29edo/Unque's compositional approach: Difference between revisions
m grammar |
Expanded functional harmony |
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|5\29 + 12\29 | |5\29 + 12\29 | ||
|G (^)maj, C (v)min | |G (^)maj, C (v)min | ||
|} | |||
Additionally, color can be created by replacing one of the fourths with an upfourth or downfourth: | |||
{| class="wikitable" | |||
|+Quartal Alterations | |||
!Symbol | |||
!Formula | |||
!Rooted | |||
!First Inversion | |||
!Second Inversion | |||
|- | |||
|C<sup>^4</sup> | |||
|13\29 + 12\29 | |||
|C - ^F - ^B♭ | |||
|C - F - vG | |||
|C - vD - G | |||
|- | |||
|C<sup>4</sup> ^7 | |||
|12\29 + 13\29 | |||
|C - F - ^B♭ | |||
|C - ^F - G | |||
|C - vD - vG | |||
|- | |||
|C<sup>v4</sup> | |||
|11\29 + 12\29 | |||
|C - vF - vB♭ | |||
|C - F - ^G | |||
|C - ^D - G | |||
|- | |||
|C<sup>4</sup> v7 | |||
|12\29 + 11\29 | |||
|C - F - vB♭ | |||
|C - vF - G | |||
|C - ^D - ^G | |||
|} | |} | ||
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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 [[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. | ||
{| class="wikitable sortable mw-collapsible" | {| class="wikitable sortable mw-collapsible" | ||
|+ style="font-size: 105%;" |Modes of 5L | |+ style="font-size: 105%;" |Modes of 5L 2s | ||
|- | |- | ||
!Gens Up | !Gens Up | ||
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|} | |} | ||
===5L 7s=== | ===5L 7s=== | ||
The [[5L 7s]] scale is an extension of 5L | The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence. Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes. | ||
{| class="wikitable sortable mw-collapsible" | {| class="wikitable sortable mw-collapsible" | ||
|+ style="font-size: 105%;" |Modes of 5L | |+ style="font-size: 105%;" |Modes of 5L 7s | ||
|- | |- | ||
!Gens Up | !Gens Up | ||
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|5 | |5 | ||
|LLLLLs | |LLLLLs | ||
|C-D-E-F♯-G♯-A♯-C | |C - D - E - F♯ - G♯ - A♯ - C | ||
|Erev | |Erev | ||
|- | |- | ||
|4 | |4 | ||
|LLLLsL | |LLLLsL | ||
|C-D-E-F♯-G♯-B♭-C | |C - D - E - F♯ - G♯ - B♭ -C | ||
|Oplen | |Oplen | ||
|- | |- | ||
|3 | |3 | ||
|LLLsLL | |LLLsLL | ||
|C-D-E-F♯-A♭-B♭-C | |C - D - E - F♯ - A♭ - B♭ - C | ||
|Layla | |Layla | ||
|- | |- | ||
|2 | |2 | ||
|LLsLLL | |LLsLLL | ||
|C-D-E-G♭-A♭-B♭-C | |C - D - E - G♭ - A♭ - B♭ - C | ||
|Shemesh | |Shemesh | ||
|- | |- | ||
|1 | |1 | ||
|LsLLLL | |LsLLLL | ||
|C-D-F♭-G♭-A♭-B♭-C | |C - D - F♭ - G♭ - A♭ - B♭ - C | ||
|Boqer | |Boqer | ||
|- | |- | ||
|0 | |0 | ||
|sLLLLL | |sLLLLL | ||
|C-E𝄫-F♭-G♭-A♭-B♭-C | |C - E𝄫 - F♭ - G♭ - A♭ - B♭ - C | ||
|Tsohorayim | |Tsohorayim | ||
|} | |} | ||
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Useful harmonic progressions may arise in a number of ways depending on the scale being used and depending on what chord the composer wishes to tonicize. Here, I will document some examples of how functional harmonic progressions may be created in the different scales of 29edo, with concepts that can be extended to apply to any scale. | Useful harmonic progressions may arise in a number of ways depending on the scale being used and depending on what chord the composer wishes to tonicize. Here, I will document some examples of how functional harmonic progressions may be created in the different scales of 29edo, with concepts that can be extended to apply to any scale. | ||
Note that I will be constructing these chord progressions | Note that I will be constructing these chord progressions nonlinearly; more specifically, I will begin with a tonic, then find a dominant, and then a predominant, etc. with mediant chords added in between to supplement the harmony if need be. | ||
=== Elements of Functional Harmony === | === Elements of Functional Harmony === | ||
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29edo has three unique types of leading tones: from narrowest to widest, they are the [[Pythagorean comma|diesis]] (1\29), the [[256/243|semitone]] (2\29), and the [[2187/2048|chroma]] (3\29). Of the three, the semitone has the strongest pull; it is narrow enough to create tension (whereas the wider chroma is often more recognizable as a regular melodic small step) while being wide enough to be recognized as a distinct interval (whereas the diesis acts more like an enharmonic alteration of the same note). | 29edo has three unique types of leading tones: from narrowest to widest, they are the [[Pythagorean comma|diesis]] (1\29), the [[256/243|semitone]] (2\29), and the [[2187/2048|chroma]] (3\29). Of the three, the semitone has the strongest pull; it is narrow enough to create tension (whereas the wider chroma is often more recognizable as a regular melodic small step) while being wide enough to be recognized as a distinct interval (whereas the diesis acts more like an enharmonic alteration of the same note). | ||
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 to create a perfect fifth, and two notes a | 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 to create a perfect fifth, and two notes a semifourth apart (23\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. | ||
=== Example: Progression in C Vivecan === | |||
The Vivecan mode of 4L 3s does not contain a perfect fifth over the root, which may make it difficult to root the mode; however, it does contain an upfifth over the root, whereas five of the other six degrees have downfifths instead, so we may be able to create believable resolutions by using harmonic patterns to "convince" ourselves that the upfifth is more resolved than the downfifth. | |||
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). | |||
By noticing that the vA and D also occur in the ''D ^min v5'' supertonic, we can use that triad as a predominant that leads nicely into the vA chord. The movement by an upfourth from the dyad ^F-vA to vB-D creates a pseudo circle-of-fifths rotation, making this progression feel more coherent than it might look at first. | |||
Finally, the ^F and vA of the D chord are shared by the chord ''^F ^min v5'' (with degrees ^F, vA, and C); additionally, the ^F-vA dyad is an upfourth above the C-^E♭ dyad in the tonic chord, which makes the ''^F ^min v5'' chord a logical mediant from the tonic to the predominant. | |||
Thus, our final progression is ''C ^min ^5 - ^F ^min v5 - D ^min v5 - vA vct ^4''. This progression uses a combination of voice leading and circle of fifths movement to create a sound that is both dynamic and functional. | |||