In 31 EDO alone there are more 3 note chords than there are of any number of notes in 12 EDO. Btw, I just found out 4EDF is underrated, anyone seeing should check it out. It's pretty beginner friendly like 5 EDO but much spicier.
In Scala, you can do Analyse->Show chord presence... on the menu. For example, in "equal 31": Scale is equal tempered, only showing first degree. 0-7-18: 31-tone Subminor Triad C Eb; G 0-8-18: 31-tone Minor Triad C Eb G 0-9-18: 31-tone Neutral Triad C E; G 0-10-18: 31-tone Major Triad C E G 0-11-18: 31-tone Supermajor Triad C E| G 0-5-10-18-23: 31-tone Added Second & Sixth "2/6" C D E G A 0-8-18-23-36: 31-tone Minor Sixth Added Ninth "m6/9" C Eb G A D.1 0-10-18-23-36: 31-tone Added Sixth & Ninth "6/9" C E G A D.1 0-10-18-25: 31-tone Harmonic Dominant Seventh C E G Bb; 0-10-18-26: 31-tone Dominant Seventh C E G Bb 0-10-18-25-36: 31-tone Harmonic Dominant Ninth C E G Bb; D.1 0-10-18-25-36-45: 31-tone Harmonic Eleventh C E G Bb; D.1 F|.1 0-10-18-25-36-45-53: 31-tone Harmonic Thirteenth C E G Bb; D.1 F|.1 A;.1 0-10-20-31: 31-tone Marvel Augmented Triad C E G# C.1 Total of 14 with 14 unique
aside from isomorphic chord shapes or the harmonic table layout, no. it doesn't really augment your potential skill playing in 12-EDO, only provide "alternate" ways of thinking about it.
Perhaps it has something to do with "Magic" linear (rank 2) temperament, which 22edo equal (rank 1) temperament supports. Magic is a temperament where the comma 3125/3072 is regularly tempered to the unison 1/1, rather than tempering the comma 81/80 regularly to unison, as is done in Meantone. Like in Meantone, usually in Magic we temper also 225/224 (Marvel) to unison, if we extend from representing only the 5-limit to also representing the 7-limit. In this case we also temper 245/243 (Sensamagic) to unison in 7-limit Magic. As a curiosity, 19edo supports both Magic and Meantone simultaneously. But in this video it seems that 22edo is explored. 41edo is also a good Magic supporting equal temperament.
Five 5/4 major thirds stacked become one 3/1 perfect twelfth in Magic temperament, such as 22edo. But i don't know what this has to do with two 6/5 minor thirds stacked. This however becomes a 10/7 in Starling temperament, where the Starling comma 126/125 is tempered. But 22edo is not a Starling temperament. However, this stacked chord of two 6/5 instead becomes a 22/15 in 22edo, because the 55/54 Telepathma is tempered in 22edo, this is thus a Telepathy temperament. I don't know if that is relevant though, but Telepathy IS an 11-limit extension of Septimal Magic.
I suppose that this 15:18:22 chord should thus be properly called the telepathic triad. It is not essentially tempered, since we can merely consider it a 5:6 followed by a 9:11, even in Just Intonation. But in Telepathic temperaments like 22edo, this 22:15 is split in two exact halfs, and we can call it a 45:55:66 chord instead, being here the same as 45:54:66 = 15:18:22. It is somewhat similar to a Diminished triad, except those exist only in temperaments where four stacked 6:5 minor thirds make one 2:1 octave, this is called Dimipent, and if 6:5 and 7:6 are also conflated, it is called Diminished. It seems that these chords are called "diminished" even in Meantone, non-Dimipent temperaments like 19edo and 31edo though. Just like two stacked 5:4 are called an "augmented" chord in Meantone, even though it is really Augmented only if three stacked 5:4 major thirds make one 2:1 octave.
SUPER AMAZING!!
Glad you think so!
In 31 EDO alone there are more 3 note chords than there are of any number of notes in 12 EDO.
Btw, I just found out 4EDF is underrated, anyone seeing should check it out. It's pretty beginner friendly like 5 EDO but much spicier.
4ed3/2?
@@Trainwreck3000 Yes.
In Scala, you can do Analyse->Show chord presence... on the menu. For example, in "equal 31":
Scale is equal tempered, only showing first degree.
0-7-18: 31-tone Subminor Triad C Eb; G
0-8-18: 31-tone Minor Triad C Eb G
0-9-18: 31-tone Neutral Triad C E; G
0-10-18: 31-tone Major Triad C E G
0-11-18: 31-tone Supermajor Triad C E| G
0-5-10-18-23: 31-tone Added Second & Sixth "2/6" C D E G A
0-8-18-23-36: 31-tone Minor Sixth Added Ninth "m6/9" C Eb G A D.1
0-10-18-23-36: 31-tone Added Sixth & Ninth "6/9" C E G A D.1
0-10-18-25: 31-tone Harmonic Dominant Seventh C E G Bb;
0-10-18-26: 31-tone Dominant Seventh C E G Bb
0-10-18-25-36: 31-tone Harmonic Dominant Ninth C E G Bb; D.1
0-10-18-25-36-45: 31-tone Harmonic Eleventh C E G Bb; D.1 F|.1
0-10-18-25-36-45-53: 31-tone Harmonic Thirteenth C E G Bb; D.1 F|.1 A;.1
0-10-20-31: 31-tone Marvel Augmented Triad C E G# C.1
Total of 14 with 14 unique
This is a really great tip, thanks for sharing!
Ahh, so vA or A; or G## is the next overtone, I only found until the eleventh
A good harmonic chord is also subminor with major sixth, so
C D# G A
Or C Eb; G A
Or Major b6 with diminished octave
C E G Ab B# C
Or C E G Ab C; C
I'm not used to microtonal scales, but those first neutral chords sounded more minor to my ear, while many of the minor chords sounded more major
Anything interesting you can do with 12 edo that you cannot do or do easily within a piano?
aside from isomorphic chord shapes or the harmonic table layout, no. it doesn't really augment your potential skill playing in 12-EDO, only provide "alternate" ways of thinking about it.
Why is the highly discordant stack of ~6.5 minor thirds in 22edo called the "magical triad"? Called by whom?
Juhani, that would be according to the Xenharmonic Wiki
Perhaps it has something to do with "Magic" linear (rank 2) temperament, which 22edo equal (rank 1) temperament supports.
Magic is a temperament where the comma 3125/3072 is regularly tempered to the unison 1/1, rather than tempering the comma 81/80 regularly to unison, as is done in Meantone.
Like in Meantone, usually in Magic we temper also 225/224 (Marvel) to unison, if we extend from representing only the 5-limit to also representing the 7-limit.
In this case we also temper 245/243 (Sensamagic) to unison in 7-limit Magic.
As a curiosity, 19edo supports both Magic and Meantone simultaneously.
But in this video it seems that 22edo is explored.
41edo is also a good Magic supporting equal temperament.
Five 5/4 major thirds stacked become one 3/1 perfect twelfth in Magic temperament, such as 22edo. But i don't know what this has to do with two 6/5 minor thirds stacked. This however becomes a 10/7 in Starling temperament, where the Starling comma 126/125 is tempered. But 22edo is not a Starling temperament. However, this stacked chord of two 6/5 instead becomes a 22/15 in 22edo, because the 55/54 Telepathma is tempered in 22edo, this is thus a Telepathy temperament. I don't know if that is relevant though, but Telepathy IS an 11-limit extension of Septimal Magic.
I suppose that this 15:18:22 chord should thus be properly called the telepathic triad. It is not essentially tempered, since we can merely consider it a 5:6 followed by a 9:11, even in Just Intonation. But in Telepathic temperaments like 22edo, this 22:15 is split in two exact halfs, and we can call it a 45:55:66 chord instead, being here the same as 45:54:66 = 15:18:22.
It is somewhat similar to a Diminished triad, except those exist only in temperaments where four stacked 6:5 minor thirds make one 2:1 octave, this is called Dimipent, and if 6:5 and 7:6 are also conflated, it is called Diminished.
It seems that these chords are called "diminished" even in Meantone, non-Dimipent temperaments like 19edo and 31edo though. Just like two stacked 5:4 are called an "augmented" chord in Meantone, even though it is really Augmented only if three stacked 5:4 major thirds make one 2:1 octave.