SKULO interval names: Difference between revisions
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A capital 'U' signals alteration upward by 33/32, and a lower case 'u' signals alteration downward by 33/32. The alteration is typically applied downward for positive Pythagorean intervals, and upward for negative Pythagorean intervals. | A capital 'U' signals alteration upward by 33/32, and a lower case 'u' signals alteration downward by 33/32. The alteration is typically applied downward for positive Pythagorean intervals, and upward for negative Pythagorean intervals. | ||
11/8 is UP4, and Uber perfect fourth and 11/6 is Um7, and Uber minor seventh. We can also add N/n, the greater and lesser neutrals, where Um is n, and uM is N, so that 11/6 is n7, the lesser neutral 7th, 11/9 is n3, the lesser neutral third, and 27/22 is N3, the greater neutral third. In tunings where the difference between a lessor and greater neutral of the same generic interval, is. 243/242 is tempered out, we can just use 'N' for 'neutral'. | 11/8 is UP4, and Uber perfect fourth and 11/6 is Um7, and Uber minor seventh. We can also add N/n, the greater and lesser neutrals, where Um is n, and uM is N, so that 11/6 is n7, the lesser neutral 7th, 11/9 is n3, the lesser neutral third, and 27/22 is N3, the greater neutral third. In tunings where the difference between a lessor and greater neutral of the same generic interval, is. 243/242 is tempered out, we can just use 'N' for 'neutral'. I also like to use N/n for fourths and fifths, where 11/8 is a (lesser) neutral 4th and 16/11 is a (greater) neutral fifth, but I have used only U4, u5, uA4 and Ud5 instead of n4, N5, N4, and n5 respectively in my edo summaries. | ||
We can use U/u and N to give familiar labels to 17edo, or to label 10edo as a neutral system, i.e., | We can use U/u and N to give familiar labels to 17edo, or to label 10edo as a neutral system, i.e., | ||
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|- | |- | ||
|Um2/n2 | |Um2/n2 | ||
|ubr-min 2nd | |ubr-min 2nd / lsr-ntl 2nd | ||
|uber minor second / lesser neutral second | |uber minor second / lesser neutral second | ||
|88/81 | |88/81 | ||
|- | |- | ||
|uM2/n2 | |uM2/n2 | ||
|unt-maj 2nd | |unt-maj 2nd / gtr-ntl 2nd | ||
|unter major second / greater neutral second | |unter major second / greater neutral second | ||
|12/11 | |12/11 | ||
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|- | |- | ||
|Um3/n3 | |Um3/n3 | ||
|ubr-min 3rd | |ubr-min 3rd / lsr-ntl 3rd | ||
|uber minor third / lesser neutral third | |uber minor third / lesser neutral third | ||
|11/9 | |11/9 | ||
|- | |- | ||
|uM3/N3 | |uM3/N3 | ||
|unt-maj 3rd | |unt-maj 3rd / gtr-ntl 3rd | ||
|unter major third / greater neutral third | |unter major third / greater neutral third | ||
|27/22 | |27/22 | ||
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|- | |- | ||
|U4 | |U4 | ||
|ubr 4th | |ubr 4th (/ lsr-ntl 4th) | ||
|uber fourth | |uber fourth (/ lesser neutral fourth) | ||
|11/8 | |11/8 | ||
|- | |- | ||
|uA4 | |uA4 | ||
|unt-aug 4th | |unt-aug 4th (/ gtr-ntl 4th) | ||
|unter augmented fourth | |unter augmented fourth (/ greater neutral fourth) | ||
|243/176 | |243/176 | ||
|- | |- | ||
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|- | |- | ||
|Ud5 | |Ud5 | ||
|ubr-dim 5th | |ubr-dim 5th (/lsr-ntl 5th) | ||
|uber diminished fifth | |uber diminished fifth (/lesser neutral fifth) | ||
|352/243 | |352/243 | ||
|- | |- | ||
|u5 | |u5 | ||
|unt 5th | |unt 5th (/gtr-ntl 5th) | ||
|unter fifth | |unter fifth (/greater neutral fifth) | ||
|16/11 | |16/11 | ||
|- | |- | ||
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|- | |- | ||
|Um6/n6 | |Um6/n6 | ||
|ubr-min 6th | |ubr-min 6th / lsr-ntl 6th | ||
|uber minor sixth / lesser neutral sixth | |uber minor sixth / lesser neutral sixth | ||
|44/27 | |44/27 | ||
|- | |- | ||
|uM6/N6 | |uM6/N6 | ||
|unt-maj 6th | |unt-maj 6th / gtr-ntl 6th | ||
|unter major sixth / greater neutral sixth | |unter major sixth / greater neutral sixth | ||
|18/11 | |18/11 | ||
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|- | |- | ||
|Um7/n7 | |Um7/n7 | ||
|ubr-min 7th | |ubr-min 7th / lsr-ntl 7th | ||
|uber minor seventh / lesser neutral seventh | |uber minor seventh / lesser neutral seventh | ||
|11/6 | |11/6 | ||
|- | |- | ||
|uM7/N7 | |uM7/N7 | ||
|unt-maj 7th | |unt-maj 7th / gtr-ntl 7th | ||
|unter minor seventh / greater neutral seventh | |unter minor seventh / greater neutral seventh | ||
|81/44 | |81/44 | ||