Alternate Tunings

What do I care if a solo performer uses one intonation over another?

I can think of a few general reasons why people care about microtonality.

One is the desire for more harmonic freedom. If you want consonance you can use Just Intonation to get a smooth and restful sound you just can't get with get 12-edo. Also, if you want a clashing chord, you can get far more dissonant with microtonality than you can with 12-edo. Upon learning that there is more to the harmonic gamut, people often want to take advantage of it, systematically. (Example: "I purposefully tuned the major third sharp in this chord so that it could be held as a common tone to this next chord which will be pure because of it...")

Another reason is the desire to explore totally new tonal structures. Sure, we have a pretty good theory of how 12-edo tends to work. We know all about parralel fifths and octaves, we know about leading tones, and we know about dominants, subdominants, subtonics and supertonics. We even know can still apply most of those tendencies to some other tunings we call meantone tunings (31-edo, 19-edo, 43-edo, etc). But what about totally out there tunings like 13-edo, 16-edo, or 10-edo? How do they work? Do some of the rules like tertian harmony still apply? Does their circle of thirds or seconds work like the circle of fifths? How can you create tension and resolution, and how would you write inspiring melodies in scales completely different from the diatonic? These are the questions that drive many microtonalists and I put myself in this category.

One of the more common reasons is to play the music of other cultures, many of which use microtonal scales. Java Gamelan ensembles, African balafons, and some Thai traditional music all use very nonwestern, non 12-edo scales.

Similarly, people also sometimes want to play historical pieces in their appropriate historical tunings. These tunings include many meantone and well-tempered tunings (Bach's Well-Tempered Clavier for instance).

I always found talking about the relative merits of x-ET over y-just to be fruitless. It's just what someone decided to use at the time. How each became entrenched is a bit more interesting, but somehow, I just can't see the benefit of a 53-note scale... why limit it there in the absence of cultural implications (the reason to limit to 12)? What makes 53-ET better than infinity-et?

You'll more often find that argument about how "x-edo is the best there ever was awesome super cool tuning and if you don't agree you are a terrible person" argument going on in the first group I mentioned where the goal is, very often, to simply approximate Just Intonation. But my (and many others') approach has been to explore the harmonic and melodic properties of many different tunings, equal and nonequal, octave and nonoctave, to make music that is expressive in its own (maybe brand new) way. So a 53-tone tuning will yield itself to some cool possibilities, and so will a 15-tone tuning.

So why would you care? Maybe because what you were first provided with is not all there is to music, and you want to explore some new ground. Maybe you are looking for new inspiration compositionally. Maybe you want to explore nonwestern cultures' music, or you want to accurately emulate the performance of a historical piece. Maybe you are interested in the maths and physics of music, which will certainly lead you to microtonality. Or maybe you are just outright curious about what the deal is with microtonality and want to experiment.

So there really isn't a "why you SHOULD care". But there are many reasons people do care, and I bet if everyone were exposed to those reasons, many of them would give it a try.

If I may offer my devalued two cents.

I find different 'natural' tunings to be quite interesting. Just intonation vs. perfect intonation, for instance. Anytime I listen to a work with some other 'adventurous' form of alternate, non-12tet tempered tuning, it just sounds out of tune.

That said, a lot of vocal and instrumental purposeful intonation alterations (such as Ligeti's "Ramifications") also get a very interesting effect, and even in pop applications it adds interest in a subtle, non-intrusive way. But usually, when something is tuned alternately, the primary effect is that it 'sounds out of tune.'

I find it most effective when writers/DJs/sound engineers acknowledge this and use it to their music's advantage rather than try to force the listeners to accept a new system of tuning and hear non-12tet as being 'in tune' to their ears.

If I may offer my devalued two cents.

I find different 'natural' tunings to be quite interesting. Just intonation vs. perfect intonation, for instance. Anytime I listen to a work with some other 'adventurous' form of alternate, non-12tet tempered tuning, it just sounds out of tune.

That said, a lot of vocal and instrumental purposeful intonation alterations (such as Ligeti's "Ramifications") also get a very interesting effect, and even in pop applications it adds interest in a subtle, non-intrusive way. But usually, when something is tuned alternately, the primary effect is that it 'sounds out of tune.'

I find it most effective when writers/DJs/sound engineers acknowledge this and use it to their music's advantage rather than try to force the listeners to accept a new system of tuning and hear non-12tet as being 'in tune' to their ears.

There is a fine line though, between just, and non-just intonation.

for example, 2187/2048 is hardly a "simple ratio", and I wouldn't call that interval a just interval.

But exactly where do intervals stop being just, and start being simply rational? the 30th harmonic? 40? 50? 70? Even stuff at the 30th (heck, even lower, depending on who is listening) harmonic sound pretey funky.

Then there is the issue of intervals being almost justly tuned, (within 3-2 cents of JI) which happens all the time in various ETs. Sure, there is a diffrence, but how significant is it really? Besides, it even brings an air of familiarity, consedring 12-tet's being slightly (or sometimes not so slightly, unless we are comparing it to pythagorean intervals) out of tune.

The 12-tet fifth is less than two cents away from a just fifth.

(just my two cents, lol)

Are you saying you also don't like quarter comma (or any comma really) meantone, or well temperaments?

I would quote-mine if i wasn't on a 5-min break. Maybe I will later.

My point isn't that I've heard everything there is to music. In fact, I've used microtones of all flavors in different works. And certainly, non-western music like Gamelan use non-western scales that have interesting properties. But if you're using a tuning system across a sufficiently large work, the ears won't be able to tell the difference - you get used to it. (Sure, those with perfect pitch to 440A will run screaming, but forget them...) But overall I'd rather be talking about wavelengths and hertz ranges than commas and steps -- seems less restrictive.

No one's answered why using ∞-tet isn't superior.

More detailed/possibly smart response later.

I would quote-mine if i wasn't on a 5-min break. Maybe I will later.

Go for it.

My point isn't that I've heard everything there is to music. In fact, I've used microtones of all flavors in different works. And certainly, non-western music like Gamelan use non-western scales that have interesting properties. But if you're using a tuning system across a sufficiently large work, the ears won't be able to tell the difference - you get used to it. (Sure, those with perfect pitch to 440A will run screaming, but forget them...) But overall I'd rather be talking about wavelengths and hertz ranges than commas and steps -- seems less restrictive.

(1st bold text) please elaborate, because I just can't comprehend how mary had a little lamb in 7-tet, and mary had a little lamb in 12-tet could ever sound indistinguishable...

(2nd bold) Why use herts? First off, they denote specific frequency, not intervals, (you could say a diffrence in hertz though) and seccondly, ratios and cents do a nice enough job.

Commas are important theoreticaly. (like for producing well temperaments) I don't know what to say about you not liking using the term "Steps" Do you not like using any other interval names?

No one's answered why using ∞-tet isn't superior.

1. there is no such thing. (actually there is, it's called: any tuning ever devised, except it is impossible to play two notes that are right next to eachother in infinity-tet, because there are infinite gradiations of pitch)

2. That would be pointless, because 205-TET is high enough to create perfect to near perfect approximations for anything you could ever think of.

There is a fine line though, between just, and non-just intonation.

for example, 2187/2048 is hardly a "simple ratio", and I wouldn't call that interval a just interval.

But exactly where do intervals stop being just, and start being simply rational? the 30th harmonic? 40? 50? 70? Even stuff at the 30th (heck, even lower, depending on who is listening) harmonic sound pretey funky.

Then there is the issue of intervals being almost justly tuned, (within 3-2 cents of JI) which happens all the time in various ETs. Sure, there is a diffrence, but how significant is it really? Besides, it even brings an air of familiarity, consedring 12-tet's being slightly (or sometimes not so slightly, unless we are comparing it to pythagorean intervals) out of tune.

The 12-tet fifth is less than two cents away from a just fifth.

My experience with compositions and/or pop songs utilizing alternate tuning is rather limited. I would assume that rational tuning systems which tune the "out of tune" notes in 12tet to be closer to "natural" tuning would not sound that odd. In fact, that's how wind instruments, strings, and voice instruments operate to remove beats from sonorities.

However, utilizing the extra notes (ie notes outside of the traditional 12 chromatic notes, yielding more than 12 notes per chromatic scale) is a huge temptation and usually ends up sounding like those notes are simply out of tune versions of the other notes.

Are you saying you also don't like quarter comma (or any comma really) meantone, or well temperaments?

*whoosh*

That was the sound of your question going entirely over my head.

One is the desire for more harmonic freedom. If you want consonance you can use Just Intonation to get a smooth and restful sound you just can't get with get 12-edo. Also, if you want a clashing chord, you can get far more dissonant with microtonality than you can with 12-edo. Upon learning that there is more to the harmonic gamut, people often want to take advantage of it, systematically. (Example: "I purposefully tuned the major third sharp in this chord so that it could be held as a common tone to this next chord which will be pure because of it...")

If the issue is harmonic freedom, I don't see why you wouldn't want to be able to put any combination of tones together. Obviously historical considerations are important, and the choice to use a historically correct tuning is one that isn't made lightly. But for "new" music, I don't see the point. Once you say "these 5 different E's are acceptable," I don't see the attraction to not going for the rest.

Another reason is the desire to explore totally new tonal structures. Sure, we have a pretty good theory of how 12-edo tends to work. We know all about parralel fifths and octaves, we know about leading tones, and we know about dominants, subdominants, subtonics and supertonics. We even know can still apply most of those tendencies to some other tunings we call meantone tunings (31-edo, 19-edo, 43-edo, etc). But what about totally out there tunings like 13-edo, 16-edo, or 10-edo? How do they work? Do some of the rules like tertian harmony still apply? Does their circle of thirds or seconds work like the circle of fifths? How can you create tension and resolution, and how would you write inspiring melodies in scales completely different from the diatonic? These are the questions that drive many microtonalists and I put myself in this category.

That's valid, but again, I don't see the attraction to limitation. It's like saying "let's experiment, but let's not get too crazy, so we'll still use increasingly less useful terms like note names."

So why would you care? Maybe because what you were first provided with is not all there is to music, and you want to explore some new ground. Maybe you are looking for new inspiration compositionally. Maybe you want to explore nonwestern cultures' music, or you want to accurately emulate the performance of a historical piece. Maybe you are interested in the maths and physics of music, which will certainly lead you to microtonality. Or maybe you are just outright curious about what the deal is with microtonality and want to experiment.

So there really isn't a "why you SHOULD care". But there are many reasons people do care, and I bet if everyone were exposed to those reasons, many of them would give it a try.

I think my admittedly brusque question was misinterpreted. Obviously, getting those "in-between" notes is important -- it's certainly in Western music too (especially if you consider Jazz to be western); but I'm confused as to why the experimentation stops at a certain point. Later, I quote something about a 205-ET or something -- that such a "tuning" exists seems almost pointless to me. At that point, you're hitting a large collection of tones such that the performance accuracy becomes a major issue.

Also, I tend not to see structures I find interesting, like uneven octaves, in most experimental tuning systems, because it seems to break down the walls of what a note is considered... but isn't that part of the whole point?

Go for it.

(1st bold text) please elaborate, because I just can't comprehend how mary had a little lamb in 7-tet, and mary had a little lamb in 12-tet could ever sound indistinguishable...

It's not that the two played side-by-side or subsequently wouldn't sound different; its that the average public can't even pull an A440 out of the air, or tell that their favorite recording was just a little flat or whatever. But I think a recognizable tune isn't really where I was heading. I'm talking about new music -- I don't think it serves as anything but an exercise to use odd tunings for well-known existing melodies, but you have a new melody for the audience, they likely won't say "oh my, that use of pythagorean tuning really accentuated the intervallic relationships" (though of course, more important sections of your audience might).

(2nd bold) Why use herts? First off, they denote specific frequency, not intervals, (you could say a diffrence in hertz though) and seccondly, ratios and cents do a nice enough job.

Commas are important theoreticaly. (like for producing well temperaments) I don't know what to say about you not liking using the term "Steps" Do you not like using any other interval names?

Yeah ratios make some sense, but I still feel that the raw numbers are more useful, especially for applications like electronic music and for developing piece-specific tuning pieces, where you can say "These are the tones I want, how do I map that to a Western staff?"

Because:

1. there is no such thing. (actually there is, it's called: any tuning ever devised, except it is impossible to play two notes that are right next to eachother in infinity-tet, because there are infinite gradiations of pitch)

2. That would be pointless, because 205-TET is high enough to create perfect to near perfect approximations for anything you could ever think of.

I mean, I won't say I can tell 440 hz vs 440.01 hz, but I can sure hear the beat pattern caused by it. Is that covered in 205 notes per octave? Maybe at that octave, but likely not in higher registers.

My experience with compositions and/or pop songs utilizing alternate tuning is rather limited. I would assume that rational tuning systems which tune the "out of tune" notes in 12tet to be closer to "natural" tuning would not sound that odd. In fact, that's how wind instruments, strings, and voice instruments operate to remove beats from sonorities.

However, utilizing the extra notes (ie notes outside of the traditional 12 chromatic notes, yielding more than 12 notes per chromatic scale) is a huge temptation and usually ends up sounding like those notes are simply out of tune versions of the other notes.

Have you listened to authentic arabic music? Does that sound out of tune? Their music is based on a theoretical division of 24 equal tones to the octave. (although the intonation varies)

*whoosh*

That was the sound of your question going entirely over my head.

Ever heard of the Well Tempered Clavier?

Well temperaments are (usually 12 tone) tunings in which all keys have a diffrent character to them, and sound reasonably in tune.

Meantone temperaments are built off of stacked perfect fifths that are tempered (lowered) by a fraction of the syntonic (unless otherwise noted) comma, since the syntonic comma is the diffrence between a pythagorean major third, and a pure major third, and a pythagorean major third is 4 perfect fifths, if we lower each fifth by a 4th of a syntonic comma, 4 of our our 1/4 comma fifths add up to a pure major third.

This tuning came out of the dis-satisfaction with pythagorean tuning, because it has very dissonant/out of tune thirds.

Meantone tunings were beginning to be abandoned in favor of well temperaments in the 18th century. (although Mozart prefered 1/6 comma meantone tuning)

It's not that the two played side-by-side or subsequently wouldn't sound different; its that the average public can't even pull an A440 out of the air, or tell that their favorite recording was just a little flat or whatever. But I think a recognizable tune isn't really where I was heading. I'm talking about new music -- I don't think it serves as anything but an exercise to use odd tunings for well-known existing melodies, but you have a new melody for the audience, they likely won't say "oh my, that use of pythagorean tuning really accentuated the intervallic relationships" (though of course, more important sections of your audience might).

What do absolute pitches have to do with this? I'll leave the a= 432 hz. stuff to the new age loons. (actually, I'm really interested to seeing a scientific study on 432 vs 440 hz, but everything i've seen on it so far is... just see for youself if yo don't know what I'm talking about: http://omega432.com/ ) Alternate tunings are about diffrences in intervals, not absolute pitches.

I think my admittedly brusque question was misinterpreted. Obviously, getting those "in-between" notes is important -- it's certainly in Western music too (especially if you consider Jazz to be western); but I'm confused as to why the experimentation stops at a certain point. Later, I quote something about a 205-ET or something -- that such a "tuning" exists seems almost pointless to me. At that point, you're hitting a large collection of tones such that the performance accuracy becomes a major issue.

So you're more interested in "why specify a specific tuning", or "what's the point of composing in some arbitrarily large division of the octave to get good harmonies" if there is no way to play it on an instrument and you might as well just use a bazillion note division and have every harmony spot on?

Well, harmony is only one aspect of a tuning to consider out of many. Granted, temperaments with harmonies closer to Just Intonation ("low error" temperaments) are the most sought out by microtonalists, but there are other important (but often overlooked) considerations to be taken into account when picking or creating a tuning.

A scale's desirability is not only dependent on it's approximation of just ratios, but also on it's melodic stability. That is, if an interval is functioning melodically the same as another interval in the scale, we as listeners tend to expect them to be the same size. If the sizes are inconsistent it can be disconcerting. Let's take, for example, the diatonic scale. The diatonic scale can be characterized by having 5 large steps (major seconds) and 2 small steps (minor seconds):

In a Just Diatonic Scale of 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8 the intervals from 1/1 to 9/8 and from 9/8 to 5/4 are interpreted to be the same because they are both functioning as major seconds. That is, they are both functioning as one of the five "large" steps of the diatonic scale. But in that Just Scale I described one major second is 9/8 whereas the other is 10/9. The fact that they are functioning as the same melodic interval but are actually different sizes can be, as I said, disconcerting for a listener. If instead we choose an equal division of the octave like 12, 19, 22, 53, or 17, among others (http://en.wikipedia.org/wiki/Syntonic_Temperament) they fit in just right with the diatonic scale so that you can have exactly 5 equally sized large steps (major seconds) and exactly 2 equally sized small steps (minor seconds). These scales will all have good melodic stability for the diatonic scale, and each will have its own characteristics in the way they line up with Just Intonation AND in the difference in size between the major and minor second, allowing for more or less expressive differences between major and minor.

For an example, I might choose 22-edo because it fits in with the diatonic scale, and though its fifths and major thirds are pretty sharp it has a stark contrast in size between major and minor seconds, allowing for very expressive melodies. I might adjust the timbre to make up for the clashing harmonies, or I might adjust my composing to fit a more melodic style.

Conversely, I could write in 19-edo because, though its major and minor seconds are very close in size leading to less contrast between major and minor and more ambiguous melodies, it has spot on minor thirds that really ring out for, let's just say, this one piece I'm writing in the minor mode.

The performance of all these different tunings becomes easy one you have an interface that supports and relates them. Then it because equally easy to play in 12-edo and 53-edo. It sounds crazy, but it's legit. If you're interested in the performance of alternate tunings, check out this synth:

http://www.dynamictonality.com/2032.htm

It maps your qwerty to this layout:

http://en.wikipedia.org/wiki/Wicki-Hayden_note_layout

Which has the same fingering for many different tunings, namely these:

http://en.wikipedia.org/wiki/Syntonic_temperament

John

So you're more interested in "why specify a specific tuning", or "what's the point of composing in some arbitrarily large division of the octave to get good harmonies" if there is no way to play it on an instrument and you might as well just use a bazillion note division and have every harmony spot on?

Well, there's always computer music... which is the applications I've used this kind of thing in. Maybe it's just that I don't care about good harmonies -- I was serious about the .01 hz difference, and considering that a chord (course it needed some playing).

But to me, microtonality is part of hearing music everywhere... Not everything fits into a staff-mindset, despite being able to be categorized.

Well, harmony is only one aspect of a tuning to consider out of many. Granted, temperaments with harmonies closer to Just Intonation ("low error" temperaments) are the most sought out by microtonalists, but there are other important (but often overlooked) considerations to be taken into account when picking or creating a tuning.

A scale's desirability is not only dependent on it's approximation of just ratios, but also on it's melodic stability. That is, if an interval is functioning melodically the same as another interval in the scale, we as listeners tend to expect them to be the same size. If the sizes are inconsistent it can be disconcerting. Let's take, for example, the diatonic scale. The diatonic scale can be characterized by having 5 large steps (major seconds) and 2 small steps (minor seconds): ...

Interesting stuff. Again, I see why I missed the point -- it's all for diatonic purposes.

I think my admittedly brusque question was misinterpreted. Obviously, getting those "in-between" notes is important -- it's certainly in Western music too (especially if you consider Jazz to be western); but I'm confused as to why the experimentation stops at a certain point. Later, I quote something about a 205-ET or something -- that such a "tuning" exists seems almost pointless to me. At that point, you're hitting a large collection of tones such that the performance accuracy becomes a major issue.

Music for your thought:

But, I agree with you for the most part. I find that even 55 tet has little use for me, except theoretically.

But the thing with the Tonal Plexus is, you don't have to think of what just intervals you want to use beforehand, and enter them into scala, or what have you, to retune your midi instrument of choice, all the notes you could ever want.

I mean, I won't say I can tell 440 hz vs 440.01 hz, but I can sure hear the beat pattern caused by it. Is that covered in 205 notes per octave? Maybe at that octave, but likely not in higher registers.

Oh really? I played a sine wave of 440 hz, and one of 440.01 at the same time, and there was no noticable beating.

So, there is such a thing as a harmonic JND. (the melodic JND is around 6 cents)

JND = Just Noticable Diffrence; diffrences in pitch that the ear can percieve.

Well, harmony is only one aspect of a tuning to consider out of many. Granted, temperaments with harmonies closer to Just Intonation ("low error" temperaments) are the most sought out by microtonalists, but there are other important (but often overlooked) considerations to be taken into account when picking or creating a tuning.

A scale's desirability is not only dependent on it's approximation of just ratios, but also on it's melodic stability. That is, if an interval is functioning melodically the same as another interval in the scale, we as listeners tend to expect them to be the same size. If the sizes are inconsistent it can be disconcerting. Let's take, for example, the diatonic scale. The diatonic scale can be characterized by having 5 large steps (major seconds) and 2 small steps (minor seconds):

In a Just Diatonic Scale of 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8 the intervals from 1/1 to 9/8 and from 9/8 to 5/4 are interpreted to be the same because they are both functioning as major seconds. That is, they are both functioning as one of the five "large" steps of the diatonic scale. But in that Just Scale I described one major second is 9/8 whereas the other is 10/9. The fact that they are functioning as the same melodic interval but are actually different sizes can be, as I said, disconcerting for a listener. If instead we choose an equal division of the octave like 12, 19, 22, 53, or 17, among others (http://en.wikipedia.org/wiki/Syntonic_Temperament) they fit in just right with the diatonic scale so that you can have exactly 5 equally sized large steps (major seconds) and exactly 2 equally sized small steps (minor seconds). These scales will all have good melodic stability for the diatonic scale, and each will have its own characteristics in the way they line up with Just Intonation AND in the difference in size between the major and minor second, allowing for more or less expressive differences between major and minor.

For an example, I might choose 22-edo because it fits in with the diatonic scale, and though its fifths and major thirds are pretty sharp it has a stark contrast in size between major and minor seconds, allowing for very expressive melodies. I might adjust the timbre to make up for the clashing harmonies, or I might adjust my composing to fit a more melodic style.

Conversely, I could write in 19-edo because, though its major and minor seconds are very close in size leading to less contrast between major and minor and more ambiguous melodies, it has spot on minor thirds that really ring out for, let's just say, this one piece I'm writing in the minor mode.

The performance of all these different tunings becomes easy one you have an interface that supports and relates them. Then it because equally easy to play in 12-edo and 53-edo. It sounds crazy, but it's legit. If you're interested in the performance of alternate tunings, check out this synth:

http://www.dynamictonality.com/2032.htm

It maps your qwerty to this layout:

http://en.wikipedia.org/wiki/Wicki-Hayden_note_layout

Which has the same fingering for many different tunings, namely these:

http://en.wikipedia.org/wiki/Syntonic_temperament

John

I disagree, variatey is the spice of life.

Well Temperaments. =D

I also think that, if you just want to be close to just intonation, you should just use just intonation. I use ETs because I like the character and flavor of notes not being exactly in tune. Well Temperaments are even better in some cases.

My experience with compositions and/or pop songs utilizing alternate tuning is rather limited. I would assume that rational tuning systems which tune the "out of tune" notes in 12tet to be closer to "natural" tuning would not sound that odd. In fact, that's how wind instruments, strings, and voice instruments operate to remove beats from sonorities.

However, utilizing the extra notes (ie notes outside of the traditional 12 chromatic notes, yielding more than 12 notes per chromatic scale) is a huge temptation and usually ends up sounding like those notes are simply out of tune versions of the other notes.

Only one problem with that; In pratice, western music uses more than 12 notes per octave. A# and Bb would be iterpreted by a violinist as having slightly diffrent intonations.

I see why I missed the point -- it's all for diatonic purposes.

Well... Sort of. It's broader than that though. Remember how I described the diatonic scale as a scale with 5 large and 2 small steps (L,L,S,L,L,L,L,S)? Given that, there were certain equal divisions of the octave that could fit that description perfectly. For example:

19-edo works if you choose your small step to be 2/19 and your large one to be 3/19. Then you're diatonic scale looks like 3,3,2,3,3,3,2. (Notice how similar in size the major and minor seconds are. They can even be a little ambiguous which, if that's what you're going for, can be cool.)

22-edo works if your small step is 1/22 and your large step is 4/22. Then your diatonic scale looks like 4,4,1,4,4,4,1. (Here the major second is 4 times the size of the minor second! Very stark difference which is noticably intense and expressive.)

That same concept can be applied to ANY other scale structure. For example, a tuning known as "mavila" or "pelogic" was observed in some african mallet instruments as well as some gamelan tunings. It has a completely reversed form from the diatonic with a combination 5 small steps and 2 large steps (instead of 5 large and 2 small). A completely different set of equal tunings line up with that scale type. For example:

16-edo works if you choose your small step to be 2/16 and your large step to be 3/16. Your mavila scale then looks like 2,2,3,2,2,2,3.

9-edo works if you choose your small step to be 1/9 and your large step to be 2/9. Your mavila scale then looks like 1,1,2,1,1,1,2.

Still yet, there are others. One last example is a 3 large step 7 small step scale that shows up in what's called the "magic temperament". As with the others, it has it's own equal tunings that line up with this configuration:

13-edo works if you choose your small step to be 1/13 and your large step to be 2/13. Your new magic scale will be 2,1,1,1,2,1,1,2,1,1.

16-edo works if you choose your small step to be 1/16 and your large step to be 3/16. The new magic scale will be 3,1,1,1,3,1,1,3,1,1. (Notice that 16 also worked for mavila/pelogic. Some equal tunings work for several different scale structures. It really just depend on how the numbers work out.)

So from my perspective, yes, a lot of the work I do is based on scales. Only then do I explore the harmonies they contain. This strategy has been very rewarding for me though, especially when coupled with adjusted timbres and the keyboards I use to play in these tunings that tie it all together. You can try it yourself with that synth I linked to before: http://www.dynamictonality.com/2032.htm if you play it with your qwerty using this layout: http://en.wikipedia.org/wiki/Wicki-Hayden_note_layout

Always a pleasure,

John