Yahoo Tuning Groups Ultimate Backup tuning "Atlantean Geometry" in Michael's "Sourest" Scale

See the "files" section, in the folder "Igliashon Jones", or visit the Xenharmonic Alliance Ning and scan through the player for "Atlantean Geometry" by City of the Asleep. This song was written in the following scale, hand-crafted by Michael to be as sour and difficult as possible (it was originally non-octave, but I discovered this actually ADDED consonances, making the scale less of a challenge):

0¢
149¢
336¢
471¢
613¢
763¢
947¢
1200¢

I think that one listen to this song will prove that while this scale would be useless in a common-practice setting, it is still capable of sounding pretty, expressive, nuanced, and gosh-darn accessible. I used a grand piano sound layered with a filtered saw-tooth sound for the main instrument, so you can rest assured there are no "tricks" going on here to hide the dissonance. I also put very little thought into the composition; by and large, it's all played by ear. I didn't sit down and calculate where the "good" chords pop up, I just let the scale speak to me (and I am UTTERLY incompetent when it comes to playing the piano! I probably have the worst keyboard technique of anyone on this list). I think the litmus test for any scale is how easy it is to improvise with, as careful calculation can often hide the weaknesses of a scale. This scale wasn't very hard at all.

My conclusion is that this scale really ain't that dissonant, despite utterly lacking a fifth (though there is a 724¢ interval on the fourth degree, a 729¢ interval on the seventh, and a 736¢ interval on the fifth, every other degree misses the fifth by at least 60¢). It has a piquant latin-jazz feel about it that I quite like.

As a companion piece, I'd like to try something in the "best" scale Michael can come up with, sort of a "Yin" to the "Yang" of this track...whenever Michael gets that scale nailed down! ;->

Anyone else want to submit an "impossible" scale in which I can try to write a song in a popular idiom? Let's keep it octave-based to ensure that I don't end up gaining extra consonances in different registers.

🔗Michael <djtrancendance@...>

Igliashon,

Bizarre...it still sounds way off to me in some ways: beats are everywhere and nearly everything sounds "jumpy" and skewed...but much much less so than I would have thought and close enough that it comes across as confident. It sounds almost like who is playing it both "can't stay in a key" but "is somehow playing in another type of intelligent pattern"...an oddly similar effect to what I got from my PHI and Silver Ratio-based scales when I heard what Chris made with them.
Seriously, I've seen several pieces composed in things like "5-limit JI" that sound more off (far as overall mood generated by the piece) than this (good job!). ;-)

Granted, the piano (which I hear loudly over the sawtooth) has a relatively in-harmonic timbre and may have given you a bit of extra leeway. Also the chords and it seems notes are hit one by one and/or as dyads at most and then "droned" at a much lower volume to create larger chords (also comes across to me as a slight cheat).

Dare I ask...can you re-generate this piece using a trumpet (very dense harmonic/overtone set) as the main instrument? I think it would reveal the sourness in some of the chords in more detail. Though even if it did/does...I think you succeeded by-and-large on "defeating" this scale and indirectly proving "over-doing dissonance can actually flip back around and lead to some consonance"..

---------------
And far as the "sweetest scale"....I'm still working on it. I have a version I'm fairly sure has all notes within about 7-8 cents of their ideal values. I'm just going to have to convert it to cents because it's "just" a highly tempered version of

12/11
5/4
11/8
3/2
5/3
11/6
2/1
............with the actual notes being up to about 7-9 cents away from the above values to preserve a fairly relaxed sounding "circle of imitation fifths" which rotate between 7/5, 22/15, 3/2, and 8/5 (and maybe 50/33 as well)...which I calculated as some of the more consonant intervals in the 7/5 to 8/5 range. I also avoided the nasty 16/11 "Wolf" 5th-like interval that keeps popping up in Ptolemy's Homalon scale by doing this.

I obviously couldn't just use a fairly pure circle of fifths or fairly pure any-other-interval...because if I did I would have no way to hit those 9/8 to 12/11 "semi-tones" I enjoy so much (IMVHO those "alternative semi-tones" are a bit tense, but sound more like 10/9 than anything else and seem not so tense they can't be stacked in chords...unlike the usual 15/14-16/15 semi-tone which to me sounds horrific when clustered like that in chords).

-Michael

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Dare I ask...can you re-generate this piece using a trumpet (very dense harmonic/overtone set) as the main instrument? I think it would reveal the sourness in some of the chords in more detail. Though even if it did/does...I think you succeeded by-and-large on "defeating" this scale and indirectly proving "over-doing dissonance can actually flip back around and lead to some consonance"..
>

Done and done. Check my folder in the "files" section. Rendered it with the filter off on the sawtooth patch, and with the piano switched to a (non-vibratoed) horn section patch. I had to look for a while just to find a brass patch that didn't incorporate a vibrato/chorus effect! Anyway, I think these timbres would be offensive no matter what scale they're played in, but hey--you asked for it! I could also try a guitar patch if you want something more "middle of the road", but I think that between these two version, the result is pretty clear: not totally "pleasant" at times, but definitely colorful, unique, and expressive!

> And far as the "sweetest scale"....I'm still working on it. I have a version I'm fairly sure has all notes within about 7-8 cents of their ideal values. I'm just going to have to convert it to cents because it's "just" a highly tempered version of
>
> 12/11
> 5/4
> 11/8
> 3/2
> 5/3
> 11/6
> 2/1

Interesting. Looks to me like it will be great for demonstrating my theory that scales based on harmonic ideals tend to suffer a loss of melodic expressiveness (given that melodic expressiveness requires intervals of a semitone or smaller to provide "ornamental flourishes"), but I am nonetheless eager to try it out. I'm quite pleased with what came from your "worst" scale, so I'm certain to be pleasantly surprised when I tune up your "best" scale. Maybe you could hit me with a prototype, I'll compose something in it, and then I can retune it as you iron out any further kinks?

-Igs

🔗Chris Vaisvil <chrisvaisvil@...>

In fact I'll add this

Igs - you are my point in the "make micro music popular debate" - the
composer - not the tuning - is the most important part of the
equation!

On Fri, Apr 30, 2010 at 8:03 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> Igs - impressive!!
>
> Your composition is nice - and it doesn't sound any more xenhar than
> other pieces I've heard - so you beat the tuning into total submission
> and came up with a memorable piece! Nice mood!
>
> Chris
>
> On Fri, Apr 30, 2010 at 2:28 AM, cityoftheasleep
> <igliashon@...> wrote:
>>
>>
>>
>> See the "files" section, in the folder "Igliashon Jones", or visit the Xenharmonic Alliance Ning and scan through the player for "Atlantean
>

🔗Michael <djtrancendance@...>

Igs>"Done and done. Check my folder in the "files" section. Rendered it with the filter off on the sawtooth patch"
Agreed...I mean, that taking the filter off a sawtooth sounds relatively offensive in just about any tuning (and obviously in the case of my "max dissonance test tuning" and your song with it). However (yes I know, I'm being picky)...try substituting the trumpet with another brass instrument (full of overtones and not unrealistically loud high ones like the sawtooth)...and I'm pretty sure it would make a more realistic test. I actually learned the "piano = semi-inharmonic timbre = cheating" from this list as I used to test most of my tunings with pianos and responses made it clear why I should not...I didn't just bring it up out of any random picky-ness. :-D

>"Interesting. Looks to me like it will be great for demonstrating my
theory that scales based on harmonic ideals tend to suffer a loss of
melodic expressiveness (given that melodic expressiveness requires
intervals of a semitone or smaller to provide "ornamental flourishes")"
At least on the surface my scale seems as an obvious disadvantage for "melodic even-ness".
TET tunings have the advantage of having a constant ratio per step, usually I find the usable scales under those tunings require 2-3 significantly different step sizes to move melodically across the scale. In 12TET, both the semi-tone and whole tone are needed and such the melodic intervals "skew" heavily between B-C and E-F, for example, because the whole-step is 2 times the size of it.
My scale has many step sizes needed to move melodically across the scale (about 12/11, 10/9, and 9/8), which seems very "uneven" at first. But realize that 12/11 is only 1.03 times the size of 9/8...a big difference from the full 2/1 difference in size between the whole and half-step in 12TET. We'll see what happens...

>"Maybe you could hit me with a prototype, I'll compose something in it,
and then I can retune it as you iron out any further kinks?"
Considering I'm pretty sure my latest proto-type has each note within about 7 cents of the final scale, that would probably be a good idea. I'll hand you over the prototype scale most likely some time this weekend.

🔗Michael <djtrancendance@...>

Chris>"Igs - you are my point in the "make micro music popular debate" - the
composer - not the tuning - is the most important part of the
equation!"

I must point out, I never dis-agreed with said-above point. I just added to it "however, improving the tuning used can make a bad composer sound decent, a good composer sound great, and a great composer sound absolutely fantastic". In other words, next to compositional skill, I think tuning is a very important factor. It's like comparing Michael Andretti's lap times in an F1 car (the equivalent of a "great" tuning) vs. in a Corvette (the equivalent of a "not-so-great tuning") to an average driver's times in an Indy car.

Of course, Andretti will likely beat the average driver's F1 times "even" in a Corvette because he's so much more of a talented driver...but you'd better believe he'll best his Corvette lap times by a good deal in an Indy car!
To test this additional theory to what we both agree on (that the composer is the most important factor)...we'll have to see what happens with Iglishon (who is kind of like Michael Andretti in the example) composes with my consonant tuning and see if he turns from "great" to "fantastic".

🔗Michael <djtrancendance@...>

🔗cityoftheasleep <igliashon@...>

Well, in the spirit of fairness, I wrote a piece with the same instruments and channel settings, same tempo and meter, same length (more or less) and same structure as "Atlantean Geometry". I'm calling this one "Lemurian Algebra" and you can find it in my folder in the files section, as well as on the Xenharmonic Alliance Ning media player.

It's an interesting scale, I will give you that, and I noticed almost no "beating" anywhere. However, there were definitely a few chords I'd be reluctant to call "consonant", and the overall feel of the scale I found to be a bit bland. Also, I think that it is very important to consider WHERE in the scale certain triads will occur, because that will determine the tension-gradient that shapes chord progressions. I felt like the scale often seemed to "fight" the direction I wanted the chords to progress, though sometimes I got some really sweet changes that surprised me.

It's certainly a nice scale, but it's not likely to replace any of my favorites. And to be honest? I like the "max dissonance" scale just as well, if not maybe a little better, at least on first blush with both of them.

And FWIW, this scale would be very well rendered in 31-tET.

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Here is the prototype "tempered" version of my "maximum average consonance" scale:
>
> 159.2154 (1.096328)
> 380.5259 (1.245828)
> 551.2827 (1.374972)
> 696.1746 (1.495)
> 878.5709 (1.661104)
> 1043.5672 (1.827206)
> 1200 (2/1)
>
> ...lets see how this does vs. my "maximum dissonance scale". :-D
>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

>"It's an interesting scale, I will give you that, and I noticed almost no "beating" anywhere."
Cool. Well at least it looks like I'm on the right track for that "side" of the goal. :-)

>"However, there were definitely a few chords I'd be reluctant to call "consonant""
Well, if you could tell me where those are I would appreciate it. Again, the version I sent you is called a prototype because (much due to only limited compositional experience which the scale myself) and there are a couple of ratios such as 18/11 which occasionally show up and I consider significantly more dissonant than the others...and between the two I realize the scale isn't quite final yet. For the record, I was aiming the get most of the 6th-ish dyads to match at either 8/5 or 13/8 or 5/3...but a couple I realize fall a bit "off"...not that they beat a whole lot but have sour "moods" (the 18/11 in particular seems to have this issue).

>"I felt like the scale often seemed to "fight" the direction I wanted
the chords to progress, though sometimes I got some really sweet
changes that surprised me."
One thing is for sure...it fights 12TET a lot in that a lot of the intervals change. The usual 5/3 is often replaced with a 8/5. The 13/8 is often replaced with an 11/6 or 9/5. The "half step" nears the 11/10 near a step in 7TET. And the whole step generally varies between 6/5 and 11/9. Thus there are no guarantees a chord will sound the same when played from a different root...but consonance/"tension" should merge toward being fairly uniform across the board IE even if the chord isn't "predictable" the consonance should be.
The "really sweet changes" you mention should ideally (if the scale is working relatively as planned) equate to "not the chord I expected, but still gives an equally-or-better consonance in sound"...does this seem to be the case or, if not, what is the case? :-D

>"And FWIW, this scale would be very well rendered in 31-tET."
Cool I will try that. :-)

>"and the overall feel of the scale I found to be a bit bland."
Bland as in...using too-well-known intervals or what exactly? I'm not here for the ego I'm here to develop the scale...so shoot me some of the chords and such you find "bland" and I'll definitely look into if I can find any patterns I can figure out a way to improve on.

I know, for one, I've been itching to fit in a 27/20 AKA 1.35 ratio in there...but can't figure out how to without screwing a whole bunch of other ratios up. Also more 7/4's (I think the original has just one 7/4-like dyad possible would be nice if I could figure out how to make it without knocking a bunch of other intervals into "beating hell")...not to say beating is bad but that I don't think I could get non-xen-tonal listeners to go for it.

BTW, dare I ask, what are, say, your 5 favorite scales ever?

>"And FWIW, this scale would be very well rendered in 31-tET."
Cool...I will definitely try that and see what the "approximation" in 31TET is. Just wondering...how did you figure out the 31TET match?

-Michael

🔗Michael <djtrancendance@...>

BTW (Igs),

Ehat's that buzz in the background in this song? Whatever it is (be it how the timbre shows weaknesses in the scale or the buzz itself)...whenever it plays everything sounds skewed and it plays for almost the entire song after the intro. For the record (if it really is just a very low saw-tooth) I agree there's no scale that's going to sound very in-tune with a saw (which is also why I suggested you use a trumpet instead of a sawtooth in my "dissonant scale" song re-make to emulate more realistic high harmonics).

Also the second chord sounds dissonant to my ears although the rest sound decent to me...I'm going to have to try and re-create that sour second chord and iron it out. Also, all else said and done...can you make a version without the buzzing sound in the background?

_,_._,___