Yahoo Tuning Groups Ultimate Backup tuning The demolished 7 chord

I kind of got a bit side-tracked from what I was saying about the many uses of the diminished 7 chord in jazz harmony. First of all, because it's the same under inversion, its indispensable for connecting different substitutions between tonal chords. This is where it's beauty lies, in context and not as a chord in itself. For eg, the 'turnaround' I VI II V7 as Cma7 A7 Dmi7 G7 becomes Cma7 C#dim7 Dmi7 Ddim7, or since the Emi group substitutes for the C (secondary relative minor), Emi7 Edim7 Dmi7 Ddim7 and so on. On the guitar for eg this gives dominant chords that are always close to any chord voicing we wish to choose because the dim's are all over the neck.

Then there is also the beautiful beating harmonies we get when we play these against the bass. If the bass player plays a G and the piano/guitar a Ddim7 we get a nice G7(b9). Over this a soloist can play a variety of scales, jazz diminished (basically Ab dim scale over G bass), Jazz melodic minor (an ascending Ab melodic minor over G bass) and so on. Other standard substitutions are the 7(b5) which descends chromatically when cycling. Since A7(b5) is enharmonically equivalent to Eb7(b5) our turnaround becomes Emi9, Eb9(b5), Dmin9, Db9(b5) for one example.

In jazz we want *options* for constant and quick variation, and it is not necessarily about dwelling on the niceties of how this or that chord sounds by itself, especially not on synthetised instruments over long durations. It is a bout playing and impro and in this respect the 12 ET system does pretty good IMO.

Rick

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>
> I kind of got a bit side-tracked from what I was saying about the many uses of the diminished 7 chord in jazz harmony. First of all, because it's the same under inversion, its indispensable for connecting different substitutions between tonal chords.

Since this is the tuning list and not the jazz list, I get to point out that the meantone dim7 chord, or the pajara version, or the 1-7/6-7/5-5/3 JI version, are also the same under inversion with suitable transposition, and sound less boring. Also, the 12:14:17:20 chord, which is not the same under inversion, can use that very fact to creep around in an oily kind of way, by alternating otonal and utonal chords. Why not try to cook up some xenharmonic jazz?

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > > Since this is the tuning list and not the jazz list, I get to
> > > point out that the meantone dim7 chord, or the pajara version,
> > > or the 1-7/6-7/5-5/3 JI version, are also the same under
> > > inversion
> >
> > How's the JI version the same under inversion? -Carl
>
> 2/intervals: 6/5-10/7-12/7-2
> 7/6 up: 7/5-5/3-2-7/3
> Top two down an octave: 1-7/6-7/5-5/3

I'm lost. I believe the inversions are

1 7/6 7/5 5/3

1 6/5 10/7 12/7

1 25/21 10/7 5/3

1 6/5 7/5 42/25

no two of which are the same, though they are close in
an interesting way and this is a neat chord.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗rick <rick_ballan@...>

Oh this strand goes right back to Marcel's JI tuning of Beethoven which sounded quite nice until it hit diminished chords. I suggested that trying to rationalise irrationals was fitting a square peg into a round hole. But you're right about meantone dim7. It sounded pretty good to me in all inversions.

I've got an old guitar here which I'm contemplating defretting.

🔗Marcel de Velde <m.develde@...>

Hi Rick,

Oh this strand goes right back to Marcel's JI tuning of Beethoven which
> sounded quite nice until it hit diminished chords.

Are you talking about my JI tuning of Beethoven done yesterday?
(before I got a lot wrong, including the diminished)

Drei Equale no1 hits the diminished seventh at 47 and 56 seconds:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_12-July-2010%29.mid

Drei Equale no2 hits the diminished sevenths at 1min 5sec and 1min 9sec:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%28M-JI_12-July-2010%29.mid

They sound absoultely beautifull to me.
Compared the 12edo diminished seventh sounds lifeless/loring and out of tune
to me:
no1:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%2812edo%29.mid
no2:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%2812edo%29.mid

Marcel

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > > > Since this is the tuning list and not the jazz list, I get to
> > > > point out that the meantone dim7 chord, or the pajara version,
> > > > or the 1-7/6-7/5-5/3 JI version, are also the same under
> > > > inversion
> > >
> > > How's the JI version the same under inversion? -Carl
> >
> > 2/intervals: 6/5-10/7-12/7-2
> > 7/6 up: 7/5-5/3-2-7/3
> > Top two down an octave: 1-7/6-7/5-5/3
>
> I'm lost. I believe the inversions are
>
> 1 7/6 7/5 5/3
>
> 1 6/5 10/7 12/7
>
> 1 25/21 10/7 5/3
>
> 1 6/5 7/5 42/25
>
> no two of which are the same, though they are close in
> an interesting way and this is a neat chord.
>
> -Carl
>
I'm with Carl here. It also doesn't come back at the 8ve. The inverted comma's around 'suitable inversions' is precisely the problem I was trying to get across to Marcel at the time. It should be at least close to the same for all keys. Personally what I find a bit boring is music that doesn't modulate i.e. pre Bach.

-Rick

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > I kind of got a bit side-tracked from what I was saying about the many uses of the diminished 7 chord in jazz harmony. First of all, because it's the same under inversion, its indispensable for connecting different substitutions between tonal chords.
>
> Since this is the tuning list and not the jazz list, I get to point out that the meantone dim7 chord, or the pajara version, or the 1-7/6-7/5-5/3 JI version, are also the same under inversion with suitable transposition, and sound less boring. Also, the 12:14:17:20 chord, which is not the same under inversion, can use that very fact to creep around in an oily kind of way, by alternating otonal and utonal chords. Why not try to cook up some xenharmonic jazz?
>
Just as an afterthought, someone saying that they find the diminished chord "boring" is, to my mind, like saying that the word "and" is boring to a writer. As I said, it's use is as a conjunctive between keys. It's 'oily' character comes from the fact that it is or is sufficiently close to the 4th root of 2. Even (6/5)^4 is closer to 2 than the JI tuning given. There is also those wonderful beats you get when you play it with clashing upper harmonics like on a piano (not with sine waves in isolation). So even if Bach played slightly different tunings of this, it is still close enough for it to have this character. And there's nothing boring about his music. I was also going to say that xenharmonia and alternate tunings are not necessarily synonymous. If we are going to explore alternate tunings to 12 tET then it's not too much to ask to have at least some understanding of it, and not to replay history by trying to turn everything into JI or fly off into the void of infinite possibilities (which also ends up being all the same, i.e. boring. How can we modulate when we have no tonal centre?).

-Rick

🔗Marcel de Velde <m.develde@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> Just as an afterthought, someone saying that they find the diminished chord "boring" is, to my mind, like saying that the word "and" is boring to a writer. As I said, it's use is as a conjunctive between keys.

Possibly because it is too boring as a sonority to serve any other purpose.

> It's 'oily' character comes from the fact that it is or is sufficiently close to the 4th root of 2.

I was talking about 12:14:17:20 specifically, and its oily movement comes from a lot more than just that. A key fact is that 24/17 and 17/12 are only six cents apart.

>I was also going to say that xenharmonia and alternate tunings are not necessarily synonymous.

And your improved definition is?

🔗Graham Breed <gbreed@...>

🔗rick <rick_ballan@...>

No not at all Marcel. I said it sounded much better didn't I? I'm talking about the very first one you did, probably a year ago now.

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Rick,
>
> Oh this strand goes right back to Marcel's JI tuning of Beethoven which
> > sounded quite nice until it hit diminished chords.
>
>
> Are you talking about my JI tuning of Beethoven done yesterday?
> (before I got a lot wrong, including the diminished)
>
> Drei Equale no1 hits the diminished seventh at 47 and 56 seconds:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_12-July-2010%29.mid
>
> Drei Equale no2 hits the diminished sevenths at 1min 5sec and 1min 9sec:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%28M-JI_12-July-2010%29.mid
>
> They sound absoultely beautifull to me.
> Compared the 12edo diminished seventh sounds lifeless/loring and out of tune
> to me:
> no1:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%2812edo%29.mid
> no2:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%2812edo%29.mid
>
> Marcel
>

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Rick,
>
> Just as an afterthought, someone saying that they find the diminished chord
> > "boring" is, to my mind, like saying that the word "and" is boring to a
> > writer.
>
>
> I said lifeless / boring and out of tune.
> Have you compared the midi files I linked to in my preious message?
> In JI the diminished seventh can fullfill all the functions you described,
> while sounding a lot better than in 12edo.
>
> Marcel
>
I was referring to Gene's comment that he said the dim7 in usual tuning sounded boring, sorry, BORING. My point was that its not a chord 'unto itself' but has many many uses. I did listen to yours and they sound pretty good to my ears. But even assuming that they sound better than 12 tET, you would still have to overcome the problem that the 12 tET system is very practical for writing/performing music with modulations. It has been said that composers like Bach, Beethoven were so prolific because they practically improvised their music on the keyboard and then wrote it down for orchestra etc...They had to be. In this respect they really are like jazz musicians. And although some people might not like to hear it, but need to, practising and studying for years and years on end to become fluent on an instrument does help to sort the wheat from the chaff. It teaches for example that music constantly *moves forward*. In order to improvise or compose prolifically, the options have to be quick and immediate and if one dwells on mistakes or small tuning errors then the music goes on without you. Have you ever tried your own hand at composition? Maybe you should Marcel.

-Rick

🔗rick <rick_ballan@...>

Again, I think you're dwelling on it too much as a sound and not a purpose. I don't have to remind you that the whole point of any ET is that the notes serve a dual function as both the notes in chords and between keys. But even with sounds, try for example Ddim7/G instead of G7 and deliberately voice it so that the G-Ab are only one 8ve apart. Not boring at all, especially in a slow moving piece.
>
> > It's 'oily' character comes from the fact that it is or is sufficiently close to the 4th root of 2.
>
> I was talking about 12:14:17:20 specifically, and its oily movement comes from a lot more than just that. A key fact is that 24/17 and 17/12 are only six cents apart.

Well I think Graham answered this question.
>
> >I was also going to say that xenharmonia and alternate tunings are not necessarily synonymous.
>
> And your improved definition is?

Well I wouldn't exactly call JI "Xenharmonic", or meantone, or...
>

🔗rick <rick_ballan@...>

About 12:14:17:20, it should also be noted that my model also predicts that b5th will have wave convergents 17/12 or 10/7 and maj 6th will have 12/7 and 17/10. Interesting. I would never have thought of that diminished.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Just as an afterthought, someone saying that they find the diminished chord "boring" is, to my mind, like saying that the word "and" is boring to a writer. As I said, it's use is as a conjunctive between keys.
>
> Possibly because it is too boring as a sonority to serve any other purpose.
>
> > It's 'oily' character comes from the fact that it is or is sufficiently close to the 4th root of 2.
>
> I was talking about 12:14:17:20 specifically, and its oily movement comes from a lot more than just that. A key fact is that 24/17 and 17/12 are only six cents apart.
>
> >I was also going to say that xenharmonia and alternate tunings are not necessarily synonymous.
>
> And your improved definition is?
>

🔗rick <rick_ballan@...>

Gene, another interesting progression that comes from dim is to have say a G and F in the bottom of the chord (LH on piano) and play triads (RH) Gmin, Gmaj, Emin, Emaj, Dbmin, Dbmaj and Bbmin, Bbmaj. Then the cycle starts again in its next inversion. These substitute for G7 leading to C. Note that these are triads moving in minor thirds (along dim notes). The scale a soloist will play will be the jazz diminished which is basically an Ab dim scale starting from G i.e. semitone, tone, semitone, tone etc...

These chords are Gmi7, G7, G13, G13(b9), G13(b9b5)...

These are the types of harmonies I have in mind when I say that trying to retune them in JI would lead to all kinds of difficulties. What key is the E triad/G7 bass in for eg? Do we tune it to C, E or both?

-Rick

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Possibly because it is too boring as a sonority to serve any other purpose.

...and 4:5:6 is exciting? Gosh, I've heard the dim7 chord described as a lot of things--discordant, piquant, rough, harsh, sinister, etc.--but this is definitely a first for "boring". Regardless, Gene, I don't think this is the right argument to make, since (IIRC), this debate is about the JI tuning of a dim7 chord, and anyone arguing for the equal-tempered "4-EDO" version is totally off-base. The proper argument against what Rick is saying is "tempered chords have no place in JI, so regardless of the purpose and character of the dim7 in tempered music, we have to look at it differently in JI." If this argument keeps going in its current direction, it's just going to devolve into an "ET vs JI" argument, and we all know how those go...

-Igs

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
> Again, I think you're dwelling on it too much as a sound and not a purpose. I don't have to remind you that the whole point of any ET is that the notes serve a dual function as both the notes in chords and between keys. But even with sounds, try for example Ddim7/G instead of G7 and deliberately voice it so that the G-Ab are only one 8ve apart. Not boring at all, especially in a slow moving piece.
>

Rick, aren't you kind of arguing apples to oranges here? Knowing that the function of a dim7 in equal temperament is contingent on the equality of spacing between the notes doesn't really solve the problem of how to tune it in JI. Are you suggesting that in a piece of JI music, dim7 chords should be tuned as they are in equal temperament? That for one chord in a piece, the JI should fall away into an equal temperament? I don't see how anyone into JI could buy that.

Your argument is more a "roundabout" way of arguing for ET over JI for certain kinds of music than it is arguing for a specific tuning of the dim7 chord in JI. If that's really the argument you want to make, a more direct approach might be more productive.

-Igs

🔗genewardsmith <genewardsmith@...>

Bah. Have you ever compared the various versions of the dim7? The 4et version stands out because of its boring quality.

>The proper argument against what Rick is saying is "tempered chords have no place in JI, so regardless of the purpose and character of the dim7 in tempered music, we have to look at it differently in JI."

Since I see no clear audible line between JI and microtempering, this argument makes no sense to me. What Marcel did would sound very much the same if you retuned it to 53, 118, or 171 I believe.

🔗Marcel de Velde <m.develde@...>

Hi Gene,

Since I see no clear audible line between JI and microtempering, this
> argument makes no sense to me. What Marcel did would sound very much the
> same if you retuned it to 53, 118, or 171 I believe.
>

Funny thing is, I thought it would too.
However, I've rendered the Drei Equale no1 in Pythagorean aswell by
extending the chain of fifths down.
So where 32/27 fifth down is 405/256 untempered, in Pythegorean I did 128/81
instead of 405/156 etc.
This way of doing Pythagorean makes a difference of only 1,5 cents (Schisma)
for 6 of the 12 tones (other 6 stay the same offcourse).
I thought this wouldn't be really audible, but to my surprise it is very
much so!.
It sounded significantly worse.
I've never been that bothered by 1,5 cents difference before really strange.
But my latest JI system is apparently very sensitive to tempering.
A 1/1 3/2 2/1 5/2 chord makes small differences audible, but I'm hearing it
in dissonant chords aswell strange enough, and I guess it's also due to the
tempering of 256/243 and 135/128 into 1 interval which seems to be
noticable.
Haven't tried 53edo yet though, but it's not very different from a chain of
pure fifths if I'm right?

Marcel

🔗Marcel de Velde <m.develde@...>

> I was referring to Gene's comment that he said the dim7 in usual tuning
> sounded boring, sorry, BORING. My point was that its not a chord 'unto
> itself' but has many many uses. I did listen to yours and they sound pretty
> good to my ears. But even assuming that they sound better than 12 tET, you
> would still have to overcome the problem that the 12 tET system is very
> practical for writing/performing music with modulations. It has been said
> that composers like Bach, Beethoven were so prolific because they
> practically improvised their music on the keyboard and then wrote it down
> for orchestra etc...They had to be. In this respect they really are like
> jazz musicians. And although some people might not like to hear it, but need
> to, practising and studying for years and years on end to become fluent on
> an instrument does help to sort the wheat from the chaff. It teaches for
> example that music constantly *moves forward*. In order to improvise or
> compose prolifically, the options have to be quick and immediate and if one
> dwells on mistakes or small tuning errors then the music goes on without
> you. Have you ever tried your own hand at composition? Maybe you should
> Marcel.
>
> -Rick
>

I will start with composing soon :)
I just needed to find my tuning system first.

As for modulations.
Yes you have "the" point there.
Honestly, I don't know what the tuning rules for modulations are.
Only that at some point it means a scale is transposed up or down (or better
said perhaps, the 2 chains of fifths are extended in one direction and
shortened in the other to get at a new 12 tone scale).

However. Even though I can't tell you exactly how this'll work, I can tell
that it does not need to be a mathematical impossibility.
Just like crazy things can be done in one key (all 3 drei equale in one key
without a single modulation), if one allows the mathematics of the 2 chains
of fifths be the judge of exactly when the modulation happends then there is
no problem.
And you'll find that the diminished 7th is indeed a perfectly ok chord that
can live in 2 "keys" at once in many circumstances (as are many other
chords).

It will only be when you are playing a diminished 7th for instance, in a
specific location in the key, and then modulate to a different key that
doesn't have the transposed version of this same diminished 7th in the same
inversion, at a moment not by choice of the "scale mathematics" but at an
artificial moment of choice by the artist/composer, that a mathematical
problem can arrise.
These are a lot of "if's". And I'm not sure if music rules would need them
or allow them.
But lets say you philosophically feel that it has to be so. Well.. then
there are 2 mathematical solutions.
Both ugly. 1 is to have a comma shift in a possibly held note. 2 is to have
a chord which doesn't fit he 12tone scale of the original key nor the 12tone
scale of the new key but has pitches that are a combination of both.
But, I personally think the above scenario will never occur in actual music,
not jazz, not classical.
I think the books need to be rewritten based on tuning, and what's called a
key and modulation (and when it exactly occurs) are not even that clear now
in normal music theory, but even in their unclarity seem to still be wrong.
JI is the thing that can give the real rules of music (and universe perhaps
haha) I feel.
The other option, 12edo, I don't think it's needed and I don't think it
sounds good.

Marcel

🔗genewardsmith <genewardsmith@...>

🔗Marcel de Velde <m.develde@...>

🔗genewardsmith <genewardsmith@...>

🔗Marcel de Velde <m.develde@...>

Hi Gene,

Here are the files:
M-JI:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_12-July-2010%29.mid
12edo:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%2812edo%29.mid
tempered to Pythagorean:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-Pythagorean%29.mid
tempered to 53edo:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI-53edo-tempered%29.mid
tempered to 118edo:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI-118edo-tempered%29.mid

I would have no problem at all picking out the Pythagorean or 53edo compared
to the M-JI, but I can't reliably tell the difference between 118edo en M-JI
indeed.
Too bad the 53edo doesn't do better. I allways though it was as good as JI.
But good that there's a new one to take it's place, 118edo :)

Marcel

On 14 July 2010 02:51, genewardsmith <genewardsmith@...> wrote:

> > > Different enough that twelve notes of it are probably more like the
> scale
> > > you are using than like Pythagorean, I think. 118 is maybe even a
> better
> > > thing to try, however.
> >
> >
> > Ok I'll make a comparison between M-JI and M-JI tempered to Pythagorean
> and
> > 53edo.
> > Not sure on how to use 118edo.
>
> In 118edo, a fifth is 69/118 octave and a major third is 38/118 octave.

🔗Marcel de Velde <m.develde@...>

Oh what's real funny..
If you listen to all the version and than as last one 12edo.
It's crazy how out of tune 12edo sounds then :)
Strong loss of clarity aswell.

Marcel

On 14 July 2010 04:10, Marcel de Velde <m.develde@...> wrote:

> Hi Gene,
>
> Here are the files:
> M-JI:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_12-July-2010%29.mid
> 12edo:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%2812edo%29.mid
> tempered to Pythagorean:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-Pythagorean%29.mid
> tempered to 53edo:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI-53edo-tempered%29.mid
> tempered to 118edo:
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI-118edo-tempered%29.mid
>
> I would have no problem at all picking out the Pythagorean or 53edo
> compared to the M-JI, but I can't reliably tell the difference between
> 118edo en M-JI indeed.
> Too bad the 53edo doesn't do better. I allways though it was as good as JI.
> But good that there's a new one to take it's place, 118edo :)
>
> Marcel

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Possibly because it is too boring as a sonority to serve any other purpose.
>
> ...and 4:5:6 is exciting? Gosh, I've heard the dim7 chord described as a lot of things--discordant, piquant, rough, harsh, sinister, etc.--but this is definitely a first for "boring". Regardless, Gene, I don't think this is the right argument to make, since (IIRC), this debate is about the JI tuning of a dim7 chord, and anyone arguing for the equal-tempered "4-EDO" version is totally off-base. The proper argument against what Rick is saying is "tempered chords have no place in JI, so regardless of the purpose and character of the dim7 in tempered music, we have to look at it differently in JI." If this argument keeps going in its current direction, it's just going to devolve into an "ET vs JI" argument, and we all know how those go...
>
> -Igs
>
I don't buy this at all Igs. Staunch JIists completely fail to distinguish between tonal and atonal (pantonal) chords. Only the former have their basis in JI and the harmonic series. For an example of atonality, look at the related b5 interval as Srt2 or a "2 EDO". JI tried to avoid this for centuries, calling it the "Devil's interval" etc...This discomfort with irrationals goes way back to Pythagoras when he discovered that the hypotenuse of a right angle triangle of sides 1 was sqrt 2 and not a rational. Musically this was emancipated with both the blues and also (eventually) serialism. Mathematically it led to the new number system of the set of reals. It's the *only* interval that is the same under 8ve inversion; sqrt2/1 = 2/sqrt2. Since each note stands precisely in the same relation to the other then, at least theoretically, it doesn't have a tonic.

However, this is to be distinguished between the #11 which *is* a tonal chord. maj7(#11) is one example (Cma7(#11) has C-E-G-D-F#-A for eg). This is completely separate from say C7(b5) which is enharmonically equal to Gb7(b5) (C-E-Gb-Bb). In 12 EDO the b5 and #11 *just so happen* to be the same note. But they are born from a very different tree, #11 is JI, b5 is EDO. EDO's appear wherever the music is passing *between* keys or roots, and dim7 is just one example. In contrast we have tonal chords which sound like they have arrived or landed.

Knowing that the word "jass" was a euphemism for sex, that pianists were hired to improvise in brothels, it's really not surprising that the b5 and its derivatives like dim7 now hold an important place in jazz music. JIists would have us all bopping to the Gregorian chant!

-Rick

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>For an example of atonality, look at the related b5 interval as Srt2 or a "2 EDO". JI tried to avoid this for centuries, calling it the "Devil's interval" etc...

"JI" did no such thing. People were not using JI when this term was invented, and even in circulating temperaments the tritone was not going to be exactly sqrt(2). In meantone, of course, the augmented fourth and diminished fifth are two different intervals.

>This discomfort with irrationals goes way back to Pythagoras when he discovered that the hypotenuse of a right angle triangle of sides 1 was sqrt 2 and not a rational.

Pythagoras probably did not discover this. Hippasus seems to be the leading candidate.

> Musically this was emancipated with both the blues and also (eventually) serialism.

Long, long before that.

>EDO's appear wherever the music is passing *between* keys or roots, and dim7 is just one example.

They do? How do they magically appear?

> JIists would have us all bopping to the Gregorian chant!

Yeah, that Harry Partch. Wild for Gregorian chant.

Have you ever looked at 22? Like 12, it tempers out 50/49, and so sqrt(2) is used for both 7/5 and 10/7 in septimal harmony. It seems amenable to jazz.

🔗cityoftheasleep <igliashon@...>

Hi Rick,

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
> I don't buy this at all Igs. Staunch JIists completely fail to distinguish between tonal and atonal (pantonal) chords.
>

And that's *exactly* my point: in JI, there's no such thing as an atonal or pantonal chord. Tuning a dim7 chord in JI requires making it tonal. What you are arguing, basically, is that in a system where atonal chords are impossible (JI), it is impossible to play an atonal chord (dim7). Or, in other words, that you cannot maintain the character of a chord whose intervals are equally-spaced if you try to translate it into a system where equal spacing between intervals in a chord is impossible. You are, essentially, critiquing the JIists for failing to do something that they are not attempting to do (which is to say, render an atonal chord in an atonal fashion).

You are using the equal temperament definition of a dim7 chord to prove that the JI definition is incorrect, which is an easy error to make because both systems share a lot of the same terminology, thus allowing people presume they are interchangeable. You can't use one system to disprove another any more than you can win a basketball game by hitting a home run. You're trying to use ET as an argument against JI, and that doesn't work.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Since I see no clear audible line between JI and microtempering, this argument makes no sense to me. What Marcel did would sound very much the same if you retuned it to 53, 118, or 171 I believe.
>

There doesn't need to be a clear audible line for there to be a clear theoretical distinction. Just because you can approximate JI to an arbitrary degree of closeness via microtempering doesn't mean you can *achieve* JI with microtempering. Sure, it's splitting hairs to insist that JI has to be absolutely *pure* frequency ratios, but that seems to be the point of JI. The basis of JI is in defining intervals as simple (or maybe not-so-simple?) integer frequency ratios, so insisting on using irrational intervals (like 2^(1/4)) is contrary to the definition of JI. If someone is asking "how should I tune a dim7 in JI" and someone else responds "use 4-EDO!", that response is clearly not an answer to the question. Tempering is by definition not JI!

-Igs

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Since I see no clear audible line between JI and microtempering, this argument makes no sense to me. What Marcel did would sound very much the same if you retuned it to 53, 118, or 171 I believe.
> >
>
> There doesn't need to be a clear audible line for there to be a clear theoretical distinction.

What "clear theoretical distinction"? I've never heard of one. There is a clear theoretical distinction between rational intonation and allowing irrationals, but this can't be used to define "just" in some theoretical sense since every odd prime limit is dense in the positive reals. What you are saying seems to be that JI must be RI, but that's a necessary condition which can't be a sufficent one.

Just because you can approximate JI to an arbitrary degree of closeness via microtempering doesn't mean you can *achieve* JI with microtempering. Sure, it's splitting hairs to insist that JI has to be absolutely *pure* frequency ratios, but that seems to be the point of JI.

It's not just splitting hairs, it's nonsensical from the point of view of physics.

> Tempering is by definition not JI!

And a necessary condition is by definition not necessarily also a sufficient condition.

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Hi Rick,
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> > I don't buy this at all Igs. Staunch JIists completely fail to distinguish between tonal and atonal (pantonal) chords.
> >
>
> And that's *exactly* my point: in JI, there's no such thing as an atonal or pantonal chord. Tuning a dim7 chord in JI requires making it tonal. What you are arguing, basically, is that in a system where atonal chords are impossible (JI), it is impossible to play an atonal chord (dim7). Or, in other words, that you cannot maintain the character of a chord whose intervals are equally-spaced if you try to translate it into a system where equal spacing between intervals in a chord is impossible. You are, essentially, critiquing the JIists for failing to do something that they are not attempting to do (which is to say, render an atonal chord in an atonal fashion).
>
> You are using the equal temperament definition of a dim7 chord to prove that the JI definition is incorrect, which is an easy error to make because both systems share a lot of the same terminology, thus allowing people presume they are interchangeable. You can't use one system to disprove another any more than you can win a basketball game by hitting a home run. You're trying to use ET as an argument against JI, and that doesn't work.
>
Hi Igs,

Yeah I completely agree. 12 EDO harmony uses the same set of notes but in entirely different ways, one tonal and the other symmetric. It becomes problematic when these two worlds merge together. However, in the original debate (which actually started probably a year ago), Marcel was trying to retune a Beethoven piece in terms of JI where he (Beethoven) was using allot of 'puns' or ambiguities on the diminished chord. The II V7 I in the minor key was using half-diminished (i.e. say Dmi7(b5), D-F-Ab-C in the key of C min) to diminished (G7 becomes D diminished, D-F-Ab-B with only one note difference from the half dim) to I minor C-Eb-G. Marcel's tuning sounded good until it hit these types of chords. He's since found other tunings that are closer to the tempered minor third for these chords and it now sounds fine (although my original idea that 19/16 is the closest I still think is correct because four of these almost hits the 8ve).

-Rick

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> What "clear theoretical distinction"? I've never heard of one. There is a clear theoretical distinction between rational intonation and allowing irrationals, but this can't be used to define "just" in some theoretical sense since every odd prime limit is dense in the positive reals. What you are saying seems to be that JI must be RI, but that's a necessary condition which can't be a sufficent one.
>

It doesn't *have to be* a sufficient condition. Look, let's convert this to sentential logic to make it clearer. Let p = "Music is in Just Intonation", and let q = "Music is in Rational Intonation". Saying RI is necessary but not sufficient for JI is saying "if p, then q"; if we wanted to say RI is necessary and sufficient, we'd say "p if and only if q". Now, the statement "music is tempered" can simply be written "music is not in rational intonation", i.e. "not q", unless you want to allow that tempered music can be in rational intonation (which I'm assuming you don't want to allow). Now, we have two premises:
1. if p, then q
2. not q
The conclusion is "therefore, not p", since "if p, then q" equates to "q or not p", and since we can affirm "not q", we have only "not p" left.

Thus, if music is not rational, it is also not Just. This doesn't tell us about sufficient conditions for being Just, but that's okay, because it at least excludes irrational (i.e. tempered) intervals.

So, the line between tempering and JI is at least RI, since JI is just a special subset of RI. Whether this line defines an audible difference or not is moot to the theoretical definition, since of course any ratio can be approximated with arbitrary closeness by an irrational, and any irrational can be approximated with arbitrary closeness by a rational (the key word being "approximated"). If we allowed "arbitrarily close to" to be logically-equivalent to "the same as", of course the distinction would vanish, but the whole point is that we DON'T, and this is how JI maintains its identity from tempered music. Maybe we SHOULD allow this, but that's a different argument, because I'm pretty sure we currently DON'T.

-Igs

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > Oh what's real funny..
> > If you listen to all the version and than as last one 12edo.
> > It's crazy how out of tune 12edo sounds then :)
> > Strong loss of clarity aswell.
> >
> > Marcel
> >
>
> What I ment to say, was.
> That Pythagorean used in this way, and 53edo are very very good compared to
> 12edo.
>
> Marcel
>
They all sound pretty much in tune to me Marcel including the 12-EDO. (I think you're letting your imagination run away with you there). Good to be able to hear them all side-by-side. Thanks. But I do think you are proving that the idea that one interval corresponds to one number is unrealistic. As a guitarist I really do know this from experience.

-Rick

🔗rick <rick_ballan@...>

Sorry Gene, missed this response. I'll answer in text.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >For an example of atonality, look at the related b5 interval as Srt2 or a "2 EDO". JI tried to avoid this for centuries, calling it the "Devil's interval" etc...
>
> "JI" did no such thing. People were not using JI when this term was invented, and even in circulating temperaments the tritone was not going to be exactly sqrt(2). In meantone, of course, the augmented fourth and diminished fifth are two different intervals.

Well I probably tend to think of whole-numberedness and JI being the same thing. What perhaps I should have said was that the b5 was strictly forbidden in traditional counterpoint.
>
> >This discomfort with irrationals goes way back to Pythagoras when he discovered that the hypotenuse of a right angle triangle of sides 1 was sqrt 2 and not a rational.
>
> Pythagoras probably did not discover this. Hippasus seems to be the leading candidate.

Yeah this is a fuzzy area. I've read that it's possible that Pyth himself did the reductio proof that a/b = sqrt2. But one of my close friends who's a classical Greek scholar says that the Greeks would often create legendary characters and then write the 'evidence' of their existence in order to back their claims. Like Homer, it's even possible that a real person named Pythagoras never existed.
>
> > Musically this was emancipated with both the blues and also (eventually) serialism.
>
> Long, long before that.

Again I should have perhaps said "fully emancipated" or something. Of course Mozart is full of diminisheds etc...
>
> >EDO's appear wherever the music is passing *between* keys or roots, and dim7 is just one example.
>
> They do? How do they magically appear?

I think of this more of a law of harmony. There is no way in the world you can tell me that ending on a diminished or augmented chord sounds 'complete' or that a C maj triad sounds like its modulating.
>
> > JIists would have us all bopping to the Gregorian chant!
>
> Yeah, that Harry Partch. Wild for Gregorian chant.

That was before his death metal phase.
>
> Have you ever looked at 22? Like 12, it tempers out 50/49, and so sqrt(2) is used for both 7/5 and 10/7 in septimal harmony. It seems amenable to jazz.
>
No I haven't. I'll check it out. The problem with extending microtonality to jazz performance is the instruments or non-existence thereof and the fact that most pro's are so fluent on their instruments that changing their ways would be like learning a new language. There's also the problem of a formalised, common language which is needed for people to impro together (you play *this* scale over *that* chord etc...). Formalise microtonality and give it a generation or two and it should start to take hold.

🔗Marcel de Velde <m.develde@...>

Hi Rick,

They all sound pretty much in tune to me Marcel including the 12-EDO. (I
> think you're letting your imagination run away with you there).
>

No, no imagination :)
I really really hear the 12edo version as out of tune. Not just the
harmonies, they don't sound nice to me, but especially the melodies.
If I follow a melody in 12edo I go "ewwww" in a lot of places. The out of
tune ewwww where I put my head between my shoulders (perhaps to try and hide
my ears haha)

> Good to be able to hear them all side-by-side. Thanks. But I do think you
> are proving that the idea that one interval corresponds to one number is
> unrealistic. As a guitarist I really do know this from experience.
>
> -Rick
>

I don't really follow what you mean.
A fifth isn't a fixed interval it can be 3 different intervals in M-JI,
neither is a major or minor third etc.
It's a fixed interval in a certain place in a key yes.

But take for instance no2. He plays the exact same notes / chord sequence
somewhere in the middle of the piece as in the beginning, only transposed.
I used to think this must surely mean a modulation as they can't be played
thesame in one key transposed.
But I've found that when it's played in the middle, the notes/chords are
actually tuned differently! They have a different emotion / feel / function
in the piece.

Marcel

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Now, the statement "music is tempered" can simply be written "music is not in rational intonation", i.e. "not q", unless you want to allow that tempered music can be in rational intonation (which I'm assuming you don't want to allow).

Of course I want to allow it. Why wouldn't I? Even a regular temperament which subdivides the octave can be tuned in RI if we allow a minuscule or even unmeasureable degree of octave tweaking, and of course for temperaments like meantone or miracle there's no problem at all.

> So, the line between tempering and JI is at least RI, since JI is just a special subset of RI.

This just doesn't work. JI ==> RI, but not RI ==> JI.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > Now, the statement "music is tempered" can simply be written "music is not in rational intonation", i.e. "not q", unless you want to allow that tempered music can be in rational intonation (which I'm assuming you don't want to allow).
>
> Of course I want to allow it. Why wouldn't I? Even a regular temperament which subdivides the octave can be tuned in RI if we allow a minuscule or even unmeasureable degree of octave tweaking, and of course for temperaments like meantone or miracle there's no problem at all.
>

This is nonsense, Gene, I'm sorry to say.

Last I checked, these terms were defined according to mathematical representations of intervals, not how they make intervals sound. RI means representing intervals as integer ratios, JI means representing intervals as "simple" integer ratios (for some value of simple), and temperament means representing intervals as irrational numbers.

Unless you want to argue that a rational number equals an irrational number, or that the term "rational intonation" (and by extension, Just intonation, since you agree that JI is a type of RI) is not defined according to a mathematical way to represent musical intervals, this argument of yours holds no water.

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

Hi Rick,
>
> Yeah I completely agree. 12 EDO harmony uses the same set of notes but in entirely different ways, one tonal and the other symmetric. It becomes problematic when these two worlds merge together.
>

Yes, because "12-EDO harmony" is not what common-practice music is based on. The skeleton of common-practice music is the spiral of relatively-pure fifths; that is how notes are named, that is how key-signatures are derived, and really all a note-name tells you is a note's position on the spiral of fifths. Puns arise in 12-EDO because a spiral is being approximated by a circle, and notes which "should" be distinct (occupying different places on the spiral) become the same, forming an enharmonic equivalent. However, any music written in 12-EDO using diatonic note names (A thru G, with various sharps and flats) is NOT essentially 12-EDO music, because it does not require the symmetry/equality of 12-EDO in order to make sense, it only requires a series of reasonably-pure fifths (presumably which do not "close" as a circle at any fewer than 12 notes).

Tonal 12-tET music can probably be retuned to JI, but the skeleton gets deformed since 5-limit or higher JI is not based on a 1-dimensional spiral of fifths (nor on a circle of fifths); hence Marcel's mathematical acrobatics and use of complex intervals like 40/27 and whatever that minor third with the huge numbers was.

I think the biggest confusion comes from jazz, which often uses the same terminology as tonal 12-EDO music in spite of the fact that the circle of fifths is usually much less relevant than the symmetrical arrangement of 12 tones. Since jazz disobeys almost all the standard rules of tonality, notating a "jazz" Cdim7 as C-Eb-Gb-Bbb could make the same amount of sense as C-Eb-F#-A. Each spelling suggests a different JI interpretation, but because neither spelling is any more "accurate" than the other, there's no argument for either JI interpretation, so retuning it to JI would make about as much sense as trying to retune a serialist piece. Not to say you can't play jazz or serialism in JI, of course, just that there's no basis for a "proper" retuning of 12-EDO jazz or serialism into JI.

-Igs

🔗cityoftheasleep <igliashon@...>

🔗Marcel de Velde <m.develde@...>

Hi Igs,

Yes, because "12-EDO harmony" is not what common-practice music is based on.
>
>

Completely agreed!

> The skeleton of common-practice music is the spiral of relatively-pure
> fifths; that is how notes are named, that is how key-signatures are derived,
> and really all a note-name tells you is a note's position on the spiral of
> fifths.
>

Well.. that's what conventional music theory has made of it.
I'm not going along with that view.

Actually what conventional music theory is doing here is saying music is
really Pythagorean.
And my ear tells me it isn't so.
Tuning lies at the basis of music theory.
Our ears and brain knows what it's about. Now it's for the mind to figure
out what it is.

> Puns arise in 12-EDO because a spiral is being approximated by a circle,
> and notes which "should" be distinct (occupying different places on the
> spiral) become the same, forming an enharmonic equivalent. However, any
> music written in 12-EDO using diatonic note names (A thru G, with various
> sharps and flats) is NOT essentially 12-EDO music, because it does not
> require the symmetry/equality of 12-EDO in order to make sense, it only
> requires a series of reasonably-pure fifths (presumably which do not "close"
> as a circle at any fewer than 12 notes).
>
> Tonal 12-tET music can probably be retuned to JI, but the skeleton gets
> deformed since 5-limit or higher JI is not based on a 1-dimensional spiral
> of fifths (nor on a circle of fifths); hence Marcel's mathematical
> acrobatics and use of complex intervals like 40/27 and whatever that minor
> third with the huge numbers was.
>

The minor triads are:
5/3 2/1 5/2 (1/1 6/5 3/2)
3/2 16/9 9/4 (1/1 32/27 3/2)
16/9 135/64 8/3 (1/1 1215/1024)
9/8 4/3 5/3 (1/1 32/27 40/27)
405/256 15/8 64/27 (1/1 32/27 (3/2 -Schisma))
Some of these occur in multiple places in one key.

> I think the biggest confusion comes from jazz, which often uses the same
> terminology as tonal 12-EDO music in spite of the fact that the circle of
> fifths is usually much less relevant than the symmetrical arrangement of 12
> tones. Since jazz disobeys almost all the standard rules of tonality,
> notating a "jazz" Cdim7 as C-Eb-Gb-Bbb could make the same amount of sense
> as C-Eb-F#-A. Each spelling suggests a different JI interpretation, but
> because neither spelling is any more "accurate" than the other, there's no
> argument for either JI interpretation, so retuning it to JI would make about
> as much sense as trying to retune a serialist piece. Not to say you can't
> play jazz or serialism in JI, of course, just that there's no basis for a
> "proper" retuning of 12-EDO jazz or serialism into JI.
>
> -Igs
>

I must strongly disagree here.
Jazz and serialism can be put in JI perfectly, just like common practice
classical music.
I'll demonstrate this soon.
All music is JI.

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Graham Breed <gbreed@...>

On 15 July 2010 02:16, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
>> I think Gene's just saying you can tune any temperament
>> with rational intervals, and of course that's right.
>> Where's the beef?
>
> What do you mean, of course that's right?? Dang it Carl, I was counting on you for back up. Have I lost my mind? What ratio is equal to 2^(1/12)?

I agree with Gene and Carl. Equal divisions of the octave are only
one kind of temperament. 58:39, for example, gives a reasonable
meantone fifth. I don't see why something generated by that interval
shouldn't be called a temperament. The defining feature of a
temperament is that it approximates just intonation, not that it's
irrational.

Graham

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > I think Gene's just saying you can tune any temperament
> > with rational intervals, and of course that's right.
> > Where's the beef?
>
> What do you mean, of course that's right?? Dang it Carl, I was counting on you for back up. Have I lost my mind? What ratio is equal to 2^(1/12)?

As I said, regular temperaments which subdivide the octave will require octave tweaking. I think you will find that step sizes of 196/185 will give an octave so slightly sharp you wouldn't notice the difference. It's a 37-limit interval, in case that matters.

If the temperament can have some slight, theoretical degree of irregularity, we don't even need to tweak the octaves. As Marcel noted, if you take 3/2 down a schisma, you in effect get a 12edo fifth. Eleven of these and a non-wolf fifth which is lower by a Kirnberger atom completes a 5-limit version of 12 equal in 5-limit rational intonation. The atom is only 0.0153 cents in size, so you will not be able to tell any difference between the big bad wolf and the other fifths, which justifies my calling this a version of 12 equal.

As for meantone, miracle, et al, you don't even need to tweak the octaves or do anything fancy; just use a rational number as the generator.

🔗cityoftheasleep <igliashon@...>

Hi Graham,

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> I agree with Gene and Carl. Equal divisions of the octave are only
> one kind of temperament. 58:39, for example, gives a reasonable
> meantone fifth. I don't see why something generated by that interval
> shouldn't be called a temperament. The defining feature of a
> temperament is that it approximates just intonation, not that it's
> irrational.

I think I see what you're trying to do, but it misses the original point. Gene asserted that there is no clear line between JI and temperament, and I said that the line exists in the definition that JI uses simple integer ratios and temperaments don't. Gene disputed this by arguing that you can get arbitrarily close to a simple ratio with a temperament, and while I used to think temperaments were by definition irrational, it doesn't matter if they can be rational too.

Your assertion that "the defining feature of a temperament is that it approximates Just Intonation" backs up my original claim that there is a clear distinction between the two, or else what is it that temperaments are approximating? Other temperaments? Then the definition of a temperament becomes recursive ("the defining feature of a temperament is that it approximates another temperament") and thus meaningless.

Come on guys, seriously: either JI is distinct from temperament, or the idea of "temperament" is meaningless.

-Igs

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> > What do you mean, of course that's right?? Dang it Carl, I was counting on you for back up. Have I lost my mind? What ratio is equal to 2^(1/12)?
>
> As I said, regular temperaments which subdivide the octave will require octave tweaking. I think you will find that step sizes of 196/185 will give an octave so slightly sharp you wouldn't notice the difference. It's a 37-limit interval, in case that matters.
>

Ye gods, has the definition of the word "equal" been stricken from everyone's brain? "Equal" does not mean "imperceptibly different", it means "the same"! This is not about physics or the limits of human perception, it's about logic, math, and the definition of terms!

> If the temperament can have some slight, theoretical degree of irregularity, we don't even need to tweak the octaves. As Marcel noted, if you take 3/2 down a schisma, you in effect get a 12edo fifth. Eleven of these and a non-wolf fifth which is lower by a Kirnberger atom completes a 5-limit version of 12 equal in 5-limit rational intonation. The atom is only 0.0153 cents in size, so you will not be able to tell any difference between the big bad wolf and the other fifths, which justifies my calling this a version of 12 equal.
>

Okay, so if this temperament is the same as 12-EDO, than any temperament which gets this close to JI is the same as JI. In which case, the temperament must be said to approximate itself, which is absurd! Come on, Gene, either there's a distinction or there isn't! And if there isn't, then the concept of a "temperament" is meaningless, since then even JI can be considered a temperament and the whole point of a temperament is to approximate JI! If JI is a temperament, than a temperament approximates a temperament, which is a meaningless definition!!

-Igs

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> What Gene and Carl mean is that ratios will get so close to 2^(1/12) that
> one can't hear or even measure the difference.
> For instance for all practical purposes, a 3/2 minus a Schisma (700.0013
> cents) is the same as an equal tempered fifth.

But this isn't about "for all practical purposes". 700.0000 cents does not equal 700.0013 cents. Next thing you're going to tell me 2+2=5!

> Also, since even time and the sound wave are themselves quantized, 2^(1/12)
> cannot even exist in real life.

Now THAT, my friend, is a bold claim! Time is quantized? Really? Pray tell, Zeno, let's hear how you prove it. I'm just itching to dust off my metaphysics texts from my days as a philosophy major.

-Igs

🔗Chris Vaisvil <chrisvaisvil@...>

Marcel you've said some very insightful things in these two messages.

I need to ask though

It seems your version of JI (which I view as an adaptive version of
JI) is based upon a definition of tonality by the music itself. What
does one do when the serialist is intentionally trying to eliminate a
tonal center?

I'm probably making an ignorant statement about Jazz here - I see at
this point Jazz in large part as an extension of Debussian harmonies
and therefore tonal just but not in a common practice sense - so here
I can understand it working though I can see parallel harmonies as
being a challenge to adaptive JI.

Chris

>
> I must strongly disagree here.
> Jazz and serialism can be put in JI perfectly, just like common practice classical music.
> I'll demonstrate this soon.
> All music is JI.
>
> Marcel

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> > As I said, regular temperaments which subdivide the octave will require octave tweaking. I think you will find that step sizes of 196/185 will give an octave so slightly sharp you wouldn't notice the difference. It's a 37-limit interval, in case that matters.
> >
>
> Ye gods, has the definition of the word "equal" been stricken from everyone's brain? "Equal" does not mean "imperceptibly different", it means "the same"!

And every step of 196/185 is equal to every other step. "The same". So what's your point?

> This is not about physics or the limits of human perception, it's about logic, math, and the definition of terms!

In mathematics, you need to first define terms.

> Okay, so if this temperament is the same as 12-EDO, than any temperament which gets this close to JI is the same as JI.

It's called microtempering, or if it gets extreme enough, nanotempering. An example of a nanotemperament is atomic temperament, which tempers out the Kirnberger atom. As I said, the line blurs in such cases; I don't think there is only one possible definition of JI, and you need to stipulate and define terms in order to exclude such things as atomic temperament.

> In which case, the temperament must be said to approximate itself, which is absurd!

It's not absurd, its tautological.

> Come on, Gene, either there's a distinction or there isn't! And if there isn't, then the concept of a "temperament" is meaningless, since then even JI can be considered a temperament and the whole point of a temperament is to approximate JI!

I can in fact give you examples where JI can be considered a temperament. Take the set of all JI intervals obtained by combining the just fourth of exactly 4/3 and the just minor third of exactly 6/5. This can be considered a just intonation subgroup of 5-limit JI, which is the obvious interpretation, but it also works, and very well, as a 7-limit temperament.

> If JI is a temperament, than a temperament approximates a temperament, which is a meaningless definition!!

It is? Temperaments do in fact approximate other temperaments, a fact in constant use. 31et, for example, approximates meantone, or at least that's one way to say it.

> -Igs
>

🔗Marcel de Velde <m.develde@...>

>
> I think I see what you're trying to do, but it misses the original point.
> Gene asserted that there is no clear line between JI and temperament, and I
> said that the line exists in the definition that JI uses simple integer
> ratios and temperaments don't. Gene disputed this by arguing that you can
> get arbitrarily close to a simple ratio with a temperament, and while I used
> to think temperaments were by definition irrational, it doesn't matter if
> they can be rational too.
>
> Your assertion that "the defining feature of a temperament is that it
> approximates Just Intonation" backs up my original claim that there is a
> clear distinction between the two, or else what is it that temperaments are
> approximating? Other temperaments? Then the definition of a temperament
> becomes recursive ("the defining feature of a temperament is that it
> approximates another temperament") and thus meaningless.
>
> Come on guys, seriously: either JI is distinct from temperament, or the
> idea of "temperament" is meaningless.
>
> -Igs

For me the defining characteristic of JI is the exact meaning of it's name
"Just Intonation".
Meaning, to tune "in tune", to tune "correct", to tune "pure".
The part to figure out is not wether this is with rational tuning or not,
the part to figure out is what exactly is "in tune" and "correct".
Should I for instance be wrong with my M-JI tuning, then I don't see it as
likely but one couldn't exclude a non rational tuning system (although one
couldn't call it a temperament then anymore as it wouldn't temper but be
pure)

Marcel

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Come on guys, seriously: either JI is distinct from temperament,
> or the idea of "temperament" is meaningless.

It's a lot like pornography -- best not to try too hard to
define it.

I started out a JI acolyte, but when I began applying JI
scales to my piano, I found I used 56/45 like 5/4 without
realizing it. That's the thing about JI numerology -- it has
nothing to do with music or the way musicians operate.

So even though my scale contained lots of consonant rational
dyads and none much more complex than 56/45 (and in fact, had
about the lowest average dyad complexity of any possible
12-note scale) I was still tempering. Well, you can say it
wasn't true temperament because the comma (225/224) wasn't
split and distributed. And I wouldn't argue with you. But
the line is clearly very thin. The reality is that there's
precious little music ever been written in any culture which
doesn't involve temperament of some kind or another.

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Your assertion that "the defining feature of a temperament is
> that it approximates Just Intonation" backs up my original claim
> that there is a clear distinction between the two,

The defining feature of regular temperament is that it is a
homomorphism. Drop the requirement that temperament be regular
and all hell breaks loose. There's no iron-clad way to look at
a score or hear a performance and determine whether it's in JI
or some temperament, and if some temperament, which. It's
conceivable such a thing could be developed but at the moment
it's hard enough just to tell temperaments apart when
considering sytems of rank > 2.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Marcel de Velde <m.develde@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> And every step of 196/185 is equal to every other step. "The same". So what's your point?
>

That 196/185 is not equal to 2^(1/12).

> In mathematics, you need to first define terms.

And I'm pretty sure that defining JI as using intervals composed exclusively of exact simple integer frequency ratios is a well-defined term.

> It's called microtempering, or if it gets extreme enough, nanotempering. An example of a nanotemperament is atomic temperament, which tempers out the Kirnberger atom. As I said, the line blurs in such cases; I don't think there is only one possible definition of JI, and you need to stipulate and define terms in order to exclude such things as atomic temperament.
>

And the definition of JI above fails to do this how?

> > If JI is a temperament, than a temperament approximates a temperament, which is a meaningless definition!!
>
> It is? Temperaments do in fact approximate other temperaments, a fact in constant use. 31et, for example, approximates meantone, or at least that's one way to say it.
>

But you can't define the concept of a temperament as "that which approximates a temperament". A tautology is not a meaningful definition.
If you say 31-tET approximates meantone temperament, and meantone temperament approximates 5-limit JI, and you stipulate that JI can be a temperament, you could start with 5-limit JI and say that it approximates meantone, and that meantone approximates 31-tET. Thus you have a circle of approximation, upon which you could use the property of transitivity of identity to assert that 31-tET approximates 31-tET. But since the definition of approximation is "something that is approximate; especially : a mathematical quantity that is close in value to ***but not the same as*** a desired quantity" (according to Merriam-Webster, anyway), that's saying that 31-tET is close to itself but not the same as itself.

Thus, if you assert that JI can approximate temperament, and temperament can approximate JI, you can assert that anything (JI, temperament, whatever) is close to (but not the same as) itself, which, again, is absurdity.

Unless you can draw a line and say that something can be approximated but is not itself an approximation, the concepts of temperament and JI are meaningless and should be discarded entirely.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> For me the defining characteristic of JI is the exact meaning of it's name
> "Just Intonation".
> Meaning, to tune "in tune", to tune "correct", to tune "pure".

According to WHAT? And for "Bob"'s sake, don't say "the human ear", because that's nonsense, as there's no "single" human ear but only the average of all of us with plenty of individual variation! What sounds "in tune" is completely context-dependent, totally based on subjective aesthetic preference. Without the standard of "small-integer frequency ratios", there's no definition of JI precise enough to be meaningful in discourse.

Though that seems to be where this is all heading, anyway. Which I guess I should be happy about, because I think JI is nonsense anyway...and that the inconsistencies of pitch-rendering on physical instruments, as well as the "fuzziness" of the human ear, render ANY exact standard of defining a scale somewhat nonsensical.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> The defining feature of regular temperament is that it is a
> homomorphism. Drop the requirement that temperament be regular
> and all hell breaks loose. There's no iron-clad way to look at
> a score or hear a performance and determine whether it's in JI
> or some temperament, and if some temperament, which. It's
> conceivable such a thing could be developed but at the moment
> it's hard enough just to tell temperaments apart when
> considering sytems of rank > 2.

Well alright then, I concede. I guess we can all agree that JI is a meaningless concept, as is temperament, and that defining any scale with discrete values is a useful-but-false convention? So we agree that 12-EDO is as much a delusion as 5-limit JI, and that all intervals are forbidden a discrete value, or even a range of values with discrete boundaries, and that practically everything we discuss on this list doesn't, in point of fact, exist?

-Igs

🔗Marcel de Velde <m.develde@...>

Hi Igs,

Well alright then, I concede. I guess we can all agree that JI is a
> meaningless concept, as is temperament, and that defining any scale with
> discrete values is a useful-but-false convention? So we agree that 12-EDO is
> as much a delusion as 5-limit JI, and that all intervals are forbidden a
> discrete value, or even a range of values with discrete boundaries, and that
> practically everything we discuss on this list doesn't, in point of fact,
> exist?
>
> -Igs
>

LOL

Just do your own thing. No point in trying to get agreement on things on
this list.
My thing is 5-limit JI delusions btw :)

Marcel

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > The defining feature of regular temperament is that it is a
> > homomorphism. Drop the requirement that temperament be regular
> > and all hell breaks loose. There's no iron-clad way to look at
> > a score or hear a performance and determine whether it's in JI
> > or some temperament, and if some temperament, which. It's
> > conceivable such a thing could be developed but at the moment
> > it's hard enough just to tell temperaments apart when
> > considering sytems of rank > 2.

I should clarify that in the last sentence, I'm no longer
talking about telling temperaments apart in a musical setting,
but rather telling them apart at all -- as in, enumerating
them with a computer program.

> Well alright then, I concede. I guess we can all agree
> that JI is a meaningless concept, as is temperament, and that
> defining any scale with discrete values is a useful-but-
> false convention? So we agree that 12-EDO is as much a
> delusion as 5-limit JI, and that all intervals are forbidden
> a discrete value, or even a range of values with discrete
> boundaries, and that practically everything we discuss on
> this list doesn't, in point of fact, exist?

Whereas you and Gene have been arguing about tunings (like
whether 300001/20000 is different than 3/2) I'm talking about
something more abstract. The abstract temperaments
(homomorphisms) give practical results and therefore exist:
they recommend scales that can be used on real instruments to
make real music, and such music will sound different than if
the theory wasn't available. Just because we won't
necessarily agree on which mapping some arbitrary music in
64-ET is using, doesn't mean it's time to start cracking
eachother's skulls open and feasting on the goo inside.

-Carl

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> > And every step of 196/185 is equal to every other step. "The same". So what's your point?
> >
>
> That 196/185 is not equal to 2^(1/12).

And it needs to be because...?

> > In mathematics, you need to first define terms.
>
> And I'm pretty sure that defining JI as using intervals composed exclusively of exact simple integer frequency ratios is a well-defined term.

Yes, but once again you've shifted ground. Now you are stipulating, whereas before you were claiming there was only one way to define JI, and there are no areas of fuzz.

> But you can't define the concept of a temperament as "that which approximates a temperament".

You are again shifting ground. We had not before been discussing how to define temperaments. I'm perfectly willing to define things, but that's different from the claim that some term already has a firmly fixed definition.

> But since the definition of approximation is "something that is approximate; especially : a mathematical quantity that is close in value to ***but not the same as*** a desired quantity" (according to Merriam-Webster, anyway), that's saying that 31-tET is close to itself but not the same as itself.

I suggest the dictionary is not the best place to find mathematical definitions. In fact, mathematicians are quite willing to say something is approximated by itself under the right circumstances. An example would be that a line is the linear approximation of itself.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Yes, but once again you've shifted ground. Now you are stipulating, whereas before you were claiming there was only one way to define JI, and there are no areas of fuzz.
>
> > But you can't define the concept of a temperament as "that which approximates a temperament".
>
> You are again shifting ground. We had not before been discussing how to define temperaments. I'm perfectly willing to define things, but that's different from the claim that some term already has a firmly fixed definition.
>

Okay, Gene. You've worn me down. Instruct me! I 've been assuming we all knew what we meant when we used terms like "JI" and "temperament". Clearly, though, you are operating under different definitions of than I am, such that the two are not mutually-exclusive. These definitions are completely unfamiliar to me. I've always been given the impression that JI is, by definition, untempered, and that temperament is, by definition, not Just. I guess you could say my definition of JI, which I've just sort of synthesized from how the term is used by people like Carl, Marcel, Jon Catler, and Harry Partch, is as follows:
"JI is a set of interval relationships which are represented exactly by integer frequency ratios, wherein no number in any of the ratios exceeds a given size." The fuzziness of the definition is, of course, how big the largest number can get, but suffice to say the set is finite and excludes all pitches except the exact ratios. I suppose that anything outside this set could be construed to be a "tempered" interval, whether it is rational or otherwise. Now I'd like to know how you define the terms "Just" and "tempered", since clearly you believe they can be meaningfully defined without being mutually exclusive. I'd also like to know why you reject the definition I've been operating under.

> I suggest the dictionary is not the best place to find mathematical definitions. In fact, mathematicians are quite willing to say something is approximated by itself under the right circumstances. An example would be that a line is the linear approximation of itself.
>

Then please define "approximation" for me as well. The plain English definition hasn't been serving me well in this discourse.

-Igs

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Rick,
>
> They all sound pretty much in tune to me Marcel including the 12-EDO. (I
> > think you're letting your imagination run away with you there).
> >
>
> No, no imagination :)
> I really really hear the 12edo version as out of tune. Not just the
> harmonies, they don't sound nice to me, but especially the melodies.
> If I follow a melody in 12edo I go "ewwww" in a lot of places. The out of
> tune ewwww where I put my head between my shoulders (perhaps to try and hide
> my ears haha)
>
> The 12-EDO version sounds perfectly in tune to me. No "ewww's" at all.
>
> > Good to be able to hear them all side-by-side. Thanks. But I do think you
> > are proving that the idea that one interval corresponds to one number is
> > unrealistic. As a guitarist I really do know this from experience.
> >
> > -Rick
> >
>
> I don't really follow what you mean.
> A fifth isn't a fixed interval it can be 3 different intervals in M-JI,
> neither is a major or minor third etc.
> It's a fixed interval in a certain place in a key yes.
>
> But take for instance no2. He plays the exact same notes / chord sequence
> somewhere in the middle of the piece as in the beginning, only transposed.
> I used to think this must surely mean a modulation as they can't be played
> the same in one key transposed.
> But I've found that when it's played in the middle, the notes/chords are
> actually tuned differently! They have a different emotion / feel / function
> in the piece.
>
> Marcel
>
What I mean is that we can glide from say 80/64 = 5/4 to 81/64 in the middle of the 'same' note and probably hear little or no difference, that there is a 'gap' around intervals as in harmonic entropy. Hindemith makes this point that if we couldn't approximate intervals it would be a disaster.

But concerning Beethoven, I don't know what you mean about playing the same thing in a different key. Didn't he compose on a tempered piano? As I said, these composers practically improvised their work. They had to in order to write so much stuff. I just can't help the feeling that by focusing too much on these tiny subtleties one can miss the point that composers like Bach Beethoven had bombastic personalities. Sometimes Beethoven would deliberately introduce notes that sound out of tune until we heard what was to follow. The introduction of the French horn in the Eroica is a perfect example. Upon hearing it, his student stood up and told off the orchestra. Beethoven then told him off and for the orchestra to continue. We then hear that this 'out of tune' theme becomes the new motif for an entire new movement. As for Bach, (ah, Bach), he was also a great swordsman. After berating his musicians for being lazy they attacked him and he beat them off with a sword.

-Rick

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> "JI is a set of interval relationships which are represented exactly by integer frequency ratios, wherein no number in any of the ratios exceeds a given size."

I have no objection to this definition, if labeled as such, but of course it concedes the point at issue, which is that there is no clear line.

> Now I'd like to know how you define the terms "Just" and "tempered", since clearly you believe they can be meaningfully defined without being mutually exclusive.

My point originally was that there was no universally accepted definition of "just" which draws a clear demarcation between just and not just. That, if you will recall, is what you objected to.

> I'd also like to know why you reject the definition I've been operating under.

If you will recall, you originally defined just intonation as rational intonation, which as I pointed out clearly will not work.

> > I suggest the dictionary is not the best place to find mathematical definitions. In fact, mathematicians are quite willing to say something is approximated by itself under the right circumstances. An example would be that a line is the linear approximation of itself.
> >
>
> Then please define "approximation" for me as well.

There isn't any single definition in use in all of mathematics,,let alone in science and engineering also. There are many mathematical terms like that--"number", "space", "tensor", "prime", etc.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
> Hindemith makes this point that if we couldn't approximate intervals it would be a disaster.

Hindemith's argument is pretty much baloney.

> But concerning Beethoven, I don't know what you mean about playing the same thing in a different key. Didn't he compose on a tempered piano? As I said, these composers practically improvised their work. They had to in order to write so much stuff.

You said that before, and it's still wrong. Beethoven would sweat for years over a piece of music, trying to get it just the way he wanted it. Bach had a bigger output, but he also was willing to recycle, and his music was carefully thought out. Of course both were well known for their ability to improvise, but that's not how they composed.

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > What "clear theoretical distinction"? I've never heard of one. There is a clear theoretical distinction between rational intonation and allowing irrationals, but this can't be used to define "just" in some theoretical sense since every odd prime limit is dense in the positive reals. What you are saying seems to be that JI must be RI, but that's a necessary condition which can't be a sufficent one.
> >
>
> It doesn't *have to be* a sufficient condition. Look, let's convert this to sentential logic to make it clearer. Let p = "Music is in Just Intonation", and let q = "Music is in Rational Intonation". Saying RI is necessary but not sufficient for JI is saying "if p, then q"; if we wanted to say RI is necessary and sufficient, we'd say "p if and only if q". Now, the statement "music is tempered" can simply be written "music is not in rational intonation", i.e. "not q", unless you want to allow that tempered music can be in rational intonation (which I'm assuming you don't want to allow). Now, we have two premises:
> 1. if p, then q
> 2. not q
> The conclusion is "therefore, not p", since "if p, then q" equates to "q or not p", and since we can affirm "not q", we have only "not p" left.
>
> Thus, if music is not rational, it is also not Just. This doesn't tell us about sufficient conditions for being Just, but that's okay, because it at least excludes irrational (i.e. tempered) intervals.
>
> So, the line between tempering and JI is at least RI, since JI is just a special subset of RI. Whether this line defines an audible difference or not is moot to the theoretical definition, since of course any ratio can be approximated with arbitrary closeness by an irrational, and any irrational can be approximated with arbitrary closeness by a rational (the key word being "approximated"). If we allowed "arbitrarily close to" to be logically-equivalent to "the same as", of course the distinction would vanish, but the whole point is that we DON'T, and this is how JI maintains its identity from tempered music. Maybe we SHOULD allow this, but that's a different argument, because I'm pretty sure we currently DON'T.
>
> -Igs
>
Hi Igs,

Concerning physics, although the others are by now sick of hearing it, I've recently been working on a theory which shows that the GCD's or periodic waves i.e. their frequency, remain when we detune notes. The standard example I've been giving is that if we take a Fourier series between the just major third 80/64 = 5/4, which has peaks at the GCD frequency 16, and detune it to the Pythagorean maj 3rd 81/64, then the peaks of this wave will occur at the approximate GCD frequency (81 + 64)/(5 + 4) = 16.1111...Without going into detail, the upshot is that non-JI waves can be seen simply as JI waves with a modulated amplitude (observe for eg that the denominator is (5 + 4), where 5/4 is its JI counterpart). You can see some of the results in my files folder.

I'll just say that when we frame the problems in terms of the correct physical approach, wave theory, then most of them either have a clear answer or disappear of their own accord. For eg, I used to think that because the b5 as sqrt 2 was irrational and had no GCD, then it cannot have a frequency and must therefore be 'atonal'. However, by looking at the actual waves I now realise that it does have an approximate GCD close to 7/5. Therefore, trying to draw a distinct line in the sand between JI and non-JI, rationals and irrationals, might be flawed from the outset.

-Rick

🔗rick <rick_ballan@...>

Yeah Igs, what you say here "Tonal 12-tET music can probably be retuned to JI, but the skeleton gets deformed" is exactly what I was saying. Pure theorists often don't realise that the 'heart' of modern 12 EDO tonal harmony is not based on tuning the fifths but on what we call *guide tones* between the thirds and sevenths, which invert as we cycle. It is these which 'spell out' the chord and the fifths are quite dispensable. It starts by noticing that as we cycle using dom7 chords the tritone between the maj 3 and b7 descends chromatically, inverting each time. C7 - F7 - Bb7 -...has guide tones (E, Bb) - (Eb, A) - (D, Ab) -...where it's seen that maj3 is flattened to become b7 and b7 is flattened to become maj3.

We then modify these to match the chord progression in question. Eg Cmi7 - F7 - Bbmaj7 has guide tones (Eb, Bb) - (Eb, A) - (D, A). Notice that the chords are perfectly spelled out but with absolute minimal voice movement. This is vital for both efficiency in composing and improvising. If I score for sax and trombone for eg and want to spell out the chords I'll automatically choose these notes.

Once you start detuning away from this tritone "skeleton" you are going to run into trouble. Sure it's possible, but why do it just because of some old idea that tempered systems don't match some Platonic ideal of 'Pure whole-numbers'? In truth, instruments have never matched these exactly anyway. String/pipe length, thickness, temperature are all factors that make things only approximate anyway.

-Rick

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Hi Rick,
> >
> > Yeah I completely agree. 12 EDO harmony uses the same set of notes but in entirely different ways, one tonal and the other symmetric. It becomes problematic when these two worlds merge together.
> >
>
> Yes, because "12-EDO harmony" is not what common-practice music is based on. The skeleton of common-practice music is the spiral of relatively-pure fifths; that is how notes are named, that is how key-signatures are derived, and really all a note-name tells you is a note's position on the spiral of fifths. Puns arise in 12-EDO because a spiral is being approximated by a circle, and notes which "should" be distinct (occupying different places on the spiral) become the same, forming an enharmonic equivalent. However, any music written in 12-EDO using diatonic note names (A thru G, with various sharps and flats) is NOT essentially 12-EDO music, because it does not require the symmetry/equality of 12-EDO in order to make sense, it only requires a series of reasonably-pure fifths (presumably which do not "close" as a circle at any fewer than 12 notes).
>
> Tonal 12-tET music can probably be retuned to JI, but the skeleton gets deformed since 5-limit or higher JI is not based on a 1-dimensional spiral of fifths (nor on a circle of fifths); hence Marcel's mathematical acrobatics and use of complex intervals like 40/27 and whatever that minor third with the huge numbers was.
>
> I think the biggest confusion comes from jazz, which often uses the same terminology as tonal 12-EDO music in spite of the fact that the circle of fifths is usually much less relevant than the symmetrical arrangement of 12 tones. Since jazz disobeys almost all the standard rules of tonality, notating a "jazz" Cdim7 as C-Eb-Gb-Bbb could make the same amount of sense as C-Eb-F#-A. Each spelling suggests a different JI interpretation, but because neither spelling is any more "accurate" than the other, there's no argument for either JI interpretation, so retuning it to JI would make about as much sense as trying to retune a serialist piece. Not to say you can't play jazz or serialism in JI, of course, just that there's no basis for a "proper" retuning of 12-EDO jazz or serialism into JI.
>
> -Igs
>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> You said that before, and it's still wrong. Beethoven would sweat
> for years over a piece of music, trying to get it just the way he
> wanted it. Bach had a bigger output, but he also was willing to
> recycle, and his music was carefully thought out. Of course both
> were well known for their ability to improvise, but that's not how
> they composed.

Definitely true of Beethoven's piano sonatas, symphonies, and
string quartets. He wrote some theme and variation sets that
have more direct roots in improv.

Bach did have to turn out cantatas pretty fast for many years,
and he recycles and refines ideas there for sure, but there's
also a demonstrated ability to write that stuff rapidly.
However he's on record saying that composers who write at a
keyboard are rank amateurs. And apparently some believe WTC1
was a dry run and that WTC2 was the intended final product.

-Carl

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > "JI is a set of interval relationships which are represented exactly by integer frequency ratios, wherein no number in any of the ratios exceeds a given size."
>
> I have no objection to this definition, if labeled as such, but of course it concedes the point at issue, which is that there is no clear line.
>

The line may be fuzzy, but the exclusion of irrationals is not. We may not be able to say whether 40/27 or 17/12 are Just or merely Rational, but we can say that 2^(1/4) is not Just. My point was that the line doesn't have to be crystal clear to exclude a specific type of interval.

> > Now I'd like to know how you define the terms "Just" and "tempered", since clearly you believe they can be meaningfully defined without being mutually exclusive.
>
> My point originally was that there was no universally accepted definition of "just" which draws a clear demarcation between just and not just. That, if you will recall, is what you objected to.
>

And my objection was not that there IS a complete definition of JI, but that a complete definition isn't necessary in order to exclude some intervals.

> > I'd also like to know why you reject the definition I've been operating under.
>
> If you will recall, you originally defined just intonation as rational intonation, which as I pointed out clearly will not work.
>

No, I gave "rational intonation" as a necessary (but not sufficient) condition for JI, which you agreed to. Anything failing to meet that necessary condition, i.e. an irrational interval, is therefore not Just. Such is the meaning of "necessary". But then you advanced the argument that there is no clear distinction between a rational interval and an irrational interval, and that's where I lost it. I mean, "rational" and "irrational" are clear antonyms. Even if you can approach arbitrarily close to one using the other, you can't surmount the final "hurdle" and make an irrational number rational (or vice versa).

Believe me, I take your point: it's a stupid way to make a distinction, it has no musical value, and you can all but sneak irrational intervals "around the guards" by using arbitrarily-close approximations. I.e. you can sort of "sneak" 2^(1/4) into JI using, say, 19/16. I get it. I never debated that. But it's not actually 2^(1/4) that makes it in, just a dead-ringer for it, and even if the distinction is practically meaningless, it's *still a distinction*. I.e. we could write a computer program to sort intervals into "possibly JI" and "definitely NOT JI" based on this definition and it could sort successfully any interval we give to it without fail, even if no one could hear the difference between intervals from one category and intervals in the other.

Unless, of course, you and Marcel are correct that there are "atoms" of time, in which case all intervals will be rational. Then there is definitely no way to clearly distinguish JI from non-JI, unless we arbitrarily set a boundary on interval complexity.

-Igs

🔗cityoftheasleep <igliashon@...>

Hi Rick,
--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>
> Yeah Igs, what you say here "Tonal 12-tET music can probably be retuned to JI, but the skeleton gets deformed" is exactly what I was saying. Pure theorists often don't realise that the 'heart' of modern 12 EDO tonal harmony is not based on tuning the fifths but on what we call *guide tones* between the thirds and sevenths, which invert as we cycle.
>

Sorry, I should have left out "12-tET" from that sentence. I don't understand really anything about these guide-tones you talk about, but the fact remains that diatonic music as we know it originated from tuning systems based on a series of fifths. Any series of seven reasonably-pure fifths will do to produce a diatonic scale. Notes were initially defined one-dimensionally; E is not "E" because it's a major third of C, but because it's a fifth of A, which is a fifth of D, which is a fifth of G, which is a fifth of C. The fact that E is a major third above C is really a contingency of the way approximately-pure fifths work. The skeleton that gets deformed by forcing 5-limit JI is that backbone of fifths, because when you make E a pure 5/4, it is no longer related to C by a chain of fifths. And as we all know, the point of temperament was (among other things) to push the harmony of C-E toward 5/4 without losing the relationship of the chain of fifths, as well as to turn the spiral of pure fifths into a closed circle, so that more keys are accessible without adding notes spaced only a comma apart. But the point is, it has to be fifths, and it has to be a series of them, or else you are abandoning the framework of diatonic music.

-Igs

🔗rick <rick_ballan@...>

Hi Carl,

Yeah what you say here is definitely true. I used to play a Bach fugue in Emin that was transcribed by Segovia from cello. I forgot allot of it so I went to the music shop to buy it. But when I got it home it had the same motif and counterpoint opening but was a different piece entirely. And I've since heard yet a third version. Even in my own experience I can compose a theme or section and sit on it for years until I find where to put it. Sometimes it pops out of nowhere while I'm mucking around, other times it takes years of fiddling to get it right. OTOH no one would doubt that they were both virtuoso performers, Bach at least on a variety of instruments. What I'm saying to Marcel is that being able to write for instruments does require knowing something about how they're played, their range, transposition etc...We wouldn't do a B-A# trill on a trombone for eg since they are at opposite ends of the slide. And there's no substitute for experience. At any rate, the line between composition and impro, discovery and creativity, is never that clear cut.

-Rick

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > You said that before, and it's still wrong. Beethoven would sweat
> > for years over a piece of music, trying to get it just the way he
> > wanted it. Bach had a bigger output, but he also was willing to
> > recycle, and his music was carefully thought out. Of course both
> > were well known for their ability to improvise, but that's not how
> > they composed.
>
> Definitely true of Beethoven's piano sonatas, symphonies, and
> string quartets. He wrote some theme and variation sets that
> have more direct roots in improv.
>
> Bach did have to turn out cantatas pretty fast for many years,
> and he recycles and refines ideas there for sure, but there's
> also a demonstrated ability to write that stuff rapidly.
> However he's on record saying that composers who write at a
> keyboard are rank amateurs. And apparently some believe WTC1
> was a dry run and that WTC2 was the intended final product.
>
> -Carl
>

🔗Michael <djtrancendance@...>

Marcel> For instance for all practical purposes, a 3/2 minus a Schisma
(700.0013
> cents) is the same as an equal tempered fifth.

Igs>But this isn't about "for all practical purposes". 700.0000 cents does not
equal 700.0013 cents. Next thing you're going to tell me 2+2=5!

I'm thinking it's more like 2 + 2 = 4.003. And considering music is an art
foremost (IMVHO) and a science second-most, 4.01 is close enough because it
still "feels exactly like a 4". I believe that's leaning toward what Gene was
saying, which is that the difference is not perceivable. It's like comparing a
256kb/s mp3 to the original...in a huge % of cases no one can tell the
difference.

I think it's fair to say temperament do approximate JI...but they appear to
focus on distributing the error EQUALLY (or at least near equally) across dyads,
rather than having a lot dyads as perfect and a handful of them "way off" (IE
over 9 cents or so off) as "straight JI" scales do (at least assuming JI doesn't
go over, say 15-odd-limit or so).
I have made plenty of JI scales and, minus writing a straight harmonic series,
have always found some dyads in the scale are imperceptably different while
others are far from it regardless of how much optimization I do. It seems to be
an apparent limitation of JI...otherwise, I figure, why temper in the first
place?

In my mind that's most of what makes the two different. Meanwhile, things
like making scales that don't approximate JI seem to be merely irrational
tunings and not temperament (IE what are the tempering from then anyhow?). Is
there any reason to doubt/obvious-loophole you can see in what I said? Because,
at least on the surface, it seems like a simple issue to me.

-Michael

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> I'm thinking it's more like 2 + 2 = 4.003. And considering music is an art
> foremost (IMVHO) and a science second-most, 4.01 is close enough because it
> still "feels exactly like a 4". I believe that's leaning toward what Gene was
> saying, which is that the difference is not perceivable. It's like comparing a
> 256kb/s mp3 to the original...in a huge % of cases no one can tell the
> difference.

A non-perceivable difference can still be a calculable difference, i.e. it can still be a real non-zero difference. My understanding of the definition of JI is that it involves exact mathematical values and is not based on whether one can "hear the difference" or not. If it were to be based on the latter, then JI would be defined in terms of something like harmonic entropy, thus stripping "simple integer ratios" of their "magic". But hey, this isn't "my" definition of JI, I'm going off of the likes of Partch, Young, Catler, etc. I frankly agree that it's silly to make numerological distinctions if they have no basis in perception, it's just that I thought the term "JI" had an accepted definition as dealing only with exact frequency ratios. If this definition isn't actually accepted by anyone, then I'm an idiot for arguing for it.

> In my mind that's most of what makes the two different. Meanwhile, things
> like making scales that don't approximate JI seem to be merely irrational
> tunings and not temperament (IE what are the tempering from then anyhow?).

Gene's argument seems to be that you can call *anything* a temperament of anything else if you want to. I could call a pure 7/6 a tempered 6/5, or a pure 3/2 a tempered 16/11. It'd be silly to do so, maybe, but there's nothing stopping me. All irrational numbers have rational approximations, so even the most irrational tuning could be called a temperament of *something*. Phi could be considered a tempered 13/8. Everything is an approximation of everything else, it's just that its "accuracy of approximation" peaks near itself.

Also, for anyone who believes that time is not infinitely divisible, i.e. that there is a shortest length of time (a "chronon"), irrational intervals don't exist, because sound frequencies can only be described to a finite degree of accuracy. Irrational numbers would require that sound frequencies can be expressed to an infinite degree of accuracy.

-Igs

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> > Hindemith makes this point that if we couldn't approximate intervals it would be a disaster.
>
> Hindemith's argument is pretty much baloney.

(Baloney, such an American word. Love it!). Sure his argument about cutting off at the 7th harmonic is nonsense, but with this point I agree.
>
> > But concerning Beethoven, I don't know what you mean about playing the same thing in a different key. Didn't he compose on a tempered piano? As I said, these composers practically improvised their work. They had to in order to write so much stuff.
>
> You said that before, and it's still wrong. Beethoven would sweat for years over a piece of music, trying to get it just the way he wanted it. Bach had a bigger output, but he also was willing to recycle, and his music was carefully thought out. Of course both were well known for their ability to improvise, but that's not how they composed.
>

🔗Michael <djtrancendance@...>

>"My understanding of the definition of JI is that it involves exact
>mathematical values and is not based on whether one can "hear the difference"
>or not."
Right, hence why I'm leaning toward the idea of temperament often leaning
more toward situations where there's a difference from "real"/"pure" JI, but one
that can't be heard.

>"Gene's argument seems to be that you can call *anything* a temperament of
>anything else if you want to."
I agree...but then the question becomes how much error are you willing to
allow while still being able to call something a "tempered version" of something
else? I would say 13 cents error at absolute max...and more likely something
under 8 cents...and I'm pretty sure many would agree on that, if not be even
more conservative (IE saying "most be no more than 3 cents").

>"Phi could be considered a tempered 13/8."
That's about a 7 cent difference or so...so yeah, I'd say that's definitely
close enough. And, of course, 13/8 could be considered a tempered PHI (agreeing
with Gene's argument). But, meanwhile, only 13/8 could be considered JI. And,
for the record 18/11 could be considered a different JI ratio that (if you count
anything below 13 cents as "close enough") could be considered a tempered 13/8.

Gene...correct me if I'm wrong but don't those sorts of examples get near
the core of what you were saying?

🔗Marcel de Velde <m.develde@...>

> I frankly agree that it's silly to make numerological distinctions if they
> have no basis in perception, it's just that I thought the term "JI" had an
> accepted definition as dealing only with exact frequency ratios. If this
> definition isn't actually accepted by anyone, then I'm an idiot for arguing
> for it.

Well I think it probably isn't silly to make the distinction.
I think JI will show the math and logic behind music.
This logic would probably be lost in numbers when viewing tempered numbers.
When working theoretically there could be a huge difference between working
with exact ratios and working with large numbers in cents.

But again. JI is a concept of "in perfect tune" more than anything else.
So if someone comes up with a theory of why a no rational temperament is
actually the thing that is in tune to our ears/brain and in the physical
world etc, then that "non rational temperament" would have a right to be
called JI in my opinion.
Not that I think that'll ever be the case though :)

Marcel

🔗Michael <djtrancendance@...>

Marcel>"I think JI will show the math and logic behind music.
This logic would probably be lost in numbers when viewing tempered numbers."

I agree with this wholeheartedly. An example: my latest scales are littered
with values such as 1.67 and 1.463...which are near JI ratios but not exact. In
cases such as those, the JI relationships they are based on aren't blatantly
obvious...but when you are told they are part of the same interval classes as
5/3 and 22/15 it, I figure, should become much more obvious.

In fact there seems to be a numeric reason (and not just a psycho-acoustic
one!) for tempering by about 7 cents or less. Which is that values are close
enough to x/15 (thus including x/13, x/11, etc.) type fractions that it's often
blatantly obvious which JI fraction the "tempered" value is approximating. Try
typing the decimal equivalent for ANY tempered value within 7 cents or so of its
"perfect" JI value in here -< http://www.mindspring.com/~alanh/fracs.html and it
will find you the nearest JI interval "class", thus revealing the logic.

>"But again. JI is a concept of "in perfect tune" more than anything else."
But it's just that...a concept...even if it does explain what a lot of human
hearing derives from notes. It's like saying "the limit of Y where x approaches
infinity". You are always giving-up/losing JI purity of one interval for gained
purity in another when making JI scales to an extent.

>"So if someone comes up with a theory of why a no rational temperament is
>actually the thing that is in tune to our ears/brain and in the physical world"
Agreed it's not...I figure it's very much a case of
A) The brain's rounding what's the to fairly low-limit JI dyads.

B) The brain trying to make an effort to de-cloud the effects of critical band.
This often causes a huge sense of tension is the ratio is closer than about
12/11 and doesn't have the 12/11 surrounded by other tones that mask the
clashing harmonics ALA frequency masking (which is also used to help calculate
which tones can be deleted in mp3s since they are inaudible).

This closeness CAN be derived from JI ratios, of course, but the point is
there are JI ratios the brain considers neither in-tune nor unique. For example
19/18 vs. 93/89...which are both so close to maximum critical band dissonance
that their "JI periodicity" becomes scrambled and somewhat irrelevant...and
telling them apart becomes quite difficult. Yes I do harbor on-and-on about
this point...but mostly because it amazes me (perhaps minus Sethares) just how
many people ignore it, especially considering what a fundamental part of
psychoacoustics it is.
---

But the question becomes...if a tempered ratio so close you can't tell the
difference in hearing it and also so close that it becomes obvious which JI
ratio it's approximating (IE you can derive the logic)...why is it a problem?

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

>Pure theorists often don't realise that the 'heart' of modern 12 EDO tonal harmony is not based on tuning the fifths but on what we call *guide tones* between the thirds and sevenths, which invert as we cycle.

I know this will come as a shock, but jazz is not all of modern 12edo music. Anyway, the guide tone idea could be argued to be a kind of throwback, since it is something like the Baroque continuo.

> Once you start detuning away from this tritone "skeleton" you are going to run into trouble. Sure it's possible, but why do it just because of some old idea that tempered systems don't match some Platonic ideal of 'Pure whole-numbers'?

Because you are bored of music which sounds like crap?

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
I'm going off of the likes of Partch, Young, Catler, etc. I frankly agree that it's silly to make numerological distinctions if they have no basis in perception, it's just that I thought the term "JI" had an accepted definition as dealing only with exact frequency ratios. If this definition isn't actually accepted by anyone, then I'm an idiot for arguing for it.

It's accepted by many, probably most, but not by everyone, as some people seem to think JI should be defined in terms of how things actually sound.

> Gene's argument seems to be that you can call *anything* a temperament of anything else if you want to.

I don't recall saying this. But where do you propose drawing the lines?

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Igs> Gene's argument seems to be that you can call *anything* a temperament of
anything else if you want to.

Gene>I don't recall saying this. But where do you propose drawing the lines?

Gene, I realize this was directed mostly at Igs...but it's a great question
IMVHO. My two cents is that anything about at or under 7 cents of a JI ratio
can count as a tempered version because to the human ear it sounds virtually
identical.

Furthermore here's an example. The 1.68179 (6th) ratio in 12TET is actually
within about 7 cents of 27/16 (1.6875) than it it to what it's "supposed to be a
tempered version of", AKA 4/3, in JI terms.
In fact, the 1.68179 is over 13 cents away from 5/3 (IMVHO not exactly valid
as a tempered 5/3)!...I think it's a crying shame how far "tempered
substitutions" are allowed and the lines should be drawn according to
psychoacoustic perception, which means at under 8 cents.

I also suggest the ability to still have something tempered between two JI
ratios and allow it to function as both, but only if it is within under 8 cents
of both. Otherwise, I figure, you are leaning far toward performer aesthetics
in how much tempering is allowed (very subjective) rather than the physics of
the human ear and to what error it perceives two tones to be relatively
identical (relatively objective).

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Marcel de Velde <m.develde@...>

> Did you see my posting on "in tune" equal temperaments for various odd
> limits, meaning with errors for the whole diamond under 256/255 = 6.776
> cents? Of course you can do the same for higher rank temperaments also.
>

6.776 cents is a lot.
I wouldn't actually call that in tune.
Since these 6.776 cents can also be at fifths that should be 3/2 for
instance, this could make the whole sound more out of tune than 12edo.
And I wouldn't call 12edo in tune.

Other than this. These temperaments give no information on which notes to
hit exactly.

I think 5-limit for instance includes 1/1 5/4 3/2 major chords and 1/1 81/64
3/2 major chords, and 1/1 5/4 40/27 major chords etc.
So the error relative to 5-limit JI would be considerably higher than 6.776
cents.

Marcel

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>Not to mention the side question of if you know of
> any custom-made/non-equal temperament tunings that hit 3,5,7,9, and 11 within 7
> cents (and, preferably, with 12-20 tones for practicality so far as instrument
> playing).

The first thing which will occur to everyone is miracle, and its 21 note MOS Blackjack in particular. But it's not the only possibility. Others are diaschismic (46&58), myna (31&58), mystery (29&58) and wizard (22&50). I could expound on these further, but don't know what you need to know. Putting the above pairs of numbers into Graham's temperament finder will bring up the basic data in any case.

Some other possibles I don't have names for, and invite anyone who cares to try to propose a name.

22&58
<<6 -12 10 -14 -33 -1 -43 57 9 -74||
1/2 octave period, 9/7 generator
[<2 1 9 2 12|, <0 3 -6 5 -7|]

41&80
<<7 26 25 -3 25 20 -29 -15 -97 -95||
octave period, 7/5 generator
[<1 5 15 15 2|, <0 7 26 25 -3|]

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Marcel>"Since these 6.776 cents can also be at fifths that should be 3/2 for
instance, this could make the whole sound more out of tune than 12edo."
I don't get it, what's up with the "all 5ths MUST be pure" Puritanism on this
list? What makes a "slightly less than pure" 5th so much worse than, say, a
slightly less than pure third or fifth?
Also I never said temperaments MUST be created by single interval generators,
which your example of "using a de-tuned 5th as a generator for a 12TET-like
scale" seems to assume. Of course a circle of 7-cent-impure fifths may make a
lousy circle of fifths...but why not, say, use alternating intervals as a
generator? Is there some mantra that says all scales we create must be
generated the same way as 12TET? If there was...microtonality would bore me to
tears.

>"I think 5-limit for instance includes 1/1 5/4 3/2 major chords and 1/1 81/64
>3/2 major chords, and 1/1 5/4 40/27 major chords etc..... So the error relative
>to 5-limit JI would be considerably higher than 6.776 cents."
81/64 and 40/27 are both pretty sour in my opinion. 81/64 nears 19/15 within
a few cents and 40/27 is near virtually nothing even remotely low-limited (even
22/15 is far more than 7 cents away). And in both cases it assumes people can
often interpret the 15th limit as sounding non-chaotic...which seems to be a bit
of a stretch. There's nothing wrong with the root-tone critical band for either
of these, but the periodicity seems to be all over the place (and I'm guessing,
the overtone critical-band alignment would be equally sour).

So , in your opinion, what makes these ratios so special?

🔗Michael <djtrancendance@...>

🔗Marcel de Velde <m.develde@...>

Hi Michael,

Marcel>"Since these 6.776 cents can also be at fifths that should be 3/2 for
> instance, this could make the whole sound more out of tune than 12edo."
> I don't get it, what's up with the "all 5ths MUST be pure" Puritanism on
> this list? What makes a "slightly less than pure" 5th so much worse than,
> say, a slightly less than pure third or fifth?
>

Nonono, all fifths definately must not be 3/2.
Often a fifth is 40/27, and sometimes it is 3/2 minus a Schisma.
It's just that when the music does indeed calls for a 3/2 fifth, if you're
off by almost 7 cents sharp for instance.. well that's going to be audible
pretty well with many sounds. It'll probably be more audibly out of tune
than 12tet, even though 12tet has a terrible major third for instance,
somehow this major third is less audible when mistuned. This may also have
something to do with there beeing a 512/405 and 81/64 close to the equal
tempered major third. But there is nothing in 5-limit JI that's close to an
almost 7 cents sharp 3/2 for isntance.

> Also I never said temperaments MUST be created by single interval
> generators, which your example of "using a de-tuned 5th as a generator for a
> 12TET-like scale" seems to assume. Of course a circle of 7-cent-impure
> fifths may make a lousy circle of fifths...but why not, say, use alternating
> intervals as a generator? Is there some mantra that says all scales we
> create must be generated the same way as 12TET? If there
> was...microtonality would bore me to tears.
>

The idea is that equal temperaments are usable in all keys.
One can modulate all one wants with them.
It's like giving up quality for convenience. Going to mcdonalds instead of
cooking a tasty healthy meal yourself.

> >"I think 5-limit for instance includes 1/1 5/4 3/2 major chords and 1/1
> 81/64 3/2 major chords, and 1/1 5/4 40/27 major chords etc..... So the error
> relative to 5-limit JI would be considerably higher than 6.776 cents."
> 81/64 and 40/27 are both pretty sour in my opinion. 81/64 nears 19/15
> within a few cents and 40/27 is near virtually nothing even remotely
> low-limited (even 22/15 is far more than 7 cents away). And in both cases
> it assumes people can often interpret the 15th limit as sounding
> non-chaotic...which seems to be a bit of a stretch. There's nothing wrong
> with the root-tone critical band for either of these, but the periodicity
> seems to be all over the place (and I'm guessing, the overtone critical-band
> alignment would be equally sour).
>
> So , in your opinion, what makes these ratios so special?
>

40/27 I looove it.
Sure, one shouldn't play a 40/27 in a place in music that calls for a 3/2.
But neither should one play a 3/2 in a place in music that calls for a
40/27.
If you listen to my Drei Equale or Lasso pieces, they have 40/27 all over
them.
Drei Equale no1 and no2 even end with one! I've tried changing it to 3/2 to
see what it sounds like (easily done) and it sounds wrong that way! :) It
really does!

As for what makes them special. Well I'll have to think about a good
explenation for that, for now I can only say that after much research into
the LOGIC behind how music MUST work, this is what it comes down to. But pff
I'll make a webpage about that soon.

Marcel

🔗Herman Miller <hmiller@...>

genewardsmith wrote:
> > --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>> Not to mention the side question of if you know of any
>> custom-made/non-equal temperament tunings that hit 3,5,7,9, and 11
>> within 7 cents (and, preferably, with 12-20 tones for practicality
>> so far as instrument playing).
> > The first thing which will occur to everyone is miracle, and its 21
> note MOS Blackjack in particular. But it's not the only possibility.
> Others are diaschismic (46&58), myna (31&58), mystery (29&58) and
> wizard (22&50). I could expound on these further, but don't know what
> you need to know. Putting the above pairs of numbers into Graham's
> temperament finder will bring up the basic data in any case.
> > Some other possibles I don't have names for, and invite anyone who
> cares to try to propose a name.
> > 22&58 <<6 -12 10 -14 -33 -1 -43 57 9 -74|| 1/2 octave period, 9/7
> generator [<2 1 9 2 12|, <0 3 -6 5 -7|]

Similar to hedgehog, but unrelated. Echidna?

> 41&80 <<7 26 25 -3 25 20 -29 -15 -97 -95|| octave period, 7/5
> generator [<1 5 15 15 2|, <0 7 26 25 -3|]

That generator is way out beyond neptune. Pluto?

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> >Pure theorists often don't realise that the 'heart' of modern 12 EDO tonal harmony is not based on tuning the fifths but on what we call *guide tones* between the thirds and sevenths, which invert as we cycle.
>
> I know this will come as a shock, but jazz is not all of modern 12edo music. Anyway, the guide tone idea could be argued to be a kind of throwback, since it is something like the Baroque continuo.

Yes and Picasso is "something like" Rubens because they both used lines and a paint brush. Don't be absurd. We've not been talking about Xanakis but how diatonic music has morphed through the centuries.
>
> > Once you start detuning away from this tritone "skeleton" you are going to run into trouble. Sure it's possible, but why do it just because of some old idea that tempered systems don't match some Platonic ideal of 'Pure whole-numbers'?
>
> Because you are bored of music which sounds like crap?
>
Now who's over-generalising? Too much xentonality can become very tedious as well.

🔗rick <rick_ballan@...>

Just another thought on this point. I've noticed that even today classical composers often make exaggerated claims about being able to write straight to score without checking on an instrument. But I suspect this is more of a fashion.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>
> Hi Carl,
>
> Yeah what you say here is definitely true. I used to play a Bach fugue in Emin that was transcribed by Segovia from cello. I forgot allot of it so I went to the music shop to buy it. But when I got it home it had the same motif and counterpoint opening but was a different piece entirely. And I've since heard yet a third version. Even in my own experience I can compose a theme or section and sit on it for years until I find where to put it. Sometimes it pops out of nowhere while I'm mucking around, other times it takes years of fiddling to get it right. OTOH no one would doubt that they were both virtuoso performers, Bach at least on a variety of instruments. What I'm saying to Marcel is that being able to write for instruments does require knowing something about how they're played, their range, transposition etc...We wouldn't do a B-A# trill on a trombone for eg since they are at opposite ends of the slide. And there's no substitute for experience. At any rate, the line between composition and impro, discovery and creativity, is never that clear cut.
>
> -Rick
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > >
> > > You said that before, and it's still wrong. Beethoven would sweat
> > > for years over a piece of music, trying to get it just the way he
> > > wanted it. Bach had a bigger output, but he also was willing to
> > > recycle, and his music was carefully thought out. Of course both
> > > were well known for their ability to improvise, but that's not how
> > > they composed.
> >
> > Definitely true of Beethoven's piano sonatas, symphonies, and
> > string quartets. He wrote some theme and variation sets that
> > have more direct roots in improv.
> >
> > Bach did have to turn out cantatas pretty fast for many years,
> > and he recycles and refines ideas there for sure, but there's
> > also a demonstrated ability to write that stuff rapidly.
> > However he's on record saying that composers who write at a
> > keyboard are rank amateurs. And apparently some believe WTC1
> > was a dry run and that WTC2 was the intended final product.
> >
> > -Carl
> >
>

🔗genewardsmith <genewardsmith@...>

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Hi Rick,
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > Yeah Igs, what you say here "Tonal 12-tET music can probably be retuned to JI, but the skeleton gets deformed" is exactly what I was saying. Pure theorists often don't realise that the 'heart' of modern 12 EDO tonal harmony is not based on tuning the fifths but on what we call *guide tones* between the thirds and sevenths, which invert as we cycle.
> >
>
> Sorry, I should have left out "12-tET" from that sentence. I don't understand really anything about these guide-tones you talk about, but the fact remains that diatonic music as we know it originated from tuning systems based on a series of fifths. Any series of seven reasonably-pure fifths will do to produce a diatonic scale. Notes were initially defined one-dimensionally; E is not "E" because it's a major third of C, but because it's a fifth of A, which is a fifth of D, which is a fifth of G, which is a fifth of C. The fact that E is a major third above C is really a contingency of the way approximately-pure fifths work. The skeleton that gets deformed by forcing 5-limit JI is that backbone of fifths, because when you make E a pure 5/4, it is no longer related to C by a chain of fifths. And as we all know, the point of temperament was (among other things) to push the harmony of C-E toward 5/4 without losing the relationship of the chain of fifths, as well as to turn the spiral of pure fifths into a closed circle, so that more keys are accessible without adding notes spaced only a comma apart. But the point is, it has to be fifths, and it has to be a series of them, or else you are abandoning the framework of diatonic music.
>
> -Igs
>
Yeah I get that Igs. But my point was that despite its initial motivation of closing off the fifths, it inadvertently created a new set of rules or connections that evolved on its own. Debussy's whole-tonality is one example. Wagner's 'pantonality' and Shoernberg's 12 tonality are others. As are all of those jazz harmonies which (unconsciously?) manipulate the properties of the n'th root of 12.

Concerning guide tones, the notes C-E is sufficient to tell the listener that its a C maj. The fifth is not needed. When we apply these thirds from the stacked fifths we get the 7th's, 9th's, 11'ths and 13'ths, all of which also cycle like guide tones. (Wagner would even extend these further so that the tonic became buried. One critic said that his music "rolled out of the orchestra pit and onto the audience like a tepid water balloon". Love it!)

Any retuning will have to take into consideration *all* of these inbetweeny intervals.

-Rick

🔗Marcel de Velde <m.develde@...>

> Yeah I get that Igs. But my point was that despite its initial motivation
> of closing off the fifths, it inadvertently created a new set of rules or
> connections that evolved on its own. Debussy's whole-tonality is one
> example. Wagner's 'pantonality' and Shoernberg's 12 tonality are others. As
> are all of those jazz harmonies which (unconsciously?) manipulate the
> properties of the n'th root of 12.
>

Well, they may think they manipulate the properties of the n'th root of 12,
but it doesn't have to be so in the actual working of music / tuning at all.
There is currently no algorythm or something based on n'th root of 12
thinking that produces anything musical.
No matter what the composer thought of 12edo, they used their ears / brain
to make their music (with some exception to totally atonal music which isn't
about music anymore.. see what true 12edo thinking gives.. complete atonal
music)

>
> Concerning guide tones, the notes C-E is sufficient to tell the listener
> that its a C maj. The fifth is not needed. When we apply these thirds from
> the stacked fifths we get the 7th's, 9th's, 11'ths and 13'ths, all of which
> also cycle like guide tones. (Wagner would even extend these further so that
> the tonic became buried. One critic said that his music "rolled out of the
> orchestra pit and onto the audience like a tepid water balloon". Love it!)
>
> Any retuning will have to take into consideration *all* of these inbetweeny
> intervals.
>
> -Rick
>

Agreed that the 3/2 and 5/4 are THE important intervals.
See my 1/1 135/128 9/8 32/27 5/4 4/3 45/32 3/2 405/256 5/3 16/9 15/8 2/1
M-JI scale.
All triads, major or minor have either a 5/4 or a 3/2 in them (or both),
with the exception of one, (which may be perhaps the least understood triad
(makes the german sixth) of them all the 405/256 2/1 64/27 (45/16) ?)
See, this kind of thing does function in JI.

Marcel

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Just another thought on this point. I've noticed that even
> > today classical composers often make exaggerated claims about
> > being able to write straight to score without checking on an
> > instrument. But I suspect this is more of a fashion.
>
> Beethoven wrote his greatest music when he was totally deaf.
> What an exaggerator.

Indeed. The difference is, probably no modern composer spends
as much time working with manuscript as a composer of Bach or
Beethoven's day. Once you turn off the TV and internet, you
still have the temptations of multitrack recording and programs
like Sibelius to renounce before you're really forced to flex
your chops. Bach spent hundreds of hours as a young man just
copying scores... good ol' German learn-by-wrote approach.
(It works, at least if you're German.) Anyway, these guys
could all write music as fast as they could wet their quills.
We've seen the last of their kind I'm sure. Handel wrote
Messiah in less than a month, and while his dotted rhythms
can be a bit formulaic ("pork and beer" according to Berlioz),
Messiah f'ing rocks and you'll be hard pressed to find any of
its themes in his other work. Telemann, according to Handel,
was even faster and remains one of the most prolific composers
of all time.

-Carl

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > > Just another thought on this point. I've noticed that even
> > > today classical composers often make exaggerated claims about
> > > being able to write straight to score without checking on an
> > > instrument. But I suspect this is more of a fashion.
> >
> > Beethoven wrote his greatest music when he was totally deaf.
> > What an exaggerator.

Carl, writing straight to score is not some type of speciality for a composer but a basic requirement. I've written symphonies, string quartets, big band charts, musicals and countless small band stuff and couldn't check things on the guitar even if I wanted to. It would also slow me down to a snails pace which ruins the flow and I can't afford. The fact that a great composer like Beethoven wrote music when he was deaf is really not that surprising (it's more remarkable for its unselfishness and pathos). What I meant was that classical composers often exaggerate to their students in order to drive this point home. One of my teachers said "If you can't compose straight to the score then you might as well take a job at the bank!". But the reality is that composers are generally good at performing on one or more instruments as well. Your Bach quote reminded me of it, that's all. He was a phenomenal organ player.
>
> Indeed. The difference is, probably no modern composer spends
> as much time working with manuscript as a composer of Bach or
> Beethoven's day. Once you turn off the TV and internet, you
> still have the temptations of multitrack recording and programs
> like Sibelius to renounce before you're really forced to flex
> your chops. Bach spent hundreds of hours as a young man just
> copying scores... good ol' German learn-by-wrote approach.
> (It works, at least if you're German.) Anyway, these guys
> could all write music as fast as they could wet their quills.
> We've seen the last of their kind I'm sure. Handel wrote
> Messiah in less than a month, and while his dotted rhythms
> can be a bit formulaic ("pork and beer" according to Berlioz),
> Messiah f'ing rocks and you'll be hard pressed to find any of
> its themes in his other work. Telemann, according to Handel,
> was even faster and remains one of the most prolific composers
> of all time.
>
> -Carl
>
Yeah, fortunately I learnt in the 80's before computers. But I write on Sibelius now, not so much for the (God awful) playback but because it is wonderful not having to transpose and copy a chart ever again (I once calculated that it took me 90 minutes to copy one instrument and x 18 for big band makes 27 hours! It's allot of time for say 5 minutes of music. No I just press extract score and print).

-Rick

🔗Daniel Forró <dan.for@...>

Why? I've been composing my polystylistic music mainly this way when not using live improvisation and direct recording into the sequencer in some music styles. And of course I write by hand using pencil and eraser... Later I put finished music from the manuscript to computer notator (I used Atari ST Notator between 1988-ca 2003, then Sibelius on Mac) and usually do some smaller changes after some time. But this way is easy with perfect pitch :-)

Daniel Forro

On 16 Jul 2010, at 11:59 AM, rick wrote:

> Just another thought on this point. I've noticed that even today > classical composers often make exaggerated claims about being able > to write straight to score without checking on an instrument. But I > suspect this is more of a fashion.
>

🔗Daniel Forró <dan.for@...>

On 16 Jul 2010, at 7:38 PM, rick wrote:

> Carl, writing straight to score is not some type of speciality for > a composer but a basic requirement. I've written symphonies, string > quartets, big band charts, musicals and countless small band stuff > and couldn't check things on the guitar even if I wanted to. It > would also slow me down to a snails pace which ruins the flow and I > can't afford. The fact that a great composer like Beethoven wrote > music when he was deaf is really not that surprising (it's more > remarkable for its unselfishness and pathos). What I meant was that > classical composers often exaggerate to their students in order to > drive this point home.

So we are on the same boat.

> One of my teachers said "If you can't compose straight to the score > then you might as well take a job at the bank!".

Only partly truth, there are more possible methods nowadays. But of course it's good to be able to do so, and every composer should know it, it's a part of professional craftsmanship...

> But the reality is that composers are generally good at performing > on one or more instruments as well. Your Bach quote reminded me of > it, that's all. He was a phenomenal organ player.

Yes, but instrumental dexterity is dangerous for composition as such composer is not able to write properly for the other instruments and orchestra. In Baroque times it was OK, music for different instruments, vocals, choirs looked the same in the score. But later with orchestra development more specific instrumentation art was necessary, with different textures for different instruments. Compare orchestral works of Schumann or Liszt with Berlioz for example, you will understand the difference. In fact their output is only orchestrated piano part. Debussy, Ravel, Stravinsky or Bartok were exception.

>>
> Yeah, fortunately I learnt in the 80's before computers. But I > write on Sibelius now, not so much for the (God awful) playback but > because it is wonderful not having to transpose and copy a chart > ever again (I once calculated that it took me 90 minutes to copy > one instrument and x 18 for big band makes 27 hours! It's allot of > time for say 5 minutes of music. No I just press extract score and > print).
>
> -Rick

Yes, Sibelius and other notators are great aid exactly in this mechanical work...

Daniel Forro

🔗Michael <djtrancendance@...>

Marcel>"It's just that when the music does indeed calls for a 3/2 fifth, if
you're off by almost 7 cents sharp for instance.. well that's going to be
audible pretty well with many sounds. It'll probably be more audibly out of
tune than 12tet, even though 12tet has a terrible major third for instance,
somehow this major third is less audible when mistuned."
This would be interesting to run a test on. I don't think it's true unless,
of course, the two tones that form the fifth represent the highest and lowest
notes in your chord (IE with non-diminished triads). But who would use bare
bones triads without fourth or fifth notes added on to make it more
interesting? I figure...not that many composers.

Me>"Also I never said temperaments MUST be created by single interval
generators,"
Marcel>"The idea is that equal temperaments are usable in all keys.
One can modulate all one wants with them.
It's like giving up quality for convenience. Going to mcdonalds instead of
cooking a tasty healthy meal yourself."
Not that I blame people for taking the option of "going to McDonalds"...but
I'm betting I'm far from the only one willing to "cook at home" for the
advantages. It's funny too...last time I lived in Holland, McDonalds was
actually considered fairly fancy, and the average diet included a lot of
bun-less hamburgers, french fries, and "frite-saus". :-D
...but you're right, TET tunings ensure perfect modulation and without any
complex calculations...that's an obvious advantage to them.

>"As for what makes them special. Well I'll have to think about a good
>explenation for that, for now I can only say that after much research into the
>LOGIC behind how music MUST work, this is what it comes down to. But pff I'll
>make a webpage about that soon."
Yeah 40/27 is a tough nut to explain. But, then again, so is 22/15 (by far
my favorite alternative 5th)...which I find much more in place than 17/11 and
even 13/9...although the fairly high numbers in the fraction 22/15 make it seem
it should be otherwise. Good luck on the page/explanation, though!

🔗Daniel Forró <dan.for@...>

On 16 Jul 2010, at 4:15 PM, Carl Lumma wrote:

> Indeed. The difference is, probably no modern composer spends
> as much time working with manuscript as a composer of Bach or
> Beethoven's day.

So I'm old-fashioned modern composer using mainly manuscripts in 42 years of my compositional work...

> Once you turn off the TV and internet, you
> still have the temptations of multitrack recording and programs
> like Sibelius to renounce before you're really forced to flex
> your chops. Bach spent hundreds of hours as a young man just
> copying scores... good ol' German learn-by-wrote approach.
> (It works, at least if you're German.)

I remember my copying of lot of scores by hand in my childhood and youth... You can't imagine how difficult was to get scores in the countries behind iron curtain, especially Western jazz, or musicals (I copied by hand whole West Side Story!) and photocopy service didn't exist long years there, until 80ies, and then quality was poor. So we had to write by hand a lot...

> Anyway, these guys
> could all write music as fast as they could wet their quills.
> We've seen the last of their kind I'm sure. Handel wrote
> Messiah in less than a month, and while his dotted rhythms
> can be a bit formulaic ("pork and beer" according to Berlioz),
> Messiah f'ing rocks and you'll be hard pressed to find any of
> its themes in his other work. Telemann, according to Handel,
> was even faster and remains one of the most prolific composers
> of all time.
>
> -Carl

But don't forget they all wrote only in one music style whole their life, and there's a lot of common patterns and figures used by all composers of the same era, and lot of recycling between different composers and even in the works of the same composer. That's the reason why many works are rather boring, especially less able composers. But even Bach, Handel and Mozart had their bad and worse days, when they created just from inertia and pure craftsmanship, without an interesting musical motifs. (Of course they could have good reasons for doing so - for example paid commission). Besides there's generally lot of redundancy in their output. We can say the same for example about such Bohuslav Martinu, or Paul Hindemith and many other composers in 20th century even. Prolific, yes. Hard working, yes. But I say lot of their music doesn't deserve to be performed at all.

What's more funny - they are not so well known composers who sometimes have sudden boom after somebody (performer, conductor, music scientist...) "find" them after years and bring their works to the light. From Czech composers for example Zelenka, Myslivecek, Dusik, Rejcha, Erwin Schulhoff, Korngold... Here I think this is good - they deserved to be living part of musical heritage, not only fashionable personalities.

Now here in Japan Leos Janacek started to be very fashionable, thanks to Murakami's bestseller 1Q84 where he often mentioned Sinfonietta. Funny enough, such reason for fame, but if it can somebody fire for deeper interest in Janacek, why not...

Daniel Forro

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> > Indeed. The difference is, probably no modern composer spends
> > as much time working with manuscript as a composer of Bach or
> > Beethoven's day.
>
> So I'm old-fashioned modern composer using mainly manuscripts
> in 42 years of my compositional work...

Yeah... I think you and Rick missed the point. I can through
compose too. You're probably better at it than I am, but
neither of us are as good as Bach.

> But don't forget they all wrote only in one music style whole
> their life, and there's a lot of common patterns and figures
> used by all composers of the same era,

I've heard this argument before and I don't think it holds
water. In reality, most composers use only a relatively small
bag of tricks no matter what "style" they're writing in.
Beethoven invented romantic music and Bach's music is probably
the most recognizable of any composer.

> From Czech composers for example Zelenka, Myslivecek,
> Dusik, Rejcha, Erwin Schulhoff, Korngold...

I'm a big Zelenka fan.

> Funny enough, such reason for fame, but if it can somebody
> fire for deeper interest in Janacek, why not...

I like Janacek.

-Carl

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> Yeah I get that Igs. But my point was that despite its initial motivation of closing off the fifths, it inadvertently created a new set of rules or connections that evolved on its own. Debussy's whole-tonality is one example. Wagner's 'pantonality' and Shoernberg's 12 tonality are others. As are all of those jazz harmonies which (unconsciously?) manipulate the properties of the n'th root of 12.
>

Yeah, I get that too, Rick. That's why it's troublesome that these composers all retained the fifth-based notation system, which assigns note-names and interval-classes according to the spiral of fifths and not according to 12-tET. There'd be less confusion on this list if those composers all used a notation that didn't (at its core) imply a circle of fifths. I guess my point is that it's the notation that implies the circle of fifths, not the music itself.

> Any retuning will have to take into consideration *all* of these inbetweeny intervals.

Not really; there's no rule stipulating what a retuning "has to" take into consideration. I can retune anything to any tuning I want, and you can't stop me! ;-> Of course, if I'm going to try to argue that my retuning is "more correct" that the original tuning, I'm going to have to do a LOT of work to prove that, and in fact it may be unprovable. The only way to define a "correct" tuning is to ask the composer what he/she intended! Trying to tell me that my 16-EDO music would be more correctly-tuned in 5-limit JI is silly, because I intended that music to have that tuning, and therefore it's the "correct" tuning for that music. Marcel knows enough not to tell people on this list that their music is "tuned wrong", though why he insists on telling Beethoven that he tuned wrong is beyond me!

-Igs

🔗Michael <djtrancendance@...>

Igs>"The only way to define a "correct" tuning is to ask the composer what
he/she intended! Trying to tell me that my 16-EDO music would be more
correctly-tuned in 5-limit JI is silly, because I intended that music to have
that tuning, and therefore it's the "correct" tuning for that music."

Well put! I'll still argue someone who likes 5-limit intervals will most
likely want their music done in a tuning which has a lot of 5-limit or
near-5-limit dyads available. However, isn't it fair to say a lot of musicians
most likely don't like a certain limit per say, but rather certain intervals
from many limit sets?

It bugs me many tuning enthusiasts make broad generalizations like "I only
like x-limit" without comparing intervals from that limit against other ones.
And I'm betting, that what a composer intended far as mood and balance usually
spans multiple sets of "limits" rather than just one. I used to hate limit sets
over 7 because of all the on list suggestions that "anything over 7 is
chaotic"...but actually trying as many dyads as I could showed me I prefered
certain 9, 11, and even occasionally 15-limit (thought almost never 13-limit)
intervals to their nearest 5 or 7 limit equivalents.

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> Well I think it probably isn't silly to make the distinction.
> I think JI will show the math and logic behind music.

There is no "one" logic behind music; JI is a complete internally-consistent logical system for making music, and so is temperament. Temperament can be thought of as a warped JI where two distinct ratios collapse into one interval, and each pair of collapsed ratios defines a unique internally-consistent logical system. The logic behind music thus comes from either defining or forbidding equivalences. If common-practice music is based on a system where 81/64 and 5/4 are the same interval, you'll have to accept inconsistencies to translate it into a system where they are different intervals--i.e. sometimes you have to use an 81/64, sometimes a 5/4. The "logic" doesn't come ONLY from how the intervals sound, it also comes from how the intervals are defined. Choosing between the two systems can only be made according to aesthetic preference; you, as a composer, prefer to have a few intervals of great complexity for the sake of having many intervals of low complexity. The fact that temperament became as popular as it did suggests that at some point, a majority of composers decided they'd prefer to spread the error out among all the intervals in some way instead of concentrate into a few intervals.

You have the right to disagree with this choice, but you don't have the right to retroactively retract the choices of dead composers regarding how their music is "supposed to be" tuned. You are free to tune it and perform it as you please, of course, but you can't alter the historical fact of the choices they made or retroactively strip them of the authority to define the "proper" tuning for their own compositions!

I don't mean to suggest it's not a worthwhile exercise to find a way to minimize the inconsistency of translating tempered music into JI, just that there's mountains of evidence against this somehow being the "one true logic" behind music.

-Igs

🔗Marcel de Velde <m.develde@...>

Hi Igs,

There is no "one" logic behind music; JI is a complete internally-consistent
> logical system for making music, and so is temperament.
>

I disagree here.
Offcourse, it's a personal belief. I don't have hard proof, though if I took
to the effort to write down a lengthy reasoning behind it, I could show that
it is likely so with good reason.

But JI beeing complete or a system for writing music?
Right now it's neither of those.
It's very very poorly understood and very incomplete.
And the worst advice for someone who wants to make music is to advice
him/her to do it in JI. Surely music making in JI right now means that
either no music is made because of getting lost in numbers, or the music is
terribly out of tune.
An aid for making music it's certainly not right now.
Though I do think that with the right progress in JI that it will become
such. The best aid for making music, that'll sound the best too.
But right now.. big no no.

> Temperament can be thought of as a warped JI where two distinct ratios
> collapse into one interval, and each pair of collapsed ratios defines a
> unique internally-consistent logical system. The logic behind music thus
> comes from either defining or forbidding equivalences. If common-practice
> music is based on a system where 81/64 and 5/4 are the same interval, you'll
> have to accept inconsistencies to translate it into a system where they are
> different intervals--i.e. sometimes you have to use an 81/64, sometimes a
> 5/4. The "logic" doesn't come ONLY from how the intervals sound, it also
> comes from how the intervals are defined. Choosing between the two systems
> can only be made according to aesthetic preference; you, as a composer,
> prefer to have a few intervals of great complexity for the sake of having
> many intervals of low complexity. The fact that temperament became as
> popular as it did suggests that at some point, a majority of composers
> decided they'd prefer to spread the error out among all the intervals in
> some way instead of concentrate into a few intervals.
>

There is no "error" in JI to spread out.
JI is like the music is in it's inner core.
Music theory is not based on 12edo or circle of fifth logic.
Notation is based on this, but music theory is a vast collection of things
that sound good found by actual practice, and semi-rules that are based on
trying to make sense of what sounds good in practice etc. Though very
incomplete this system is.

>
> You have the right to disagree with this choice, but you don't have the
> right to retroactively retract the choices of dead composers regarding how
> their music is "supposed to be" tuned. You are free to tune it and perform
> it as you please, of course, but you can't alter the historical fact of the
> choices they made or retroactively strip them of the authority to define the
> "proper" tuning for their own compositions!
>

Yes one can.
Since JI is how music really works it doesn't matter in which temperament a
composer wrote.
Harmony and counterpoint have logic of their own. Once a composer wrote
music the music itself speaks, not the composer.

>
> I don't mean to suggest it's not a worthwhile exercise to find a way to
> minimize the inconsistency of translating tempered music into JI, just that
> there's mountains of evidence against this somehow being the "one true
> logic" behind music.
>
> -Igs
>

There's in my opinion a bigger mountain of evidence and likelyhood that
music does have "one true logic" :)

Marcel

🔗Marcel de Velde <m.develde@...>

🔗jonszanto <jszanto@...>

🔗genewardsmith <genewardsmith@...>

🔗jonszanto <jszanto@...>

🔗Marcel de Velde <m.develde@...>

🔗jonszanto <jszanto@...>

🔗caleb morgan <calebmrgn@...>

Marcel, I listened to this, most of it sounded good, despite the quacky brass sound.

But towards the end, I think there are some little mistakes that make it sound quite out of tune. Such as some out of tune octaves, I think.

I bet you'd find 4 or 5 little things you might want to tweak. (I have no idea if they are theoretically important or if they're trivial.)

Caleb

On Jul 17, 2010, at 12:58 AM, Marcel de Velde wrote:

>
> Again, lol. Harry knew what he was up against.
>
> lol lol lol :-p
>
> Harry couldn't do this:
> www.develde.net
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_no1_%28M-JI_2010-07-17%29.mp3
>
> And neither can any of you ;)
> And I just did :-)
>
> Marcel
>
>

🔗rick <rick_ballan@...>

Yes I knew we're on the same page. I've just never been good at communicating (when I was a kid I used to start stories right at the end and get annoyed why others didn't understand me). I'll just add that I'd much prefer Chopin to Rachmaninoff. But Bach (ah, Bach) has something special about his 'virtuosity'. This is especially evident when we compare his music to his son's. They all have the same style but there is that indefinable quality, that turn of phrase which is both unexpected and correct in retrospect, that J. S has.

-Rick

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 16 Jul 2010, at 7:38 PM, rick wrote:
>
> > Carl, writing straight to score is not some type of speciality for
> > a composer but a basic requirement. I've written symphonies, string
> > quartets, big band charts, musicals and countless small band stuff
> > and couldn't check things on the guitar even if I wanted to. It
> > would also slow me down to a snails pace which ruins the flow and I
> > can't afford. The fact that a great composer like Beethoven wrote
> > music when he was deaf is really not that surprising (it's more
> > remarkable for its unselfishness and pathos). What I meant was that
> > classical composers often exaggerate to their students in order to
> > drive this point home.
>
> So we are on the same boat.
>
>
> > One of my teachers said "If you can't compose straight to the score
> > then you might as well take a job at the bank!".
>
> Only partly truth, there are more possible methods nowadays. But of
> course it's good to be able to do so, and every composer should know
> it, it's a part of professional craftsmanship...
>
> > But the reality is that composers are generally good at performing
> > on one or more instruments as well. Your Bach quote reminded me of
> > it, that's all. He was a phenomenal organ player.
>
> Yes, but instrumental dexterity is dangerous for composition as such
> composer is not able to write properly for the other instruments and
> orchestra. In Baroque times it was OK, music for different
> instruments, vocals, choirs looked the same in the score. But later
> with orchestra development more specific instrumentation art was
> necessary, with different textures for different instruments. Compare
> orchestral works of Schumann or Liszt with Berlioz for example, you
> will understand the difference. In fact their output is only
> orchestrated piano part. Debussy, Ravel, Stravinsky or Bartok were
> exception.
>
> >>
> > Yeah, fortunately I learnt in the 80's before computers. But I
> > write on Sibelius now, not so much for the (God awful) playback but
> > because it is wonderful not having to transpose and copy a chart
> > ever again (I once calculated that it took me 90 minutes to copy
> > one instrument and x 18 for big band makes 27 hours! It's allot of
> > time for say 5 minutes of music. No I just press extract score and
> > print).
> >
> > -Rick
>
>
> Yes, Sibelius and other notators are great aid exactly in this
> mechanical work...
>
> Daniel Forro
>

🔗Marcel de Velde <m.develde@...>

Hi Caleb,

Marcel, I listened to this, most of it sounded good, despite the quacky
> brass sound.
>
> But towards the end, I think there are some little mistakes that make it
> sound quite out of tune. Such as some out of tune octaves, I think.
>
> I bet you'd find 4 or 5 little things you might want to tweak. (I have no
> idea if they are theoretically important or if they're trivial.)
>
> Caleb
>

Thanks for listening!

But there are no out of tune octaves.
All notes are theoretically important to me, however this time I got them
all right :)
I'm not sure where in the piece you think you're hearing these things, but
they are really not there.
There are a couple of wolfs, but these are correct and Beethoven actually
placed the fundamental bass correct relative to these (there is never a
fundamental bass under any wolf)

Btw this will probably be my last message on this (if it even gets through)
as Carl has once again decided to moderate me.
I will not stand this and will unsubscribe from this list untill moderation
is removed.

Marcel
www.develde.net

🔗caleb morgan <calebmrgn@...>

timings of places where I'm hearing badness:

1:02 slight

1:04 next chord (dom chord) slight

1:32 very bad, this sounds like out-of-tune octave, perhaps it's an overtone

1:39 slight

1:44 very bad

1:48 very very slight

On Jul 17, 2010, at 11:25 AM, Marcel de Velde wrote:

> Hi Caleb,
> Marcel, I listened to this, most of it sounded good, despite the quacky brass sound.
>
>
> But towards the end, I think there are some little mistakes that make it sound quite out of tune. Such as some out of tune octaves, I think.
>
> I bet you'd find 4 or 5 little things you might want to tweak. (I have no idea if they are theoretically important or if they're trivial.)
>
> Caleb
>
>
> Thanks for listening!
>
> But there are no out of tune octaves.
> All notes are theoretically important to me, however this time I got them all right :)
> I'm not sure where in the piece you think you're hearing these things, but they are really not there.
> There are a couple of wolfs, but these are correct and Beethoven actually placed the fundamental bass correct relative to these (there is never a fundamental bass under any wolf)
>
> Btw this will probably be my last message on this (if it even gets through) as Carl has once again decided to moderate me.
> I will not stand this and will unsubscribe from this list untill moderation is removed.
>
> Marcel
> www.develde.net
>
>
>

🔗genewardsmith <genewardsmith@...>

🔗Marcel de Velde <m.develde@...>

Hi Caleb,

Thanks for taking the effort!

timings of places where I'm hearing badness:
>
> 1:02 slight
>

Yes this has a wolf. It's a 1/1 5/4 27/16 sixth chord.
It also occurs at 0:20

>
> 1:04 next chord (dom chord) slight
>

It's the same dominant major chord in minor that's used throughout the
piece.
It's also the chord that's used every time to modulate between D minor and C
major, like it is here.

> 1:32 very bad, this sounds like out-of-tune octave, perhaps it's an
> overtone
>

This is a 9/8 4/3 5/3 chord (same as the 1/1 5/4 27/16 sixth, only here the
bass is put at the bottom of the wolf fifth)
I belief it is correct. It has a dissonant tension as it should, it serves
the same function here as the diminished 7th chords that are used at 0:46
and 0:55 that lead to the same chord as the 9/8 4/3 5/3 leads to in this
case.

> 1:39 slight
>

The 1/1 5/4 27/16 sixth chord again.

> 1:44 very bad
>

Oh yes thank you soooo much!!!!
Unbelievable.
I heard this myself too and thought neh it's a 1/1 5/4 3/2 2/1 major chord,
I wrote it myself. It's fine and didn't pay attention to it anymore.
But you refocussed my attention to it, and upon close listening it indeed
didn't sound like a 1/1 5/4 3/2 2/1 major..
So I checked my Scala sequence file..
And indeed I made a stupid sloppy error there!
One of the modulation messages I accidently put one note too late!
And exactly on the one track where it matters in practice..
Thanks again! This one really slipped passed me.

I re-rendered the MP3 and updated the MIDI and .seq files.
MP3:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_no1_%28M-JI_2010-07-17%29.mp3
MIDI:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_2010-07-17%29.mid
.seq:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%28M-JI_2010-07-17%29.seq

Amazing how I had put this away from the attention of my ears by the
mistaken belief that it was a 1/1 5/4 3/2 2/1 chord..
(btw the error made it a 1/1 5/4 40/27 2/1 chord, due to one note staying
stuck in the previous key for one note)

Kind regards,
Marcel

🔗cityoftheasleep <igliashon@...>

🔗Andy <a_sparschuh@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> Too bad the 53edo doesn't do better.
> I allways though it was as good as JI.

Hi Marcel,

then in that case try out to do 53 better in rational fractions,
with epimoric temperings inbetween some 5ths as here suggested

+-0: D. 1/1 unsion
+ 1: A. 3/4
+ 2: E. 9/8
+ 3: B. 32/27
+ 4: F# 27/32
~~ 1215/1216 ~~
+ 5: C# 19/20
~~ 400/399 ~~
+ 6: G# 5/7
~~ 434/435
+ 7: D# 31/29
~~ 464/465
+ 8: A# 4/5
+ 9: F/ 6/5
+10: C/ 9/10
~~ 460/459 ~~
+11: G/ 23/17
~~ 1105/1104 ~~
+12: D/ 65/64
~~ 4096/4095 ~~
+13: A/ 16/21
+14: E/ 8/7
+15: B/ 6/7
+16: F& 9/7
~~ 350/351 ~~
+17: C& 25/26
~~ 675/676 ~~
+18: G& 13/18
+19: D& 13/12
+20: A& 13/16
~~ 352/351 ~~
+21: F+ 11/9
+22: C+ 11/12
+23: G+ 11/8
+24: D+ 33/32
~~ 512/513 ~~
+25: A+ 44/57
~~ 495/494 ~~
+26: E+ 52/45 F-
~~ 675/676 ~~
-26: C- 45/52 B+
~~ 494/494 ~~
-25: G- 57/44
~~ 512/513 ~~
-24: D- 32/33
-23: A- 8/11
-22: E- 12/11
-21: B- 9/11
~~ 352/351 ~~
-20: GB 16/13
-19: DB 12/13
-18: AB 18/13
~~ 675/676 ~~
-17: EB 26/25
~~ 350/351
-16: BB 7/9
-15: F\ 7/6
-14: C\ 7/8
-13: G\ 21/16
~~ 4096/4095 ~~
-12: D\ 64/65
~~ 1105/1104 ~~
-11: A\ 17/23
~~ 459/460 ~~
-10: E\ 10/9
- 9: B\ 5/6
- 8: Gb 5/4
~~ 464/465 ~~
- 7: Db 29/31
~~ 434/435 ~~
- 6: Ab 7/5
~~ 400/399 ~~
- 5: Eb 20/19
~~ 1215/1216 ~~
- 4: Bb 64/81
- 3: F. 32/27
- 2: C. 8/9
- 1: G. 2/3
+-0: D. 1/1

or when arranged in ascending order stepwise comma by comma

z -26 G# 5/7
y -25 G& 13/18
x -24 A- 8/11
w -23 A\ 17/23
v -22 A. 3/4
u -21 A/ 16/21
t -20 A+ 44/57
s -19 BB 7/9
r -18 Bb 64/81
q -17 A# 4/5
p -16 A& 13/16
o -15 B- 9/11
n -14 B/ 5/6
m -13 B. 27/32
l -12 B/ 6/7
k -11 B+ 45/52 C-
j -10 C\ 7/8
i - 9 C. 8/9
h - 8 C/ 9/10
g - 7 C+ 10/11
f - 6 DB 12/13
e - 5 Db 15/16
d - 4 C# 19/20
c - 3 C& 25/26
b - 2 D- 32/33
a - 1 D\ 64/65
@ +-0 D. 1/1
A + 1 D/ 65/64
B + 2 D+ 33/32
C + 3 EB 26/25
D + 4 Eb 20/19
E + 5 D# 16/15
F + 6 D& 13/12
G + 7 E- 11/10
H + 8 E\ 10/9
I + 9 E. 9/8
J +10 E/ 8/7
K +11 E+ 52/45 F-
L +12 F\ 7/6
M +13 F. 32/27
N +14 F/ 6/5
O +15 F+ 11/9
P +16 GB 16/13
Q +17 Gb 5/4
R +18 F# 81/64
S +19 F& 9/7
T +20 G- 57/44
U +21 G\ 21/16
V +22 G. 4/3
W +23 G/ 23/17
X +24 G+ 11/8
Y +25 AB 18/13
Z +26 Ab 7/5

!Sp53rat.scl
Sparschuh's [2010] rational 53-tone with some epimoric biased 5ths
53
!
65/64 ! A
33/32 ! B
26/25 ! C
20/19 ! D
16/15 ! E
13/12 ! F
11/10 ! G
10/9 ! H
9/8 ! I
8/7 ! J
52/45 ! K
7/6 ! L
32/27 ! M
6/5 ! N
11/9 ! O
16/13 ! P
5/4 ! Q
81/64 ! R
9/7 ! S
57/44 ! T
21/16 ! U
4/3 ! V
23/17 ! W
11/8 ! X
18/13 ! Y
7/5 ! Z
10/7 ! z'
13/9 ! y'
16/11 ! x'
34/23 ! w'
3/2 ! v'
32/21 ! u'
88/57 ! t'
14/9 ! s'
128/81 ! r'
8/5 ! q'
13/8 ! p'
18/11 ! o'
5/3 ! n'
27/16 ! m'
12/7 ! l'
45/26 ! k'
7/4 ! j'
16/9 ! i'
9/5 ! h'
20/11 ! g'
24/13 ! f'
15/8 ! e'
19/10 ! d'
25/13 ! c'
64/33 ! b'
128/65 ! a'
2/1 ! @'
!
!
![eof]

Remark:
Attend the many mirror-symmetries within that,
that went particulary lost in the 'scala'-reprensentation,
when the lower-case note-namnes got octaved.

bye
Andy