Is 7 edo really Xenharmonic?

I didn't know the meaning of Xenharmonic, so I looked it up on Wikipedia. It says: "Xenharmonic is a term used to describe tuning systems, or music using those systems, which does not conform to or closely approximate the common 12-tone equal temperament."

And "The term is meant to include tunings such as 5- and 7-tone equal temperament"

I feel that this is not accurate. When I hear or play 7 edo, I find it sounds to me very very similar to a diatonic scale in 12 edo. To me, 7 edo sometimes sounds like a major scale in 12 edo and sometimes sounds like a minor scale in 12 edo (or dorian or myxolydian), but doesn't sound incredibly different from either.

My experience of playing non 12 edo music to "ordinary" audiences in Southern England (Either with or without warning that I'm playing non 12 edo music) is that 7 edo is one of the most acceptable non 12 edo tunings for "Ordinary" people (also, a friend of mine who plays instruments for fun but not on stage recently asked me to remember that it was a 7 edo ukelele that he particularly enjoyed playing. But then he may no longer be "ordinary" since he has known me for over ten years and before I started making fretted non 12 edo instruments I played fretless guitar). The other tunings they seem to find more acceptable (of the ones I have tried) are pythagorean intonation, quarter comma meantone and 12 note just intonation with a 5 limit (1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2). 9 edo and 10 edo sometimes seem to go down well and sometimes very badly. I should explain that this refers to me playing electric guitar (or sometimes acoustic banjo guitar) and my style often uses a lot of strummed barre chords (with vocals). I think 10 edo is more acceptable to "ordinary" people if it is used for fingerpicking or lead playing rather than strummed chords. I have also tried playing bass whilst singing and I think that "ordinary" people find most scales acceptable then because I'm only playing one note at a time and the issue of instrumental chords does not come up.

I am aware that the third of 7 edo, at about 342.857 cents, is close to the middle of one of the gaps in 12 edo, but the overall scale doesn't sound that different to me (so sometimes I think it does not have the "fun" of some of other tunings I've tried in that it does not sound different enough from 12 edo to be interesting to me). (whereas 8 edo, appart from the diminished seventh chord sounds very different from 12 edo to me)

> I feel that this is not accurate. When I hear or play 7 edo, I find it sounds to me very very similar to a diatonic scale in 12 edo. To me, 7 edo sometimes sounds like a major scale in 12 edo and sometimes sounds like a minor scale in 12 edo (or dorian or myxolydian), but doesn't sound incredibly different from either.

I agree with this and I'm also at a loss to explain it. This
realization spurred my whole rant for the last few months about the
brain forming a "JI map" of the chord/scale going on, but that's
clearly not the case all of the time (as evidenced by the fact that
12-tet comma pumps don't make you go nuts). I think that studying
7-tet and seeing how our perception of large intervals being tempered
out works will yield some information into how we perceive small
intervals being tempered out as well (although there may be different
psychoacoustic mechanisms that come into play when small intervals are
involved).

Anyway, end rant. But what you're saying is true, and I have no idea
why. I wonder if there's a way to get out of "diatonic mode" when you
listen to 7-tet and hear the whole thing as a series of possibly 11 or
13 limit neutral thirds. Then it would certainly be xenharmonic.

However, I would DEFINITELY say that 5-edo is xenharmonic, despite its
pseudo-realization as a detuned 5-limit pentatonic scale. Very
xenharmonic, and a fantastic sound.

-Mike

Markallan>"I feel that this is not accurate. When I hear or play 7 edo, I find it
sounds to me very very similar to a diatonic scale in 12 edo. To me, 7
edo sometimes sounds like a major scale in 12 edo and sometimes sounds
like a minor scale in 12 edo (or dorian or myxolydian), but doesn't
sound incredibly different from either."
I've found 7EDO already have many good approximations of 12TET intervals like the minor third, perfect fourth, perfect fifth, and so on. So if you only use those intervals it does by-and-large sound like 12TET.
The "7th", however, is dramatically changed to about 9/5 (about 1.8) from about 15/8 (1.875) and the minor second becomes a "whole new class" of interval slightly below the major second...around 11/10 (1.1) thus below the usual 9/8 (1.125) major second but far above the 15/14 minor second. To me the "new" second in 7TET and the "new" 7th make a huge difference in this scale and allow chords impossible with 12TET, such as chords with consecutive intervals below the major second, to work.

So to me 7TET is "a good dose if familiar 12TET intervals but also a good 30% does of something completely different".

>"The other tunings they seem to find more acceptable (of the ones I have
tried) are pythagorean intonation, quarter comma meantone and 12 note
just intonation with a 5 limit (1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5
5/3 9/5 15/8 2). "
But, to me, those are within cents of 12TET and sound almost exactly the same for ALL intervals as 12TET...unlike 7EDO which has the two classes I described above which are significantly different.

Now if you enjoy 7TET and some of your friends do I'd highly recommend my own tuning which closely co-insides with intervals from 7TET, but it tuned for significantly more pure harmony:(currently called the "Infinity" scale).

1/1 11/10 5/4 11/8 3/2 5/3 11/6 2/1

-Michael

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>
> Now if you enjoy 7TET and some of your friends do I'd highly recommend my own tuning which closely co-insides with intervals from 7TET, but it tuned for significantly more pure harmony:(currently called the "Infinity" scale).
>
> 1/1 11/10 5/4 11/8 3/2 5/3 11/6 2/1
>
> -Michael
>
>
> [Non-text portions of this message have been removed]
>
Thank you very much for that. I'll check it out. I suspect that it will be easier on harp/zither like instruments (or perhaps modified tin whistle or other wind instruments) or synthesised instruments than the fretted instruments I usually make. I've got scala so I can test it with synth sounds before attempting Ukelele or guitar fingerboards.

Me>"Now if you enjoy 7TET and some of your friends do I'd highly
recommend my own tuning which closely co-insides with intervals from
7TET, but is tuned for significantly more pure harmony (currently called the "Infinity" scale).
> 1/1 11/10 5/4 11/8 3/2 5/3 11/6 2/1"

Markallanbarnes>"Thank you very much for that. I'll check it out. I suspect that it will
be easier on harp/zither like instruments (or perhaps modified tin
whistle or other wind instruments) or synthesised instruments than the
fretted instruments I usually make. I've got scala so I can test it with synth sounds before attempting Ukelele or guitar fingerboards."
Awesome...and when you get it all working I'd love to hear sound samples of your instruments playing it. :-)

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Hmm...well, melodically, 7-EDO can quite resemble diatonic 12, as can pretty much any relatively-even heptatonic scale. But harmonically? I think if you play 7-EDO with full triadic harmony, you'll find the similarity drops away a little. Or maybe not? In some of my work with neutral-third scales (particularly the Mosh heptatonic in 17-EDO), I've certainly found that the way the brain deals with neutral thirds is often to "round them" up or down to a major or minor, depending on the logic of the chord progression. I haven't played much with 7-EDO, maybe I should.... Little-known fact about 7-EDO though is that a few of its intervals are very close to some higher harmonics: look at the 29th, 39th, and 43rd harmonics in comparison to the 7-EDO 7th, 3rd, and 4th. This may account for the "stability" it displays.

I should say though that in my experience, the longer I play microtonally (and the weirder scales I use), the less xenharmonic ANYTHING sounds. Why, I found myself playing in 8-EDO the other day and it felt so NORMAL...yet I remember just a few years ago even 22-EDO could sound intolerably weird to me. What is happening to me???

-Igs

--- In MakeMicroMusic@yahoogroups.com, "markallanbarnes" <mark.barnes3@...> wrote:
>
> I didn't know the meaning of Xenharmonic, so I looked it up on Wikipedia. It says: "Xenharmonic is a term used to describe tuning systems, or music using those systems, which does not conform to or closely approximate the common 12-tone equal temperament."
>
> And "The term is meant to include tunings such as 5- and 7-tone equal temperament"
>
> I feel that this is not accurate. When I hear or play 7 edo, I find it sounds to me very very similar to a diatonic scale in 12 edo. To me, 7 edo sometimes sounds like a major scale in 12 edo and sometimes sounds like a minor scale in 12 edo (or dorian or myxolydian), but doesn't sound incredibly different from either.
>
> My experience of playing non 12 edo music to "ordinary" audiences in Southern England (Either with or without warning that I'm playing non 12 edo music) is that 7 edo is one of the most acceptable non 12 edo tunings for "Ordinary" people (also, a friend of mine who plays instruments for fun but not on stage recently asked me to remember that it was a 7 edo ukelele that he particularly enjoyed playing. But then he may no longer be "ordinary" since he has known me for over ten years and before I started making fretted non 12 edo instruments I played fretless guitar). The other tunings they seem to find more acceptable (of the ones I have tried) are pythagorean intonation, quarter comma meantone and 12 note just intonation with a 5 limit (1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2). 9 edo and 10 edo sometimes seem to go down well and sometimes very badly. I should explain that this refers to me playing electric guitar (or sometimes acoustic banjo guitar) and my style often uses a lot of strummed barre chords (with vocals). I think 10 edo is more acceptable to "ordinary" people if it is used for fingerpicking or lead playing rather than strummed chords. I have also tried playing bass whilst singing and I think that "ordinary" people find most scales acceptable then because I'm only playing one note at a time and the issue of instrumental chords does not come up.
>
> I am aware that the third of 7 edo, at about 342.857 cents, is close to the middle of one of the gaps in 12 edo, but the overall scale doesn't sound that different to me (so sometimes I think it does not have the "fun" of some of other tunings I've tried in that it does not sound different enough from 12 edo to be interesting to me). (whereas 8 edo, appart from the diminished seventh chord sounds very different from 12 edo to me)
>

>Michael: I've found 7EDO already have many good approximations of 12TET intervals like the minor third, perfect fourth, perfect fifth, and so on. So if you only use those intervals it does by-and-large sound like 12TET.
> The "7th", however, is dramatically changed to about 9/5 (about 1.8) from about 15/8 (1.875) and the minor second becomes a "whole new class" of interval slightly below the major second...around 11/10 (1.1) thus below the usual 9/8 (1.125) major second but far above the 15/14 minor second. To me the "new" second in 7TET and the "new" 7th make a huge difference in this scale and allow chords impossible with 12TET, such as chords with consecutive intervals below the major second, to work.
>
> So to me 7TET is "a good dose if familiar 12TET intervals but also a good 30% does of something completely different".
>
> >Mark Barnes: "The other tunings they seem to find more acceptable (of the ones I have
> tried) are pythagorean intonation, quarter comma meantone and 12 note
> just intonation with a 5 limit (1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5
> 5/3 9/5 15/8 2). "

>Michael: But, to me, those are within cents of 12TET and sound almost exactly the same for ALL intervals as 12TET...unlike 7EDO which has the two classes I described above which are significantly different.
>

> -Michael
>

Whereas quarter comma meantone and 12 note just intonation with a 5 limit (1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2). Might well sound the same as 12 edo to you and often sound very similar to me, it is worth bearing in mind that some intervals in these scales can sound very different and the difference in cents is not really that small. For example, if playing 12 note quarter comma meantone with a b flat to f wolf fifth, the minor 2nd, a to b flat is to my ear very different from a 12 edo minor second and at about 76.049 it is almost 24 cents different, which is more than a pythagorean comma (the difference between a pure 3/2 fifth and a pythagorean wolf fifth). This minor 2nd is almost as small as 25/24. Similarly, in such a scale if you make d the tonic then you have a narrow minor 2nd and a noticably flatter than normal minor 6th, at about 772.627 (equal to 25/16). This is almost the same difference from 12 edo in cents as your 2nd and 7th of 7 edo differ from 12 edo. If you don't mind selecting a tonic that gives a wolf 5th, you also get a minor sixth (or augmented 5th) of about 737.637 cents, which is further in cents from 12 edo than your 2nd and 7th of 7 edo are.

The 5 limit just intonation scale I mention includes, among other intervals, 25/24 and 27/25. These are about 70.672 cents and 133.238 cents. Both of these intervals are further from 12 edo intervals (in cents atleast) than the 2nd and 7th of 7 edo are.

I find that to my ear the 25/24 minor 2nd of this scale usually sounds distinctively different from a 12 edo minor 2nd. I think the just scale I have given sounds much more similar to 12 edo when you take the note I have given as 1 as the tonic, but often very different if other notes of the scale are used as the tonic.

I'd like to go into more detail and edit this message more, but I have a gig I need to get to (probably pythagorean or quarter comma, but I'll take other fretboards, probably 7 edo and 10 edo, maybe something else, for more options).

Markallan>"Might well sound the same as 12 edo to you and often sound very similar to me, it is worth bearing in mind that some intervals in these scales
can sound very different and the difference in cents is not really that
small. For example, if playing 12 note quarter comma meantone with a b
flat to f wolf fifth"
To note. I have also noticed fifths are incredibly sensitive to even the slightest change...perhaps more so than any other type of interval. Depending on the interval, I've found even something as small as a 9 cent or so change such as that between 9/5 to 20/11 can make a huge difference since in certain areas nearby intervals sound completely different in character.

>"This minor 2nd is almost as small as 25/24. "
So no wonder it stings. The critical band dissonance must be horrid for something that close. You're right though I only briefly have glanced over quarter-comma mean-tone and didn't notice those differences from 12TET.

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I dunno - I feel the same. One would hope that with enough compelling
compositions (and I'm meaning towards pop here like Elaine Walker) the
public can find acceptance. Things obviously change (Pythagorean to
mean tone to 12tet) - so the real question is how fast?

Though if one is honest about pop music (in general) it is probably
less about music than it is about making social statements (I kissed a
girl and I liked it, like a virgin, poker face) than it is about
music. The lack of harmonic variety (and really lack of rhythmic
variety too in many cases) is made up by a huge range of timbres and
extravagant appearance and lyrics.

Now I'm not really familiar with the more electronic side though I do
find people like Bjork refreshingly different (and out right weird).
My "pop" listening is in the form of my teenage daughter with whom I
play guitar/keys for her so she can sing the pop songs she likes.

So opposing / differing / clarifying opinions are most welcome.

Chris

On Wed, May 5, 2010 at 12:54 PM, cityoftheasleep
<igliashon@...> wrote:
>

I should say though that in my experience, the longer I play
microtonally (and the weirder scales I use), the less xenharmonic
ANYTHING sounds. Why, I found myself playing in 8-EDO the other day
and it felt so NORMAL...yet I remember just a few years ago even
22-EDO could sound intolerably weird to me. What is happening to me???

-Igs
>

>"The lack of harmonic variety (and really lack of rhythmic variety too in many cases) is made up by a huge range of timbres and extravagant appearance and lyrics."
I agreed here completely. This echoes many of my discussions about how music has evolved a lot recently in many ways just, unfortunately, not in terms of the tunings used to compose it. People are programming bizarre timbres, making vocals with new types of fluctuations, purposefully making odd noises with guitars (IE Tom Morello, Primus, etc.), doing some really clever things with beat accents (though sadly not often things like altering the position of loud/"key" snare drums on off-beats and such). And I strongly suspect this is done at least partly out of the realization that using just one tuning (12TET) that's been experimented with for so long often yields relatively un-original and un-surprising results.

>"Though if one is honest about pop music (in general) it is probably less about music than it is about making social statements (I kissed a girl and I liked it, like a virgin, poker face) than it is about
music. "
I will agree it's somewhat more about social statements. Yet I figure, we can't optimize the social statements...but we can optimize things like the tunings and theories available to compose with IE the other half of the equation. Of course, there are some (although not a ton) of artists who get along fine in the pop world without social statement or, in fact, without lyrics. Chicane, Joe Satriani, Brian Eno, Orbital, Hybrid...there are lots of groups making a living off instrumental-only "non-social" pop. So would micro-tonal music with lyrics help...sure, but the flip-side is I also think micro-tonal instrumentalist can go pop and should in no way be called "unrealistic" if they want to make lyric-less micro-tonal pop music.

So to bring it "back to 7TET"...I think such "kind of the same, but in many ways different" tunings do qualify as Xenharmonic as the intervals and chords they make often have completely different feelings than their nearest "12TET equivalents". Aside from 7TET also, I think Bohlen Pierce, Wilson's Six Hexanies tuning, and 22TET Deca-tonic scales all make good easy-to-access scales for micro-tonal pop. And perhaps 17TET as well. Sure, virtually any scale can ultimately be made to sound popular (and artists like Igs are proof of this)...but I think those few are among the most accessible scales which are also distinct enough from 12TET to make people take instant notice of their originality...in a good way. :-)

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