5L 9s: Difference between revisions
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{{Infobox MOS | |||
| Periods = 1 | | Periods = 1 | ||
| nLargeSteps = 5 | | nLargeSteps = 5 | ||
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| Neutralized = 2L 6s | | Neutralized = 2L 6s | ||
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{{MOS intro}} | |||
The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel [[5L_2s|diatonic]] scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a [[meantone]] or [[superpyth]] 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for [[The_Archipelago#Barbados|barbados]] subgroup harmonies. | The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel [[5L_2s|diatonic]] scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a [[meantone]] or [[superpyth]] 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for [[The_Archipelago#Barbados|barbados]] subgroup harmonies. | ||
Revision as of 18:17, 22 February 2024
| ↖ 4L 8s | ↑ 5L 8s | 6L 8s ↗ |
| ← 4L 9s | 5L 9s | 6L 9s → |
| ↙ 4L 10s | ↓ 5L 10s | 6L 10s ↘ |
ssLssLssLssLsL
5L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 9 small steps, repeating every octave. 5L 9s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 942.9 ¢ to 960 ¢, or from 240 ¢ to 257.1 ¢. The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel diatonic scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a meantone or superpyth 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for barbados subgroup harmonies.
| 1/5 | 240 | ||||
| 7/34 | 247.059 | ||||
| 6/29 | 248.276 | ||||
| 11/53 | 249.057 | ||||
| 249.7135 | |||||
| 5/24 | 250 | ||||
| 250.6235 | |||||
| 14/67 | 250.746 | ||||
| 250.865 | |||||
| 9/43 | 251.163 | ||||
| 13/62 | 251.613 | ||||
| 4/19 | 252.632 | ||||
| 15/71 | 253.521 | ||||
| 253.59 | |||||
| 11/52 | 253.846 | ||||
| 254.043 | |||||
| 18/85 | 254.118 | ||||
| 254.24 | |||||
| 7/33 | 254.5455 | ||||
| 17/80 | 255 | ||||
| 10/47 | 255.319 | ||||
| 13/61 | 255.738 | ||||
| 3/14 | 257.143 |