL LLLLsL }} || || {{ LsLLLL LsLLLL LsL }} ||
| | <td style="text-align: center;"><br /> |
| || {{ sLL LLLsLL LLLsLL }} || || {{ sLLLLL sLLLLL sLL }} ||
| | </td> |
| || || || {{ LLLLLs LLLLLs LLs }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ LLLLsL LLLLsL LsL }} ||
| | </td> |
| || || || {{ LLLsLL LLLsLL sLL }} ||
| | <td style="text-align: center;"><br /> |
| | | </td> |
| | | </tr> |
| ==17 tones (7+3+7)==
| | <tr> |
| | | <td style="text-align: center;"><strong>4</strong><br /> |
| ===[[5L 12s|5L+12s]]===
| | </td> |
| [[Superpyth]] / ultrapyth MOS. Imperfect, best at low L/s. Many modes may be split two ways.
| | <td style="text-align: center;"><br /> |
| | | </td> |
| [[image:TN_17_05_12_sssLssL_ssL_sssLssL.png link="file:17_05_12_sssLssL_ssL_sssLssL.png"]]
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| | | </td> |
| generator = 2L+5s (480.0 to 494.1 cents)
| | <td style="text-align: center;"><br /> |
| notable EDOs: 22, 27, 32, 37, 39
| | </td> |
| | | <td style="text-align: center;"><br /> |
| modes:
| | </td> |
| || {{ Lss LssLsss LssLsss }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ ssL ssLsssL ssLsssL }} || || {{ ssLssLs ssLssLs ssL }} ||
| | </td> |
| || {{ sLs sLsssLs sLsssLs }} || || {{ sLssLss sLssLss sLs }} ||
| | <td style="text-align: center;"><br /> |
| || {{ Lss LsssLss LsssLss }} || || {{ LssLsss LssLsss Lss }} ||
| | </td> |
| || {{ sLs ssLssLs ssLssLs }} || || {{ sLsssLs sLsssLs sLs }} ||
| | <td style="text-align: center;"><br /> |
| || {{ Lss sLssLss sLssLss }} || || {{ LsssLss LsssLss Lss }} ||
| | </td> |
| || || || {{ sssLssL sssLssL ssL }} ||
| | <td style="text-align: center;"><br /> |
| || || {{ ssLssLs ssL ssLssLs }} || {{ ssLssLs ssLssLs sLs }} ||
| | </td> |
| || || {{ sLssLss sLs sLssLss }} || {{ sLssLss sLssLss Lss }}||
| | <td style="text-align: center;"><br /> |
| || || {{ LssLsss Lss LssLsss }} || ||
| | </td> |
| || || {{ ssLsssL ssL ssLsssL }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ sLsssLs sLs sLsssLs }} || ||
| | </td> |
| || || {{ LsssLss Lss LsssLss }} || ||
| | <td style="text-align: center;"><br /> |
| || || {{ sssLssL ssL sssLssL }} || ||
| | </td> |
| || || {{ sssLssL ssL sssLssL }} || ||
| | <td style="text-align: center;"><br /> |
| || {{ ssL ssLssLs ssLssLs }} || {{ ssLssLs sLs ssLssLs }} || ||
| | </td> |
| || {{ sLs sLssLss sLssLss }} || {{ sLssLss Lss sLssLss }} || ||
| | <td style="text-align: center;"><br /> |
| | | </td> |
| | | <td style="text-align: center;"><br /> |
| ===[[12L 5s|12L+5s]]===
| | </td> |
| Helmholtz / [[Schismatic family|schismatic]] MOS; full L/s range very good [[{$page}#ref1|(1)]]
| | <td style="text-align: center;"><br /> |
| | | </td> |
| [[image:TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png link="file:17_12_05_LLLsLLs_LLs_LLLsLLs.png"]]
| | <td style="text-align: center;"><br /> |
| | | </td> |
| Pythagorean (3-limit JI): L=256/243, s=531441/524288
| | <td style="text-align: center;"><br /> |
| P = 3.8459060415
| | </td> |
| generator = 5L+2s (494.1 to 500.0 cents)
| | <td style="text-align: center;"><br /> |
| notable EDOs: 29, 41, 46, 53, 65
| | </td> |
| | | <td style="text-align: center;"><br /> |
| modes:
| | </td> |
| || {{ LLs LLsLLsL LLsLLsL }} || {{ LLsLLsL LsL LLsLLsL }} || ||
| | <td style="text-align: center;"><br /> |
| || {{ LsL LsLLsLL LsLLsLL }} || {{ LsLLsLL sLL LsLLsLL }} || ||
| | </td> |
| || {{ sLL sLLsLLL sLLsLLL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ LLs LLsLLLs LLsLLLs }} || || {{ LLsLLsL LLsLLsL LLs }} ||
| | </td> |
| || {{ LsL LsLLLsL LsLLLsL }} || || {{ LsLLsLL LsLLsLL LsL }} ||
| | <td style="text-align: center;"><br /> |
| || {{ sLL sLLLsLL sLLLsLL }} || || {{ sLLsLLL sLLsLLL sLL }} ||
| | </td> |
| || {{ LLs LLLsLLs LLLsLLs }} || || {{ LLsLLLs LLsLLLs LLs }} ||
| | <td style="text-align: center;"><br /> |
| || {{ LsL LLsLLsL LLsLLsL }} || || {{ LsLLLsL LsLLLsL LsL }} ||
| | </td> |
| || {{ sLL LsLLsLL LsLLsLL }} || || {{ sLLLsLL sLLLsLL sLL }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ LLLsLLs LLLsLLs LLs }} ||
| | </td> |
| || || {{ LLsLLsL LLs LLsLLsL }} || {{ LLsLLsL LLsLLsL LsL }} ||
| | <td style="text-align: center;"><br /> |
| || || {{ LsLLsLL LsL LsLLsLL }} || {{ LsLLsLL LsLLsLL sLL }} ||
| | </td> |
| || || {{ sLLsLLL sLL sLLsLLL }} || ||
| | </tr> |
| || || {{ LLsLLLs LLs LLsLLLs }} || ||
| | <tr> |
| || || {{ LsLLLsL LsL LsLLLsL }} || ||
| | <td style="text-align: center;"><strong>5</strong><br /> |
| || || {{ sLLLsLL sLL sLLLsLL }} || ||
| | </td> |
| || || {{ LLLsLLs LLs LLLsLLs }} || ||
| | <td style="text-align: center;"><br /> |
| | | </td> |
| | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%205s">x</a><br /> |
| ===[[7L 10s|7L+10s]]===
| | </td> |
| [[Mohajira]] / [[Neutral third scales|neutral-thirds]] MODMOS; full L/s range good
| | <td style="text-align: center;"><br /> |
| | | </td> |
| [[image:TN_17_07_10_LssLssL_ssL_LssLssL.png link="file:17_07_10_LssLssL_ssL_LssLssL.png"]]
| | <td style="text-align: center;"><br /> |
| | | </td> |
| P = 1.5872804832
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%205s">x</a><br /> |
| generator = 2L+3s (342.9 to 352.9 cents)
| | </td> |
| notable EDOs: 24, 31, 41, 65
| | <td style="text-align: center;"><br /> |
| | | </td> |
| {{ ssLsLssLsLssLsLsL }} (MOS)
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%205s">x</a><br /> |
| {{ || || || }}
| | </td> |
| {{ ssLLssLssLssLLssL }} (OTC MODMOS)
| | <td style="text-align: center;"><br /> |
| | | </td> |
| modes:
| | <td style="text-align: center;"><br /> |
| || {{ Lss LssLssL LssLssL }} || {{ LssLssL ssL LssLssL }} || ||
| | </td> |
| || {{ ssL ssLssLL ssLssLL }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ sLs sLssLLs sLssLLs }} || || ||
| | </td> |
| || {{ Lss LssLLss LssLLss }} || || ||
| | <td style="text-align: center;"><br /> |
| || {{ ssL ssLLssL ssLLssL }} || || {{ ssLssLL ssLssLL ssL }} ||
| | </td> |
| || {{ sLs sLLssLs sLLssLs }} || || {{ sLssLLs sLssLLs sLs }} ||
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%205s">x</a><br /> |
| || {{ Lss LLssLss LLssLss }} || || {{ LssLLss LssLLss Lss }} ||
| | </td> |
| || {{ ssL LssLssL LssLssL }} || || {{ ssLLssL ssLLssL ssL }} ||
| | <td style="text-align: center;"><br /> |
| || || || {{ sLLssLs sLLssLs sLs }} ||
| |
| || || || {{ LLssLss LLssLss Lss }} ||
| |
| || || {{ LssLssL Lss LssLssL }} || {{ LssLssL LssLssL ssL }} ||
| |
| || || {{ ssLssLL ssL ssLssLL }} || ||
| |
| || || {{ sLssLLs sLs sLssLLs }} || ||
| |
| || || {{ LssLLss Lss LssLLss }} || ||
| |
| || || {{ ssLLssL ssL ssLLssL }} || ||
| |
| || || {{ sLLssLs sLs sLLssLs }} || ||
| |
| || || {{ LLssLss Lss LLssLss }} || ||
| |
| | |
| | |
| ===[[10L 7s|10L+7s]]===
| |
| Beatles? / [[Dicot family|dicot]]? MODMOS; imperfect; full L/s range mostly good
| |
| | |
| [[image:TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png link="file:17_10_07_sLLsLLs_LLs_sLLsLLs.png"]]
| |
| | |
| generator = 3L+2s (352.9 to 360.0 cents)
| |
| notable EDOs: 27, 37, 44, 61
| |
| | |
| {{ sLsLsLLsLsLLsLsLL }} (MOS)
| |
| {{ || || || }}
| |
| {{ ssLLsLLssLLsLLsLL }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || {{ sLL sLLsLLs sLLsLLs }} || {{ sLLsLLs LLs sLLsLLs }} || ||
| |
| || {{ LLs LLsLLss LLsLLss }} || || ||
| |
| || {{ LsL LsLLssL LsLLssL }} || || ||
| |
| || {{ sLL sLLssLL sLLssLL }} || || {{ sLLsLLs sLLsLLs sLL }} ||
| |
| || {{ LLs LLssLLs LLssLLs }} || || {{ LLsLLss LLsLLss LLs }} ||
| |
| || {{ LsL LssLLsL LssLLsL }} || || {{ LsLLssL LsLLssL LsL }} ||
| |
| || {{ sLL ssLLsLL ssLLsLL }} || || {{ sLLssLL sLLssLL sLL }} ||
| |
| || {{ LLs sLLsLLs sLLsLLs }} || || {{ LLssLLs LLssLLs LLs }} ||
| |
| || || || {{ LssLLsL LssLLsL LsL }} ||
| |
| || || || {{ ssLLsLL ssLLsLL sLL }} ||
| |
| || || {{ sLLsLLs sLL sLLsLLs }} || {{ sLLsLLs sLLsLLs LLs }} ||
| |
| || || {{ LLsLLss LLs LLsLLss }} || ||
| |
| || || {{ LsLLssL LsL LsLLssL }} || ||
| |
| || || {{ sLLssLL sLL sLLssLL }} || ||
| |
| || || {{ LLssLLs LLs LLssLLs }} || ||
| |
| || || {{ LssLLsL LsL LssLLsL }} || ||
| |
| || || {{ ssLLsLL sLL ssLLsLL }} || ||
| |
| | |
| | |
| ==18 tones (7+4+7)==
| |
| | |
| ===[[7L 11s|7L+11s]]===
| |
| Sixix?; best for L/s>2
| |
| | |
| [[image:TN_18_07_11_sssLsLL_sssL_sssLsLL.png link="file:18_07_11_sssLsLL_sssL_sssLsLL.png"]]
| |
| | |
| P = 5.968201208
| |
| generator = 2L+3s (333.3 to 342.9 cents)
| |
| notable EDOs: 25, 32, 39, 46, 53
| |
| | |
| {{ LsLssLsLssLsLssLss }} (MOS)
| |
| {{ || | | || }}
| |
| {{ LLsssLsLLsssLsssLs }} (OTC MODMOS?)
| |
| | |
| modes:
| |
| || || {{ LsssLsL Lsss LsssLsL }} || ||
| |
| || || {{ sssLsLL sssL sssLsLL }} || ||
| |
| || || {{ ssLsLLs ssLs ssLsLLs }} || ||
| |
| || || {{ sLsLLss sLss sLsLLss }} || ||
| |
| || || {{ LsLLsss Lsss LsLLsss }} || ||
| |
| || || {{ sLLsssL sssL sLLsssL }} || ||
| |
| || || {{ LLsssLs ssLs LLsssLs }} || ||
| |
| || {{ Lsss LsssLsL LsssLsL }} || || ||
| |
| || {{ sssL sssLsLL sssLsLL }} || || ||
| |
| || {{ ssLs ssLsLLs ssLsLLs }} || || ||
| |
| || {{ sLss sLsLLss sLsLLss }} || || ||
| |
| || {{ Lsss LsLLsss LsLLsss }} || || {{ LsssLsL LsssLsL Lsss }} ||
| |
| || {{ sssL sLLsssL sLLsssL }} || || {{ sssLsLL sssLsLL sssL }} ||
| |
| || {{ ssLs LLsssLs LLsssLs }} || || {{ ssLsLLs ssLsLLs ssLs }} ||
| |
| || || || {{ sLsLLss sLsLLss sLss }} ||
| |
| || || || {{ LsLLsss LsLLsss Lsss }} ||
| |
| || || || {{ sLLsssL sLLsssL sssL }} ||
| |
| || || || {{ LLsssLs LLsssLs ssLs }} ||
| |
| | |
| | |
| ==19 tones (8+3+8)==
| |
| | |
| ===[[7L 12s|7L+12s]]===
| |
| [[Meantone family#Flattone|Flattone]] MOS; [[{$page}#perfect|P]]<0; [[{$page}#ref1|(1)]]
| |
| | |
| [[image:TN_19_07_12_LssLsLss_Lss_LssLsLss.png link="file:19_07_12_LssLsLss_Lss_LssLsLss.png"]]
| |
| | |
| generator = 3L+5s (505.3 to 514.3 cents)
| |
| notable EDOs: 26, 33, 40, 45
| |
| | |
| modes:
| |
| || {{ sLs sLssLssL sLssLssL }} || {{ sLssLssL ssL sLssLssL }} || ||
| |
| || {{ Lss LssLssLs LssLssLs }} || {{ LssLssLs sLs LssLssLs }} || ||
| |
| || {{ ssL ssLssLsL ssLssLsL }} || || ||
| |
| || {{ sLs sLssLsLs sLssLsLs }} || || {{ sLssLssL sLssLssL sLs }} ||
| |
| || {{ Lss LssLsLss LssLsLss }} || || {{ LssLssLs LssLssLs Lss }} ||
| |
| || {{ ssL ssLsLssL ssLsLssL }} || || {{ ssLssLsL ssLssLsL ssL }} ||
| |
| || {{ sLs sLsLssLs sLsLssLs }} || || {{ sLssLsLs sLssLsLs sLs }} ||
| |
| || {{ Lss LsLssLss LsLssLss }} || || {{ LssLsLss LssLsLss Lss }} ||
| |
| || {{ ssL sLssLssL sLssLssL }} || || {{ ssLsLssL ssLsLssL ssL }} ||
| |
| || {{ sLs LssLssLs LssLssLs }} || || {{ sLsLssLs sLsLssLs sLs }} ||
| |
| || || || {{ LsLssLss LsLssLss Lss }} ||
| |
| || || {{ sLssLssL sLs sLssLssL }} || {{ sLssLssL sLssLssL ssL }} ||
| |
| || || {{ LssLssLs Lss LssLssLs }} || {{ LssLssLs LssLssLs sLs }} ||
| |
| || || {{ ssLssLsL ssL ssLssLsL }} || ||
| |
| || || {{ sLssLsLs sLs sLssLsLs }} || ||
| |
| || || {{ LssLsLss Lss LssLsLss }} || ||
| |
| || || {{ ssLsLssL ssL ssLsLssL }} || ||
| |
| || || {{ sLsLssLs sLs sLsLssLs }} || ||
| |
| || || {{ LsLssLss Lss LsLssLss }} || ||
| |
| | |
| | |
| ===[[12L 7s|12L+7s]]===
| |
| [[Meantone]] MOS; [[{$page}#perfect|P]]<0 (oddly, neither this scale nor its [[{$page}#dual|dual]] can be tuned with a perfect 3/2!) [[{$page}#ref1|(1)]]
| |
| | |
| [[image:TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png link="file:19_12_07_sLLsLsLL_sLL_sLLsLsLL.png"]]
| |
| | |
| generator = 5L+3s (500.0 to 505.3 cents)
| |
| notable EDOs: 31, 43, 50, 55
| |
| | |
| modes:
| |
| || {{ LsL LsLLsLLs LsLLsLLs }} || {{ LsLLsLLs LLs LsLLsLLs }} || ||
| |
| || {{ sLL sLLsLLsL sLLsLLsL }} || {{ sLLsLLsL LsL sLLsLLsL }} || ||
| |
| || {{ LLs LLsLLsLs LLsLLsLs }} || || ||
| |
| || {{ LsL LsLLsLsL LsLLsLsL }} || || {{ LsLLsLLs LsLLsLLs LsL }} ||
| |
| || {{ sLL sLLsLsLL sLLsLsLL }} || || {{ sLLsLLsL sLLsLLsL sLL }} ||
| |
| || {{ LLs LLsLsLLs LLsLsLLs }} || || {{ LLsLLsLs LLsLLsLs LLs }} ||
| |
| || {{ LsL LsLsLLsL LsLsLLsL }} || || {{ LsLLsLsL LsLLsLsL LsL }} ||
| |
| || {{ sLL sLsLLsLL sLsLLsLL }} || || {{ sLLsLsLL sLLsLsLL sLL }} ||
| |
| || {{ LLs LsLLsLLs LsLLsLLs }} || || {{ LLsLsLLs LLsLsLLs LLs }} ||
| |
| || {{ LsL sLLsLLsL sLLsLLsL }} || || {{ LsLsLLsL LsLsLLsL LsL }} ||
| |
| || || || {{ sLsLLsLL sLsLLsLL sLL }} ||
| |
| || || {{ LsLLsLLs LsL LsLLsLLs }} || {{ LsLLsLLs LsLLsLLs LLs }} ||
| |
| || || {{ sLLsLLsL sLL sLLsLLsL }} || {{ sLLsLLsL sLLsLLsL LsL }} ||
| |
| || || {{ LLsLLsLs LLs LLsLLsLs }} || ||
| |
| || || {{ LsLLsLsL LsL LsLLsLsL }} || ||
| |
| || || {{ sLLsLsLL sLL sLLsLsLL }} || ||
| |
| || || {{ LLsLsLLs LLs LLsLsLLs }} || ||
| |
| || || {{ LsLsLLsL LsL LsLsLLsL }} || ||
| |
| || || {{ sLsLLsLL sLL sLsLLsLL }} || ||
| |
| | |
| | |
| ===[[5L 14s|5L+14s]]===
| |
| Godzilla? MODMOS; full L/s range good
| |
| | |
| [[image:TN_19_05_14_ssLssssL_ssL_ssLssssL.png link="file:19_05_14_ssLssssL_ssL_ssLssssL.png"]]
| |
| | |
| P = 2.5200335053
| |
| generator = L+3s (240.0 to 252.6 cents)
| |
| notable EDOs: 24, 29, 34, 39, 43, 53
| |
| | |
| {{ sssLsssLsssLsssLssL }} (MOS)
| |
| {{ || || }}
| |
| {{ ssLssssLssLssssLssL }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || {{ ssL ssLssLss ssLssLss }} || {{ ssLssLss Lss ssLssLss }} || ||
| |
| || {{ sLs sLssLsss sLssLsss }} || || ||
| |
| || {{ Lss LssLssss LssLssss }} || || ||
| |
| || {{ ssL ssLssssL ssLssssL }} || || {{ ssLssLss ssLssLss ssL }} ||
| |
| || {{ sLs sLssssLs sLssssLs }} || || {{ sLssLsss sLssLsss sLs }} ||
| |
| || {{ Lss LssssLss LssssLss }} || || {{ LssLssss LssLssss Lss }} ||
| |
| || {{ ssL ssssLssL ssssLssL }} || || {{ ssLssssL ssLssssL ssL }} ||
| |
| || {{ sLs sssLssLs sssLssLs }} || || {{ sLssssLs sLssssLs sLs }} ||
| |
| || {{ Lss ssLssLss ssLssLss }} || || {{ LssssLss LssssLss Lss }} ||
| |
| || || || {{ ssssLssL ssssLssL ssL }} ||
| |
| || || || {{ sssLssLs sssLssLs sLs }} ||
| |
| || || {{ ssLssLss ssL ssLssLss }} || {{ ssLssLss ssLssLss Lss }} ||
| |
| || || {{ sLssLsss sLs sLssLsss }} || ||
| |
| || || {{ LssLssss Lss LssLssss }} || ||
| |
| || || {{ ssLssssL ssL ssLssssL }} || ||
| |
| || || {{ sLssssLs sLs sLssssLs }} || ||
| |
| || || {{ LssssLss Lss LssssLss }} || ||
| |
| || || {{ ssssLssL ssL ssssLssL }} || ||
| |
| || || {{ sssLssLs sLs sssLssLs }} || ||
| |
| | |
| | |
| ===[[14L 5s|14L+5s]]===
| |
| [[Semaphore and godzilla|Semaphore / godzilla]] MODMOS; imperfect; full L/s range good
| |
| | |
| [[image:TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png link="file:19_14_05_LLsLLLLs_LLs_LLsLLLLs.png"]]
| |
| | |
| generator = 3L+s (252.6 to 257.1 cents)
| |
| notable EDOs: 33, 47, 52
| |
| | |
| {{ LLLsLLLsLLLsLLLsLLs }} (MOS)
| |
| {{ || || }}
| |
| {{ LLLLsLLsLLLLsLLsLLs }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || || {{ LLsLLLLs LLs LLsLLLLs }} || ||
| |
| || || {{ LsLLLLsL LsL LsLLLLsL }} || ||
| |
| || || {{ sLLLLsLL sLL sLLLLsLL }} || ||
| |
| || || {{ LLLLsLLs LLs LLLLsLLs }} || ||
| |
| || || {{ LLLsLLsL LsL LLLsLLsL }} || ||
| |
| || {{ LLs LLsLLsLL LLsLLsLL }} || {{ LLsLLsLL sLL LLsLLsLL }} || ||
| |
| || {{ LsL LsLLsLLL LsLLsLLL }} || || ||
| |
| || {{ sLL sLLsLLLL sLLsLLLL }} || || ||
| |
| || {{ LLs LLsLLLLs LLsLLLLs }} || || {{ LLsLLsLL LLsLLsLL LLs }} ||
| |
| || {{ LsL LsLLLLsL LsLLLLsL }} || || {{ LsLLsLLL LsLLsLLL LsL }} ||
| |
| || {{ sLL sLLLLsLL sLLLLsLL }} || || {{ sLLsLLLL sLLsLLLL sLL }} ||
| |
| || {{ LLs LLLLsLLs LLLLsLLs }} || || {{ LLsLLLLs LLsLLLLs LLs }} ||
| |
| || {{ LsL LLLsLLsL LLLsLLsL }} || || {{ LsLLLLsL LsLLLLsL LsL }} ||
| |
| || {{ sLL LLsLLsLL LLsLLsLL }} || || {{ sLLLLsLL sLLLLsLL sLL }} ||
| |
| || || || {{ LLLLsLLs LLLLsLLs LLs }} ||
| |
| || || || {{ LLLsLLsL LLLsLLsL LsL }} ||
| |
| || || {{ LLsLLsLL LLs LLsLLsLL }} || {{ LLsLLsLL LLsLLsLL sLL }} ||
| |
| || || {{ LsLLsLLL LsL LsLLsLLL }} || ||
| |
| || || {{ sLLsLLLL sLL sLLsLLLL }} || ||
| |
| | |
| | |
| ==22 tones (9+4+9)==
| |
| | |
| ===[[7L 15s|7L+15s]]===
| |
| [[Porcupine]] MODMOS; full L/s range good
| |
| | |
| [[image:TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png link="file:22_07_15_sssLsssLL_sssL_sssLsssLL.png"]]
| |
| | |
| P = 2.3809207248
| |
| generator = L+2s (163.6 to 171.4 cents)
| |
| notable EDOs: 29, 36, 43, 50, 51
| |
| | |
| {{ LssLssLssLssLssLssLsss }} (MOS)
| |
| {{ |||| |||| }}
| |
| {{ LsssLLsssLsssLLsssLsss }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || || {{ sssLsssLL sssL sssLsssLL }} || ||
| |
| || || {{ ssLsssLLs ssLs ssLsssLLs }} || ||
| |
| || || {{ sLsssLLss sLss sLsssLLss }} || ||
| |
| || || {{ LsssLLsss Lsss LsssLLsss }} || ||
| |
| || || {{ sssLLsssL sssL sssLLsssL }} || ||
| |
| || || {{ ssLLsssLs ssLs ssLLsssLs }} || ||
| |
| || || {{ sLLsssLss sLss sLLsssLss }} || ||
| |
| || || {{ LLsssLsss Lsss LLsssLsss }} || ||
| |
| || {{ Lsss LsssLsssL LsssLsssL }} || {{ LsssLsssL sssL LsssLsssL }} || ||
| |
| || {{ sssL sssLsssLL sssLsssLL }} || || ||
| |
| || {{ ssLs ssLsssLLs ssLsssLLs }} || || ||
| |
| || {{ sLss sLsssLLss sLsssLLss }} || || ||
| |
| || {{ Lsss LsssLLsss LsssLLsss }} || || {{ LsssLsssL LsssLsssL Lsss }} ||
| |
| || {{ sssL sssLLsssL sssLLsssL }} || || {{ sssLsssLL sssLsssLL sssL }} ||
| |
| || {{ ssLs ssLLsssLs ssLLsssLs }} || || {{ ssLsssLLs ssLsssLLs ssLs }} ||
| |
| || {{ sLss sLLsssLss sLLsssLss }} || || {{ sLsssLLss sLsssLLss sLss }} ||
| |
| || {{ Lsss LLsssLsss LLsssLsss }} || || {{ LsssLLsss LsssLLsss Lsss }} ||
| |
| || {{ sssL LsssLsssL LsssLsssL }} || || {{ sssLLsssL sssLLsssL sssL }} ||
| |
| || || || {{ ssLLsssLs ssLLsssLs ssLs }} ||
| |
| || || || {{ sLLsssLss sLLsssLss sLss }} ||
| |
| || || || {{ LLsssLsss LLsssLsss Lsss }} ||
| |
| || || {{ LsssLsssL Lsss LsssLsssL }} || {{ LsssLsssL LsssLsssL sssL }} ||
| |
| | |
| | |
| ===[[15L 7s|15L+7s]]===
| |
| [[Porcupine]] MODMOS; imperfect; full L/s range mostly good
| |
| | |
| [[image:TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png link="file:22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png"]]
| |
| | |
| generator = 2L+s (160.0 to 163.6 cents)
| |
| notable EDOs: 37, 52b, 59
| |
| | |
| {{ sLLsLLsLLsLLsLLsLLsLLL }} (MOS)
| |
| {{ |||| |||| }}
| |
| {{ sLLLssLLLsLLLssLLLsLLL }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || || {{ LLLsLLLss LLLs LLLsLLLss }} || ||
| |
| || || {{ LLsLLLssL LLsL LLsLLLssL }} || ||
| |
| || || {{ LsLLLssLL LsLL LsLLLssLL }} || ||
| |
| || || {{ sLLLssLLL sLLL sLLLssLLL }} || ||
| |
| || || {{ LLLssLLLs LLLs LLLssLLLs }} || ||
| |
| || || {{ LLssLLLsL LLsL LLssLLLsL }} || ||
| |
| || || {{ LssLLLsLL LsLL LssLLLsLL }} || ||
| |
| || || {{ ssLLLsLLL sLLL ssLLLsLLL }} || ||
| |
| || {{ sLLL sLLLsLLLs sLLLsLLLs }} || {{ sLLLsLLLs LLLs sLLLsLLLs }} || ||
| |
| || {{ LLLs LLLsLLLss LLLsLLLss }} || || ||
| |
| || {{ LLsL LLsLLLssL LLsLLLssL }} || || ||
| |
| || {{ LsLL LsLLLssLL LsLLLssLL }} || || ||
| |
| || {{ sLLL sLLLssLLL sLLLssLLL }} || || {{ sLLLsLLLs sLLLsLLLs sLLL }} ||
| |
| || {{ LLLs LLLssLLLs LLLssLLLs }} || || {{ LLLsLLLss LLLsLLLss LLLs }} ||
| |
| || {{ LLsL LLssLLLsL LLssLLLsL }} || || {{ LLsLLLssL LLsLLLssL LLsL }} ||
| |
| || {{ LsLL LssLLLsLL LssLLLsLL }} || || {{ LsLLLssLL LsLLLssLL LsLL }} ||
| |
| || {{ sLLL ssLLLsLLL ssLLLsLLL }} || || {{ sLLLssLLL sLLLssLLL sLLL }} ||
| |
| || {{ LLLs sLLLsLLLs sLLLsLLLs }} || || {{ LLLssLLLs LLLssLLLs LLLs }} ||
| |
| || || || {{ LLssLLLsL LLssLLLsL LLsL }} ||
| |
| || || || {{ LssLLLsLL LssLLLsLL LsLL }} ||
| |
| || || || {{ ssLLLsLLL ssLLLsLLL sLLL }} ||
| |
| || || {{ sLLLsLLLs sLLL sLLLsLLLs }} || {{ sLLLsLLLs sLLLsLLLs LLLs }} ||
| |
| | |
| | |
| ===[[12L 10s|12L+10s]]===
| |
| [[Pajara]] / [[Diaschismic family|srutal (diaschismic)]] MODMOS [[{$page}#ref1|(1)]]
| |
| | |
| [[image:TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png link="file:22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png"]]
| |
| | |
| P = 7.6918120831
| |
| generator = L+s (100.0 to 109.1 cents)
| |
| period = 1/2 octave
| |
| notable EDOs: 34, 46, 56, 58, 70
| |
| | |
| {{ sLsLsLsLsLLsLsLsLsLsLL }} (MOS)
| |
| {{ || }}
| |
| {{ sLsLsLsLsLsLLsLsLsLsLL }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || {{ LsLs LsLsLsLsL LsLsLsLsL }} || {{ LsLsLsLsL sLsL LsLsLsLsL }} || ||
| |
| || {{ sLsL sLsLsLsLL sLsLsLsLL }} || || ||
| |
| || {{ LsLs LsLsLsLLs LsLsLsLLs }} || || ||
| |
| || {{ sLsL sLsLsLLsL sLsLsLLsL }} || || ||
| |
| || {{ LsLs LsLsLLsLs LsLsLLsLs }} || || {{ LsLsLsLsL LsLsLsLsL LsLs }} ||
| |
| || {{ sLsL sLsLLsLsL sLsLLsLsL }} || || {{ sLsLsLsLL sLsLsLsLL sLsL }} ||
| |
| || {{ LsLs LsLLsLsLs LsLLsLsLs }} || || {{ LsLsLsLLs LsLsLsLLs LsLs }} ||
| |
| || {{ sLsL sLLsLsLsL sLLsLsLsL }} || || {{ sLsLsLLsL sLsLsLLsL sLsL }} ||
| |
| || {{ LsLs LLsLsLsLs LLsLsLsLs }} || || {{ LsLsLLsLs LsLsLLsLs LsLs }} ||
| |
| || {{ sLsL LsLsLsLsL LsLsLsLsL }} || || {{ sLsLLsLsL sLsLLsLsL sLsL }} ||
| |
| || || || {{ LsLLsLsLs LsLLsLsLs LsLs }} ||
| |
| || || || {{ sLLsLsLsL sLLsLsLsL sLsL }} ||
| |
| || || || {{ LLsLsLsLs LLsLsLsLs LsLs }} ||
| |
| || || {{ LsLsLsLsL LsLs LsLsLsLsL }} || {{ LsLsLsLsL LsLsLsLsL sLsL }} ||
| |
| || || {{ sLsLsLsLL sLsL sLsLsLsLL }} || ||
| |
| || || {{ LsLsLsLLs LsLs LsLsLsLLs }} || ||
| |
| || || {{ sLsLsLLsL sLsL sLsLsLLsL }} || ||
| |
| || || {{ LsLsLLsLs LsLs LsLsLLsLs }} || ||
| |
| || || {{ sLsLLsLsL sLsL sLsLLsLsL }} || ||
| |
| || || {{ LsLLsLsLs LsLs LsLLsLsLs }} || ||
| |
| || || {{ sLLsLsLsL sLsL sLLsLsLsL }} || ||
| |
| || || {{ LLsLsLsLs LsLs LLsLsLsLs }} || ||
| |
| | |
| | |
| ===[[10L 12s|10L+12s]]===
| |
| Pajara? MODMOS; imperfect; full L/s range good
| |
| | |
| [[image:TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png link="file:22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png"]]
| |
| | |
| notable EDOs: 32, 42, 54
| |
| generator = L+s (10.91 to 120.0 cents)
| |
| period = 1/2 octave
| |
| | |
| {{ LsLsLsLsLssLsLsLsLsLss }} (MOS)
| |
| {{ || }}
| |
| {{ LsLsLsLsLsLssLsLsLsLss }} (OTC MODMOS)
| |
| | |
| modes:
| |
| || {{ sLsL sLsLsLsLs sLsLsLsLs }} || {{ sLsLsLsLs LsLs sLsLsLsLs }} || ||
| |
| || {{ LsLs LsLsLsLss LsLsLsLss }} || || ||
| |
| || {{ sLsL sLsLsLssL sLsLsLssL }} || || ||
| |
| || {{ LsLs LsLsLssLs LsLsLssLs }} || || ||
| |
| || {{ sLsL sLsLssLsL sLsLssLsL }} || || {{ sLsLsLsLs sLsLsLsLs sLsL }} ||
| |
| || {{ LsLs LsLssLsLs LsLssLsLs }} || || {{ LsLsLsLss LsLsLsLss LsLs }} ||
| |
| || {{ sLsL sLssLsLsL sLssLsLsL }} || || {{ sLsLsLssL sLsLsLssL sLsL }} ||
| |
| || {{ LsLs LssLsLsLs LssLsLsLs }} || || {{ LsLsLssLs LsLsLssLs LsLs }} ||
| |
| || {{ sLsL ssLsLsLsL ssLsLsLsL }} || || {{ sLsLssLsL sLsLssLsL sLsL }} ||
| |
| || {{ LsLs sLsLsLsLs sLsLsLsLs }} || || {{ LsLssLsLs LsLssLsLs LsLs }} ||
| |
| || || || {{ sLssLsLsL sLssLsLsL sLsL }} ||
| |
| || || || {{ LssLsLsLs LssLsLsLs LsLs }} ||
| |
| || || || {{ ssLsLsLsL ssLsLsLsL sLsL }} ||
| |
| || || {{ sLsLsLsLs sLsL sLsLsLsLs }} || {{ sLsLsLsLs sLsLsLsLs LsLs }} ||
| |
| || || {{ LsLsLsLss LsLs LsLsLsLss }} || ||
| |
| || || {{ sLsLsLssL sLsL sLsLsLssL }} || ||
| |
| || || {{ LsLsLssLs LsLs LsLsLssLs }} || ||
| |
| || || {{ sLsLssLsL sLsL sLsLssLsL }} || ||
| |
| || || {{ LsLssLsLs LsLs LsLssLsLs }} || ||
| |
| || || {{ sLssLsLsL sLsL sLssLsLsL }} || ||
| |
| || || {{ LssLsLsLs LsLs LssLsLsLs }} || ||
| |
| || || {{ ssLsLsLsL sLsL ssLsLsLsL }} || ||
| |
| | |
| | |
| ----
| |
| | |
| =Scales with 3 step sizes=
| |
| | |
| ===22-tone Indian 'sruti' scale===
| |
| (5-limit [[Just intonation|JI]])
| |
| | |
| ||= **scale step** ||= **ratio** ||> **cents** ||
| |
| ||= 0 ||= 1/1 ||> 0.000 ||
| |
| ||= 1 ||= 256/243 ||> 90.225 ||
| |
| ||= 2 ||= 16/15 ||> 111.731 ||
| |
| ||= 3 ||= 10/9 ||> 182.404 ||
| |
| ||= 4 ||= 9/8 ||> 203.910 ||
| |
| ||= 5 ||= 32/27 ||> 294.135 ||
| |
| ||= 6 ||= 6/5 ||> 315.641 ||
| |
| ||= 7 ||= 5/4 ||> 386.314 ||
| |
| ||= 8 ||= 81/64 ||> 407.820 ||
| |
| ||= 9 ||= 4/3 ||> 498.045 ||
| |
| ||= 10 ||= 27/20 ||> 519.551 ||
| |
| ||= 11 ||= 45/32 ||> 590.224 ||
| |
| ||= 12 ||= 729/512 ||> 611.730 ||
| |
| ||= 13 ||= 3/2 ||> 701.955 ||
| |
| ||= 14 ||= 128/81 ||> 792.180 ||
| |
| ||= 15 ||= 8/5 ||> 813.686 ||
| |
| ||= 16 ||= 5/3 ||> 884.359 ||
| |
| ||= 17 ||= 27/16 ||> 905.865 ||
| |
| ||= 18 ||= 16/9 ||> 996.090 ||
| |
| ||= 19 ||= 9/5 ||> 1017.596 ||
| |
| ||= 20 ||= 15/8 ||> 1088.269 ||
| |
| ||= 21 ||= 243/128 ||> 1109.775 ||
| |
| ||= 22 ||= 2/1 ||> 1200.000 ||
| |
| | |
| A = 256/243
| |
| b = 81/80
| |
| c = 25/24
| |
| A+2b+c = 9/8
| |
| 3A+4b+2c = 4/3
| |
| 7A+10b+5c = 2/1
| |
| | |
| modes:
| |
| || {{ Abcb AbcbAbcbA AbcbAbcbA }} || {{ AbcbAbcbA bcbA AbcbAbcbA }} || ||
| |
| || {{ bcbA bcbAbcbAA bcbAbcbAA }} || || ||
| |
| || {{ cbAb cbAbcbAAb cbAbcbAAb }} || || ||
| |
| || {{ bAbc bAbcbAAbc bAbcbAAbc }} || || ||
| |
| || {{ Abcb AbcbAAbcb AbcbAAbcb }} || || {{ AbcbAbcbA AbcbAbcbA Abcb }} ||
| |
| || {{ bcbA bcbAAbcbA bcbAAbcbA }} || || {{ bcbAbcbAA bcbAbcbAA bcbA }} ||
| |
| || {{ cbAb cbAAbcbAb cbAAbcbAb }} || || {{ cbAbcbAAb cbAbcbAAb cbAb }} ||
| |
| || {{ bAbc bAAbcbAbc bAAbcbAbc }} || || {{ bAbcbAAbc bAbcbAAbc bAbc }} ||
| |
| || {{ Abcb AAbcbAbcb AAbcbAbcb }} || || {{ AbcbAAbcb AbcbAAbcb Abcb }} ||
| |
| || {{ bcbA AbcbAbcbA AbcbAbcbA }} || || {{ bcbAAbcbA bcbAAbcbA bcbA }} ||
| |
| || || || {{ cbAAbcbAb cbAAbcbAb cbAb }} ||
| |
| || || || {{ bAAbcbAbc bAAbcbAbc bAbc }} ||
| |
| || || || {{ AAbcbAbcb AAbcbAbcb Abcb }} ||
| |
| || || {{ AbcbAbcbA Abcb AbcbAbcbA }} || {{ AbcbAbcbA AbcbAbcbA bcbA }} ||
| |
| || || {{ bcbAbcbAA bcbA bcbAbcbAA }} || ||
| |
| || || {{ cbAbcbAAb cbAb cbAbcbAAb }} || ||
| |
| || || {{ bAbcbAAbc bAbc bAbcbAAbc }} || ||
| |
| || || {{ AbcbAAbcb Abcb AbcbAAbcb }} || ||
| |
| || || {{ bcbAAbcbA bcbA bcbAAbcbA }} || ||
| |
| || || {{ cbAAbcbAb cbAb cbAAbcbAb }} || ||
| |
| || || {{ bAAbcbAbc bAbc bAAbcbAbc }} || ||
| |
| || || {{ AAbcbAbcb Abcb AAbcbAbcb }} || ||
| |
| | |
| | |
| ---- | |
| | |
| =Definitions and formulas= | |
| | |
| [[#dual]]**"Dual"** refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, {{ sLssL }} and {{ LsLLs }} are duals.
| |
| | |
| [[#perfect]]**"Perfect"** means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo subgroup]].) In this case the value **"P"** is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> ``=`` L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> ``=`` s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ).
| |
| | |
| In some cases, P may be less than zero. I'm not yet sure what this means :)
| |
| | |
| The value of P is calculated as follows:
| |
| | |
| a = the number of L steps per 2/1
| |
| b = the number of s steps per 2/1
| |
| c = the number of L steps per 3/2
| |
| d = the number of s steps per 3/2
| |
| x = log<span style="vertical-align: sub;">2</span>(3/2) = ~0.58496 octaves = ~701.955 cents
| |
| | |
| aL+bs = log<span style="vertical-align: sub;">2</span>(2/1) = 1
| |
| cL+ds = x
| |
| | |
| s = (c-ax)/(bc-ad)
| |
| L = (x-ds)/c
| |
| P = L/s
| |
| | |
| **"L/s range"**: For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.
| |
| | |
| | |
| ----
| |
| | |
| =References= | |
| | |
| * [[#ref1]](1) Several of these scales were noted as omnitetrachordal by Paul Erlich in 2002 (if not before). See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987|10987]].
| |
| </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>Gallery of omnitetrachordal scales</title></head><body><!-- ws:start:WikiTextTocRule:136:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 1em;"><a href="#Scales with two step sizes">Scales with two step sizes</a></div>
| |
| <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-5 tones (2+1+2)">5 tones (2+1+2)</a></div> | |
| <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-5 tones (2+1+2)-2L+3s">2L+3s</a></div> | |
| <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-5 tones (2+1+2)-3L+2s">3L+2s</a></div> | |
| <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-7 tones (3+1+3)">7 tones (3+1+3)</a></div> | |
| <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-7 tones (3+1+3)-2L+5s">2L+5s</a></div> | |
| <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-7 tones (3+1+3)-5L+2s">5L+2s</a></div> | |
| <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-10 tones (4+2+4)">10 tones (4+2+4)</a></div> | |
| <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-5L+5s">5L+5s</a></div> | |
| <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-7L+3s">7L+3s</a></div> | |
| <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-3L+7s">3L+7s</a></div> | |
| <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-2L+8s">2L+8s</a></div> | |
| <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-8L+2s">8L+2s</a></div> | |
| <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-12 tones (5-2-5)">12 tones (5-2-5)</a></div> | |
| <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-5L+7s">5L+7s</a></div> | |
| <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-7L+5s">7L+5s</a></div> | |
| <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-10L+2s">10L+2s</a></div> | |
| <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-2L+10s">2L+10s</a></div> | |
| <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-13 tones (5+3+5)">13 tones (5+3+5)</a></div> | |
| <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-13 tones (5+3+5)-7L+6s">7L+6s</a></div> | |
| <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-14 tones (6+2+6)">14 tones (6+2+6)</a></div> | |
| <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-14 tones (6+2+6)-5L+9s">5L+9s</a></div> | |
| <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-14 tones (6+2+6)-12L+2s">12L+2s</a></div> | |
| <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-15 tones (6+3+6)">15 tones (6+3+6)</a></div> | |
| <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-15 tones (6+3+6)-7L+8s">7L+8s</a></div> | |
| <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-15 tones (6+3+6)-12L+3s">12L+3s</a></div> | |
| <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-17 tones (7+3+7)">17 tones (7+3+7)</a></div> | |
| <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-5L+12s">5L+12s</a></div> | |
| <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-12L+5s">12L+5s</a></div> | |
| <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-7L+10s">7L+10s</a></div> | |
| <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-10L+7s">10L+7s</a></div> | |
| <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-18 tones (7+4+7)">18 tones (7+4+7)</a></div> | |
| <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-18 tones (7+4+7)-7L+11s">7L+11s</a></div> | |
| <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-19 tones (8+3+8)">19 tones (8+3+8)</a></div> | |
| <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-7L+12s">7L+12s</a></div> | |
| <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-12L+7s">12L+7s</a></div> | |
| <!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-5L+14s">5L+14s</a></div> | |
| <!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-14L+5s">14L+5s</a></div> | |
| <!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-22 tones (9+4+9)">22 tones (9+4+9)</a></div> | |
| <!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-7L+15s">7L+15s</a></div>
| |
| <!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-15L+7s">15L+7s</a></div> | |
| <!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-12L+10s">12L+10s</a></div> | |
| <!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-10L+12s">10L+12s</a></div> | |
| <!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><div style="margin-left: 1em;"><a href="#Scales with 3 step sizes">Scales with 3 step sizes</a></div> | |
| <!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><div style="margin-left: 3em;"><a href="#Scales with 3 step sizes--22-tone Indian 'sruti' scale">22-tone Indian 'sruti' scale</a></div>
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| <!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --><div style="margin-left: 1em;"><a href="#Definitions and formulas">Definitions and formulas</a></div>
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| <!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><div style="margin-left: 1em;"><a href="#References">References</a></div>
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| <!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --></div>
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| <!-- ws:end:WikiTextTocRule:184 --><br />
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| An (incomplete) list of <a class="wiki_link" href="/Omnitetrachordality">omnitetrachordal</a> (OTC) scale patterns.<br />
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| <br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc0"><a name="Scales with two step sizes"></a><!-- ws:end:WikiTextHeadingRule:42 -->Scales with two step sizes</h1>
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| (not necessarily <a class="wiki_link" href="/MOS">MOS</a> or <a class="wiki_link" href="/Distributional%20Evenness">DE</a>)<br />
| |
| <a class="wiki_link" href="/Omnitetrachordal%20scale">Omnitetrachordal scales</a> are mostly tempered (irrational) scales. In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit <a class="wiki_link" href="/Just%20intonation">JI</a>) version is possible.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc1"><a name="Scales with two step sizes-5 tones (2+1+2)"></a><!-- ws:end:WikiTextHeadingRule:44 -->5 tones (2+1+2)</h2>
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc2"><a name="Scales with two step sizes-5 tones (2+1+2)-2L+3s"></a><!-- ws:end:WikiTextHeadingRule:46 --><a class="wiki_link" href="/2L%203s">2L+3s</a></h3>
| |
| The familiar classic pentatonic scale. Can include <a class="wiki_link" href="/superpyth">superpyth</a>, <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow">Pythagorean</a>, <a class="wiki_link" href="/meantone">meantone</a>, and <a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">mavila</a> tunings. Is <a class="wiki_link" href="/MOS">MOS</a>. <!-- ws:start:WikiTextVariableComponentRule:03:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:03 --><br />
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| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3890:&lt;a href=&quot;/file/view/05_02_03_sL_s_sL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_05_02_03_sL_s_sL.png/589273922/TN_05_02_03_sL_s_sL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/05_02_03_sL_s_sL.png"><img src="/file/view/TN_05_02_03_sL_s_sL.png/589273922/TN_05_02_03_sL_s_sL.png" alt="TN_05_02_03_sL_s_sL.png" title="TN_05_02_03_sL_s_sL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3890 --><br />
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| <br />
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| Pythagorean (3-limit JI): L=<a class="wiki_link" href="/32_27">32/27</a>, s=9/8<br />
| |
| generator = L+s (480.0 to 600.0 cents)<br />
| |
| <!-- ws:start:WikiTextVariableComponentRule:05:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:05 --> = 1.4424745962<br />
| |
| notable <a class="wiki_link" href="/EDO">EDO</a>s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31<br />
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| <br />
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| modes:<br />
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| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sL s sL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2014L%205s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> Ls s Ls </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2017L%205s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2019L%205s">x</a><br /> |
| <tr>
| |
| <td><tt> s sL sL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> s Ls Ls </tt><br /> | | <td style="text-align: center;"><strong>6</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sL sL s </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> Ls Ls s </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h3&gt; --><h3 id="toc3"><a name="Scales with two step sizes-5 tones (2+1+2)-3L+2s"></a><!-- ws:end:WikiTextHeadingRule:48 --><a class="wiki_link" href="/3L%202s">3L+2s</a></h3>
| |
| Father? MOS; <!-- ws:start:WikiTextVariableComponentRule:07:[[{$page}#perfect|imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">imperfect</a><!-- ws:end:WikiTextVariableComponentRule:07 -->; <!-- ws:start:WikiTextVariableComponentRule:09:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:09 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3892:&lt;a href=&quot;/file/view/05_03_02_Ls_L_Ls.png&quot;&gt;&lt;img src=&quot;/file/view/TN_05_03_02_Ls_L_Ls.png/589273924/TN_05_03_02_Ls_L_Ls.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/05_03_02_Ls_L_Ls.png"><img src="/file/view/TN_05_03_02_Ls_L_Ls.png/589273924/TN_05_03_02_Ls_L_Ls.png" alt="TN_05_03_02_Ls_L_Ls.png" title="TN_05_03_02_Ls_L_Ls.png" /></a><!-- ws:end:WikiTextLocalImageRule:3892 --><br />
| |
| <br />
| |
| generator = L+s (400.0 to 480.0 cents)<br />
| |
| notable EDOs: 8, 11b, 13, 18, 23b<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> Ls L Ls </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%206s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sL L sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> L Ls Ls </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> L sL sL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> Ls Ls L </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sL sL L </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| | </td> |
| | | <td style="text-align: center;"><br /> |
| <br />
| | </td> |
| <br />
| | <td style="text-align: center;"><br /> |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc4"><a name="Scales with two step sizes-7 tones (3+1+3)"></a><!-- ws:end:WikiTextHeadingRule:50 -->7 tones (3+1+3)</h2>
| |
| <br /> | |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc5"><a name="Scales with two step sizes-7 tones (3+1+3)-2L+5s"></a><!-- ws:end:WikiTextHeadingRule:52 --><a class="wiki_link" href="/2L%205s">2L+5s</a></h3>
| |
| <a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">Mavila</a> diatonic MOS. <!-- ws:start:WikiTextVariableComponentRule:011:[[{$page}#perfect|Imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">Imperfect</a><!-- ws:end:WikiTextVariableComponentRule:011 -->. <!-- ws:start:WikiTextVariableComponentRule:013:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:013 --><br /> | |
| <br /> | |
| <!-- ws:start:WikiTextLocalImageRule:3894:&lt;a href=&quot;/file/view/07_02_05_sLs_s_sLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_07_02_05_sLs_s_sLs.png/589273926/TN_07_02_05_sLs_s_sLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/07_02_05_sLs_s_sLs.png"><img src="/file/view/TN_07_02_05_sLs_s_sLs.png/589273926/TN_07_02_05_sLs_s_sLs.png" alt="TN_07_02_05_sLs_s_sLs.png" title="TN_07_02_05_sLs_s_sLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3894 --><br /> | |
| <br />
| |
| generator = L+2s (514.3 to 600.0 cents)<br />
| |
| notable EDOs: 9, 11, 16, 23<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sLs s sLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>7</strong><br /> |
| </td> | | </td> |
| <td><tt> Lss s Lss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%203L%207s">x</a><br /> |
| <tr>
| | </td> |
| <td><tt> s ssL ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%207s">x</a><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%207s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2010L%207s">x</a><br /> |
| <tr>
| |
| <td><tt> s sLs sLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssL ssL s </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%207s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> s Lss Lss </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLs sLs s </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2015L%207s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2017L%207s">x</a><br /> |
| </td> | | </td> |
| <td><tt> Lss Lss s </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> ssL s ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc6"><a name="Scales with two step sizes-7 tones (3+1+3)-5L+2s"></a><!-- ws:end:WikiTextHeadingRule:54 --><a class="wiki_link" href="/5L%202s">5L+2s</a></h3>
| |
| Classic diatonic scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>); MOS. <!-- ws:start:WikiTextVariableComponentRule:015:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:015 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3896:&lt;a href=&quot;/file/view/07_05_02_LsL_L_Ls.png&quot;&gt;&lt;img src=&quot;/file/view/TN_07_05_02_LsL_L_Ls.png/589273928/TN_07_05_02_LsL_L_Ls.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/07_05_02_LsL_L_Ls.png"><img src="/file/view/TN_07_05_02_LsL_L_Ls.png/589273928/TN_07_05_02_LsL_L_Ls.png" alt="TN_07_05_02_LsL_L_Ls.png" title="TN_07_05_02_LsL_L_Ls.png" /></a><!-- ws:end:WikiTextLocalImageRule:3896 --><br />
| |
| <br />
| |
| Pythagorean (3-limit JI): L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a><br />
| |
| P = 2.2600167527<br />
| |
| generator = 2L+s (480.0 to 514.3 cents)<br />
| |
| notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> LLs L LLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Ionian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>8</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%208s">x</a><br /> |
| </td> | | </td> |
| <td><tt> LsL L LsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Dorian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%208s">x</a><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLL L sLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%208s">x</a><br /> |
| </td> | | </td> |
| <td>Phrygian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> L LLs LLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Lydian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> L LsL LsL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLs LLs L </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Mixolydian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> L sLL sLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsL LsL L </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Aeolian<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>9</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLL sLL L </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Locrian<br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%209s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| | </td> |
| | | <td style="text-align: center;"><br /> |
| <br />
| | </td> |
| <br />
| | <td style="text-align: center;"><br /> |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc7"><a name="Scales with two step sizes-10 tones (4+2+4)"></a><!-- ws:end:WikiTextHeadingRule:56 -->10 tones (4+2+4)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h3&gt; --><h3 id="toc8"><a name="Scales with two step sizes-10 tones (4+2+4)-5L+5s"></a><!-- ws:end:WikiTextHeadingRule:58 --><a class="wiki_link" href="/5L%205s">5L+5s</a></h3>
| |
| Blackwood MOS. This omnitetrachordal scale has some unusual properties:<br />
| |
| <ul><li>it has only two modes</li><li>either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)</li><li>it is its own dual (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tuning of 3/2 is independent of L/s ratio (fixed at exactly 720 cents)</li></ul><br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3898:&lt;a href=&quot;/file/view/10_05_05_LsLs_Ls_LsLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_10_05_05_LsLs_Ls_LsLs.png/589273946/TN_10_05_05_LsLs_Ls_LsLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/10_05_05_LsLs_Ls_LsLs.png"><img src="/file/view/TN_10_05_05_LsLs_Ls_LsLs.png/589273946/TN_10_05_05_LsLs_Ls_LsLs.png" alt="TN_10_05_05_LsLs_Ls_LsLs.png" title="TN_10_05_05_LsLs_Ls_LsLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3898 --><br /> | |
| <br /> | |
| generator = s (0 to 120 cents)<br />
| |
| <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/5 octave<br /> | |
| notable EDOs: 15, 20, 25<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> Ls LsLs LsLs </tt><br />
| |
| </td> | | </td> |
| <td><tt> LsLs Ls LsLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLs LsLs Ls </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2010L%209s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL sLsL sLsL </tt><br /> | |
| </td> | | </td> |
| <td><tt> sLsL sL sLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsL sLsL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc9"><a name="Scales with two step sizes-10 tones (4+2+4)-7L+3s"></a><!-- ws:end:WikiTextHeadingRule:60 --><a class="wiki_link" href="/7L%203s">7L+3s</a></h3>
| |
| <a class="wiki_link" href="/Mohajira">Mohajira</a> / <a class="wiki_link" href="/Neutral%20third%20scales">neutral-thirds</a> <a class="wiki_link" href="/MODMOS">MODMOS</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3900:&lt;a href=&quot;/file/view/10_07_03_sLLL_sL_sLLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_10_07_03_sLLL_sL_sLLL.png/589273948/TN_10_07_03_sLLL_sL_sLLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/10_07_03_sLLL_sL_sLLL.png"><img src="/file/view/TN_10_07_03_sLLL_sL_sLLL.png/589273948/TN_10_07_03_sLLL_sL_sLLL.png" alt="TN_10_07_03_sLLL_sL_sLLL.png" title="TN_10_07_03_sLLL_sL_sLLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3900 --><br />
| |
| <br />
| |
| P = 2.5872804832<br />
| |
| generator = 2L+s (342.9 to 360.0 cents)<br />
| |
| notable EDOs: 17, 24, 27, 31, 41<br />
| |
| <br />
| |
| <tt> sLLsLLsLLL </tt> (MOS)<br />
| |
| <tt> || </tt> <br />
| |
| <tt> sLLLsLsLLL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> LsLL Ls LsLL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2015L%209s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLL sL sLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLs Ls LLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>10</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">x</a><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLsL sL LLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2010s">x</a><br /> |
| <tr>
| | </td> |
| <td><tt> Ls LsLL LsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%2010s">x</a><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2014L%2010s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL sLLL sLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LLLs LLLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLL LsLL Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL LLsL LLsL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLLL sLLL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>11</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td><tt> LLLs LLLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLsL LLsL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2011s">x</a><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h3&gt; --><h3 id="toc10"><a name="Scales with two step sizes-10 tones (4+2+4)-3L+7s"></a><!-- ws:end:WikiTextHeadingRule:62 --><a class="wiki_link" href="/3L%207s">3L+7s</a></h3>
| |
| The <!-- ws:start:WikiTextVariableComponentRule:017:[[{$page}#dual|dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a><!-- ws:end:WikiTextVariableComponentRule:017 --> of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3902:&lt;a href=&quot;/file/view/10_03_07_Lsss_Ls_Lsss.png&quot;&gt;&lt;img src=&quot;/file/view/TN_10_03_07_Lsss_Ls_Lsss.png/589273940/TN_10_03_07_Lsss_Ls_Lsss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/10_03_07_Lsss_Ls_Lsss.png"><img src="/file/view/TN_10_03_07_Lsss_Ls_Lsss.png/589273940/TN_10_03_07_Lsss_Ls_Lsss.png" alt="TN_10_03_07_Lsss_Ls_Lsss.png" title="TN_10_03_07_Lsss_Ls_Lsss.png" /></a><!-- ws:end:WikiTextLocalImageRule:3902 --><br />
| |
| <br />
| |
| notable EDOs: 13, 16b<br />
| |
| <br />
| |
| modes: LsssLsLsss, etc.<br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h3&gt; --><h3 id="toc11"><a name="Scales with two step sizes-10 tones (4+2+4)-2L+8s"></a><!-- ws:end:WikiTextHeadingRule:64 --><a class="wiki_link" href="/2L%208s">2L+8s</a></h3>
| |
| <a class="wiki_link" href="/Pajara">Pajara</a> MODMOS. Best at lower ratios of L/s. <!-- ws:start:WikiTextVariableComponentRule:019:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:019 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3904:&lt;a href=&quot;/file/view/10_02_08_sLss_ss_sLss.png&quot;&gt;&lt;img src=&quot;/file/view/TN_10_02_08_sLss_ss_sLss.png/589273936/TN_10_02_08_sLss_ss_sLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/10_02_08_sLss_ss_sLss.png"><img src="/file/view/TN_10_02_08_sLss_ss_sLss.png/589273936/TN_10_02_08_sLss_ss_sLss.png" alt="TN_10_02_08_sLss_ss_sLss.png" title="TN_10_02_08_sLss_ss_sLss.png" /></a><!-- ws:end:WikiTextLocalImageRule:3904 --><br />
| |
| <br />
| |
| P = 1.8849491924<br />
| |
| generator = s (0 to 120 cents)<br />
| |
| <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
| |
| notable EDOs: 12, 14, 16, 22, 26<br />
| |
| <br />
| |
| <tt> LssssLssss </tt> (MOS)<br />
| |
| <tt> || </tt> <br />
| |
| <tt> LsssssLsss </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sssL ss sssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Standard Pentachordal Minor<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> ssLs ss ssLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLss ss sLss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>Alternate Pentachordal Major<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> Lsss ss Lsss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><br /> |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ss sssL sssL </tt><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> ss ssLs ssLs </tt><br /> | | <td style="text-align: center;"><strong>12</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td>Alternate Pentachordal Minor<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> ss sLss sLss </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%2012s">x</a><br /> |
| </td> | | </td> |
| <td><tt> sssL sssL ss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2012s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> ss Lsss Lsss </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLs ssLs ss </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2010L%2012s">x</a><br /> |
| </td> | | </td> |
| <td>Standard Pentachordal Major<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2012L%2012s">x</a><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLss sLss ss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> Lsss Lsss ss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td>-<br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| (The names of the modes are Paul Erlich's - see <a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">http://lumma.org/tuning/erlich/erlich-decatonic.pdf</a>.)<br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h3&gt; --><h3 id="toc12"><a name="Scales with two step sizes-10 tones (4+2+4)-8L+2s"></a><!-- ws:end:WikiTextHeadingRule:66 --><a class="wiki_link" href="/8L%202s">8L+2s</a></h3>
| |
| The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3906:&lt;a href=&quot;/file/view/10_08_02_LsLL_LL_LsLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_10_08_02_LsLL_LL_LsLL.png/589273954/TN_10_08_02_LsLL_LL_LsLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/10_08_02_LsLL_LL_LsLL.png"><img src="/file/view/TN_10_08_02_LsLL_LL_LsLL.png/589273954/TN_10_08_02_LsLL_LL_LsLL.png" alt="TN_10_08_02_LsLL_LL_LsLL.png" title="TN_10_08_02_LsLL_LL_LsLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3906 --><br />
| |
| <br />
| |
| notable EDOs: 18, 26b<br />
| |
| <br />
| |
| modes: LsLLLLLsLL, etc.<br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc13"><a name="Scales with two step sizes-12 tones (5-2-5)"></a><!-- ws:end:WikiTextHeadingRule:68 -->12 tones (5-2-5)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h3&gt; --><h3 id="toc14"><a name="Scales with two step sizes-12 tones (5-2-5)-5L+7s"></a><!-- ws:end:WikiTextHeadingRule:70 --><a class="wiki_link" href="/5L%207s">5L+7s</a></h3>
| |
| 12-tone MOS of the helmholtz / garibaldi / <a class="wiki_link" href="/Schismatic%20family">schismatic</a> and <a class="wiki_link" href="/superpyth">superpyth</a> temperaments (slightly sharp 3/2). Very usable at any L/s ratio. Many modes may be pentachordally split in two ways.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3908:&lt;a href=&quot;/file/view/12_05_07_sLssL_sL_sLssL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_12_05_07_sLssL_sL_sLssL.png/589273964/TN_12_05_07_sLssL_sL_sLssL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/12_05_07_sLssL_sL_sLssL.png"><img src="/file/view/TN_12_05_07_sLssL_sL_sLssL.png/589273964/TN_12_05_07_sLssL_sL_sLssL.png" alt="TN_12_05_07_sLssL_sL_sLssL.png" title="TN_12_05_07_sLssL_sL_sLssL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3908 --><br />
| |
| <br />
| |
| Pythagorean (3-limit JI): L=2187/2048, s=256/243<br />
| |
| P = 1.2600167527<br />
| |
| generator = 2L+3s (480.0 to 500.0 cents)<br />
| |
| notable EDOs: 17, 22, 27, 29, 41, 53, etc.<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sLsLs sL sLsLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsLs sLsLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LsLss Ls LsLss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>13</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLssL sL sLssL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LssLs Ls LssLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2013s">x</a><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> ssLsL sL ssLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL sLsLs sLsLs </tt><br /> | |
| </td> | | </td> |
| <td><tt> sLsLs Ls sLsLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><tt> Ls LsLss LsLss </tt><br />
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL sLssL sLssL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsLs sLsLs sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LssLs LssLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLss LsLss Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL ssLsL ssLsL </tt><br /> | |
| </td> | | </td> |
| <td><tt> sLssL sL ssLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> Ls sLsLs sLsLs </tt><br /> | | <td style="text-align: center;"><strong>14</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LssLs LssLs Ls </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLsL ssLsL sL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%2014s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:72:&lt;h3&gt; --><h3 id="toc15"><a name="Scales with two step sizes-12 tones (5-2-5)-7L+5s"></a><!-- ws:end:WikiTextHeadingRule:72 --><a class="wiki_link" href="/7L%205s">7L+5s</a></h3>
| |
| 12-tone MOS of the <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/Meantone%20family#Flattone">flattone</a> temperaments (slightly flat 3/2). <!-- ws:start:WikiTextVariableComponentRule:021:[[{$page}#perfect|Imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">Imperfect</a><!-- ws:end:WikiTextVariableComponentRule:021 -->, but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3910:&lt;a href=&quot;/file/view/12_07_05_LsLLs_Ls_LsLLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_12_07_05_LsLLs_Ls_LsLLs.png/589273968/TN_12_07_05_LsLLs_Ls_LsLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/12_07_05_LsLLs_Ls_LsLLs.png"><img src="/file/view/TN_12_07_05_LsLLs_Ls_LsLLs.png/589273968/TN_12_07_05_LsLLs_Ls_LsLLs.png" alt="TN_12_07_05_LsLLs_Ls_LsLLs.png" title="TN_12_07_05_LsLLs_Ls_LsLLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3910 --><br />
| |
| <br />
| |
| generator = 3L+2s (500.0 to 514.3 cents)<br />
| |
| notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> LsLLs Ls LsLLs </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2014s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLsL sL sLLsL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%2010L%2014s">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLsLs Ls LLsLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LsLsL LsLsL </tt><br /> | |
| </td> | | </td> |
| <td><tt> LsLsL sL LsLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><tt> sL sLsLL sLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LsLLs LsLLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLsL LsLsL Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> sL sLLsL sLLsL </tt><br /> | | <td style="text-align: center;"><strong>15</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsLL sLsLL sL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LLsLs LLsLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLLs LsLLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL LsLsL LsLsL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2015s">x</a><br /> |
| </td> | | </td> |
| <td><tt> sLLsL sLLsL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLsLs LLsLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LsLsL Ls LsLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLsL LsLsL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLsLL sL sLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h3&gt; --><h3 id="toc16"><a name="Scales with two step sizes-12 tones (5-2-5)-10L+2s"></a><!-- ws:end:WikiTextHeadingRule:74 --><a class="wiki_link" href="/10L%202s">10L+2s</a></h3>
| |
| <a class="wiki_link" href="/Pajara">Pajara</a> MODMOS. Good for most any ratio of L to s.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3912:&lt;a href=&quot;/file/view/12_10_02_LLsLL_LL_LLsLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_12_10_02_LLsLL_LL_LLsLL.png/589273970/TN_12_10_02_LLsLL_LL_LLsLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/12_10_02_LLsLL_LL_LLsLL.png"><img src="/file/view/TN_12_10_02_LLsLL_LL_LLsLL.png/589273970/TN_12_10_02_LLsLL_LL_LLsLL.png" alt="TN_12_10_02_LLsLL_LL_LLsLL.png" title="TN_12_10_02_LLsLL_LL_LLsLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3912 --><br />
| |
| <br />
| |
| P = 1.1300083763<br />
| |
| generator = L (100.0 to 120.0 cents)<br />
| |
| <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
| |
| notable EDOs: 22, 32, 34, 46<br />
| |
| <br />
| |
| <tt> LLLLLsLLLLLs </tt> (MOS)<br />
| |
| <tt> || </tt> <br />
| |
| <tt> LLLLLLsLLLLs </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> LL LLLLs LLLLs </tt><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><tt> LL LLLsL LLLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> LL LLsLL LLsLL </tt><br /> | | <td style="text-align: center;"><strong>16</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLLs LLLLs LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%2016s">x</a><br /> |
| <tr>
| |
| <td><tt> LL LsLLL LsLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLsL LLLsL LL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2016s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LL sLLLL sLLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLsLL LLsLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLLL LsLLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLLLL sLLLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLLs LL LLLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLsL LL LLLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLsLL LL LLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>17</strong><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| <td><tt> LsLLL LL LsLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%2017s">x</a><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sLLLL LL sLLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%207L%2017s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:76:&lt;h3&gt; --><h3 id="toc17"><a name="Scales with two step sizes-12 tones (5-2-5)-2L+10s"></a><!-- ws:end:WikiTextHeadingRule:76 --><a class="wiki_link" href="/2L%2010s">2L+10s</a></h3>
| |
| <!-- ws:start:WikiTextVariableComponentRule:023:[[{$page}#dual|Dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">Dual</a><!-- ws:end:WikiTextVariableComponentRule:023 --> of 10L+2s. Probably only useful for small values of L/s.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3914:&lt;a href=&quot;/file/view/12_02_10_ssLss_ss_ssLss.png&quot;&gt;&lt;img src=&quot;/file/view/TN_12_02_10_ssLss_ss_ssLss.png/589273958/TN_12_02_10_ssLss_ss_ssLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/12_02_10_ssLss_ss_ssLss.png"><img src="/file/view/TN_12_02_10_ssLss_ss_ssLss.png/589273958/TN_12_02_10_ssLss_ss_ssLss.png" alt="TN_12_02_10_ssLss_ss_ssLss.png" title="TN_12_02_10_ssLss_ss_ssLss.png" /></a><!-- ws:end:WikiTextLocalImageRule:3914 --><br />
| |
| <br />
| |
| notable EDOs: 14, 16<br />
| |
| <br />
| |
| modes: ssLssssssLss, etc.<br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc18"><a name="Scales with two step sizes-13 tones (5+3+5)"></a><!-- ws:end:WikiTextHeadingRule:78 -->13 tones (5+3+5)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:80:&lt;h3&gt; --><h3 id="toc19"><a name="Scales with two step sizes-13 tones (5+3+5)-7L+6s"></a><!-- ws:end:WikiTextHeadingRule:80 --><a class="wiki_link" href="/7L%206s">7L+6s</a></h3>
| |
| <a class="wiki_link" href="/Tetracot%20family">Tetracot</a> MODMOS. Best tuned at high values of L/s.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3916:&lt;a href=&quot;/file/view/13_07_06_ssLLL_ssL_ssLLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_13_07_06_ssLLL_ssL_ssLLL.png/589273972/TN_13_07_06_ssLLL_ssL_ssLLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/13_07_06_ssLLL_ssL_ssLLL.png"><img src="/file/view/TN_13_07_06_ssLLL_ssL_ssLLL.png/589273972/TN_13_07_06_ssLLL_ssL_ssLLL.png" alt="TN_13_07_06_ssLLL_ssL_ssLLL.png" title="TN_13_07_06_ssLLL_ssL_ssLLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3916 --><br />
| |
| <br />
| |
| P = 5.1745609664<br />
| |
| generator = L+s (171.4 to 184.6 cents)<br />
| |
| notable EDOs: 20, 27, 34, 41<br />
| |
| <br />
| |
| <tt> sLsLsLsLsLsLL </tt> (MOS) <br />
| |
| <tt> || || || </tt> <br />
| |
| <tt> ssLLLssLssLLL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> Lss LssLL LssLL </tt><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> ssL ssLLL ssLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sLs sLLLs sLLLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Lss LLLss LLLss </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LssLL LssLL Lss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> ssL LLssL LLssL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLLL ssLLL ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLLLs sLLLs sLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>18</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLss LLLss Lss </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLssL LLssL ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LssLL Lss LssLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLLL ssL ssLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLLs sLs sLLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLss Lss LLLss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLssL ssL LLssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc20"><a name="Scales with two step sizes-14 tones (6+2+6)"></a><!-- ws:end:WikiTextHeadingRule:82 -->14 tones (6+2+6)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:84:&lt;h3&gt; --><h3 id="toc21"><a name="Scales with two step sizes-14 tones (6+2+6)-5L+9s"></a><!-- ws:end:WikiTextHeadingRule:84 --><a class="wiki_link" href="/5L%209s">5L+9s</a></h3>
| |
| <a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore / godzilla</a> MODMOS. Usable at any L/s ratio.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3918:&lt;a href=&quot;/file/view/14_05_09_LsssLs_Ls_LsssLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_14_05_09_LsssLs_Ls_LsssLs.png/589273978/TN_14_05_09_LsssLs_Ls_LsssLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/14_05_09_LsssLs_Ls_LsssLs.png"><img src="/file/view/TN_14_05_09_LsssLs_Ls_LsssLs.png/589273978/TN_14_05_09_LsssLs_Ls_LsssLs.png" alt="TN_14_05_09_LsssLs_Ls_LsssLs.png" title="TN_14_05_09_LsssLs_Ls_LsssLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3918 --><br />
| |
| <br />
| |
| P = 3.5200335053<br />
| |
| generator = L+2s (240.0 to 257.1 cents)<br />
| |
| notable EDOs: 19, 24, 29, 33, 34, 53<br />
| |
| <br />
| |
| <tt> ssLssLssLssLsL </tt> (<a class="wiki_link" href="/MOS">MOS</a>)<br />
| |
| <tt> || || </tt><br />
| |
| <tt> sssLsLsssLsLsL </tt> (OTC <a class="wiki_link" href="/MODMOS">MODMOS</a>)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> sL sLsLss sLsLss </tt><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> Ls LsLsss LsLsss </tt><br /> | | <td style="text-align: center;"><strong>19</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sL sLsssL sLsssL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsLss sLsLss sL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%205L%2019s">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls LsssLs LsssLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLsss LsLsss Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><tt> sL sssLsL sssLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsssL sLsssL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Ls ssLsLs ssLsLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsssLs LsssLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sssLsL sssLsL sL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLsLs ssLsLs Ls </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>20</strong><br /> |
| </td> | | </td> |
| <td><tt> sLsLss sL sLsLss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLsss Ls LsLsss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLsssL sL sLsssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LsssLs Ls LsssLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sssLsL sL sssLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> ssLsLs Ls ssLsLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:86:&lt;h3&gt; --><h3 id="toc22"><a name="Scales with two step sizes-14 tones (6+2+6)-12L+2s"></a><!-- ws:end:WikiTextHeadingRule:86 --><a class="wiki_link" href="/12L%202s">12L+2s</a></h3>
| |
| <a class="wiki_link" href="/Injera">Injera</a> MODMOS. Imperfect (P&lt;0); best for L/s &gt;= 1.5 <!-- ws:start:WikiTextVariableComponentRule:025:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:025 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3920:&lt;a href=&quot;/file/view/14_12_02_sLLLLL_LL_sLLLLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_14_12_02_sLLLLL_LL_sLLLLL.png/589273982/TN_14_12_02_sLLLLL_LL_sLLLLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/14_12_02_sLLLLL_LL_sLLLLL.png"><img src="/file/view/TN_14_12_02_sLLLLL_LL_sLLLLL.png/589273982/TN_14_12_02_sLLLLL_LL_sLLLLL.png" alt="TN_14_12_02_sLLLLL_LL_sLLLLL.png" title="TN_14_12_02_sLLLLL_LL_sLLLLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3920 --><br />
| |
| <br />
| |
| generator = L (85.7 to 100.0 cents)<br />
| |
| <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
| |
| notable EDOs: 26, 38, 40, 50<br />
| |
| <br />
| |
| <tt> LLLLLLsLLLLLLs </tt> (MOS)<br />
| |
| <tt> || </tt><br />
| |
| <tt> LLLLLLLsLLLLLs </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> LL LLLLLs LLLLLs </tt><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LL LLLLsL LLLLsL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> LL LLLsLL LLLsLL </tt><br /> | | <td style="text-align: center;"><strong>21</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLLLs LLLLLs LL </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LL LLsLLL LLsLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLLsL LLLLsL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LL LsLLLL LsLLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLLsLL LLLsLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LL sLLLLL sLLLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLsLLL LLsLLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLLLL LsLLLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLLLLL sLLLLL LL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLLLs LL LLLLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLLsL LL LLLLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLsLL LL LLLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>22</strong><br /> |
| </td> | | </td> |
| <td><tt> LLsLLL LL LLsLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LsLLLL LL LsLLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLLLL LL sLLLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc23"><a name="Scales with two step sizes-15 tones (6+3+6)"></a><!-- ws:end:WikiTextHeadingRule:88 -->15 tones (6+3+6)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:90:&lt;h3&gt; --><h3 id="toc24"><a name="Scales with two step sizes-15 tones (6+3+6)-7L+8s"></a><!-- ws:end:WikiTextHeadingRule:90 --><a class="wiki_link" href="/7L%208s">7L+8s</a></h3>
| |
| <a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3922:&lt;a href=&quot;/file/view/15_07_08_ssLsLL_ssL_ssLsLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_15_07_08_ssLsLL_ssL_ssLsLL.png/589273986/TN_15_07_08_ssLsLL_ssL_ssLsLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/15_07_08_ssLsLL_ssL_ssLsLL.png"><img src="/file/view/TN_15_07_08_ssLsLL_ssL_ssLsLL.png/589273986/TN_15_07_08_ssLsLL_ssL_ssLsLL.png" alt="TN_15_07_08_ssLsLL_ssL_ssLsLL.png" title="TN_15_07_08_ssLsLL_ssL_ssLsLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3922 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextVariableComponentRule:027:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:027 --> = 3.3809207248<br />
| |
| generator = L+s (160.0 to 171.4 cents)<br />
| |
| notable EDOs: 22, 29, 36, 37, 43, 65<br />
| |
| <br />
| |
| <tt> LsLsLsLsLsLsLss </tt> (MOS)<br />
| |
| <tt> || || </tt><br />
| |
| <tt> LsLLssLsLLssLss </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> LssLsL Lss LssLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> ssLsLL ssL ssLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> sLsLLs sLs sLsLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LsLLss Lss LsLLss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLssL ssL sLLssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLssLs sLs LLssLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> Lss LssLsL LssLsL </tt><br /> | | <td style="text-align: center;"><strong>23</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><tt> ssL ssLsLL ssLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sLs sLsLLs sLsLLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> Lss LsLLss LsLLss </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LssLsL LssLsL Lss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> ssL sLLssL sLLssL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> ssLsLL ssLsLL ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> sLs LLssLs LLssLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLsLLs sLsLLs sLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLLss LsLLss Lss </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> sLLssL sLLssL ssL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><br /> | | <td style="text-align: center;"><strong>24</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LLssLs LLssLs sLs </tt><br /> | | <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%20ns">x</a><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:92:&lt;h3&gt; --><h3 id="toc25"><a name="Scales with two step sizes-15 tones (6+3+6)-12L+3s"></a><!-- ws:end:WikiTextHeadingRule:92 --><a class="wiki_link" href="/12L%203s">12L+3s</a></h3>
| |
| <a class="wiki_link" href="/Augmented">Augmented</a> MODMOS. Best at higher L/s ratios.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3924:&lt;a href=&quot;/file/view/15_12_03_LLLLLs_LLs_LLLLLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_15_12_03_LLLLLs_LLs_LLLLLs.png/589273990/TN_15_12_03_LLLLLs_LLs_LLLLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/15_12_03_LLLLLs_LLs_LLLLLs.png"><img src="/file/view/TN_15_12_03_LLLLLs_LLs_LLLLLs.png/589273990/TN_15_12_03_LLLLLs_LLs_LLLLLs.png" alt="TN_15_12_03_LLLLLs_LLs_LLLLLs.png" title="TN_15_12_03_LLLLLs_LLs_LLLLLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3924 --><br />
| |
| <br />
| |
| P = 12.5377181246<br />
| |
| generator = L (80.0 to 100.0 cents)<br />
| |
| period = 1/3 octave<br />
| |
| notable EDOs: 27, 39, 51<br />
| |
| <br />
| |
| <tt> LLLLsLLLLsLLLLs </tt> (MOS)<br />
| |
| <tt> || || </tt><br />
| |
| <tt> LLLLLsLLsLLLLLs </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><tt> LLsLLL LLs LLsLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| | </td> |
| | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><tt> LsLLLL LsL LsLLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> sLLLLL sLL sLLLLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLLLs LLs LLLLLs </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLLsL LsL LLLLsL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><br /> | |
| </td> | | </td> |
| <td><tt> LLLsLL sLL LLLsLL </tt><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><br /> |
| <tr>
| |
| <td><tt> LLs LLsLLL LLsLLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td><tt> LsL LsLLLL LsLLLL </tt><br /> | | <td style="text-align: center;"><strong>s</strong><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| | </td> |
| <td><tt> sLL sLLLLL sLLLLL </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><tt> LLs LLLLLs LLLLLs </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><tt> LsL LLLLsL LLLLsL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><tt> LsLLLL LsLLLL LsL </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><tt> sLL LLLsLL LLLsLL </tt><br /> | |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><tt> sLLLLL sLLLLL sLL </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><tt> LLLLLs LLLLLs LLs </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><tt> LLLLsL LLLLsL LsL </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr>
| | <td style="text-align: center;"><tt> </tt><br /> |
| <tr>
| |
| <td><br />
| |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| <td><tt> LLLsLL LLLsLL sLL </tt><br /> | | <td style="text-align: center;"><tt> </tt><br /> |
| | </td> |
| | <td style="text-align: center;"><tt> </tt><br /> |
| </td> | | </td> |
| </tr> | | </tr> |
| Line 2,627: |
Line 1,780: |
|
| |
|
| <br /> | | <br /> |
| | <hr /> |
| | <br /> |
| | <!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc25"><a name="Scales with 3 step sizes"></a><!-- ws:end:WikiTextHeadingRule:76 -->Scales with 3 step sizes</h1> |
| | <ul><li><a class="wiki_link" href="/OTC%2022%20sruti">22-tone Indian 'sruti' scale</a></li></ul><br /> |
| | <hr /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc26"><a name="Scales with two step sizes-17 tones (7+3+7)"></a><!-- ws:end:WikiTextHeadingRule:94 -->17 tones (7+3+7)</h2> | | <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc26"><a name="Definitions and formulas"></a><!-- ws:end:WikiTextHeadingRule:78 -->Definitions and formulas</h1> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:96:&lt;h3&gt; --><h3 id="toc27"><a name="Scales with two step sizes-17 tones (7+3+7)-5L+12s"></a><!-- ws:end:WikiTextHeadingRule:96 --><a class="wiki_link" href="/5L%2012s">5L+12s</a></h3> | | <!-- ws:start:WikiTextAnchorRule:109:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@dual&quot; title=&quot;Anchor: dual&quot;/&gt; --><a name="dual"></a><!-- ws:end:WikiTextAnchorRule:109 --><strong>&quot;Dual&quot;</strong> refers to the &quot;inverse&quot; of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals. If a scale is OTC, its dual is often OTC as well, but not always!<br /> |
| <a class="wiki_link" href="/Superpyth">Superpyth</a> / ultrapyth MOS. Imperfect, best at low L/s. Many modes may be split two ways.<br /> | |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextLocalImageRule:3926:&lt;a href=&quot;/file/view/17_05_12_sssLssL_ssL_sssLssL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_17_05_12_sssLssL_ssL_sssLssL.png/589273994/TN_17_05_12_sssLssL_ssL_sssLssL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/17_05_12_sssLssL_ssL_sssLssL.png"><img src="/file/view/TN_17_05_12_sssLssL_ssL_sssLssL.png/589273994/TN_17_05_12_sssLssL_ssL_sssLssL.png" alt="TN_17_05_12_sssLssL_ssL_sssLssL.png" title="TN_17_05_12_sssLssL_ssL_sssLssL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3926 --><br /> | | <!-- ws:start:WikiTextAnchorRule:110:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@perfect&quot; title=&quot;Anchor: perfect&quot;/&gt; --><a name="perfect"></a><!-- ws:end:WikiTextAnchorRule:110 --><strong>&quot;Perfect&quot;</strong> means that values for L and s exist such that L &gt; s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>.)<br /> |
| <br /> | | <br /> |
| generator = 2L+5s (480.0 to 494.1 cents)<br />
| | In this case the value <strong>P</strong> is given, where P = L/s. For a perfect scale, P &gt; 1. Note that if a scale &quot;a&quot; is perfect (P<span style="vertical-align: sub;">a</span> <!-- ws:start:WikiTextRawRule:00:``=`` -->=<!-- ws:end:WikiTextRawRule:00 --> L/s), its dual &quot;b&quot; will have the value P<span style="vertical-align: sub;">b</span> <!-- ws:start:WikiTextRawRule:01:``=`` -->=<!-- ws:end:WikiTextRawRule:01 --> s/L <!-- ws:start:WikiTextRawRule:02:``=`` -->=<!-- ws:end:WikiTextRawRule:02 --> 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> &gt; 1, then P<span style="vertical-align: sub;">b</span> &lt; 1 ).<br /> |
| notable EDOs: 22, 27, 32, 37, 39<br />
| |
| <br /> | | <br /> |
| modes:<br />
| | In some cases, P may be less than zero. I'm not yet sure what this means :)<br /> |
| | | <br /> |
| | | The value of P is calculated as follows:<br /> |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> Lss LssLsss LssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLsssL ssLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLs ssLssLs ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLsssLs sLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLss sLssLss sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LsssLss LsssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsss LssLsss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs ssLssLs ssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsssLs sLsssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss sLssLss sLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLss LsssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLssL sssLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLs ssL ssLssLs </tt><br />
| |
| </td>
| |
| <td><tt> ssLssLs ssLssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLss sLs sLssLss </tt><br />
| |
| </td>
| |
| <td><tt> sLssLss sLssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsss Lss LssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsssL ssL ssLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsssLs sLs sLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLss Lss LsssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLssL ssL sssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLssL ssL sssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLssLs ssLssLs </tt><br />
| |
| </td>
| |
| <td><tt> ssLssLs sLs ssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLssLss sLssLss </tt><br />
| |
| </td>
| |
| <td><tt> sLssLss Lss sLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:98:&lt;h3&gt; --><h3 id="toc28"><a name="Scales with two step sizes-17 tones (7+3+7)-12L+5s"></a><!-- ws:end:WikiTextHeadingRule:98 --><a class="wiki_link" href="/12L%205s">12L+5s</a></h3>
| |
| Helmholtz / <a class="wiki_link" href="/Schismatic%20family">schismatic</a> MOS; full L/s range very good <!-- ws:start:WikiTextVariableComponentRule:029:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:029 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3928:&lt;a href=&quot;/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png/589274008/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png"><img src="/file/view/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png/589274008/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" alt="TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" title="TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3928 --><br />
| |
| <br />
| |
| Pythagorean (3-limit JI): L=256/243, s=531441/524288<br />
| |
| P = 3.8459060415<br /> | |
| generator = 5L+2s (494.1 to 500.0 cents)<br />
| |
| notable EDOs: 29, 41, 46, 53, 65<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> LLs LLsLLsL LLsLLsL </tt><br />
| |
| </td>
| |
| <td><tt> LLsLLsL LsL LLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLsLL LsLLsLL </tt><br />
| |
| </td>
| |
| <td><tt> LsLLsLL sLL LsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLsLLL sLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLLLs LLsLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsL LLsLLsL LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLLsL LsLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLL LsLLsLL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLLsLL sLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLL sLLsLLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLLsLLs LLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLs LLsLLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LLsLLsL LLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLsL LsLLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL LsLLsLL LsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLsLL sLLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLs LLLsLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsL LLs LLsLLsL </tt><br />
| |
| </td>
| |
| <td><tt> LLsLLsL LLsLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLL LsL LsLLsLL </tt><br />
| |
| </td>
| |
| <td><tt> LsLLsLL LsLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLL sLL sLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLs LLs LLsLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLsL LsL LsLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLsLL sLL sLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLs LLs LLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:100:&lt;h3&gt; --><h3 id="toc29"><a name="Scales with two step sizes-17 tones (7+3+7)-7L+10s"></a><!-- ws:end:WikiTextHeadingRule:100 --><a class="wiki_link" href="/7L%2010s">7L+10s</a></h3>
| |
| <a class="wiki_link" href="/Mohajira">Mohajira</a> / <a class="wiki_link" href="/Neutral%20third%20scales">neutral-thirds</a> MODMOS; full L/s range good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3930:&lt;a href=&quot;/file/view/17_07_10_LssLssL_ssL_LssLssL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_17_07_10_LssLssL_ssL_LssLssL.png/589273998/TN_17_07_10_LssLssL_ssL_LssLssL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/17_07_10_LssLssL_ssL_LssLssL.png"><img src="/file/view/TN_17_07_10_LssLssL_ssL_LssLssL.png/589273998/TN_17_07_10_LssLssL_ssL_LssLssL.png" alt="TN_17_07_10_LssLssL_ssL_LssLssL.png" title="TN_17_07_10_LssLssL_ssL_LssLssL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3930 --><br />
| |
| <br />
| |
| P = 1.5872804832<br />
| |
| generator = 2L+3s (342.9 to 352.9 cents)<br />
| |
| notable EDOs: 24, 31, 41, 65<br />
| |
| <br />
| |
| <tt> ssLsLssLsLssLsLsL </tt> (MOS)<br />
| |
| <tt> || || || </tt><br />
| |
| <tt> ssLLssLssLssLLssL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> Lss LssLssL LssLssL </tt><br />
| |
| </td>
| |
| <td><tt> LssLssL ssL LssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLssLL ssLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLssLLs sLssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LssLLss LssLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLLssL ssLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLL ssLssLL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLLssLs sLLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLLs sLssLLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LLssLss LLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLss LssLLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL LssLssL LssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLssL ssLLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLssLs sLLssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLss LLssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLssL Lss LssLssL </tt><br />
| |
| </td>
| |
| <td><tt> LssLssL LssLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLL ssL ssLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLLs sLs sLssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLss Lss LssLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLssL ssL ssLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLssLs sLs sLLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLss Lss LLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:102:&lt;h3&gt; --><h3 id="toc30"><a name="Scales with two step sizes-17 tones (7+3+7)-10L+7s"></a><!-- ws:end:WikiTextHeadingRule:102 --><a class="wiki_link" href="/10L%207s">10L+7s</a></h3>
| |
| Beatles? / <a class="wiki_link" href="/Dicot%20family">dicot</a>? MODMOS; imperfect; full L/s range mostly good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3932:&lt;a href=&quot;/file/view/17_10_07_sLLsLLs_LLs_sLLsLLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png/589274004/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/17_10_07_sLLsLLs_LLs_sLLsLLs.png"><img src="/file/view/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png/589274004/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" alt="TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" title="TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3932 --><br />
| |
| <br />
| |
| generator = 3L+2s (352.9 to 360.0 cents)<br />
| |
| notable EDOs: 27, 37, 44, 61<br />
| |
| <br />
| |
| <tt> sLsLsLLsLsLLsLsLL </tt> (MOS)<br />
| |
| <tt> || || || </tt><br />
| |
| <tt> ssLLsLLssLLsLLsLL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> sLL sLLsLLs sLLsLLs </tt><br />
| |
| </td>
| |
| <td><tt> sLLsLLs LLs sLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLLss LLsLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLssL LsLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLssLL sLLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLs sLLsLLs sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLssLLs LLssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLss LLsLLss LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LssLLsL LssLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLssL LsLLssL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL ssLLsLL ssLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLssLL sLLssLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs sLLsLLs sLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLLs LLssLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLsL LssLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLsLL ssLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLs sLL sLLsLLs </tt><br />
| |
| </td>
| |
| <td><tt> sLLsLLs sLLsLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLss LLs LLsLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLssL LsL LsLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLssLL sLL sLLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLLs LLs LLssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLsL LsL LssLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLsLL sLL ssLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc31"><a name="Scales with two step sizes-18 tones (7+4+7)"></a><!-- ws:end:WikiTextHeadingRule:104 -->18 tones (7+4+7)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:106:&lt;h3&gt; --><h3 id="toc32"><a name="Scales with two step sizes-18 tones (7+4+7)-7L+11s"></a><!-- ws:end:WikiTextHeadingRule:106 --><a class="wiki_link" href="/7L%2011s">7L+11s</a></h3>
| |
| Sixix?; best for L/s&gt;2<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3934:&lt;a href=&quot;/file/view/18_07_11_sssLsLL_sssL_sssLsLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_18_07_11_sssLsLL_sssL_sssLsLL.png/589274012/TN_18_07_11_sssLsLL_sssL_sssLsLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/18_07_11_sssLsLL_sssL_sssLsLL.png"><img src="/file/view/TN_18_07_11_sssLsLL_sssL_sssLsLL.png/589274012/TN_18_07_11_sssLsLL_sssL_sssLsLL.png" alt="TN_18_07_11_sssLsLL_sssL_sssLsLL.png" title="TN_18_07_11_sssLsLL_sssL_sssLsLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3934 --><br />
| |
| <br />
| |
| P = 5.968201208<br />
| |
| generator = 2L+3s (333.3 to 342.9 cents)<br />
| |
| notable EDOs: 25, 32, 39, 46, 53<br />
| |
| <br />
| |
| <tt> LsLssLsLssLsLssLss </tt> (MOS)<br />
| |
| <tt> || | | || </tt><br />
| |
| <tt> LLsssLsLLsssLsssLs </tt> (OTC MODMOS?)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLsL Lsss LsssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLsLL sssL sssLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLLs ssLs ssLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLss sLss sLsLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsss Lsss LsLLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsssL sssL sLLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsssLs ssLs LLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lsss LsssLsL LsssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sssL sssLsLL sssLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssLs ssLsLLs ssLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLss sLsLLss sLsLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lsss LsLLsss LsLLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLsL LsssLsL Lsss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sssL sLLsssL sLLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLsLL sssLsLL sssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssLs LLsssLs LLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLLs ssLsLLs ssLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLss sLsLLss sLss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsss LsLLsss Lsss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsssL sLLsssL sssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsssLs LLsssLs ssLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:108:&lt;h2&gt; --><h2 id="toc33"><a name="Scales with two step sizes-19 tones (8+3+8)"></a><!-- ws:end:WikiTextHeadingRule:108 -->19 tones (8+3+8)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:110:&lt;h3&gt; --><h3 id="toc34"><a name="Scales with two step sizes-19 tones (8+3+8)-7L+12s"></a><!-- ws:end:WikiTextHeadingRule:110 --><a class="wiki_link" href="/7L%2012s">7L+12s</a></h3>
| |
| <a class="wiki_link" href="/Meantone%20family#Flattone">Flattone</a> MOS; <!-- ws:start:WikiTextVariableComponentRule:031:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:031 -->&lt;0; <!-- ws:start:WikiTextVariableComponentRule:033:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:033 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3936:&lt;a href=&quot;/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png&quot;&gt;&lt;img src=&quot;/file/view/TN_19_07_12_LssLsLss_Lss_LssLsLss.png/589274018/TN_19_07_12_LssLsLss_Lss_LssLsLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png"><img src="/file/view/TN_19_07_12_LssLsLss_Lss_LssLsLss.png/589274018/TN_19_07_12_LssLsLss_Lss_LssLsLss.png" alt="TN_19_07_12_LssLsLss_Lss_LssLsLss.png" title="TN_19_07_12_LssLsLss_Lss_LssLsLss.png" /></a><!-- ws:end:WikiTextLocalImageRule:3936 --><br />
| |
| <br />
| |
| generator = 3L+5s (505.3 to 514.3 cents)<br />
| |
| notable EDOs: 26, 33, 40, 45<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> sLs sLssLssL sLssLssL </tt><br />
| |
| </td>
| |
| <td><tt> sLssLssL ssL sLssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LssLssLs LssLssLs </tt><br />
| |
| </td>
| |
| <td><tt> LssLssLs sLs LssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLssLsL ssLssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLssLsLs sLssLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLssL sLssLssL sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LssLsLss LssLsLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLssLs LssLssLs Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLsLssL ssLsLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLsL ssLssLsL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLsLssLs sLsLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsLs sLssLsLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LsLssLss LsLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsLss LssLsLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL sLssLssL sLssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLssL ssLsLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs LssLssLs LssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLssLs sLsLssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLssLss LsLssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLssL sLs sLssLssL </tt><br />
| |
| </td>
| |
| <td><tt> sLssLssL sLssLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLssLs Lss LssLssLs </tt><br />
| |
| </td>
| |
| <td><tt> LssLssLs LssLssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLsL ssL ssLssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsLs sLs sLssLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsLss Lss LssLsLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLssL ssL ssLsLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLssLs sLs sLsLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLssLss Lss LsLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:112:&lt;h3&gt; --><h3 id="toc35"><a name="Scales with two step sizes-19 tones (8+3+8)-12L+7s"></a><!-- ws:end:WikiTextHeadingRule:112 --><a class="wiki_link" href="/12L%207s">12L+7s</a></h3>
| |
| <a class="wiki_link" href="/Meantone">Meantone</a> MOS; <!-- ws:start:WikiTextVariableComponentRule:035:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:035 -->&lt;0 (oddly, neither this scale nor its <!-- ws:start:WikiTextVariableComponentRule:037:[[{$page}#dual|dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a><!-- ws:end:WikiTextVariableComponentRule:037 --> can be tuned with a perfect 3/2!) <!-- ws:start:WikiTextVariableComponentRule:039:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:039 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3938:&lt;a href=&quot;/file/view/19_12_07_sLLsLsLL_sLL_sLLsLsLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png/589274022/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/19_12_07_sLLsLsLL_sLL_sLLsLsLL.png"><img src="/file/view/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png/589274022/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" alt="TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" title="TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3938 --><br />
| |
| <br />
| |
| generator = 5L+3s (500.0 to 505.3 cents)<br />
| |
| notable EDOs: 31, 43, 50, 55<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> LsL LsLLsLLs LsLLsLLs </tt><br />
| |
| </td>
| |
| <td><tt> LsLLsLLs LLs LsLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLsLLsL sLLsLLsL </tt><br />
| |
| </td>
| |
| <td><tt> sLLsLLsL LsL sLLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLLsLs LLsLLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLsLsL LsLLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLLs LsLLsLLs LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLsLsLL sLLsLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLsL sLLsLLsL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLsLLs LLsLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsLs LLsLLsLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLsLLsL LsLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLsL LsLLsLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLsLLsLL sLsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLsLL sLLsLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LsLLsLLs LsLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLsLLs LLsLsLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL sLLsLLsL sLLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLLsL LsLsLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLsLL sLsLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLLs LsL LsLLsLLs </tt><br />
| |
| </td>
| |
| <td><tt> LsLLsLLs LsLLsLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLsL sLL sLLsLLsL </tt><br />
| |
| </td>
| |
| <td><tt> sLLsLLsL sLLsLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsLs LLs LLsLLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLsL LsL LsLLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLsLL sLL sLLsLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLsLLs LLs LLsLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLLsL LsL LsLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLsLL sLL sLsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:114:&lt;h3&gt; --><h3 id="toc36"><a name="Scales with two step sizes-19 tones (8+3+8)-5L+14s"></a><!-- ws:end:WikiTextHeadingRule:114 --><a class="wiki_link" href="/5L%2014s">5L+14s</a></h3>
| |
| Godzilla? MODMOS; full L/s range good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3940:&lt;a href=&quot;/file/view/19_05_14_ssLssssL_ssL_ssLssssL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_19_05_14_ssLssssL_ssL_ssLssssL.png/589274014/TN_19_05_14_ssLssssL_ssL_ssLssssL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/19_05_14_ssLssssL_ssL_ssLssssL.png"><img src="/file/view/TN_19_05_14_ssLssssL_ssL_ssLssssL.png/589274014/TN_19_05_14_ssLssssL_ssL_ssLssssL.png" alt="TN_19_05_14_ssLssssL_ssL_ssLssssL.png" title="TN_19_05_14_ssLssssL_ssL_ssLssssL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3940 --><br />
| |
| <br />
| |
| P = 2.5200335053<br />
| |
| generator = L+3s (240.0 to 252.6 cents)<br />
| |
| notable EDOs: 24, 29, 34, 39, 43, 53<br />
| |
| <br />
| |
| <tt> sssLsssLsssLsssLssL </tt> (MOS)<br />
| |
| <tt> || || </tt><br />
| |
| <tt> ssLssssLssLssssLssL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> ssL ssLssLss ssLssLss </tt><br />
| |
| </td>
| |
| <td><tt> ssLssLss Lss ssLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLssLsss sLssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LssLssss LssLssss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssLssssL ssLssssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLss ssLssLss ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sLssssLs sLssssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsss sLssLsss sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss LssssLss LssssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLssss LssLssss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssL ssssLssL ssssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssssL ssLssssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLs sssLssLs sssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssssLs sLssssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lss ssLssLss ssLssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssssLss LssssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssssLssL ssssLssL ssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLssLs sssLssLs sLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssLss ssL ssLssLss </tt><br />
| |
| </td>
| |
| <td><tt> ssLssLss ssLssLss Lss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsss sLs sLssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLssss Lss LssLssss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLssssL ssL ssLssssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssssLs sLs sLssssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssssLss Lss LssssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssssLssL ssL ssssLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLssLs sLs sssLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:116:&lt;h3&gt; --><h3 id="toc37"><a name="Scales with two step sizes-19 tones (8+3+8)-14L+5s"></a><!-- ws:end:WikiTextHeadingRule:116 --><a class="wiki_link" href="/14L%205s">14L+5s</a></h3>
| |
| <a class="wiki_link" href="/Semaphore%20and%20godzilla">Semaphore / godzilla</a> MODMOS; imperfect; full L/s range good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3942:&lt;a href=&quot;/file/view/19_14_05_LLsLLLLs_LLs_LLsLLLLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png/589274028/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/19_14_05_LLsLLLLs_LLs_LLsLLLLs.png"><img src="/file/view/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png/589274028/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" alt="TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" title="TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3942 --><br />
| |
| <br />
| |
| generator = 3L+s (252.6 to 257.1 cents)<br />
| |
| notable EDOs: 33, 47, 52<br />
| |
| <br />
| |
| <tt> LLLsLLLsLLLsLLLsLLs </tt> (MOS)<br />
| |
| <tt> || || </tt><br />
| |
| <tt> LLLLsLLsLLLLsLLsLLs </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLLs LLs LLsLLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLLsL LsL LsLLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLLsLL sLL sLLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLLsLLs LLs LLLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLsL LsL LLLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLLsLL LLsLLsLL </tt><br />
| |
| </td>
| |
| <td><tt> LLsLLsLL sLL LLsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLsLLL LsLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLsLLLL sLLsLLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLsLLLLs LLsLLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsLL LLsLLsLL LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LsLLLLsL LsLLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLLL LsLLsLLL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL sLLLLsLL sLLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLLL sLLsLLLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLs LLLLsLLs LLLLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLLs LLsLLLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsL LLLsLLsL LLLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLLsL LsLLLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLL LLsLLsLL LLsLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLLsLL sLLLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLLsLLs LLLLsLLs LLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLsL LLLsLLsL LsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLsLL LLs LLsLLsLL </tt><br />
| |
| </td>
| |
| <td><tt> LLsLLsLL LLsLLsLL sLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLLL LsL LsLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLLLL sLL sLLsLLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:118:&lt;h2&gt; --><h2 id="toc38"><a name="Scales with two step sizes-22 tones (9+4+9)"></a><!-- ws:end:WikiTextHeadingRule:118 -->22 tones (9+4+9)</h2>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:120:&lt;h3&gt; --><h3 id="toc39"><a name="Scales with two step sizes-22 tones (9+4+9)-7L+15s"></a><!-- ws:end:WikiTextHeadingRule:120 --><a class="wiki_link" href="/7L%2015s">7L+15s</a></h3>
| |
| <a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS; full L/s range good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3944:&lt;a href=&quot;/file/view/22_07_15_sssLsssLL_sssL_sssLsssLL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png/589274032/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/22_07_15_sssLsssLL_sssL_sssLsssLL.png"><img src="/file/view/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png/589274032/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" alt="TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" title="TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3944 --><br />
| |
| <br />
| |
| P = 2.3809207248<br />
| |
| generator = L+2s (163.6 to 171.4 cents)<br />
| |
| notable EDOs: 29, 36, 43, 50, 51<br />
| |
| <br />
| |
| <tt> LssLssLssLssLssLssLsss </tt> (MOS)<br />
| |
| <tt> |||| |||| </tt><br />
| |
| <tt> LsssLLsssLsssLLsssLsss </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLsssLL sssL sssLsssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsssLLs ssLs ssLsssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsssLLss sLss sLsssLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLLsss Lsss LsssLLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLLsssL sssL sssLLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLsssLs ssLs ssLLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsssLss sLss sLLsssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsssLsss Lsss LLsssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lsss LsssLsssL LsssLsssL </tt><br />
| |
| </td>
| |
| <td><tt> LsssLsssL sssL LsssLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sssL sssLsssLL sssLsssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssLs ssLsssLLs ssLsssLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLss sLsssLLss sLsssLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lsss LsssLLsss LsssLLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLsssL LsssLsssL Lsss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sssL sssLLsssL sssLLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLsssLL sssLsssLL sssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssLs ssLLsssLs ssLLsssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsssLLs ssLsssLLs ssLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLss sLLsssLss sLLsssLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsssLLss sLsssLLss sLss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Lsss LLsssLsss LLsssLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLLsss LsssLLsss Lsss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sssL LsssLsssL LsssLsssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLLsssL sssLLsssL sssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLsssLs ssLLsssLs ssLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsssLss sLLsssLss sLss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsssLsss LLsssLsss Lsss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsssLsssL Lsss LsssLsssL </tt><br />
| |
| </td>
| |
| <td><tt> LsssLsssL LsssLsssL sssL </tt><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:122:&lt;h3&gt; --><h3 id="toc40"><a name="Scales with two step sizes-22 tones (9+4+9)-15L+7s"></a><!-- ws:end:WikiTextHeadingRule:122 --><a class="wiki_link" href="/15L%207s">15L+7s</a></h3>
| |
| <a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS; imperfect; full L/s range mostly good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3946:&lt;a href=&quot;/file/view/22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png&quot;&gt;&lt;img src=&quot;/file/view/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png/589274046/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png"><img src="/file/view/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png/589274046/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" alt="TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" title="TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" /></a><!-- ws:end:WikiTextLocalImageRule:3946 --><br />
| |
| <br />
| |
| generator = 2L+s (160.0 to 163.6 cents)<br />
| |
| notable EDOs: 37, 52b, 59<br />
| |
| <br />
| |
| <tt> sLLsLLsLLsLLsLLsLLsLLL </tt> (MOS)<br />
| |
| <tt> |||| |||| </tt><br />
| |
| <tt> sLLLssLLLsLLLssLLLsLLL </tt> (OTC MODMOS)<br />
| |
| <br /> | |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLLss LLLs LLLsLLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLssL LLsL LLsLLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLssLL LsLL LsLLLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLssLLL sLLL sLLLssLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLssLLLs LLLs LLLssLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLLLsL LLsL LLssLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLLsLL LsLL LssLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLLsLLL sLLL ssLLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLLL sLLLsLLLs sLLLsLLLs </tt><br />
| |
| </td>
| |
| <td><tt> sLLLsLLLs LLLs sLLLsLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLLs LLLsLLLss LLLsLLLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLsL LLsLLLssL LLsLLLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLL LsLLLssLL LsLLLssLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLLL sLLLssLLL sLLLssLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLsLLLs sLLLsLLLs sLLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLLs LLLssLLLs LLLssLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLsLLLss LLLsLLLss LLLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLsL LLssLLLsL LLssLLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLLLssL LLsLLLssL LLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLL LssLLLsLL LssLLLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLLssLL LsLLLssLL LsLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLLL ssLLLsLLL ssLLLsLLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLssLLL sLLLssLLL sLLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LLLs sLLLsLLLs sLLLsLLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLLssLLLs LLLssLLLs LLLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLssLLLsL LLssLLLsL LLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLLLsLL LssLLLsLL LsLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLLLsLLL ssLLLsLLL sLLL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLLsLLLs sLLL sLLLsLLLs </tt><br />
| |
| </td>
| |
| <td><tt> sLLLsLLLs sLLLsLLLs LLLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:124:&lt;h3&gt; --><h3 id="toc41"><a name="Scales with two step sizes-22 tones (9+4+9)-12L+10s"></a><!-- ws:end:WikiTextHeadingRule:124 --><a class="wiki_link" href="/12L%2010s">12L+10s</a></h3>
| |
| <a class="wiki_link" href="/Pajara">Pajara</a> / <a class="wiki_link" href="/Diaschismic%20family">srutal (diaschismic)</a> MODMOS <!-- ws:start:WikiTextVariableComponentRule:041:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:041 --> <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3948:&lt;a href=&quot;/file/view/22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png&quot;&gt;&lt;img src=&quot;/file/view/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png/589274040/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png"><img src="/file/view/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png/589274040/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" alt="TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" title="TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" /></a><!-- ws:end:WikiTextLocalImageRule:3948 --><br />
| |
| <br />
| |
| P = 7.6918120831<br /> | |
| generator = L+s (100.0 to 109.1 cents)<br />
| |
| period = 1/2 octave<br />
| |
| notable EDOs: 34, 46, 56, 58, 70<br />
| |
| <br />
| |
| <tt> sLsLsLsLsLLsLsLsLsLsLL </tt> (MOS)<br />
| |
| <tt> || </tt><br />
| |
| <tt> sLsLsLsLsLsLLsLsLsLsLL </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> LsLs LsLsLsLsL LsLsLsLsL </tt><br />
| |
| </td>
| |
| <td><tt> LsLsLsLsL sLsL LsLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLsLsLsLL sLsLsLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLsLsLLs LsLsLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLsLsLLsL sLsLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLsLLsLs LsLsLLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLsL LsLsLsLsL LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLsLLsLsL sLsLLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLL sLsLsLsLL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLLsLsLs LsLLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLLs LsLsLsLLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLLsLsLsL sLLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLLsL sLsLsLLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LLsLsLsLs LLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLLsLs LsLsLLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL LsLsLsLsL LsLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLsLsL sLsLLsLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLsLs LsLLsLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLsLsL sLLsLsLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLsLsLs LLsLsLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLsL LsLs LsLsLsLsL </tt><br />
| |
| </td>
| |
| <td><tt> LsLsLsLsL LsLsLsLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLL sLsL sLsLsLsLL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLLs LsLs LsLsLsLLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLLsL sLsL sLsLsLLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLLsLs LsLs LsLsLLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLLsLsL sLsL sLsLLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLLsLsLs LsLs LsLLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLLsLsLsL sLsL sLLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LLsLsLsLs LsLs LLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:126:&lt;h3&gt; --><h3 id="toc42"><a name="Scales with two step sizes-22 tones (9+4+9)-10L+12s"></a><!-- ws:end:WikiTextHeadingRule:126 --><a class="wiki_link" href="/10L%2012s">10L+12s</a></h3>
| |
| Pajara? MODMOS; imperfect; full L/s range good<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:3950:&lt;a href=&quot;/file/view/22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png&quot;&gt;&lt;img src=&quot;/file/view/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png/589274036/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/a&gt; --><a href="/file/view/22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png"><img src="/file/view/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png/589274036/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" alt="TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" title="TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" /></a><!-- ws:end:WikiTextLocalImageRule:3950 --><br />
| |
| <br />
| |
| notable EDOs: 32, 42, 54<br />
| |
| generator = L+s (10.91 to 120.0 cents)<br />
| |
| period = 1/2 octave<br />
| |
| <br />
| |
| <tt> LsLsLsLsLssLsLsLsLsLss </tt> (MOS)<br />
| |
| <tt> || </tt><br />
| |
| <tt> LsLsLsLsLsLssLsLsLsLss </tt> (OTC MODMOS)<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> sLsL sLsLsLsLs sLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLs LsLs sLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLsLsLss LsLsLsLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLsLsLssL sLsLsLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLsLssLs LsLsLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLsLssLsL sLsLssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLs sLsLsLsLs sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LsLssLsLs LsLssLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLss LsLsLsLss LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL sLssLsLsL sLssLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLssL sLsLsLssL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs LssLsLsLs LssLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLssLs LsLsLssLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> sLsL ssLsLsLsL ssLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLssLsL sLsLssLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> LsLs sLsLsLsLs sLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLssLsLs LsLssLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsLsL sLssLsLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsLsLs LssLsLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLsLsL ssLsLsLsL sLsL </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLs sLsL sLsLsLsLs </tt><br />
| |
| </td>
| |
| <td><tt> sLsLsLsLs sLsLsLsLs LsLs </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLsLss LsLs LsLsLsLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLsLssL sLsL sLsLsLssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLsLssLs LsLs LsLsLssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsLssLsL sLsL sLsLssLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LsLssLsLs LsLs LsLssLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLssLsLsL sLsL sLssLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> LssLsLsLs LsLs LssLsLsLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLsLsLsL sLsL ssLsLsLsL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <hr />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:128:&lt;h1&gt; --><h1 id="toc43"><a name="Scales with 3 step sizes"></a><!-- ws:end:WikiTextHeadingRule:128 -->Scales with 3 step sizes</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:130:&lt;h3&gt; --><h3 id="toc44"><a name="Scales with 3 step sizes--22-tone Indian 'sruti' scale"></a><!-- ws:end:WikiTextHeadingRule:130 -->22-tone Indian 'sruti' scale</h3>
| |
| (5-limit <a class="wiki_link" href="/Just%20intonation">JI</a>)<br />
| |
| <br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td style="text-align: center;"><strong>scale step</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>ratio</strong><br />
| |
| </td>
| |
| <td style="text-align: right;"><strong>cents</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">1/1<br />
| |
| </td>
| |
| <td style="text-align: right;">0.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td style="text-align: center;">256/243<br />
| |
| </td>
| |
| <td style="text-align: right;">90.225<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td style="text-align: center;">16/15<br />
| |
| </td>
| |
| <td style="text-align: right;">111.731<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td style="text-align: center;">10/9<br />
| |
| </td>
| |
| <td style="text-align: right;">182.404<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">4<br />
| |
| </td>
| |
| <td style="text-align: center;">9/8<br />
| |
| </td>
| |
| <td style="text-align: right;">203.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td style="text-align: center;">32/27<br />
| |
| </td>
| |
| <td style="text-align: right;">294.135<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td style="text-align: center;">6/5<br />
| |
| </td>
| |
| <td style="text-align: right;">315.641<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td style="text-align: center;">5/4<br />
| |
| </td>
| |
| <td style="text-align: right;">386.314<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td style="text-align: center;">81/64<br />
| |
| </td>
| |
| <td style="text-align: right;">407.820<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9<br />
| |
| </td>
| |
| <td style="text-align: center;">4/3<br />
| |
| </td>
| |
| <td style="text-align: right;">498.045<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10<br />
| |
| </td>
| |
| <td style="text-align: center;">27/20<br />
| |
| </td>
| |
| <td style="text-align: right;">519.551<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11<br />
| |
| </td>
| |
| <td style="text-align: center;">45/32<br />
| |
| </td>
| |
| <td style="text-align: right;">590.224<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">12<br />
| |
| </td>
| |
| <td style="text-align: center;">729/512<br />
| |
| </td>
| |
| <td style="text-align: right;">611.730<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">13<br />
| |
| </td>
| |
| <td style="text-align: center;">3/2<br />
| |
| </td>
| |
| <td style="text-align: right;">701.955<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">14<br />
| |
| </td>
| |
| <td style="text-align: center;">128/81<br />
| |
| </td>
| |
| <td style="text-align: right;">792.180<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">15<br />
| |
| </td>
| |
| <td style="text-align: center;">8/5<br />
| |
| </td>
| |
| <td style="text-align: right;">813.686<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">16<br />
| |
| </td>
| |
| <td style="text-align: center;">5/3<br />
| |
| </td>
| |
| <td style="text-align: right;">884.359<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17<br />
| |
| </td>
| |
| <td style="text-align: center;">27/16<br />
| |
| </td>
| |
| <td style="text-align: right;">905.865<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">18<br />
| |
| </td>
| |
| <td style="text-align: center;">16/9<br />
| |
| </td>
| |
| <td style="text-align: right;">996.090<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19<br />
| |
| </td>
| |
| <td style="text-align: center;">9/5<br />
| |
| </td>
| |
| <td style="text-align: right;">1017.596<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">20<br />
| |
| </td>
| |
| <td style="text-align: center;">15/8<br />
| |
| </td>
| |
| <td style="text-align: right;">1088.269<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">21<br />
| |
| </td>
| |
| <td style="text-align: center;">243/128<br />
| |
| </td>
| |
| <td style="text-align: right;">1109.775<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">22<br />
| |
| </td>
| |
| <td style="text-align: center;">2/1<br />
| |
| </td>
| |
| <td style="text-align: right;">1200.000<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| A = 256/243<br />
| |
| b = 81/80<br />
| |
| c = 25/24<br />
| |
| A+2b+c = 9/8<br />
| |
| 3A+4b+2c = 4/3<br />
| |
| 7A+10b+5c = 2/1<br />
| |
| <br />
| |
| modes:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><tt> Abcb AbcbAbcbA AbcbAbcbA </tt><br />
| |
| </td>
| |
| <td><tt> AbcbAbcbA bcbA AbcbAbcbA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> bcbA bcbAbcbAA bcbAbcbAA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> cbAb cbAbcbAAb cbAbcbAAb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> bAbc bAbcbAAbc bAbcbAAbc </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Abcb AbcbAAbcb AbcbAAbcb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AbcbAbcbA AbcbAbcbA Abcb </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> bcbA bcbAAbcbA bcbAAbcbA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bcbAbcbAA bcbAbcbAA bcbA </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> cbAb cbAAbcbAb cbAAbcbAb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> cbAbcbAAb cbAbcbAAb cbAb </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> bAbc bAAbcbAbc bAAbcbAbc </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bAbcbAAbc bAbcbAAbc bAbc </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> Abcb AAbcbAbcb AAbcbAbcb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AbcbAAbcb AbcbAAbcb Abcb </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> bcbA AbcbAbcbA AbcbAbcbA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bcbAAbcbA bcbAAbcbA bcbA </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> cbAAbcbAb cbAAbcbAb cbAb </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bAAbcbAbc bAAbcbAbc bAbc </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AAbcbAbcb AAbcbAbcb Abcb </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AbcbAbcbA Abcb AbcbAbcbA </tt><br />
| |
| </td>
| |
| <td><tt> AbcbAbcbA AbcbAbcbA bcbA </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bcbAbcbAA bcbA bcbAbcbAA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> cbAbcbAAb cbAb cbAbcbAAb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bAbcbAAbc bAbc bAbcbAAbc </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AbcbAAbcb Abcb AbcbAAbcb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bcbAAbcbA bcbA bcbAAbcbA </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> cbAAbcbAb cbAb cbAAbcbAb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> bAAbcbAbc bAbc bAAbcbAbc </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> AAbcbAbcb Abcb AAbcbAbcb </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <hr />
| |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:132:&lt;h1&gt; --><h1 id="toc45"><a name="Definitions and formulas"></a><!-- ws:end:WikiTextHeadingRule:132 -->Definitions and formulas</h1> | | a <!-- ws:start:WikiTextRawRule:03:``=`` -->=<!-- ws:end:WikiTextRawRule:03 --> the number of L steps per 2/1<br /> |
| | b <!-- ws:start:WikiTextRawRule:04:``=`` -->=<!-- ws:end:WikiTextRawRule:04 --> the number of s steps per 2/1<br /> |
| | c <!-- ws:start:WikiTextRawRule:05:``=`` -->=<!-- ws:end:WikiTextRawRule:05 --> the number of L steps per 4/3<br /> |
| | d <!-- ws:start:WikiTextRawRule:06:``=`` -->=<!-- ws:end:WikiTextRawRule:06 --> the number of s steps per 4/3<br /> |
| | x <!-- ws:start:WikiTextRawRule:07:``=`` -->=<!-- ws:end:WikiTextRawRule:07 --> log<span style="vertical-align: sub;">2</span>(4/3) <!-- ws:start:WikiTextRawRule:08:``=`` -->=<!-- ws:end:WikiTextRawRule:08 --> ~0.41504 octaves <!-- ws:start:WikiTextRawRule:09:``=`` -->=<!-- ws:end:WikiTextRawRule:09 --> ~498.045 cents<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextAnchorRule:185:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@dual&quot; title=&quot;Anchor: dual&quot;/&gt; --><a name="dual"></a><!-- ws:end:WikiTextAnchorRule:185 --><strong>&quot;Dual&quot;</strong> refers to the &quot;inverse&quot; of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals.<br /> | | aL+bs <!-- ws:start:WikiTextRawRule:010:``=`` -->=<!-- ws:end:WikiTextRawRule:010 --> log<span style="vertical-align: sub;">2</span>(2/1) = 1<br /> |
| | cL+ds <!-- ws:start:WikiTextRawRule:011:``=`` -->=<!-- ws:end:WikiTextRawRule:011 --> x<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextAnchorRule:186:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@perfect&quot; title=&quot;Anchor: perfect&quot;/&gt; --><a name="perfect"></a><!-- ws:end:WikiTextAnchorRule:186 --><strong>&quot;Perfect&quot;</strong> means that values for L and s exist such that L &gt; s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>.) In this case the value <strong>&quot;P&quot;</strong> is given, where P = L/s. For a perfect scale, P &gt; 1. Note that if a scale &quot;a&quot; is perfect (P<span style="vertical-align: sub;">a</span> <!-- ws:start:WikiTextRawRule:00:``=`` -->=<!-- ws:end:WikiTextRawRule:00 --> L/s), its dual &quot;b&quot; will have the value P<span style="vertical-align: sub;">b</span> <!-- ws:start:WikiTextRawRule:01:``=`` -->=<!-- ws:end:WikiTextRawRule:01 --> s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> &gt; 1, then P<span style="vertical-align: sub;">b</span> &lt; 1 ).<br /> | | s <!-- ws:start:WikiTextRawRule:012:``=`` -->=<!-- ws:end:WikiTextRawRule:012 --> (c-ax)/(bc-ad)<br /> |
| | L <!-- ws:start:WikiTextRawRule:013:``=`` -->=<!-- ws:end:WikiTextRawRule:013 --> (x-ds)/c<br /> |
| | P <!-- ws:start:WikiTextRawRule:014:``=`` -->=<!-- ws:end:WikiTextRawRule:014 --> L/s<br /> |
| <br /> | | <br /> |
| In some cases, P may be less than zero. I'm not yet sure what this means :)<br />
| | Note that the same procedure could be used to calculate the L/s ratio necessary to give any other just interval, such as 5/4, 11/8, etc.<br /> |
| <br /> | | <br /> |
| The value of P is calculated as follows:<br />
| | <!-- ws:start:WikiTextAnchorRule:111:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Q&quot; title=&quot;Anchor: Q&quot;/&gt; --><a name="Q"></a><!-- ws:end:WikiTextAnchorRule:111 --><strong>Q</strong> is calculated similarly to P, but indicates a limit of sorts -- a point on the L/s continuum beyond which the omnitetrachordality of the scale can be considered to 'break down' in some way.<br /> |
| <br /> | | <br /> |
| a = the number of L steps per 2/1<br />
| | Consider for example the 2L+8s pajara MODMOS, LsssssLsss -- at P <!-- ws:start:WikiTextRawRule:015:``=`` -->=<!-- ws:end:WikiTextRawRule:015 --> L/s <!-- ws:start:WikiTextRawRule:016:``=`` -->=<!-- ws:end:WikiTextRawRule:016 --> 1.885, L+3s forms a just 4/3. As L/s increases, L gets larger and s smaller; at Q <!-- ws:start:WikiTextRawRule:017:``=`` -->=<!-- ws:end:WikiTextRawRule:017 --> L/s <!-- ws:start:WikiTextRawRule:018:``=`` -->=<!-- ws:end:WikiTextRawRule:018 --> 4.827, a just 4/3 is not L+3s, but L+2.5s. Past this point, L+2s will therefore be closer to a just 4/3 than L+3s:<br /> |
| b = the number of s steps per 2/1<br />
| |
| c = the number of L steps per 3/2<br />
| |
| d = the number of s steps per 3/2<br />
| |
| x = log<span style="vertical-align: sub;">2</span>(3/2) = ~0.58496 octaves = ~701.955 cents<br />
| |
| <br /> | | <br /> |
| aL+bs = log<span style="vertical-align: sub;">2</span>(2/1) = 1<br />
| | <!-- ws:start:WikiTextLocalImageRule:1525:&lt;img src=&quot;/file/view/P_Q_C_LsssssLsss.png/590309824/P_Q_C_LsssssLsss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/P_Q_C_LsssssLsss.png/590309824/P_Q_C_LsssssLsss.png" alt="P_Q_C_LsssssLsss.png" title="P_Q_C_LsssssLsss.png" /><!-- ws:end:WikiTextLocalImageRule:1525 --><br /> |
| cL+ds = x<br />
| |
| <br /> | | <br /> |
| s = (c-ax)/(bc-ad)<br />
| | For some scales, Q will not exist. For others, a second Q may exist that is less than P, placing a lower bound on the L/s ratio as well as an upper one.<br /> |
| L = (x-ds)/c<br />
| |
| P = L/s<br /> | |
| <br /> | | <br /> |
| <strong>&quot;L/s range&quot;</strong>: For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as &quot;full L/s range is good&quot; simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's &quot;goodness&quot; is intended.<br /> | | We can also consider a point C, where the number of steps &quot;crosses&quot; the just 4/3 entirely - in the example above, this corresponds to 4/3 <!-- ws:start:WikiTextRawRule:019:``=`` -->=<!-- ws:end:WikiTextRawRule:019 --> L+2s. Q is then halfway between P and C, i.e.<br /> |
| <br /> | | C <!-- ws:start:WikiTextRawRule:020:``=`` -->=<!-- ws:end:WikiTextRawRule:020 --> 2Q-P<br /> |
| <br /> | | Q <!-- ws:start:WikiTextRawRule:021:``=`` -->=<!-- ws:end:WikiTextRawRule:021 --> (C+P)/2<br /> |
| <hr /> | | P <!-- ws:start:WikiTextRawRule:022:``=`` -->=<!-- ws:end:WikiTextRawRule:022 --> 2Q-C<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:134:&lt;h1&gt; --><h1 id="toc46"><a name="References"></a><!-- ws:end:WikiTextHeadingRule:134 -->References</h1> | | ...which leads to the curious result that, although P is undefined when calculated by the normal method (due to division by zero) for a scale such as blackwood[10] (LsLsLsLsLs), C and Q can be calculated, and thus a value of P <!-- ws:start:WikiTextRawRule:023:``=`` -->=<!-- ws:end:WikiTextRawRule:023 --> -1 can be found anyway, even though it seems not to be of any use :)<br /> |
| <br /> | | <br /> |
| <ul><li><!-- ws:start:WikiTextAnchorRule:187:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref1&quot; title=&quot;Anchor: ref1&quot;/&gt; --><a name="ref1"></a><!-- ws:end:WikiTextAnchorRule:187 -->(1) Several of these scales were noted as omnitetrachordal by Paul Erlich in 2002 (if not before). See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html></pre></div> | | <strong>&quot;L/s range&quot;</strong>: For any L+s scale pattern, the ratio L/s may range from 1 (L<!-- ws:start:WikiTextRawRule:024:``=`` -->=<!-- ws:end:WikiTextRawRule:024 -->s, in which case the scale is (L+s)edo ) to ~infinity (s<!-- ws:start:WikiTextRawRule:025:``=`` -->=<!-- ws:end:WikiTextRawRule:025 -->0, in which case the scale is (L)edo ). A note such as &quot;full L/s range is good&quot; simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's &quot;goodness&quot; is intended.</body></html></pre></div> |