Trachytonic: Difference between revisions

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'''~~Screamapillar''' or '''trachytonic~~''' is the 7-note MODMOS LLmmLLs. 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 [[Rothenberg_propriety|strictly proper]], whereas the 17edo diatonic scale is not proper at all, and the 12edo diatonic scale is proper but not strictly so.

'''Trachytonic''' is the 7-note MODMOS LLmmLLs, which is the pattern of the maqam [[Bayati]] taken as a scale in the context of Western xenharmonic theory. 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 [[Rothenberg_propriety|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 [[Mohajira|rast]] scale, so it has resemblance to both Western and Middle-Eastern scales~~. In fact, melodically, it corresponds to the [http://www.maqamworld.com/maqamat/bayati.html bayati] maqam~~.

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 trachytonic. Trachytonic is also one modification away from the [[Mohajira|rast]] scale, so it has resemblance to both Western and Middle-Eastern scales.

The ~~name~~ "screamapillar" comes from an analogy with [[Scorp|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 scale and its modes have alternative "Simpsonsesque" names by Mason Green, where the scale itself is called "'''screamapillar'''", which comes from an analogy with [[Scorp|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 ''[https://en.wikipedia.org/wiki/The_Simpsons_Theme Simpsons theme]'' uses a scale which, although not exactly screamapillar, does contain a sharpened fourth~~. The name "trachytonic" comes from the Greek "τρᾱχῠ́ς", meaning "rough".

The sharpened fourth could also be called a "red note" (opposite of a blue note) due to the mood it creates. The name "trachytonic" comes from the Greek "τρᾱχῠ́ς", 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.

Because trachytonic 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.

Trachytonic 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 [https://en.wikipedia.org/wiki/Mu_chord 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.

Other high-limit chords and tone clusters can also be realized in trachytonic, 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:

The modes of trachytonic are as follows:

{| class="wikitable"

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=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.

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

While 17edo itself is an excellent choice for such a temperament, there are other options, notably [[61edo|61edo]], whose version of the ~~screamapillar~~ scale has step pattern 11 11 7 7 11 11 3. [[78edo|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.

While 17edo itself is an excellent choice for such a temperament, there are other options, notably [[61edo|61edo]], whose version of the trachytonic scale has step pattern 11 11 7 7 11 11 3. [[78edo|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|44edo]] and [[27edo|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).

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 {{Idiosyncratic terms}}
-'''Screamapillar''' or '''trachytonic''' is the 7-note MODMOS LLmmLLs. 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 [[Rothenberg_propriety|strictly proper]], whereas the 17edo diatonic scale is not proper at all, and the 12edo diatonic scale is proper but not strictly so.
+'''Trachytonic''' is the 7-note MODMOS LLmmLLs, which is the pattern of the maqam [[Bayati]] taken as a scale in the context of Western xenharmonic theory. 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 [[Rothenberg_propriety|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 [[Mohajira|rast]] scale, so it has resemblance to both Western and Middle-Eastern scales. In fact, melodically, it corresponds to the [http://www.maqamworld.com/maqamat/bayati.html bayati] maqam.
+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 trachytonic. Trachytonic is also one modification away from the [[Mohajira|rast]] scale, so it has resemblance to both Western and Middle-Eastern scales.
-The name "screamapillar" comes from an analogy with [[Scorp|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 scale and its modes have alternative "Simpsonsesque" names by Mason Green, where the scale itself is called "'''screamapillar'''", which comes from an analogy with [[Scorp|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 ''[https://en.wikipedia.org/wiki/The_Simpsons_Theme Simpsons theme]'' uses a scale which, although not exactly screamapillar, does contain a sharpened fourth. The name "trachytonic" comes from the Greek "τρᾱχῠ́ς", meaning "rough".
+The sharpened fourth could also be called a "red note" (opposite of a blue note) due to the mood it creates. The name "trachytonic" comes from the Greek "τρᾱχῠ́ς", 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.
+Because trachytonic 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.
+Trachytonic 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 [https://en.wikipedia.org/wiki/Mu_chord 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.
+Other high-limit chords and tone clusters can also be realized in trachytonic, 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:
+The modes of trachytonic are as follows:
 {| class="wikitable"
 |-
@@ Line 39: / Line 39: @@
 =<span style="line-height: 1.5;">As a temperament</span>=
-<span style="line-height: 1.5;">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.</span>
+<span style="line-height: 1.5;">Quite a few commas are tempered out including 64:63, 78:77, 99:98, 144:143, 243:242, etc. in the temperament that provides the harmonic equivalencies featured in the trachytonic scale.</span>
-While 17edo itself is an excellent choice for such a temperament, there are other options, notably [[61edo|61edo]], whose version of the screamapillar scale has step pattern 11 11 7 7 11 11 3. [[78edo|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<span style="line-height: 1.5;"> the 3rd and 11th.</span>
+While 17edo itself is an excellent choice for such a temperament, there are other options, notably [[61edo|61edo]], whose version of the trachytonic scale has step pattern 11 11 7 7 11 11 3. [[78edo|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<span style="line-height: 1.5;"> the 3rd and 11th.</span>
 Other options include [[44edo|44edo]] and [[27edo|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).