User:Aura/Aura's Ideas on Tonality: Difference between revisions
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This still leaves the matters of what happens when we modify 3-limit Augmented and Diminished intervals by 33/32, what happens when we modify Perfect Fourths and Perfect Fifths by 1331/1296, and, what happens when we either lower Major intervals or raise Minor intervals by 1331/1296. However, we can cover these topics in the next section, as we need to delve even deeper into the 11-limit to cover these intervals on account of their complexity. Before we do that, however, we first need to both take stock of the rules for the current naming system, and compile a list of relatively simple 11-limit intervals which are all classified as Alpharabian intervals, as we have now covered most of the basics for 11-limit interval terminology in this system. Do note that when composite interval terms like "Greater Neutral" are qualified by tuning terms like "Alpharabian", at least in English, the tuning term is inserted between the elements of the interval term, thus, for instance, [[88/81]], the Greater Neutral Second in Alpharabian tuning, is labeled as the "Greater Alpharabian Neutral Second". | This still leaves the matters of what happens when we modify 3-limit Augmented and Diminished intervals by 33/32, what happens when we modify Perfect Fourths and Perfect Fifths by 1331/1296, and, what happens when we either lower Major intervals or raise Minor intervals by 1331/1296. However, we can cover these topics in the next section, as we need to delve even deeper into the 11-limit to cover these intervals on account of their complexity. Before we do that, however, we first need to both take stock of the rules for the current naming system, and compile a list of relatively simple 11-limit intervals which are all classified as Alpharabian intervals, as we have now covered most of the basics for 11-limit interval terminology in this system. Do note that when composite interval terms like "Greater Neutral" are qualified by tuning terms like "Alpharabian", at least in English, the tuning term is inserted between the elements of the interval term, thus, for instance, [[88/81]], the Greater Neutral Second in Alpharabian tuning, is labeled as the "Greater Alpharabian Neutral Second". | ||
(Todo: Add more intervals and columns to the chart, with one extra column containing monzos) | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
| Line 68: | Line 70: | ||
| 53.272943 | | 53.272943 | ||
| Alpharabian Parasuperprime, Alpharabian Parachromatic Quartertone, al-Farabi Quartertone | | Alpharabian Parasuperprime, Alpharabian Parachromatic Quartertone, al-Farabi Quartertone | ||
|- | |||
| [[729/704]] | |||
| 60.412063 | |||
| Alpharabian Parasubaugmented Unison | |||
|- | |||
| [[177147/170368]] | |||
| 67.551182 | |||
| Alpharabian Subaugmented Unison | |||
|- | |- | ||
| [[1089/1024]] | | [[1089/1024]] | ||
| Line 84: | Line 94: | ||
| 97.364115 | | 97.364115 | ||
| Alpharabian Minor Second, Alpharabian Diatonic Semitone | | Alpharabian Minor Second, Alpharabian Diatonic Semitone | ||
|- | |||
| [[21296/19683]] | |||
| 136.358819 | |||
| Alpharabian Supraminor Second | |||
|- | |- | ||
| [[88/81]] | | [[88/81]] | ||
| Line 92: | Line 106: | ||
| 150.637059 | | 150.637059 | ||
| Greater Alpharabian Neutral Second | | Greater Alpharabian Neutral Second | ||
|- | |||
| [[1458/1331]] | |||
| 157.776178 | |||
| Alpharabian Submajor Second | |||
|- | |- | ||
| [[1331/1152]] | | [[1331/1152]] | ||
| Line 112: | Line 130: | ||
| 301.274117 | | 301.274117 | ||
| Alpharabian Minor Third | | Alpharabian Minor Third | ||
|- | |||
| [[2662/2187]] | |||
| 340.268821 | |||
| Alpharabian Supraminor Third | |||
|- | |- | ||
| [[11/9]] | | [[11/9]] | ||
| Line 120: | Line 142: | ||
| 354.547060 | | 354.547060 | ||
| Greater Alpharabian Neutral Third | | Greater Alpharabian Neutral Third | ||
|- | |||
| [[6561/5324]] | |||
| 361.686180 | |||
| Alpharabian Submajor Third | |||
|- | |- | ||
| [[121/96]] | | [[121/96]] | ||
| Line 136: | Line 162: | ||
| 444.772056 | | 444.772056 | ||
| Alpharabian Paraminor Fourth | | Alpharabian Paraminor Fourth | ||
|- | |||
| [[1728/1331]] | |||
| 451.911176 | |||
| Alpharabian Subfourth | |||
|- | |- | ||
| [[11/8]] | | [[11/8]] | ||
| 551.317942 | | 551.317942 | ||
| Alpharabian Paramajor Fourth, Just Paramajor Fourth | | Alpharabian Paramajor Fourth, Just Paramajor Fourth | ||
|- | |||
| [[1331/972]] | |||
| 544.178823 | |||
| Alpharabian Superfourth | |||
|- | |- | ||
| [[363/256]] | | [[363/256]] | ||
| Line 233: | Line 267: | ||
From this particular sample, we can deduce that there are three fundamental premises of the Alpharabian tuning system: | From this particular sample, we can deduce that there are three fundamental premises of the Alpharabian tuning system: | ||
* Intervals that are in the 2.11 subgroup are all considered | * Intervals that are in the 2.11 subgroup are all considered Alpharabian intervals. | ||
* Intervals that result from the modification of a Pythagorean interval by 1089/1024 are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval. | * Intervals that result from the modification of a Pythagorean interval by 1089/1024 are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval. | ||
* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by 33/32 always results in an interval that is considered "Alpharabian". | * Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by 33/32 always results in an interval that is considered "Alpharabian". | ||