Kite's Genchain mode numbering: Difference between revisions

| | sLsL sLL sLsLL

| | sLsL LsL sLsLL

| | sLsL LsL sLLsL

| | sLLs LsL sLLsL

| | sLLs LsL LsLsL

| | LsLs LsL LsLsL

| | LsLs LLs LsLsL

| | ssL ssL sL

| | ssL sL ssL

| | sL ssL ssL

| | sL ssL sL s

| | sL sL ssL s

| | Lss Lss Ls

| | Lss Ls Lss

| | Ls Lss Lss

[[MODMOS scales]] are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone[7] #6 #7. The "#" symbol means moved N steps forwards on the genchain when the generator is chroma-positive, and N steps backwards when it isn't. This ensures a higher pitch. Note that Meantone[5] is chroma-negative. However, an exception is made for superflat edos like 16edo when the generator is a 3/2 fifth, because in those edos, G# is actually flat of G. Another exception is when the generator is close to the "tipping point" between chroma-positive and chroma-negative. A good alternative in these and other situations, including non-heptatonic and non-fifth-generated scales, is to use + for forwards in the genchain and - for backwards, as in 5th Meantone[7] +6 +7.

! | LMs pattern

| | MsMM sLs

| | MsLs sLs

| | sLsM sLs

| | MsLs sMM

| | sLsM sMM

! | LMs pattern

If a rank-2 temperament's [[pergen]] has a split octave, the temperament has multiple genchains running in parallel, using ups and downs. 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 must be complete.

'''[[Srutal]] aka Diaschismatic aka Sagugu''' has a half-8ve period. All five Srutal[10] modes. Every other scale note has a down.

| | 1st Srutal[10]

| | 1st Sagugu[10]

| | 2nd Srutal[10]

| | 2nd Sagugu[10]

| | 3rd Srutal[10]

| | 3rd Sagugu[10]

| | 4th Srutal[10]

| | 4th Sagugu[10]

| | 5th Srutal[10]

| | 5th Sagugu[10]

Srutal's period is written as a vA4, but could instead be written as an ^d5. The generator is written as a P5. If the period is a fraction of an octave, 3/2 is still preferred over 4/3, even though that makes the generator larger than the period. The generator could instead be written as ~16/15 (3/2 minus a period), because that would still create the same mode numbers and thus the same scale names. The first genchain of 1st Srutal[10] would be C C#v D D#v E, just like the first half of the scale.

'''[[Octatonic_scale|Diminished]] aka Quadgu''' has a quarter-8ve period. The generator is ~3/2, which is equivalent to ~5/4 or ~25/24 or even ~9/5. The Diminished[8] scale has only two modes, because there are four very short genchains of only two notes. The comma is fifthward, so the 5th is flattened, and the 32/27 minor 3rd is > 300¢. Therefore the 300¢ period is narrower than a m3, and must be a vm3. The four genchains:

C ---------- G

 

A^ --------- E^

 

F#^^ ------ C#^^

 

C ---------- C#^^

 

 

 

Both Diminished[8] modes, using ups and downs:

! | sL pattern

| | 1st Diminished[8]

| | 1st Quadgu[8]

| | sLsL sLsL

| | 2nd Diminished[8]

|2nd Quadgu[8]

| | LsLs LsLs

[[Blackwood|'''Blackwood''']] '''aka 5-edo+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][10] modes. Ups and downs indicate the generator, not the period. Both Blackwood modes, using ups and downs:

! | sL pattern

| | 1st Blackwood[10]

|1st 5edo+ya[10]

| | 2nd Blackwood[10]

|2nd 5-edo+ya[10]

! | sMLX pattern

| | LLMs MLLM

| | LLMs MLML

| | LMLs MMXM

| | LLMsM LMsM

| | LMLsM MLsM

| | MML MMs

| | MLM MMs

| | MML Xs

| style="text-align:center;" | "

| | MsL sL

!color name

! | sL pattern

| | sL sL ssLs

| | sL sL sssL