User:VectorGraphics/16edo theory: Difference between revisions
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Vector's 16edo theory was created for Earth#16. 16edo is an extremely easy equal scale to tune, since it ultimately just requires taking lots of square roots, which can be done by geometric methods. | Vector's 16edo theory was created for [[Beyond the Xenverse|Earth#16]]. 16edo is an extremely easy equal scale to tune, since it ultimately just requires taking lots of square roots, which can be done by geometric methods. | ||
==Introduction: note names and intervals== | ==Introduction: note names and intervals== | ||
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== Staff notation == | == Staff notation == | ||
[[File:Staff 16.png|left|thumb|16edo staff]]This is a 16edo staff. There are 6 lines per staff, to accommodate the size of the decim in scale steps. The treble clef is the same G clef you're familiar with, but the bass clef is a new shape, because it marks the note H below middle C, as opposed to F (according to VQDMN convention for 9-note scales). The C clef is still the same as well | [[File:Staff 16.png|left|thumb|16edo staff]]This is a 16edo staff. There are 6 lines per staff, to accommodate the size of the decim in scale steps. The treble clef is the same G clef you're familiar with, but the bass clef is a new shape, because it marks the note H below middle C, as opposed to F (according to VQDMN convention for 9-note scales). The C clef is still the same as well. | ||
== Functional harmony == | |||
Functional harmony is a system for assigning functions to different triads in a scale. Chords that are separated by a third often have the same function in 12edo; this generalizes to 16edo, where the cycle of mediants is 18 entries long (due to the two options for mediants for each root). | |||
The following table shows the functions for the Ionian nonatonic; more chords are available in Alsatian, however they are not covered here, as the difference between the Alsatian nonatonics is similar to the difference between minor scales in 12edo. | |||
(xxxa = arto, xxx = minor, XXX=major, XXXT = tendo) | |||
{| class="wikitable" | |||
|+ | |||
!Function | |||
!Chords with Alsatian root notes | |||
!Other chords | |||
!Resolves to | |||
|- | |||
|Function 1 | |||
|i, III, *VII | |||
| | |||
|Function 2, Function 5 | |||
|- | |||
|Function 2 | |||
|iiia, VT, *II, v | |||
| | |||
|Function 3 | |||
|- | |||
|Function 3 | |||
|*vii, VIT | |||
|IXMdim, ixadim | |||
|Function 4, Function 5 | |||
|- | |||
|Function 4 | |||
|viii, IT | |||
|iva | |||
|Function 2, Function 5 | |||
|- | |||
|Function 5 | |||
|*ii | |||
|IV | |||
|Function 6 | |||
|- | |||
|Function 6 | |||
|vi, VIII | |||
| | |||
|Function 1 | |||
|} | |||
<nowiki>*</nowiki>A resolution can also be done from a minor chord to its parallel major chord. | |||
Functions 6 and 3 are similar to the dominant, functions 5 and 2 are similar to the subdominant, and functions 4 and 1 are similar to the tonic. | |||
The functional names of notes are the same as in diatonic, except that "mediant" and "submediant" cover 2 pitch classes as opposed to 1. | |||
[[Category:Method]] | [[Category:Method]] | ||
[[Category:Approaches to tuning systems]] | [[Category:Approaches to tuning systems]] | ||