29edo/Unque's compositional approach: Difference between revisions

!Native Fifths

|A7

|[[Diesis (interval region)|Diesis]]

|d3

|[[Chthonic]]

|[[Extraclassical tonality|Arto]] 3rd

|[[Naiadic]]

|[[Extraclassical tonality|Tendo]] 3rd

|[[Cocytic]]

|Arto 6th

|[[Ouranic]]

|Tendo 6th/arto 7th

|d2

|Tendo 7th

=== Tertian Triads ===

One of the most common types of chord formations in Western music is tertian harmony, where triads are formed by stacking two types of thirds.  In 29edo, this type of structure can be extended to include several types of diesis-altered thirds that are not present in the diatonic scale, which allows for many new colors that were once unavailable.

{| class="wikitable sortable mw-collapsible mw-collapsed"

|+Tertian Triads

!Chord

!Symbol

!Notation

!Formula

!Notes

The [[5L 2s]] scale is generated by taking seven adjacent tones from the Circle of Fifths, just as it is in 12edo.  Melodies and chords made using this scale will sound nearly identical to those that can be made using 12edo.

The [[4L 3s]] scale can be thought of as an alteration of the Harmonic Minor scale, which is unique to 29edo.  If we notice that the augmented second is precisely three steps larger than a major second, we can distribute this error amongst the three semitones that occur in the scale, which reduces the scale to a maximum variety of two.  We may also notice that this scale's pattern creates a circle of augmented seconds, which can be used to quantify the brightness of the seven modes.

The [[4L 5s]] scale takes the role of a diminished scale in 29edo.  Since four minor thirds fall short of the octave, the chain of minor thirds can be extended into this enneatonic form.  Note how the four bright modes resemble the pattern of the familiar octatonic scale, with one of the small steps duplicated, and the four darkest modes resemble the rotated variant of that scale; additionally, there is a symmetrical mode that is entirely new to 29edo.

Similarly to the minor third, the major third of 29edo also does not close at the octave, allowing us to create an octatonic augmented scale.  Just like the diminished scale, notice how the three brightest modes resemble the bright mode of the [[3L 6s|Tcherepnin scale]], with one of the nine steps omitted; the three darkest modes similarly resemble the dark mode of that scale; and the remaining two modes both resemble the symmetrical mode of Tcherepnin.

The first truly unheard-of scale that 29edo pulls off is its approximation of the neutral scale by stacking the downmajor third seven times.  Like 4L 3s, this scale uses harmony based on upfifths and downfifths rather than normal perfect fifths, which makes its harmony more distant from familiar structures.  Just like 5L 3s, it can be compared to the Tcherepnin scale, and as such it relies on augmented triads as its source of harmony; however, this scale pattern removes two of the nine Tcherepnin steps rather than three, reducing it to a more standard heptatonic form.

Just like the thirds, we can notice that the whole tones in 29edo do not close at the octave; instead, we see that five whole tones exceed the minor seventh by an edostep.  However, the octave can still be closed by employing a diminished third to act as a "wolf" version of the whole tone; this leads to the scale having six distinct modes, rather than having an identical pattern on every degree as 12edo had.

=== 5L 4s ===

The [[5L 4s]] scale is the first truly unusual scale in 29edo, being created via a stack of perfect chthonic intervals.  This means that every second interval in the chain will represent an interval from the familiar circle of fifths, whereas each interval between them will be an entirely alien interordinal.

The mode names for this scale are given by [[User:Inthar|Inthar]].

|+Modes of 5L 4s

!Name (Inthar)

|C - D - E - ^E - ^F♯ - G - A - vB♭ - ^B - C

|C - D - ^D - ^E - ^F♯ - G - A - vB♭ - ^B - C

|C - D - ^D - ^E - F - G - A - vB♭ - ^B - C

|C - D - ^D - ^E - F - G - ^G - vB♭ - ^B - C

|C - D - ^D - ^E - F - G - ^G - vB♭ - B♭ - C

|C - ^C - ^D - ^E - F - G - ^G - vB♭ - B♭ - C

|C - ^C - ^D - E♭ - F - G - ^G - vB♭ - B♭ - C

|C - ^C - ^D - E♭ - F - ^F - ^G - vB♭ - B♭ - C

In terms of its harmonies and melodies, [[Nicetone|3L 2M 2s]] acts as a half-way point between 5L 2s and 3L 4s.  The scale is generated using an alternating stack of wide and narrow neutral thirds; as such, the thirds are neutral like 3L 4s, but its fifths are perfect like 5L 2s, which makes it a very interesting extension of ideas from both MOS scales.  Additionally, the wide neutral third is closer to 5/4 than the diatonic major third is (though admittedly not by a lot), which makes the downmajor triad a decent analog to the [[4:5:6]] triad that is so prevalent in 5-limit music.

The [[Blackdye|5L 2M 3s]] scale is an extension of 3L 2M 2s that adds three additional tones, created by inserting a dietic step into each of the large steps, and unifies the two chiralities of the modes.  It can also be constructed using two pentatonic scales of 2L 3s, where the roots of the scales differ by an interval of 4\29; this construction allows us to separate the ten modes into five "acute" modes and five "grave" modes, with the grave modes place the root somewhere in the flatter pentatonic, and the acute modes place the root on the sharper one.

By noticing that the spacer 4\29 differs from the pentatonic large step by a chroma, we can most effectively notate the scale by treating that spacer as a diminished third; while the usage of double-flats in the grave modes and double-sharps in the acute modes makes this notation seem a bit unruly at first, it bypasses the additional ups and downs that would be necessitated if we were to treat the spacer as a downmajor second or an upchroma.

Finally, it is important to recognize certain tense intervals that resolve via contrary motion to certain perfect consonances.  Notably, 14th century composer and theorist [[wikipedia:Marchetto_da_Padova|Marchetto de Padova]] used the interordinal intervals as counterpoint dissonances: two notes a semisixth apart (11\29) can resolve outwards by a chroma (or more accurately, the enharmonically equivalent upminor second) to create a perfect fifth, and two notes a semifourth apart (6\29) can resolve outwards by a chroma to reach a perfect fourth, or outwards to reach a unison.  These paradigms can be reversed to account for the octave complements of those notes.

Firstly, we can notice that vA and vB are separated by a downchthonic, which can resolve by contrary motion to ^G and C; this mimics the perfect chthonic's tendency to resolve to the perfect fifth in a similar fashion.  Thus, we can use the ''vA vct ^4'' chord (with degrees vA, vB, and D) as a useful lead into the ''C ^min ^5'' tonic (with degrees C, ^E♭, and ^G).