Yahoo Tuning Groups Ultimate Backup tuning Magic Bullets

I've always hated the look of the Magic[10] MOS. Three clusters of very small steps, separated from each other by large ~7/6's...melodically, it looks dreadful. But for harmony, it's one of the lower-badness temperaments, right about on par with Porcupine or so. The lattice is kind of insane, you have 5 consonant 5-limit triads, and they're all both major and minor, and they're located on the first five "links" of the chain of tempered 5/4's that defines Magic's MOS's. However, in my never-ending quest to defy my own biases, I decided to try writing something in Magic[10] just to see what would happen. Turns out I didn't hate the scale as much as I thought I would. I wrote this cheezy pop song:

/tuning/files/IgliashonJones/Magic%20Bullets.mp3

Give it a whirl. The melodies are very basic, because the scale doesn't really allow for much more than arpeggiation with some chromatic "blue notes" here and there, but I really like these chords. It's really neat having a chain of 5/4's where 128/125 is NOT tempered out.

-Igs

🔗jlmoriart <JlMoriart@...>

🔗Jake Freivald <jdfreivald@...>

Igs,

I'm really not a fan of the sustained synth chords at the beginning.
They sound like someone trying to sound microtonal. You could do the
song a favor by excising that chunk, in my opinion.

As soon as the drums start, though, the song gets fun. The chords
sound much better in the guitars than in the synth; the lead handles
the blue notes nicely. The percussion is straightforward and works for
the song. I liked it a lot.

Regards,
Jake

On 5/20/11, cityoftheasleep <igliashon@...> wrote:
> I've always hated the look of the Magic[10] MOS. Three clusters of very
> small steps, separated from each other by large ~7/6's...melodically, it
> looks dreadful. But for harmony, it's one of the lower-badness
> temperaments, right about on par with Porcupine or so. The lattice is kind
> of insane, you have 5 consonant 5-limit triads, and they're all both major
> and minor, and they're located on the first five "links" of the chain of
> tempered 5/4's that defines Magic's MOS's. However, in my never-ending
> quest to defy my own biases, I decided to try writing something in Magic[10]
> just to see what would happen. Turns out I didn't hate the scale as much as
> I thought I would. I wrote this cheezy pop song:
>
> /tuning/files/IgliashonJones/Magic%20Bullets.mp3
>
> Give it a whirl. The melodies are very basic, because the scale doesn't
> really allow for much more than arpeggiation with some chromatic "blue
> notes" here and there, but I really like these chords. It's really neat
> having a chain of 5/4's where 128/125 is NOT tempered out.
>
> -Igs
>
>
>
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🔗Chris Vaisvil <chrisvaisvil@...>

Starts out very gothic for me. I like what happens after the intro a lot
better too.

Your lead guitar sound is great!

Here is a question - so you have bass guitars in all of these various
tunings you use or are you using an octave divider?

On Fri, May 20, 2011 at 3:37 AM, cityoftheasleep <igliashon@...>wrote:

>
>
> I've always hated the look of the Magic[10] MOS. Three clusters of very
> small steps, separated from each other by large ~7/6's...melodically, it
> looks dreadful. But for harmony, it's one of the lower-badness temperaments,
> right about on par with Porcupine or so. The lattice is kind of insane, you
> have 5 consonant 5-limit triads, and they're all both major and minor, and
> they're located on the first five "links" of the chain of tempered 5/4's
> that defines Magic's MOS's. However, in my never-ending quest to defy my own
> biases, I decided to try writing something in Magic[10] just to see what
> would happen. Turns out I didn't hate the scale as much as I thought I
> would. I wrote this cheezy pop song:
>
>
> /tuning/files/IgliashonJones/Magic%20Bullets.mp3
>
> Give it a whirl. The melodies are very basic, because the scale doesn't
> really allow for much more than arpeggiation with some chromatic "blue
> notes" here and there, but I really like these chords. It's really neat
> having a chain of 5/4's where 128/125 is NOT tempered out.
>
> -Igs
>
>
>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 3:37 AM, cityoftheasleep
<igliashon@...> wrote:
>
> I've always hated the look of the Magic[10] MOS. Three clusters of very small steps, separated from each other by large ~7/6's...melodically, it looks dreadful. But for harmony, it's one of the lower-badness temperaments, right about on par with Porcupine or so. The lattice is kind of insane, you have 5 consonant 5-limit triads, and they're all both major and minor, and they're located on the first five "links" of the chain of tempered 5/4's that defines Magic's MOS's. However, in my never-ending quest to defy my own biases, I decided to try writing something in Magic[10] just to see what would happen. Turns out I didn't hate the scale as much as I thought I would. I wrote this cheezy pop song:
>
> /tuning/files/IgliashonJones/Magic%20Bullets.mp3
>
> Give it a whirl. The melodies are very basic, because the scale doesn't really allow for much more than arpeggiation with some chromatic "blue notes" here and there, but I really like these chords. It's really neat having a chain of 5/4's where 128/125 is NOT tempered out.

Very cool! I need to get a hang on when you modulate by the normal
major third vs the larger one. I think that Magic is another good
candidate for getting away from the MOS's - the fact that 5 5/4's
become one 3/2 is a pretty neat property to have. There are lots of
ways to exploit that besides forcing yourself to move directly by
major thirds because the 5/4 is the "generator."

-Mike

🔗Michael <djtrancendance@...>

These have to be some of the most steady leads I've ever seen from Igs. You can feel the melodic clustering of the scale...but the confident phrasing here seems to compensate for this well. A little bit Satriani-ish for the lead, gothic for the general chord feel. Sounds incredibly stable...almost to the point I think I could trick someone into thinking it's not microtonal...and manages a strong lead/mood despite the melodic limitations of the scale. Bravo!

--- On Fri, 5/20/11, Chris Vaisvil <chrisvaisvil@...> wrote:

From: Chris Vaisvil <chrisvaisvil@...>
Subject: Re: [tuning] Magic Bullets
To: tuning@...m
Date: Friday, May 20, 2011, 8:25 AM

Starts out very gothic for me. I like what happens after the intro a lot better too.

Your lead guitar sound is great!

Here is a question - so you have bass guitars in all of these various tunings you use or are you using an octave divider?

On Fri, May 20, 2011 at 3:37 AM, cityoftheasleep <igliashon@...> wrote:

/tuning/files/IgliashonJones/Magic%20Bullets.mp3

-Igs

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Very cool! I need to get a hang on when you modulate by the normal
> major third vs the larger one.

When I move by a third, it's always a 5/4 or 6/5. When I move by a sixth, it's usually 25/16 (or 14/9 if you prefer the 7-limit interpretation). I use the E-B# movement a lot, and also the reverse--at the end of the song, for instance, the B#-E cadence works surprisingly well, probably because there's a leading-tone resolution from D##-E (or D#-E if the B# is played minor...I think the lead played the minor 3rd over the rhythm playing the major 3rd, that happened a lot by accident but still worked pretty well).

> I think that Magic is another good candidate for getting away from the MOS's.

Is there a way to do this without decimating the number of roots that form consonant triads, though? With a 10-note scale only half the roots form consonant 5-limit triads as it is, and that's pretty spare by my standards. I wouldn't want to go any lower. How could I go about finding a good MODMOS that keeps the chord-count but loses some of the clustering?

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 1:26 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Is there a way to do this without decimating the number of roots that form consonant triads, though? With a 10-note scale only half the roots form consonant 5-limit triads as it is, and that's pretty spare by my standards. I wouldn't want to go any lower. How could I go about finding a good MODMOS that keeps the chord-count but loses some of the clustering?

You would change the scale that you play over every chord and start
thinking more in terms of 5-limit harmony and comma pumps, just like
jazz musicians have been doing for years. In jazz, if I said to play
Emb5 -> A7b13 -> Dm7, you might play E locrian #2 over the first chord
(from D mixo b6), A altered over the second chord (from Bb harmonic
minor (!), makes use of 128/125 tempering), and D Dorian over the last
chord. All of those scales are MODMOS's of meantone[7]. So although
the whole thing loosely makes use of the 81/80 comma pump, you'd play
whatever scales you want over it to design the colors you want and not
get trapped into the usual diatonic sound.

I'd recommend doing the same thing with magic - find some cool scales
for each chord, and then modulate by major third as you want - that
way you aren't trapped into this dark, magic, augmented "sound" all
the time. I think that scales that incorporate all of the chords we'll
ever need are more the exception rather than the rule - in dicot
temperament, for example, there's only one minor scale, but in
meantone you need three to adequately represent common practice
harmony.

You could try things like (in 19-equal) Cmaj - Gmaj - Emaj - Bmaj -
G#maj - D#maj - Cbmaj - Gbmaj - Ebmaj - Bbmaj - Gmaj -> back to Cmaj.
Or maybe that chord progression is too drawn out for you, but the
point is that there's no reason you can't move around by a fifth if
you want. As for actually designing MODMOS's, just find the chroma
(L-s) and move random notes around by it until you're happy. Since we
don't really know how the MODMOS's work yet (probably will depend on a
better generalization of propriety), I leave the rest to you.

In fact, why do you only have to play magic MOS scales over the magic
tempered lattice at all? You could play a magic-tempered JI major
scale over all of those chords, or if you want something a little more
xenharmonic then you could try playing some mavila scales over each
one in 16-equal, which supports both magic and mavila. Or what's more
likely is you could decide to not just stick to one approach, play
magic-ish scales sometimes, play mavila-ish scales other times, maybe
throw diminished[8] in there if you want, etc.

Cliffnotes: There is more to "magic temperament" than playing major
chords that move around by 5/4.

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> These have to be some of the most steady leads I've ever seen from Igs.

Thanks, Michael. I guess it's a good proof-of-concept for the regular temperament paradigm. One of the many smooth things you can do in 19-EDO, which is probably the EDO most plentiful in low-badness 5-limit temperaments until you get above 41. It beats out 12, 22, 29, 31, 34, and 41 (the only reasonably-small EDOs that can compete with 19 in terms of accuracy in the 5-limit) in terms of sheer number of available low-badness temperaments in the 5-limit, meaning it has lots of scales that aren't too big but are well-supplied with consonant triads. I think it's safe to say that for 5-limit music, 19-EDO "wins".

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 1:59 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Thanks, Michael. I guess it's a good proof-of-concept for the regular temperament paradigm. One of the many smooth things you can do in 19-EDO, which is probably the EDO most plentiful in low-badness 5-limit temperaments until you get above 41. It beats out 12, 22, 29, 31, 34, and 41 (the only reasonably-small EDOs that can compete with 19 in terms of accuracy in the 5-limit) in terms of sheer number of available low-badness temperaments in the 5-limit, meaning it has lots of scales that aren't too big but are well-supplied with consonant triads. I think it's safe to say that for 5-limit music, 19-EDO "wins".

How are you measuring badness? 15-equal has Blackwood, porcupine,
Hanson, and augmented. For more accuracy, 22-equal gives you
porcupine, magic, diaschismasrutaljarasmic. 34-tet gives you tetracot,
diaschismrutalarja, Hanson.

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> You would change the scale that you play over every chord and start
> thinking more in terms of 5-limit harmony and comma pumps, just like
> jazz musicians have been doing for years.

Huh, yeah, I suppose I could do that easily enough. Base the progression itself on the 10-note MOS (or even a larger MOS, I suppose) and just treat each chord change as a modulation.

> As for actually designing MODMOS's, just find the chroma
> (L-s) and move random notes around by it until you're happy.

That would be 4-1=3 in 19-EDO. I'll see what that leads to.

> In fact, why do you only have to play magic MOS scales over the magic
> tempered lattice at all? You could play a magic-tempered JI major
> scale over all of those chords

Which in 19 would be the meantone major scale, which would end up just sounding like a bunch of meantone riffing that modulates around by major 3rds a lot. Probably not the best approach.

> Cliffnotes: There is more to "magic temperament" than playing major
> chords that move around by 5/4.

Yeah, the whole "every triad has a major and a minor 3rd" is pretty clutch, too. I immediately thought of Radiohead's "Creep", which goes Gmaj-Bmaj-Cmaj-Cmin, which of course wouldn't work in Magic (it would probably turn into Gmaj-Bmaj-B#maj-B#min or something), but that device of going from a major to a minor on the same root is pretty cool. Also the Gmaj-G#min (or Gmaj-G#dim), which I do a few times in "Magic Bullets", is something I've always like for a dramatic "here comes the chorus" kind of effect. So melodic woes aside, the Magic[10] MOS diatonicizes some good progressions that require chromatic alterations in other temperaments/scales. In other words, it supplies some familiar "cues" and ends up sounding rather natural because of it.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 2:12 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Huh, yeah, I suppose I could do that easily enough. Base the progression itself on the 10-note MOS (or even a larger MOS, I suppose) and just treat each chord change as a modulation.

You get bonus points if you can figure out how to create a very
clearly "tonal" cadence that sounds completely novel while doing it.

> > As for actually designing MODMOS's, just find the chroma
> > (L-s) and move random notes around by it until you're happy.
>
> That would be 4-1=3 in 19-EDO. I'll see what that leads to.

We've only been looking at proper scales so far, so we have no way of
predicting what will sound good. Maybe you'll find some pattern in
what works and what doesn't.

> > In fact, why do you only have to play magic MOS scales over the magic
> > tempered lattice at all? You could play a magic-tempered JI major
> > scale over all of those chords
>
> Which in 19 would be the meantone major scale, which would end up just sounding like a bunch of meantone riffing that modulates around by major 3rds a lot. Probably not the best approach.

You could also find which singular ET it is that tempers out both
3125/3072 and 256/243 and then get Blackwood and magic in one. My
spider sense is suggesting 25-equal. Or you could mess with other
scales than just bright-sounding fifths based ones as well, but the
point is that you're not locked into Magic[7] as an MOS by any means.

> > Cliffnotes: There is more to "magic temperament" than playing major
> > chords that move around by 5/4.
>
> Yeah, the whole "every triad has a major and a minor 3rd" is pretty clutch, too. I immediately thought of Radiohead's "Creep", which goes Gmaj-Bmaj-Cmaj-Cmin, which of course wouldn't work in Magic (it would probably turn into Gmaj-Bmaj-B#maj-B#min or something)

It seems like it would work to me, but the D# over the Bmaj wouldn't
be the same as the Eb over the C. So you could use that technique too.

> but that device of going from a major to a minor on the same root is pretty cool. Also the Gmaj-G#min (or Gmaj-G#dim), which I do a few times in "Magic Bullets", is something I've always like for a dramatic "here comes the chorus" kind of effect. So melodic woes aside, the Magic[10] MOS diatonicizes some good progressions that require chromatic alterations in other temperaments/scales. In other words, it supplies some familiar "cues" and ends up sounding rather natural because of it.

I'm confused, how so? I know magic predominantly because it merges
25/24 and 128/125. You just mean that the generator chain puts those
notes in the scales, or that the above chord progressions come from
something actually being tempered out in a useful way?

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> How are you measuring badness?

Roughly damage*complexity.

> 15-equal has Blackwood, porcupine, Hanson, and augmented.
> For more accuracy, 22-equal gives you porcupine, magic, diaschismasrutaljarasmic.
> 34-tet gives you tetracot, diaschismrutalarja, Hanson.

19-EDO gives you five 5-limit temperaments: Negri, Godzilla, Hanson, Magic, and Meantone (I may have erroneously included Sensi, which is very high complexity), and you might also count Triton, too, though it's borderline on excessive complexity. All of which are very accurate. No other EDO from 41 or lower gives you more while maintaining a comparable level of accuracy. I'm not sure any EDO in that range gives you more even with much lower accuracy.

-Igs

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> You get bonus points if you can figure out how to create a very
> clearly "tonal" cadence that sounds completely novel while doing it.

I thought the B#-E cadence sounded pretty cool. B#-E in 12 wouldn't allow a leading-tone resolution from D## to E, because they'd be the same note.

> We've only been looking at proper scales so far, so we have no way of
> predicting what will sound good. Maybe you'll find some pattern in
> what works and what doesn't.

That'll be my project for the day: MODMOS's of Magic[10].

> You could also find which singular ET it is that tempers out both
> 3125/3072 and 256/243 and then get Blackwood and magic in one. My
> spider sense is suggesting 25-equal.

Bingo. The 3-limit takes a hit but the 5 is near-perfect.

> You just mean that the generator chain puts those notes in the scales

Yes.

-Igs

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:

> 19-EDO gives you five 5-limit temperaments: Negri,
> Godzilla, Hanson, Magic, and Meantone (I may have
> erroneously included Sensi, which is very high
> complexity), and you might also count Triton, too, though
> it's borderline on excessive complexity. All of which
> are very accurate. No other EDO from 41 or lower gives
> you more while maintaining a comparable level of
> accuracy. I'm not sure any EDO in that range gives you
> more even with much lower accuracy.

What counts as a comparable level of accuracy? Which of
Diaschismic(Srutal), Schismatic(Helmholtz), Augmented,
Injera, Compton, or Diminished have an incomparable level?
I suppose Compton would be excluded for the same reasons as
Sensi, but I still count six for 12.

Generally, the best equal temperaments lead to the best
temperaments of higher rank. I don't see there's anything
special about 19. It's pretty good in the 5-limit but
always beaten by 12 or 53 (Helmholtz, Hanson, Amity, Orson,
Vulture) in terms of 5-limit Cangwu badness. It has a lower
error than 12, which also cascades to higher ranks.

This is a list that makes 19 look reasonably good:

http://x31eq.com/cgi-bin/more.cgi?r=2&limit=5&error=3

There are some higher limits where 19 EDO seems to dominate,
but I can't reproduce a list offhand. The reason is that
there are two different mappings. 19 EDO is ambigous in
the 13-limit and beyond.

Graham

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> What counts as a comparable level of accuracy? Which of
> Diaschismic(Srutal), Schismatic(Helmholtz), Augmented,
> Injera, Compton, or Diminished have an incomparable level?
> I suppose Compton would be excluded for the same reasons as
> Sensi, but I still count six for 12.

I'm only counting temperaments that lead to unique scales. Schismatic leads to the same scales as Meantone in 12-TET, and Injera the same as Diaschismic. That knocks 12 down to four.

> Generally, the best equal temperaments lead to the best
> temperaments of higher rank. I don't see there's anything
> special about 19. It's pretty good in the 5-limit but
> always beaten by 12 or 53 (Helmholtz, Hanson, Amity, Orson,
> Vulture) in terms of 5-limit Cangwu badness. It has a lower
> error than 12, which also cascades to higher ranks.

I didn't look at 53. 12 is tough to beat in terms of sheer badness.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 3:46 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> > What counts as a comparable level of accuracy? Which of
> > Diaschismic(Srutal), Schismatic(Helmholtz), Augmented,
> > Injera, Compton, or Diminished have an incomparable level?
> > I suppose Compton would be excluded for the same reasons as
> > Sensi, but I still count six for 12.
>
> I'm only counting temperaments that lead to unique scales. Schismatic leads to the same scales as Meantone in 12-TET, and Injera the same as Diaschismic. That knocks 12 down to four.

Alright, but it's not fair for you to count Godzilla[9] then when
there's hardly any 5-limit harmony in it at all. So that knocks 19
down to 4. And are we going by error here? Because 15 has Blackwood,
Hanson, Porcupine, and Augmented, and these are temperaments of
exceptional mojo, once you get past the lack of periodicity buzz and
need to use clever timbres.

But I think you've convinced me anyways, I'll put the 15-tet guitar on
hold for a bit and get a 19-tet one first.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 3:56 PM, Mike Battaglia <battaglia01@...> wrote:
>
> Alright, but it's not fair for you to count Godzilla[9] then when
> there's hardly any 5-limit harmony in it at all.

Taking this further, what are you counting as 5-limit Godzilla? That
two 75/64's gives you a 4/3? Because if so, that's just Negri. It's
the every-other-generator MOS of Negri, like how Deutone is the
every-other-generator MOS of meantone. The difference between
(75/64)^2 and 4/3 is 16875/16384.

So that's four! Four good 19-tet 5-limit temperaments. But I think I'm
still convinced that that's the way to go.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Alright, but it's not fair for you to count Godzilla[9] then when
> there's hardly any 5-limit harmony in it at all.

Fair enough. 2 out of 9 triads isn't really much, I'll admit.

> So that knocks 19 down to 4.

Back to being tied with 12 for variety, behind 12 for complexity, and ahead of 12 for accuracy.

> And are we going by error here? Because 15 has Blackwood,
> Hanson, Porcupine, and Augmented, and these are temperaments of
> exceptional mojo, once you get past the lack of periodicity buzz and
> need to use clever timbres.

Well, we're going by error. But 15 is a power-house, too; see below. In any case, 19 beats the pants off of 31 for 5-limit stuff, insofar as complexity and variety are concerned. The next-best 5-limit temperament in 31 after Meantone is Wuerschmidt, which is a good bit more complex. 19 also handily beats 22, being both more accurate and simpler and having more variety. 34 is more accurate but larger and also less varied. 41's not even on the radar.

> But I think you've convinced me anyways, I'll put the 15-tet guitar on
> hold for a bit and get a 19-tet one first.

Hey, this is just the 5-limit we're talking about. 19 doesn't look quite so compelling in higher limits. 19 has Negrisept, which is reasonably accurate and reasonably simple, but 15 has Blacksmith...crikey, man, it's hard to argue with 5 full otonal tetrads and 5 full utonal tetrads, 100% root coverage with target harmonies. You just can't beat that level of efficiency. 15 beats 19 in the 2.5.11 subgroup, Porcupine DUH. And It's also almost impossible to fool anyone into thinking 15 is normal, unless you're playing ambient music with it. An added benefit might be that your friends are less likely to scoff at the fretboard of a 15-EDO guitar...they might not even see the difference at first!

Honestly, every time I get a new guitar refretted, I think about 15 but then opt for something else at the last minute. I almost went 15 before 16, before 20, and before 23, and I'm half expecting that when I try to do my own re-fret on my classical guitar, I'll freak out at the last minute and go 18 instead. I get so hung up the fact that 15-EDO has the weak 5-EDO fifth and the weak 3-EDO major 3rd that I totally ignore that it's got intervals less than 10 cents from 11/4 and 7/4, a killer 5/3 and 11/5, and all those good temperaments you mentioned. 19's great, but I'm kind of kicking myself for putting off 15 for so long.

-Igs

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 6:29 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > 34 is more accurate but larger and also less varied. 41's not even > on the radar.
>
> 34 has 2048/2025, 15625/15552, 20000/19683, 393216/390625 and 1638400/1594323, and is much more accurate than 19. Plus, its fifth kicks the 19 fifth's sorry ass.

Yes, it does. The only thing is that 19-equal has the benefit of being
easily playable on a guitar. If it weren't for that, 34-equal would
dominate all. But wait, what's this?

http://www.c-thru-music.com/images/bass.jpg

Maybe that'll solve that problem.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Yes, it does. The only thing is that 19-equal has the benefit of being
> easily playable on a guitar. If it weren't for that, 34-equal would
> dominate all.

Speaking of slightly sharp fifths, 46 doesn't get any respect as a 5-limit system, but it does have 2048/2025, 78732/78125, 1600000/1594323, and 1990656/1953125. If that's not enough for you, toss in 34359738368/32958984375 and 131072000/129140163, which are better than they look.

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 7:27 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Yes, it does. The only thing is that 19-equal has the benefit of being
> > easily playable on a guitar. If it weren't for that, 34-equal would
> > dominate all.
>
> Speaking of slightly sharp fifths, 46 doesn't get any respect as a 5-limit system, but it does have 2048/2025, 78732/78125, 1600000/1594323, and 1990656/1953125. If that's not enough for you, toss in 34359738368/32958984375 and 131072000/129140163, which are better than they look.

34359738368/32958984375 seems cool, how are you analyzing it? It looks
like the generator is 256/225 and three of them put you at 5/4. And
then 131072000/129140163 is 5-limit Rodan again.

I wonder if this whole thing suggests a new type of badness measure to
analyze comma pumps. If we're talking about repeated motions by
something like 81/80 turning into something like 16/15, or whatever it
is we're trying to do, then not only do the numbers involved quickly
get huge, but we've effectively just created some leverage with which
to maneuver around the 5-limit lattice. I never thought something like
amity would be useful for anything other than purely theoretical
reasons, but this approach makes it possible to traverse huge portions
of the JI lattice very easily and practically. Cmaj -> A-m -> D-m ->
G-maj -> C-maj is a pretty simple motion that can move you by 81/80,
so by doing that a number of times you can easily explore something
like Amity or Gravity or Immunity or etc.

Perhaps we could come up with a "pun badness" score based on the
number of 5/4, 3/2, and 6/5 motions that it takes to get to the comma
in question (and hence traverse the pump). Two ways I can think of
doing this

1) represent the comma in 2.3.5 space, drop the 2, and look at what
you have left in the monzo for 3 and 5. Then come up with a third
column representing 6/5 - condense as many +3 -5 motions into a single
+6/5 motion as possible. Then either compute the naive score, or
weight it so that motion by 3 is better than motion by 5, both are
better than motion by 6/5, etc. If you pick the weighting to be a
certain way you might be able to skip the condensation of everything
into 6/5.

2) work out the minimal pump for the comma, and then take every step
in this minimal pump that isn't 5/4, 3/2, or 6/5 and break it down
into that. I can't tell if this will be the same as the above.

Any thoughts?

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> 34359738368/32958984375 seems cool, how are you analyzing it? It looks
> like the generator is 256/225 and three of them put you at 5/4.

That's pretty cheesy; in fact, it's three 2048/1875 intervals to get to 5/4. It extends to the 7-limit by tempering out 686/675 and 6144/6125, giving the 9&37 temperament with an ~15/14 generator. It looks even better in the 11-limit, tempering out 121/120, 176/175 and 686/675. The 13-limit looks better yet, tempering out 91/90 and 169/168 in addition to the previously cited commas. This needs to be named and cataloged.

🔗Mike Battaglia <battaglia01@...>

On Fri, May 20, 2011 at 10:21 PM, genewardsmith
<genewardsmith@...t> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > 34359738368/32958984375 seems cool, how are you analyzing it? It looks
> > like the generator is 256/225 and three of them put you at 5/4.
>
> That's pretty cheesy; in fact, it's three 2048/1875 intervals to get to 5/4.

Is that tempered equal to what I said, or did I screw up?

> It extends to the 7-limit by tempering out 686/675 and 6144/6125, giving the 9&37 temperament with an ~15/14 generator. It looks even better in the 11-limit, tempering out 121/120, 176/175 and 686/675. The 13-limit looks better yet, tempering out 91/90 and 169/168 in addition to the previously cited commas. This needs to be named and cataloged.

If it tempers out 91/90 then it can go in the Biosphere page as well.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Chris Vaisvil <chrisvaisvil@...>

if its cheesy then its all about curds and whey - and the bacteria that
create cheese from milk are obviously in the biosphere

I suggest the name "whey" temperament.

On Fri, May 20, 2011 at 10:45 PM, genewardsmith <genewardsmith@...
> wrote:

>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > That's pretty cheesy; in fact, it's three 2048/1875 intervals to get to
> 5/4.
> >
> > Is that tempered equal to what I said, or did I screw up?
>
> You screwed up, sorry.
>
>
> > If it tempers out 91/90 then it can go in the Biosphere page as well.
>
> What's a good biospheroidal name for it?
>
>
>

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

Although I'm certainly more of a fan of 34 than 19, 19 does have neat things, like the equation of the minor chroma and the diesis. This makes for things like going from #V to bVI slinkily, which is like slapping 12-tET upside the head with a silk pillow.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, May 20, 2011 at 6:29 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > 34 is more accurate but larger and also less varied. 41's not even > on the radar.
> >
> > 34 has 2048/2025, 15625/15552, 20000/19683, 393216/390625 and 1638400/1594323, and is much more accurate than 19. Plus, its fifth kicks the 19 fifth's sorry ass.
>
> Yes, it does. The only thing is that 19-equal has the benefit of being
> easily playable on a guitar. If it weren't for that, 34-equal would
> dominate all. But wait, what's this?
>
> http://www.c-thru-music.com/images/bass.jpg
>
> Maybe that'll solve that problem.
>
> -Mike
>

🔗lobawad <lobawad@...>

bvi I meant (but you can ooze around all "sixes", as you can demonstrate to yourself by starting I, I+, #V, and going from there)

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Although I'm certainly more of a fan of 34 than 19, 19 does have neat things, like the equation of the minor chroma and the diesis. This makes for things like going from #V to bVI slinkily, which is like slapping 12-tET upside the head with a silk pillow.
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Fri, May 20, 2011 at 6:29 PM, genewardsmith
> > <genewardsmith@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > > 34 is more accurate but larger and also less varied. 41's not even > on the radar.
> > >
> > > 34 has 2048/2025, 15625/15552, 20000/19683, 393216/390625 and 1638400/1594323, and is much more accurate than 19. Plus, its fifth kicks the 19 fifth's sorry ass.
> >
> > Yes, it does. The only thing is that 19-equal has the benefit of being
> > easily playable on a guitar. If it weren't for that, 34-equal would
> > dominate all. But wait, what's this?
> >
> > http://www.c-thru-music.com/images/bass.jpg
> >
> > Maybe that'll solve that problem.
> >
> > -Mike
> >
>