User:Astaryuu/15edo Notes/Scales and modes

15edo is a medium-sized temperament. By this, I mean that it is big enough that the edostep/chromatic scale might be unwieldy (temperaments that do not do this, like 8edo, are often called "macrotonal", because quite frankly, 12edo itself has a somewhat unwieldy chromatic scale), but not big enough that an edostep is noticeably distinct from the semitone (such as 24edo, whose edosteps are small enough that they're typically called "quarter tones"). However, while most medium-sized scales can at least approximate things you may know and love from the favorite temperament of the West, each also has its own flair that makes certain scales more enticing than they would be in 12edo, and also can impart some of that same flair onto the scales that are approximations of the West's favorite scales. This page catalogues some of the scales that work well in 15edo. However, note that basically any set of 15edo notes can create a scale that will be effective if used well. For example, I don't talk about sephiroth, because 15edo cannot approximate it well (due to the hepta- and decatonic versions both using notes very close to odd 30edo intervals), but that could be seen as a feature and not a bug.

15edo "sephiroth[10]"

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For every scale I will be showing an "edobox," like the one you see to the right. This is something I got from Levi McClain's xenharmony videos. Each number represents the number of edosteps (in 15edo, these are semitones, but he typically does work in 31edo, where an edostep is a diesis) you have to go from the root to reach the note we wish to include. The root can be any note in the temperament. While I will be referencing different names for notes in 15edo, these edoboxes abstract the system from any given notation type, since that's a subject for another page.

Suboctave-period scales

Suboctave-period scales have a period of fewer than, in this case, 15 (as the octave is split into 15). Such scales have limited transposition, meaning they only have as many keys as their period, and as many modes as the number of notes in the period.

Chromatic scale

Valentine

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The chromatic scale is the only scale with a period of 1. Every edo has a chromatic scale, taken by simply allowing every note in the temperament. However, the 15edo chromatic scale is often referred to as the "valentine scale", as it implements valentine temperament. As stated on the main page, valentine is essentially 15edo with a compressed octave.

The period of 1 means there is no key for valentine in 15edo. This also means the number of notes per period cannot be plural, and so there are no modes.

Slendric scales

As seen in the Astaryuu/15edo Notes/Notes and Chords page, the slendric chord uses scale degrees 0, 3, and 6. Adding the perfect fifth, the minor seventh, and the octave gives the slendric hexagon chord. A scale with a period of 3 will have this chord in it at least once.

The scale comprised entirely of major tones is usually referred to as the "slendric scale" itself. It's equivalent to 5edo "chromatic", so despite having five notes, it doesn't really resemble 12edo pentatonic at all. There are only two scales that can be made out of subdividing slendric, one of whom is valentine from before.

Blackwood major

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Blackwood

Blackwood is almost certainly the most famous 15edo scale, and it is definitely the one that feels the most 15edo, at least in my opinion. Easley Blackwood Jr. himself is partially to blame for 15edo's popularity, and therefore probably the reason you're on this page, or the reason someone did something that caused you to find this page.

The blackwood scale is basically a superpowered version of the diatonic scale, despite being suboctave-periodic (unlike the diatonic scale in both 12edo and 15edo). It has two modes: major and minor, depending on if you include the 2 (as I do in the edobox, making it major) or the 1 (minor). For each mode, every note that isn't threeven is either major or minor depending on the mode, making blackwood major and minor essentially super-lydian and super-phrygian, if you are familiar with the modes of the major scale.

Augmented scales

As seen in the Astaryuu/15edo Notes/Notes and chords page, the major augmented seventh (or just augmented seventh, as the seventh is usually assumed to be major) chord uses scale degrees 0, 5, 10, and 15. This means all scales whose period is 5 can be considered to be either the augmented seventh, or divisions thereof; I refer to these as augmented scales as a result. For some reason, of all the things that come in threes, both of the augmented scales commonly associated with 15edo are named after The Legend of Zelda, but that's fine by me.

Triforce lorule

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Triforce

Triforce is considered to be a more approachable alternative to the hyrulic scale seen next, as it only has six notes. Like blackwood, it only has two modes. Vector's equivalent to this page refers to this scale as the whole tone scale, as it uses the two kinds of whole tone in 15edo in alternating states.

The modes could simply be called "major" and "minor" again as in blackwood. However, since it is named after the Triforce, I prefer to use a naming convention from my first Zelda game: hyrule for the mode with the wolfinor chord with only one of the augmented notes (0-3-8), and lorule for the one with the wolfminor chord with the two of the augmented notes (2-5-10).

Hyrulic ganon

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Hyrulic

Hyrulic is to the augmented third what blackwood is to the perfect fifth: dividing the interval into as many neutral second intervals as possible. It is considered to be triforce on hard mode, although it appears easier on the surface due to containing true major and minor chords.

There are three modes to this scale, but they do not have names that I can find, so I will be giving them my own names. From this point on, there will also be a table comparing every mode and, if possible, comparing it to a major mode. This means the table will give a rough idea of how major or minor each mode is, but you should click the link to the scale to find out more.

UDP code	Name	Majorness	Major-centric name
0	Link	6	Lydian
1	Zelda	3	Dorian
2	Ganon	0	Phrygian

If the small interval of each triad is absorbed into an adjacent large triad, hyrulic becomes triforce. Interestingly, though, that flips the majorness on its head: hyrulic ganon is a superset of triforce hyrule, while hyrulic link is a superset of triforce lorule. Hyrulic zelda, then, is a superset of both modes of triforce. This arguably makes hyrulic zelda the most versatile mode, but the other two modes are still good for setting the tone.

Octave-periodic scales

Octave-periodic scales in 15edo have a period of 15. Technically, all scales are octave-periodic, but I use the term to refer to scales that aren't suboctave-periodic.

The diatonic (major) scale is a 12edo example of a scale that is octave-periodic. That scale is generated using perfect fifths, but in 15edo, the closest approximation of a perfect fifth is 9 steps wide. In 12edo, the perfect fifth is 7 semitones, and 7 and 12 are coprime - this is what makes it octave-periodic instead of suboctave-periodic. 9 is not coprime with 15, which is why it generates the slendric scales (like blackwood). It just so happens that two of the other fifths - diminished (7) and wolf (8) are coprime with 15, so they can be used instead for a similar effect.

Wolf fifth scales

The wolf fifth is usually not used as a generator itself. However, in 15edo, four neutral seconds, or two minor thirds, equals a wolf fifth, so a scale using either of these is a wolf fifth scale.

Pine octopus

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Pine

After blackwood, pine is arguably the most popular scale in 15edo. Eight stacked neutral seconds give this interval. The neutral second is between a minor second (also called a semitone) and major second, so notes that differ by it don't quite sound either major or minor. However, majority or minority can still be felt in intervals of multiple neutral seconds, especially since the 15edo neutral second leans a little major.

Here, I use the names suggested by William Lynch in Unque's guide for pine modes. In this scale, the mode number is equal to the number of bright generators stacked on top of the root. Note that the major mode names aren't recommended, as pine isn't a diatonic scale. However, they can serve as a reference for what a given mode might be expected to feel like.

The eighth mode here is difficult to name properly. I use "orleanian" for the eighth mode's major-centric name, as a reference to the jazz minor scale, whose brightest mode is even more major than lydian thanks to more augmented notes. However, I prefer to see octopus as the major equivalent to whale/locrian, as it, in a sense, "breaks out" of the major/minor distinction.

UDP code	Name	Majorness	Major-centric name
0	Octopus	7	Orleanian
1	Mantis	6	Lydian
2	Dolphin	5	Ionian
3	Crab	4	Mixolydian
4	Tuna	3	Dorian
5	Salmon	2	Aeolian
6	Starfish	1	Phrygian
7	Whale	0	Locrian

Sardonyx

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Onyx

Onyx uses 7 stacked neutral seconds instead of 8. You can think of it as removing the "pine note" from pine, as long as it's fine that the majority reverses! In fact, if you take the brightest modes of pine and onyx, you'll find that their intervals are exactly opposite each other (as long as one of the middle notes is removed).

Onyx modes also don't have names, so I refer to them using variants of chalcedony, the rock family to which onyx belongs.