15edo/Unque's compositional approach: Difference between revisions

|10\15

|G#

|G# = Ab

|-

|-

|12\15

|A# = Bb

|G# = Bb

|13\15

|A#

|A# = Cb

|Bb

|C

|C

|B# = C

|}

Throughout the rest of this page, wherever notation is used, I will directly specify which notation.

Many attempts have been made to categorize the chords that can be made in 15edo.  I have [[User:Unque/15edo-Chords|my own chord organization]] that is most useful for Blackwood structures, but other methods of organization also exist for various other purposes.  The choice between different categorization methods for chords in 15edo depends primarily on which structure you are focusing on, and what kind of modal harmony complements that structure.

In the Porcupine scales, chords are made by stacking intervals of 4, 5, and 6 steps; this provides a 3x3 contrast for chord types, comparable to the three way distinction between Major, Minor, and Suspended in common-practice Western music.

{| class="wikitable"

|+Chords of Porcupine

!Symbol

!Formula

|c°

|4 + 4

|Patdim 2

|15:18:22

|Minor (root position)

|c

|10:12:15

|[[Delta-rational chord|Delta-Rational]]

|Major (first inversion)

|H/C

|Pataug 2

|5:6:8

|-

|Major (root posiion)

|5 + 4

|C - Fb - Hb

|f/c

|6 + 4

|Pataug 4

|15:20:24

|

|-

|F/C

|6 + 5

|Metdim 4

|3:4:5

|C⁴

|6 + 6

|Met 4

|9:12:16

Note that each of these chords is either symmetrical or DR in at least one inversion; no chord has both properties.

15edo supports a plethora of useful scales, each with its own unique character.  While I of course can't detail every scale in the tuning, I will document the ones that I find to be the most important to its structure.

The [[7L 1s]] scale is one of the most popular scales in 15edo, and it is much more versatile than its seeming uniformity would suggest.  William Lynch suggests names for the modes based on sea creatures, with octopus being relevant to the number 8.

{| class="wikitable"

!Step pattern

!Notation (Porcupine)

!I chords

!N/I chords

|<nowiki>7|0</nowiki>

|LLLLLLLs

|Octupus

|c°, C⁴

|LLLLLsLL

|C - D - E - F - G - H - A - B - C

|c°

|F/C

|LLLLsLLL

|C - D - E - F - G - Hb - A - B - C

|c°

|F/C

|}

The [[5L 5s]] scale is another extremely popular scale, due to its relative simplicity and incorporation of useful melodic and harmonic ideas.  It is an example of a mode of limited transposition, which means that certain modes of the scale are just transpositions of the same mode into different keys; for instance, the Bright Mode in the key of C has the same notes as the bright mode in the key of D, but they start on different root pitches.

{| class="wikitable"

|+Modes of 5L5s

!Step Pattern

|-

|Bright

|LsLsLsLsLs

|-

|Dark

|}

The [[4L 3s]] scale, while not nearly as commonly used as the previous two, is another important structural scale.  In this scale, the large step is ''three'' steps of 15edo, rather than two as in the previous scales; as such, the different modes provide much more contrast with one another than in the previous scales.  [[User:Ayceman|Ayceman]] offers to name the seven modes in relation to the Almsivi in Morrowmind (from the Elder Scrolls).  The tonic chord can be made by taking degrees I-III-V, I-III-VI, or I-IV-VI of the scale.

{| class="wikitable"

!Step Pattern

!Notation (Kleismic)

!I-III-V chord

!I-IV-VI chord

|-

|<nowiki>6|0</nowiki>

|LLsLsLs

|Nerevarine

|Pataug 4

|-

|<nowiki>5|1</nowiki>

|Vivecan

|Pataug 2

|-

|<nowiki>4|2</nowiki>

|LsLsLLs

|Lorkhanic

|Patdim2

|sLLsLsL

|C - Db - Eb - F - Gb - A - Bb - C

|Patdim2

|Metdim 2

|sLsLsLL

|C - Db - Eb - Fb - Gb - Ab - Bb - C

|Pat 2

|Pat 3

|}

The [[Nicetone|3L 2M 2s]] scale is often used as an analog to Diatonic in 15edo, as its step pattern resembles that of the Zarlino scale that was historically used as a ternary version of Diatonic that was considered to have more consonant thirds.  Whereas the true Zarlino scale was made by alternating 5/4 and 6/5 as generators, 15edo's 3L2M2s scale can be made by alternating 5\15 and 4\15 generators.  Rather than tempering out the [[81/80|syntonic comma]] (the difference between the two types of whole tone) as in common-practice Western music, 15edo tempers the scale such that the syntonic comma is equal to the semitone.

There are two versions of the 3L 2M 2s scale; the left hand version results when the number of minor third generators outnumber the major third generators, and the right hand version results when the opposite is true.  Each of these versions has seven unique modes.

{| class="wikitable"

|LMLsLMs

|C - D - E - Fx - G - A# - B - C

|-

|<nowiki>5|1</nowiki>

|<nowiki>0|6</nowiki>

|MsLMLsL

|Dorian

|Patdim 1

|LsLMLsM

|C - D - Eb - F# - G - A# - Bb - C

|Pat 2

|-

|Susaug 1

|}