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{{Infobox MOS
{{Infobox MOS
|Tuning=5L 3s<15/7>}}The minor ninth of a diatonic scale has a '''5L 3s''' [[MOS]] structure with generators ranging from 2\5 (two degrees of [[5ed15/7]] = 527.8¢) to 3\8 (three degrees of [[8ed15/7]] = 494.8¢). In the case of 8edo, L and s are the same size; in the case of 5ed15/7, s becomes so small it disappears (and all that remains are the five equal L's).
|Tuning=5L 3s<15/7>}}{{MOS intro|Scale Signature=5L 3s<15/7>}}


Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest edIX with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
==Standing assumptions==
==Standing assumptions==
The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.
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|minor 3rd
|minor 3rd
|3\13, 304.487
|3\13, 304.487
|4\18, 293.2095
|4\18, 293.210
|5\21, 314.153
|5\21, 314.153
|Bf
|Bf
Line 241: Line 241:
| rowspan="2" |9\13, 913.460
| rowspan="2" |9\13, 913.460
|13\18, 952.931
|13\18, 952.931
|14\21, 879.6285
|14\21, 879.629
|D
|D
|  +7
|  +7
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|12\18, 879.6285
|12\18, 879.629
|15\21, 942.459
|15\21, 942.459
|Ef
|Ef
Line 341: Line 341:
|minor 3rd
|minor 3rd
|3\13, 304.487
|3\13, 304.487
|4\18, 293.2095
|4\18, 293.210
|7\31, 297.939
|7\31, 297.939
|Bf
|Bf
Line 403: Line 403:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|12\18, 879.6285
|12\18, 879.629
|21\31, 893.816
|21\31, 893.816
|Ef
|Ef
Line 525: Line 525:
|perfect 5th
|perfect 5th
|11\31, 691.137
|11\31, 691.137
|18\34, 698.5285
|18\34, 698.529
|Q
|Q
|3/2
|3/2
Line 538: Line 538:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|14\21, 879.6285
|14\21, 879.629
|23\34, 892.564
|23\34, 892.564
|D
|D
Line 546: Line 546:
|minor 7th
|minor 7th
|15\21, 942.459
|15\21, 942.459
|24\34, 931.3713
|24\34, 931.371
|Ef
|Ef
|12/7
|12/7
Line 592: Line 592:
|s (-5g + 2 minor 9ths)
|s (-5g + 2 minor 9ths)
|3\29, 136.494
|3\29, 136.494
|4\37, 142.6425
|4\37, [[Tel:142.6425|142.6425]]
|}
|}
====Intervals====
====Intervals====
Line 707: Line 707:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 6th
|diminished 6th
|17\29, 773.4665
|17\29, 773.466
|Dff
|Dff
|[[11/7]], [[14/9]]
|[[11/7]], [[14/9]]
Line 713: Line 713:
|-
|-
|minor 6th
|minor 6th
|18\29, 818.9645
|18\29, 818.965
|Df
|Df
|[[13/8]], [[8/5]]
|[[13/8]], [[8/5]]
Line 719: Line 719:
|-
|-
|major 6th
|major 6th
|19\29, 864.4625
|19\29, 864.463
|D
|D
|[[5/3]], [[224/135]]
|[[5/3]], [[224/135]]
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|-
|-
|dim. 4th
|dim. 4th
|6\23, 344.2025
|6\23, 344.202
|Cf
|Cf
|6/5
|6/5
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|L (3g - minor 9th)
|L (3g - minor 9th)
|7/38, 243.055
|7/38, 243.055
|10/53, 248.9515
|10/53, 248.951
|12/63, 251.322
|12/63, 251.322
|231.51
|231.51
Line 977: Line 977:
|1/38, 34.722
|1/38, 34.722
|1/53, 24.895
|1/53, 24.895
|1/63, 20.9345
|1/63, 20.934
|21.05  
|21.05  
|50/49 81/80 91/90
|50/49 81/80 91/90
Line 1,005: Line 1,005:
|2
|2
|7/38, 243.055
|7/38, 243.055
|10/53, 248.9515
|10/53, 248.951
|12/63, 251.322
|12/63, 251.322
|231.51
|231.51
Line 1,013: Line 1,013:
|-
|-
|3
|3
|14\38, 486.1105
|14\38, 486.111
|20\53, 497.903
|20\53, 497.903
|24\63, 502.645
|24\63, 502.645
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