Slendric: Difference between revisions
mNo edit summary |
added discussion of extended diatonic categories |
||
| Line 22: | Line 22: | ||
== Intervals == | == Intervals == | ||
=== Interval categories === | |||
It is possible to define the intervals of slendric in terms of diatonic categories, for at three steps is the perfect fifth, and at every three steps further are all of the standard fifth-generated intervals. For the remaining steps, a single pair of inflections suffices: "super"/"sub", which can be abbreviated with the prefixes S and s, respectively. We define the slendric generator to be the supermajor second, and therefore the 2-generator interval is a subfourth (as a major second and a perfect fourth together reach a perfect fifth) as well as a supersupermajor third. Between a major third and perfect fourth is a minor second, which is therefore equivalent to three repetitions of "super" (implying that "super" is rigorously an inflection by the "quark" of 49/48~64/63); because of this equivalence, it is never necessary to attach more than one "super"/"sub" to a diatonic interval. | |||
=== Interval chains === | === Interval chains === | ||
In the following tables, odd harmonics and subharmonics 1–27 are labeled in '''bold'''. | In the following tables, odd harmonics and subharmonics 1–27 are labeled in '''bold'''. | ||
| Line 30: | Line 33: | ||
|- | |- | ||
! # | ! # | ||
! class="unsortable" | Extended diatonic category | |||
! Cents* | ! Cents* | ||
! class="unsortable" | Approximate ratios | ! class="unsortable" | Approximate ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| P1 | |||
| 0.0 | | 0.0 | ||
| '''1/1''' | | '''1/1''' | ||
|- | |- | ||
| 1 | | 1 | ||
| SM2 | |||
| 233.7 | | 233.7 | ||
| '''8/7''' | | '''8/7''' | ||
|- | |- | ||
| 2 | | 2 | ||
| s4 | |||
| 467.5 | | 467.5 | ||
| '''21/16''', 64/49 | | '''21/16''', 64/49 | ||
|- | |- | ||
| 3 | | 3 | ||
| P5 | |||
| 701.2 | | 701.2 | ||
| '''3/2''' | | '''3/2''' | ||
|- | |- | ||
| 4 | | 4 | ||
| SM6 | |||
| 935.0 | | 935.0 | ||
| 12/7 | | 12/7 | ||
|- | |- | ||
| 5 | | 5 | ||
| s8 | |||
| 1168.7 | | 1168.7 | ||
| 63/32, 96/49 | | 63/32, 96/49 | ||
|- | |- | ||
| 6 | | 6 | ||
| M2 | |||
| 202.5 | | 202.5 | ||
| '''9/8''' | | '''9/8''' | ||
|- | |- | ||
| 7 | | 7 | ||
| SM3 | |||
| 436.2 | | 436.2 | ||
| 9/7 | | 9/7 | ||
|- | |- | ||
| 8 | | 8 | ||
| s5 | |||
| 670.0 | | 670.0 | ||
| 72/49 | | 72/49 | ||
|- | |- | ||
| 9 | | 9 | ||
| M6 | |||
| 903.7 | | 903.7 | ||
| '''27/16''' | | '''27/16''' | ||
|- | |- | ||
| 10 | | 10 | ||
| SM7 | |||
| 1137.5 | | 1137.5 | ||
| 27/14 | | 27/14 | ||
|- | |- | ||
| 11 | | 11 | ||
| sM2 | |||
| 171.2 | | 171.2 | ||
| 54/49 | | 54/49 | ||
| Line 90: | Line 106: | ||
|- | |- | ||
| 0 | | 0 | ||
| P1 | |||
| 0.0 | | 0.0 | ||
| '''1/1''' | | '''1/1''' | ||
|- | |- | ||
| −1 | | −1 | ||
| sm7 | |||
| 966.3 | | 966.3 | ||
| '''7/4''' | | '''7/4''' | ||
|- | |- | ||
| −2 | | −2 | ||
| S5 | |||
| 732.5 | | 732.5 | ||
| '''32/21''', 49/32 | | '''32/21''', 49/32 | ||
|- | |- | ||
| −3 | | −3 | ||
| P4 | |||
| 498.8 | | 498.8 | ||
| '''4/3''' | | '''4/3''' | ||
|- | |- | ||
| −4 | | −4 | ||
| sm3 | |||
| 265.0 | | 265.0 | ||
| 7/6 | | 7/6 | ||
|- | |- | ||
| −5 | | −5 | ||
| S1 | |||
| 31.3 | | 31.3 | ||
| 49/48, 64/63 | | 49/48, 64/63 | ||
|- | |- | ||
| −6 | | −6 | ||
| m7 | |||
| 997.5 | | 997.5 | ||
| '''16/9''' | | '''16/9''' | ||
|- | |- | ||
| −7 | | −7 | ||
| sm6 | |||
| 763.8 | | 763.8 | ||
| 14/9 | | 14/9 | ||
|- | |- | ||
| −8 | | −8 | ||
| S4 | |||
| 530.0 | | 530.0 | ||
| 49/36 | | 49/36 | ||
|- | |- | ||
| −9 | | −9 | ||
| m3 | |||
| 296.3 | | 296.3 | ||
| '''32/27''' | | '''32/27''' | ||
|- | |- | ||
| −10 | | −10 | ||
| sm2 | |||
| 62.5 | | 62.5 | ||
| 28/27 | | 28/27 | ||
|- | |- | ||
| −11 | | −11 | ||
| Sm7 | |||
| 1028.8 | | 1028.8 | ||
| 49/27 | | 49/27 | ||