3L 4s: Difference between revisions

[[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme|mos naming scheme]] by [[Graham Breed]]. The name is a contraction of "mohajira-ish".

=== Proposed names ===

The first set of mode nicknames was coined by [[Andrew Heathwaite]]. The other set was coined by [[User:CellularAutomaton|CellularAutomaton]] and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to Heathwaite's names. The third shows which modes are a mixture of which diatonic modes, as discussed in [[#Theory]].

{{MOS modes

| Table Headers=

Mode names<br>(Heathwaite) $

Mode names<br>(CA) $

| Table Entries=

Dalmatian $

Galatian $

Cilician $

Bithynian $

Pisidian $

Illyrian $

Lycian $

}}

* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral third (around 350{{c}}) and two of them make a 3/2 (702{{c}}).

* [[Magic]], in which the generator is 5/4 (386{{c}}) and five of them make a 3/1 (1902{{c}}), though the step ratios in this range are very hard to the point of being lopsided.

3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make mos [[7L&nbsp;3s]] (dicoid); the other scales make mos [[3L&nbsp;7s]] (sephiroid).

[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than {{nowrap| 7\24 {{=}} 350{{c}} }}.

Ultrasoft mosh edos include [[24edo]], [[31edo]], [[38edo]], and [[55edo]].

| L ({{nowrap| 4g − octave }})

| s ({{nowrap| octave − 3g }})

Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than {{nowrap| 5\17 {{=}} 352.94{{c}} }} and flatter than {{nowrap| 8\27 {{=}} 355.56{{c}} }}.

| L ({{nowrap| 4g − octave }})

| s ({{nowrap| octave − 3g }})

Hypohard tunings of mosh have a step ratio between 2 and 3, implying a generator sharper than {{nowrap| 3\10 {{=}} 360{{c}} }} and flatter than {{nowrap| 4\13 {{=}} 369.23{{c}} }}.

The large step ranges from a semifourth to a subminor third in these tunings. The small step is now clearly a semitone, ranging from 1\10 (120{{c}}) to 1\13 (92.31{{c}}).

| L ({{nowrap| 4g − octave }})

| s ({{nowrap| octave − 3g }})

Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than {{nowrap| 5\16 {{=}} 375{{c}} }}. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note mos only has two perfect fifths, so extending the chain to bigger mosses, such as the [[3L&nbsp;7s]] 10-note mos, is suggested for getting 5-limit harmony.

| L ({{nowrap| 4g − octave }})

| s ({{nowrap| octave − 3g }})

* Chroma-positive generator: 342.8571{{c}} (2\7) to 400.0000{{c}} (1\3)

* Chroma-negative generator: 800.0000{{c}} (2\3) to 857.1429{{c}} (5\7)

{{MOS tuning spectrum

| 6/5 = [[Mohaha]] / ptolemy&nbsp;↑

| 5/4 = Mohaha / migration / [[mohajira]]  

| 11/8 = Mohaha / mohamaq  

| 7/5 = Mohaha / [[neutrominant]]  

| 10/7 = [[Hemif]] / [[hemififths]]  

| 11/7 = [[Suhajira]]  

| 13/8 = Golden suhajira (354.8232{{c}})  

| 5/3 = Suhajira / [[ringo]]  

| 12/7 = [[Beatles]]  

| 13/5 = Unnamed golden tuning (366.2564{{c}})  

| 7/2 = [[Sephiroth]]  

| 9/2 = [[Muggles]]  

| 5/1 = [[Magic]]  

| 6/1 = [[Würschmidt]]&nbsp;↓