User:Eufalesio/PLIN: Difference between revisions
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Any single region has infinite intervals represented in it, and thus it is important to distinguish the breadth of the buckets any JI interval can fall into. So, while there are an infinite amount of minor thirds, and of superminor thirds, and of qu superminorthirds, and of twomins qu superminor thirds, all of them will 6/5; with 12-PLIN being quite rough, 53-PLIN being very accurate, and 665-PLIN and 7315-PLIN further refining the accuracy to extreme levels to the point where all of those will sound indistinguishable from 6/5, since the difference will be only of 0.16 c per region. | Any single region has infinite intervals represented in it, and thus it is important to distinguish the breadth of the buckets any JI interval can fall into. So, while there are an infinite amount of minor thirds, and of superminor thirds, and of qu superminorthirds, and of twomins qu superminor thirds, all of them will 6/5; with 12-PLIN being quite rough, 53-PLIN being very accurate, and 665-PLIN and 7315-PLIN further refining the accuracy to extreme levels to the point where all of those will sound indistinguishable from 6/5, since the difference will be only of 0.16 c per region. | ||
12-PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. | |||
One glaring design feature about PLINs is the lack of ''neutral'' categories, and of ''augmented'', ''diminished'' and ''perfect''. The reason to avoid those is that for one, true neutral intervals do not exist in integer pythagorean, but even if they did, using this term is unnecessary. 11/9 is commonly called a neutral interval, but it is closer to a minor third. So it is roughly a minor third. More precisely, it is a hyperminor third, at the extreme of minor thirds. Same thing applies to the interordinals like chthonics, naiadics, cocytics and ouranics. You can do fine with using hyper/hypo to refer to them at the edges of the nominals. All of this ''sonically speaking''. | One glaring design feature about PLINs is the lack of ''neutral'' categories, and of ''augmented'', ''diminished'' and ''perfect''. The reason to avoid those is that for one, true neutral intervals do not exist in integer pythagorean, but even if they did, using this term is unnecessary. 11/9 is commonly called a neutral interval, but it is closer to a minor third. So it is roughly a minor third. More precisely, it is a hyperminor third, at the extreme of minor thirds. Same thing applies to the interordinals like chthonics, naiadics, cocytics and ouranics. You can do fine with using hyper/hypo to refer to them at the edges of the nominals. All of this ''sonically speaking''. | ||
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* Mercator commas ([π]mu/[Π]mi) Available in 665-PLIN [sat], functionally only in 53/159-PLIN | * Mercator commas ([π]mu/[Π]mi) Available in 665-PLIN [sat], functionally only in 53/159-PLIN | ||
* Sasktel commas (qu/'''Q'''i) Available in 665-PLIN [sat] | * Sasktel commas (qu/'''Q'''i) Available in 665-PLIN [sat] | ||
* Sasktel comma elevenths ([0~5]plus/[0~5]-minus) Available '''only''' in 7315-PLIN [spot | * Sasktel comma elevenths ([0~5]plus/[0~5]-minus) Available '''only''' in 7315-PLIN [spot | ||
The choice of giving no center descriptor to 53-PLIN is that I believe that for the average xennie, 53 regions is precise enough to accurately name most intervals, and simple enough that the regions cannot be confused. | The choice of giving no center descriptor to 53-PLIN is that I believe that for the average xennie, 53 regions is precise enough to accurately name most intervals, and simple enough that the regions cannot be confused. | ||
Of course, the names would have many synonyms, so hypo/hyper = infra/ultra, minor second = limma, major second = tone, unison = prime, major third = ditone. | Of course, the names would have many synonyms, so hypo/hyper = infra/ultra, minor second = limma, major second = tone, unison = prime, major third = ditone. | ||
==== Syntax of a PLIN ==== | |||
* 12-PLIN : rough + diatonic nominal | |||
* 53-PLIN: hypo/sub/∅/super/hyper + diatonic nominal | |||
* 159-PLIN arto/fix/tendo + hypo/sub/∅/super/hyper + diatonic nominal | |||
* 665-PLIN [∅/qi/qu + [∅/two/three][mi/mu]]/sat + hypo/sub/∅/super/hyper + diatonic nominal | |||
* 7315-PLIN [[∅/two/three/four/five][plus/min(u)s]]/spot+[∅/qi/qu+[∅/two/three][mi/mu]]+hypo/sub/∅/super/hyper+diatonic nominal | |||
{| class="wikitable" | {| class="wikitable" | ||
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!Example 3 | !Example 3 | ||
|- | |- | ||
| | |rough unison | ||
|1r | |1r | ||
|0.000c | |0.000c | ||
| Line 71: | Line 81: | ||
|128/125 | |128/125 | ||
|- | |- | ||
| | |rough minor second | ||
|m2r | |m2r | ||
|90.225c | |90.225c | ||
| Line 80: | Line 90: | ||
|11/10 | |11/10 | ||
|- | |- | ||
| | |rough major second | ||
|M2r | |M2r | ||
|203.91c | |203.91c | ||
| Line 89: | Line 99: | ||
|15/13 | |15/13 | ||
|- | |- | ||
| | |rough minor third | ||
|m3r | |m3r | ||
|294.135c | |294.135c | ||
| Line 98: | Line 108: | ||
|11/9 | |11/9 | ||
|- | |- | ||
| | |rough major third | ||
|M3r | |M3r | ||
|407.82c | |407.82c | ||
| Line 107: | Line 117: | ||
|16/13 | |16/13 | ||
|- | |- | ||
| | |rough fourth | ||
|4r | |4r | ||
|498.045c | |498.045c | ||
| Line 116: | Line 126: | ||
|21/16 | |21/16 | ||
|- | |- | ||
| | |rough tritone | ||
|Tr | |Tr | ||
|611.73c | |611.73c | ||
| Line 125: | Line 135: | ||
|23/16 | |23/16 | ||
|- | |- | ||
| | |rough fifth | ||
|5r | |5r | ||
|701.955c | |701.955c | ||
| Line 134: | Line 144: | ||
|32/21 | |32/21 | ||
|- | |- | ||
| | |rough minor sixth | ||
|m6r | |m6r | ||
|792.18c | |792.18c | ||
| Line 143: | Line 153: | ||
|13/8 | |13/8 | ||
|- | |- | ||
| | |rough major sixth | ||
|M6r | |M6r | ||
|905.865c | |905.865c | ||
| Line 152: | Line 162: | ||
|18/11 | |18/11 | ||
|- | |- | ||
| | |rough minor seventh | ||
|m7r | |m7r | ||
|996.09c | |996.09c | ||
| Line 161: | Line 171: | ||
|11/6 | |11/6 | ||
|- | |- | ||
| | |rough major seventh | ||
|M7r | |M7r | ||
|1109.775c | |1109.775c | ||
| Line 170: | Line 180: | ||
|48/25 | |48/25 | ||
|- | |- | ||
| | |rough octave, counison | ||
|8r, c1r | |8r, c1r | ||
|1200c | |1200c | ||