Kite's Genchain mode numbering: Difference between revisions
m Internal link format, misc. edit |
m TallKite moved page Genchain mode numbering to Kite's Genchain mode numbering: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me. |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 211: | Line 211: | ||
|} | |} | ||
[[Porcupine]] aka Triyo has a [[pergen]] of (P8, P4/3) and a generator of ~10/9, notated as a vM2 or a ^^m2 using [[ups and downs notation]]. The enharmonic | [[Porcupine]] aka Triyo has a [[pergen]] of (P8, P4/3) and a generator of ~10/9, notated as a vM2 or a ^^m2 using [[ups and downs notation]]. The [[Enharmonic unisons in ups and downs notation|enharmonic unison]] is v<sup>3</sup>A1. Because the generator is a 2nd, the genchain resembles the scale. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 265: | Line 265: | ||
|} | |} | ||
[[Sensi]] aka Sepgu has pergen (P8, ccP5/7). The ~9/7 generator is both a ^<sup>3</sup>d4 and a v<sup>4</sup>A3, and the enharmonic | [[Sensi]] aka Sepgu has pergen (P8, ccP5/7). The ~9/7 generator is both a ^<sup>3</sup>d4 and a v<sup>4</sup>A3, and the [[Enharmonic unisons in ups and downs notation|enharmonic unison]] is ^<sup>7</sup>dd2. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Sensi[8]/Sepgu[8] modes | |+ Sensi[8]/Sepgu[8] modes | ||
| Line 500: | Line 500: | ||
== Temperaments with split octaves == | == Temperaments with split octaves == | ||
If a rank-2 temperament's [[pergen]] has a split octave, the temperament has multiple genchains running in parallel | If a rank-2 temperament's [[pergen]] has a split octave, the temperament has multiple genchains running in parallel. Using ups and downs notation, each genchain has its own height. There is a plain one, an up one, perhaps a down one, etc. In order to be a MOS scale, the parallel genchains must not only be the right length, and without any gaps, but also must line up exactly, so that each note has a neighbor immediately above and/or below. In other words, every column of the lattice generated by the 5th and the up must be complete. The number in the brackets becomes two numbers, and the Ls pattern as written here is grouped by period, using hyphens. | ||
[[Srutal]] aka Diaschismatic aka Sagugu has a half-8ve period of ~45/32. All five Srutal[2x5] modes. Every other scale note has a down. | [[Srutal]] aka Diaschismatic aka Sagugu has a half-8ve period of ~45/32. All five Srutal[2x5] modes. Every other scale note has a down. | ||
| Line 625: | Line 625: | ||
Using ~25/24 as the generator yields the same scales and mode numbers. 1st Diminished[4x2] would have genchains C – ^^C#, vEb – ^E, ^^F# – G and ^A – vBb, just like the scale. | Using ~25/24 as the generator yields the same scales and mode numbers. 1st Diminished[4x2] would have genchains C – ^^C#, vEb – ^E, ^^F# – G and ^A – vBb, just like the scale. | ||
[[Blackwood|'''Blackwood''']] '''aka | [[Blackwood|'''Blackwood''']] '''aka Sawa+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][5x2] modes. Ups and downs indicate the generator, not the period. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 854: | Line 854: | ||
The modes of the sister MOS 3L 5s are the same, just exchange L and s: | The modes of the sister MOS 3L 5s are the same, just exchange L and s: | ||
* 1st | * 1st 3L 5s = ssLssLsL | ||
* 2nd | * 2nd 3L 5s = ssLsLssL | ||
* 3rd | * 3rd 3L 5s = sLssLssL | ||
* etc. | * etc. | ||
For a MOS pattern with a fifth-sized generator, the fifth is still prioritized over the fourth. Otherwise the generator is the mingen. | |||
== Rationale == | == Rationale == | ||