Trachytonic

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Screamapillar, the 7-note MODMOS LLmmLLs, and the temperament which characterizes this scale, is also called "trachytonic." It is usually tuned in 17edo (that is, 3322331). It is not a maximally even scale (since seconds, thirds, sixths, and sevenths all come in three rather than two sizes). However, it is notable for being strictly proper, whereas the 17edo diatonic scale is not proper at all, and the 12edo diatonic scale is proper but not strictly so.

The scale can be obtained by a single chromatic modification of the diatonic scale; if we take 17edo's diatonic major (Ionian) mode, and raise the fourth by one step, we get screamapillar. Screamapillar is also one modification away from the rast scale, so it has resemblance to both Western and Middle-Eastern scales. In fact, melodically, it corresponds to the bayati maqam.

The name "screamapillar" comes from an analogy with scorp (as both names are related to arthropod creatures starting with "sc", which in this case is a reference to a character from the Simpsons TV show), and also because the major fourth of 17edo (which functions as 11:8, among others) has a very bright sound as though it is "screaming"'; ambulance sirens often use similar intervals. Timbres where the eleventh harmonic is strong tend to take on a similar character.

The sharpened fourth could also be called a "red note" (opposite of a blue note) due to the mood it creates. Also, the Simpsons theme uses a scale which, although not exactly screamapillar, does contain a sharpened fourth.

The name "trachytonic" comes from the Greek "trachys", meaning "rough".

Because screamapillar is so similar to the diatonic scale, it's not as xen as one might expect a no-fives 13-limit system to be, and as a result it makes a good starting point for someone who wants to explore these higher harmonies without sounding too foreign.

Screamapillar contains five types of tertian (root-third-fifth) triads. These include 2 supermajor, 2 subminor, 1 neutral, 1 neutral-diminished, and 1 subminor-diminished. Of these, the neutral triad is harmonically somewhat rough and so it might be a good idea to modify it, fortunately, there are several options for doing this, such as changing it to a sus2, sus4, or even sus4add2. On the other hand, the neutral-diminished triad is actually very nice sounding since it very closely approximates 9:11:13, and its fifth is still clearly a fifth (albeit a narrow one) rather than being ambiguous like the 12edo tritone.

The subminor and supermajor chords can be harmonically stabilized by adding, respectively, the 4th or the 2nd. This especially makes a difference in the latter case because supermajor triads sound somewhat unstable on their own.

Other high-limit chords and tone clusters can also be realized in screamapillar, including the approximations of 8:9:11:12 (which is like a sus chord but with more tension) and 12:13:14:16:18.

The modes of screamapillar are as follows:

Ionian d7/Mixolydian ‡7: 3 3 1 3 3 2 2

Dorian d6/Aeolian ‡6: 3 1 3 3 2 2 3

Phrygian d5/Locrian ‡5: 1 3 3 2 2 3 3

Lydian d4/Ionian ‡4: 3 3 2 2 3 3 1

Mixolydian d3/Dorian ‡3: 3 2 2 3 3 1 3

Aeolian d2/Dorian ‡2: 2 2 3 3 1 3 3

No clear diatonic equivalent, can be thought of as Lydian d1/Locrian ‡1: 2 3 3 1 3 3 2

As a temperament

What is the temperament that provides the harmonic equivalencies featured in the screamapillar scale? Quite a few commas are tempered out including 64:63, 78:77, 99:98, 144:143, 243:242, etc.

While 17edo itself is an excellent choice for such a temperament, there are other options, notably 61edo, whose version of the screamapillar scale has step pattern 11 11 7 7 11 11 3. 78edo works as well (with step pattern 14 14 9 9 14 14 4); both of these improve the 7th and 13th harmonics at the expense of the 3rd and 11th.

Other options include 44edo and 27edo, although the latter is a borderline case because it doesn't have a very good 11 (it maps 11:8 to 577.78 cents).