User:KingHyperio

Hey, I’m Hyperio. I’m most knowledgeable about 31edo, and I’ve done work in 17/34d and 41. I’m currently learning about ethnomusicology.

My website is 31edo.com.

31edo Solfege


31edo	solfege names	ups and downs names	edosteps
1sns	Do Du	P1 ^1	0-1
2nds	Ruh Re Ru Ra Ri	vm2 m2 ~2 M2 ^M2	2-6
3rds	Muh Me Mu Ma Mi	vm3 m3 ~3 M3 ^M3	7-11
4ths	Fuh Fo/Fe Fu	v4 P4 ^4	12-14
tritones	Fa/Suh Fi/Se	A4/vd5 ^A4/d5	15-16
5ths	Su So/Sa Si	v5 P5 ^5	17-19
6ths	Luh Le Lu La Li	vm6 m6 ~6 M6 ^M6	20-24
7ths	Tuh Te Tu Ta Ti	vm7 m7 ~7 M7 ^M7	25-29
8ves	Duh Do (Du)	v8 P8 (^8)	30-31 (32)

Example scales


Major scale	Do	Ra	Ma	Fo	So	La	Ta	Do
Minor scale	Do	Ra	Me	Fo	So	Le	Te	Do
Upmajor scale	Do	Ra	Mi	Fo	So	Li	Ti	Do
Downminor scale	Do	Ra	Muh	Fo	So	Luh	Tuh	Do
Mid scale	Do	Ra	Mu	Fo	So	Lu	Tu	Do

Additional Information

The system shown preserved vowels in perfect fifths in any scale that only uses notes from meantone[7] modes, mohajira[7] modes, and substitutions of meantone intervals with corresponding septimal subminor or supermajor intervals, allowing for any diatonic type scale to be simple as easy to learn, except for So-Ra and Te-Fo, inconsistencies which already come from the standard solfege system. Du is used for the up unison because it helps consistency, is generally used as a quartertone in scales like Centaurus, and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.

The system is built on this consistency, and preserves the standard minor intervals names, as well as -a as the standard major from La, and Ti as the strongest leading tone, here being the upmajor seventh. The remaining vowels of -uh for sub and -u for neutral are used because they correspond to the vowel sounds from their respective words.

Expanding the System

To expand into intervals that surpass these, such as the A1 or the ^A5, we will extend to Augmented, Diminished, Upaugmented, and Downdiminished intervals. The vowels for these are -ah (short a sound), -ih (for the short i in diminished), oy, and ow (for down) respectively. They work similarly to the others, and are first used in the second set of unisons, allowing the M7-A4 and d5-m2 perfect fifths and others of the sort to still use consistent vowels, as they show up in diatonic scales.

If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.

31edo Functional Harmony

My personal view of harmony in 12edo is that each note in a key has a role in any chord, which I use the names Stable, Modal, Hollow, Unstable, Leading, and Odd for. Stable describes the P1 and P5, Modal describes the m3 and M3, Hollow describes the M6 and m7, Unstable describes the M2 and P4, Leading describes the m6 and M7, and Odd describes the m2 and A4. The summary is that a chord having unstable and leading notes in it makes it a Dominant, a chord having just unstable notes in it makes it a Subdominant, a chord having just leading notes in it makes it a Mediant, and a chord having neither makes it a Tonic or Substitute Tonic. It works best for triads and tetrads, and can extend reasonably well to 31edo, and I use the follow classifications for the notes: S: P1,P5, M: s3,m3,M3,S3, H: ~6,M6,S6,s7,m7,~7, U: ~2,M2,S2,~3,v4,P4,^4, L: s6,m6,M7,S7, O: ^1,s2,m2,A4,d5,v5,^5,v8. Some notes, like the ~2 and ^4, can change roles depending on the chord, but in general the system works well. This is useful when trying to compose using microtonal scales in 31, so a table below will list some important chords (mainly triads) for each role (O means Orwell tetrad, h means harmonic):

Example Scales
	Tonic	Subdominant	Dominant	Mediant
Major	I, VIm	IIm, IV	V, VII^o	IIIm
Orwell[9] 1	Ih11(no3,9)*, Is, IS, dbIIIS	dIIO, dbIIIs	dbIIIO, tIVO, bVIO	VIIO
Squares[8] 5	IS, tIIIS(#5), dVIS(#5)**	In***, dVIn, dVIS	dbIIsn7, dIIIS(#5), tIIIs, dbVIS(#5), dVIs, tVIIS(#5)	IS(#5), dbIIn, tIIIs, tIIIn
Dylathian	I(v5)****, I(x5), IIIO	Isus2(v5)*****, Isusv4(v5), IIsus2(v5), IIsusv4(v5), dVsS6(^5), tVIsS6(^5), tVIsusv4(v5)	IIsS6(^5), dIV(v5), dIVsus2(v5), dIVsusv4(v5), dVIO, tVIIsS6(^5)	tVIsus2(v5)
Harrison Major	IS, VIm(^5)******	IIm, IV	IImS6, VS, tVIIs(vb5)	tIIIs
Graham Orwell	Ih11(no9), Is, dbIIIS	dbIIIs	bIIS, dbIIIO	IO, bIIs, IIIm, IIIS
Neutral Lydian	Ih11(no3,7)	In, IIn, dIIIh11(no3,7), dIIIn, Vn, dbVIIn
Mothra[11]	IS9, dVs7(bb5), tVIs7	IIs7, tIIS(add2)*******, dIVS6, VIs7(bb5), dIs7	VSs7, tVIIs7(bb5)	tIIIs(add4)
Greeley[8] 8	IsM6n7$********, Is(vb5), VIm(vb5)	dbIII+(#3), tIII^o	tVm(vb5), dVIIsM6n7$, dVIIs(vb5)	bII^o
Mode 8	Ih7	IIn(v5), tIVm(v5), Vs(add4)	V, VIIm(v5)	IIIm

*: The notation here is a bit strange. no3 says that there's no 3 in the chord, not no 3rd harmonic. This only comes up for the 3rd and 5th harmonics, for the rest the harmonic name matches the position in the chord. Also, in many of these extended chords, the super eleven will act as an Odd, not Unstable interval, like a #11.

**: This chord can be played as a slide, and isn't used as a tonic is the standard way.

***: This chord acts sort of like a sus chord, "resolving" to a sub or super chord on the same root.

****: These chords are called Delta Rational chords, and chords of this variety make up a significant portion of Oneirotonic chords. Specifically major v5 chords often have an add2. The major x5 chord is treated as tonic because the v6 acts as a thirteenth harmonic, mimicking a perfect fifth in a major triad.

*****: These sus chords approximate (within about a cent) 19/17/13 utonal and 13:17:19 otonal chords.

******: This is a "wolf tonic", with all tonic components but a superfifth in a scale that has mostly perfect fifths, so it prevents tonicization of the sixth, and makes it clear that there's still movement to go to get to the real tonic.

*******: The italics are purely instructional, meaning that the added note doesn't affect the role. This applies to many other chords in this scale, with some s7(bb5) chords able to be reduced to Orgone Triads for consistency without affecting anything.

********: $ here signifies a shell voicing. no5 can also be used, though in long chord names like this $ is cleaner. Additionally, in this scale, the b2 acts as a leading tone due to the absence of any remote fifth, and the ~6 generally acts as an unstable note.

31edo Keyboard Setup

For a Lumatone style Bosanquet-Wilson keyboard, I split the notes up based on their roles in the keys of CGDAE, which generally carry over well into other common keys. The coloring of the keys is a version of Kite's Color notation, with white being for C, G, D, A, and E, yellow being for B, F#, C#, and G#, green being for F, Bb, Eb, and Ab, blue being for D#/Edb, A#/Bdb, E#/Fd, and B#/Cd, red being for Db/C#t, Gb/F#t, Cb/Bt, and Fb/Et, light/grayish blue being for Gd, Dd, Ad, and Ed, grayish red/pink being for At, Dt, Gt, and Ct, and gray being for Bd and Ft. Using this coloring system, the standard key for a scale is that which uses all or as many white keys as possible, with examples shown below:


Scale	Keys
Major	F, C, G
Minor	D, A, E
Melodic Minor	G
Neapolitan Major	G, A
Harrison Major	G
Rast	G
Bayati	A, E
Neutral Lydian	C, G
YB Altered	Gb
Mode 8	C
Dylathian	C, Gt
Whole Tone	C, Bb, Ab, Gb