Yahoo Tuning Groups Ultimate Backup tuning [tuning] harmonic series as the basis for harmony and scales

I've been playing with the idea of music beeing based on the harmonic series
in a much more direct way than I previously thought.
What if the minor chord with a fundamental base of 1/1 is 1/1 19/16 3/2. It
sounds correct to me.
And the dominant 7th as 1/1 5/4 3/2 57/32
And the 9th as 1/1 5/4 3/2 57/32 9/4
They sound better to me than with 16/9 as minot 7th
Also 1/1 19/16 3/2 57/32 makes sense now.

And scales constructed like this:
1/1 17/16 9/8 19/16 5/4 4/3 17/12? (or 45/32?) 3/2 51/32 27/16 57/32 15/8
2/1
and same scale on a different degree: 1/1 17/16 9/8 19/16 5/4 4/3 17/12 3/2
19/12 5/3 16/9 17/9? (or 15/8?) 2/1
They are subsets of series of 15:16:17:18:19:20 repeated in fourths.
Music seems to me to make a lot of sense by seeing it as the harmonic series
overlapping itself in fifths (or fourths).

I'm sure many theories have allready been based on this.
If someone knows where to find them please let me know.

Marcel

🔗Michael Sheiman <djtrancendance@...>

---"1/1 17/16 9/8 19/16 5/4 4/3 17/12" -Marcel
I'm not an expert on this. But I will say that, in the past, I've found using a combination of fractions which can be stated with perfect accuracy x/16 and x/12 fractions to sound ideal far as directly harmonic-series-based scales. Thus...I don't think your "mystery" 17/12 fraction is there as a fluke (instead of 45/32). This would "ruin" the ability to simplify to x/32 "perfect harmonic series" format...but, at least personally, I believe x/12 format fractions mix with x/16 ones quite nicely in mixed "dual harmonic series" type scales.

-Michael

--- On Thu, 4/16/09, Marcel de Velde <m.develde@gmail.com> wrote:

From: Marcel de Velde <m.develde@...>
Subject: [tuning] harmonic series as the basis for harmony and scales
To: tuning@yahoogroups.com
Date: Thursday, April 16, 2009, 7:31 AM

I've been playing with the idea of music beeing based on the harmonic series in a much more direct way than I previously thought.
What if the minor chord with a fundamental base of 1/1 is 1/1 19/16 3/2. It sounds correct to me.
And the dominant 7th as 1/1 5/4 3/2 57/32And the 9th as 1/1 5/4 3/2 57/32 9/4They sound better to me than with 16/9 as minot 7thAlso 1/1 19/16 3/2 57/32 makes sense now.

And scales constructed like this:1/1 17/16 9/8 19/16 5/4 4/3 17/12? (or 45/32?) 3/2 51/32 27/16 57/32 15/8 2/1and same scale on a different degree: 1/1 17/16 9/8 19/16 5/4 4/3 17/12 3/2 19/12 5/3 16/9 17/9? (or 15/8?) 2/1
They are subsets of series of 15:16:17:18: 19:20 repeated in fourths.Music seems to me to make a lot of sense by seeing it as the harmonic series overlapping itself in fifths (or fourths).

I'm sure many theories have allready been based on this.If someone knows where to find them please let me know.
Marcel

🔗Mike Battaglia <battaglia01@...>

> I've been playing with the idea of music beeing based on the harmonic series
> in a much more direct way than I previously thought.
>
> What if the minor chord with a fundamental base of 1/1 is 1/1 19/16 3/2. It
> sounds correct to me.
> And the dominant 7th as 1/1 5/4 3/2 57/32
> And the 9th as 1/1 5/4 3/2 57/32 9/4
> They sound better to me than with 16/9 as minot 7th
> Also 1/1 19/16 3/2 57/32 makes sense now.
> And scales constructed like this:
> 1/1 17/16 9/8 19/16 5/4 4/3 17/12? (or 45/32?) 3/2 51/32 27/16 57/32 15/8
> 2/1
> and same scale on a different degree: 1/1 17/16 9/8 19/16 5/4 4/3 17/12 3/2
> 19/12 5/3 16/9 17/9? (or 15/8?) 2/1
> They are subsets of series of 15:16:17:18:19:20 repeated in fourths.
> Music seems to me to make a lot of sense by seeing it as the harmonic series
> overlapping itself in fifths (or fourths).
> I'm sure many theories have allready been based on this.
> If someone knows where to find them please let me know.
> Marcel

I think a 16:19:24 minor chord is one thing, and a 10:12:15 is
another. They can both be implied by a 12-tet 0-300-700 cent triad.

🔗Petr Parízek <p.parizek@...>

🔗djtrancendance@...

Petr,
I will definitely check those out so far as educating myself on the possibilities of equally consonant intervals within the high realms of the harmonic series (something I admittedly have not tried or heard much of yet), thank you. :-)

BTW, when I post the latest (non-fraction-based) version of my scale, it would be interesting to see if you could find a good way to convert the ratios to higher numbered fractions you think would work well together.
The result would likely be akin to what I did my estimating my PHI scale into rational fractions...only it would hopefully sound more intelligently evened out in terms of how dissonance is distributed throughout it.

-Michael

--- On Thu, 4/16/09, Petr Parízek
<p.parizek@...> wrote:

From: Petr Parízek <p.parizek@chello.cz>
Subject: Re: [tuning] harmonic series as the basis for harmony
and scales
To: tuning@yahoogroups.com
Date: Thursday, April 16, 2009, 11:18 AM

Marcel,

if you have a copy of Manuel's "Scale Archive"
handy, maybe these scales could be interesting to you:
ganassi.scl
parizek_jiweltmp. scl
parizek_jiwt2. scl
parizek_jiwt3. scl

And I'm planning to make one more in the near
future.

Petr

🔗Petr Parízek <p.parizek@...>

🔗John H. Chalmers <JHCHALMERS@...>

Marcel, Mike, et al.: Erv Wilson has studied scales of this type. His "Diaphonic Cycles" generally consist of a linearly divided 5th conjoined with a similarly linearly divided 4th (though the 4ths and 5ths are not necessarily 4/3 and 3/2 and may be 11/8-16/11 or 7/5-10/7 etc. in more finely divided cases). He also invented some simpler scales such as Helix Song, which, IIRC, consists of two short segments of the harmonic series a 5th part (within an octave). The details may be at the anaphoria.com Wilson Archives site.

Some decades ago, someone named Gwynn, IIRC, published a couple of abstracts in the annual meeting of the Acoustic Society of America on successive ratio interval approximations to the 12-tone gamut. There were also a couple of abstracts on "coupled incremental scales," which in JI would be scales of this type. I'm sorry, but I don't recall more details at the moment or even where they would be in my files.

--John

🔗Marcel de Velde <m.develde@...>

I think it's beeing misunderstood what I mean here.
I don't mean a fixed scale that is a ratio aproximation and gives slightly
false fifths and things like that in some cases.
What I mean is an infinately large "tuning" that is the harmonic series
repeated in fifths.
The example scale I gave is simply a subset for 1 single fundamental bass.
(and based on common practice western music)
In music where the fundamental bass changes all the time (just about all
music) the example scale is relative to the fundamental bass. (and comma
shifts can occur)

I've actually found the above scale about 2 years ago allready.
But I was a bit green then, and thought of the scale as a fixed scale which
doesn't work very well and abandoned it.

Btw it seems very likely now to me that the minor triad is allways 1/1 19/16
3/2 when the fundamental bass is 1/1.
I can see a 1/1 6/5 3/2 with a bass of 1/1 but then this bass seems now to
me to not be the fundamental bass.

Marcel

🔗Marcel de Velde <m.develde@...>

Here is my (I think VERY convincing) example of Harmonic-JI vs "Classic"-JI
vs 12tet:
Harmonic-JI:
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Harmonic-JI.mid

Classic-JI:
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Classic-JI.mid

12tet:
/tuning/files/Marcel/Harmonic-JI_test1/woo30_12tet.mid

The Harmonic-JI version is according to my new theory.
The fundamental bass is moves in fifths/fourths and it's products.
The minor triads are 1/1 19/16 3/2 relative to the fundamental bass.
The dominant 7th is 1/1 5/4 3/2 57/32 relative to fundamental bass.
Etc. The scale is shifting according to the fundamental bass (which is not
allways thesame as the sounding bass or lowest note)
It sounds to my ears as absolutely right.
Please understand that the system I propose I do not see as a "tempering" or
ratio aproximation to something.
I see it as the way the music is in it's deepest core, and I think this may
very well be it, my long hard search may be over :)

The Classic-JI version is a normal 5-limit JI rendering.
The minor triads are 1/1 6/5 3/2 (and sound way to high to me)
The dominant 7th is 1/1 5/4 3/2 16/9 (which sounds slightly too low to me
but it's a very small difference to Harmonic-JI)
The fundamental bass is moving in fifths/fourths and their products
(nessecary otherwise it would be very easy to construct music which shifts
as a whole amongst other things)
All chords are pure according to 1/1 6/5 3/2 and 1/1 5/4 3/2 "classic"-JI.

I've also uploaded my Scala sequence files if you wish to check the tuning:
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Harmonic-JI.seq
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Classic-JI.seq
/tuning/files/Marcel/Harmonic-JI_test1/woo30_12tet.seq(set
scale to 12tet in Scala before rendering)

Marcel

🔗Michael Sheiman <djtrancendance@...>

Yay, sound samples, thank you Marcel! :-)

For the record, I like your version a bit better than 12TET this time around (much better than the last time). However only certain chords sound significantly better than "classic JI" and it seems a toss-up between your JI and "classic JI" as to which is the best.

For example (taking examples of the chord that creep near the edge between what I consider consonant and dissonant):
A) The chords hit at about 25 and 28 seconds sound clearer in your JI
B) The chords at 14 and 15 seconds sound better in your JI
C) The chords at 1 and 17 seconds sounds better in classic JI
D) The chords at 33 and 38 seconds sounds better in classic JI

So they seem virtually neck and neck just....different.
You might want to look into the JI constructions for the chords that sound better in classic JI and tweak those in your own scale...then you might have a winner.
Also...if I were you I might try more fractions in x/3, x/6, x/12 and even x/24 format...and not just those that can be expressed in x/32, x/16, x/8, x/4, x/2...format. I have found using such a "second harmonic series" can help you find tones that fit "close enough to perfect" to more chords in more ways so far as JI goes. I realize, of course, this just my opinion...and realize this technique bares little 'respect' for odd-limits in JI scales (IE 27/24 in the form x/24 would be something like 23-limit...far north of 11-odd-limit!)...however, my ears still like the result of the above technique.

-Michael

--- On Fri, 4/17/09, Marcel de Velde <m.develde@...> wrote:

From: Marcel de Velde <m.develde@gmail.com>
Subject: Re: [tuning] Re: harmonic series as the basis for harmony and scales
To: tuning@yahoogroups.com
Date: Friday, April 17, 2009, 10:24 AM

Here is my (I think VERY convincing) example of Harmonic-JI vs "Classic"-JI vs 12tet:
Harmonic-JI:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_Harmonic- JI.mid

Classic-JI:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_Classic- JI.mid

12tet:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_12tet. mid

The Harmonic-JI version is according to my new theory.The fundamental bass is moves in fifths/fourths and it's products.The minor triads are 1/1 19/16 3/2 relative to the fundamental bass.
The dominant 7th is 1/1 5/4 3/2 57/32 relative to fundamental bass.Etc. The scale is shifting according to the fundamental bass (which is not allways thesame as the sounding bass or lowest note)
It sounds to my ears as absolutely right.Please understand that the system I propose I do not see as a "tempering" or ratio aproximation to something.I see it as the way the music is in it's deepest core, and I think this may very well be it, my long hard search may be over :)

The Classic-JI version is a normal 5-limit JI rendering.The minor triads are 1/1 6/5 3/2 (and sound way to high to me)The dominant 7th is 1/1 5/4 3/2 16/9 (which sounds slightly too low to me but it's a very small difference to Harmonic-JI)
The fundamental bass is moving in fifths/fourths and their products (nessecary otherwise it would be very easy to construct music which shifts as a whole amongst other things)All chords are pure according to 1/1 6/5 3/2 and 1/1 5/4 3/2 "classic"-JI.

I've also uploaded my Scala sequence files if you wish to check the tuning:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_Harmonic- JI.seq

http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_Classic- JI.seq

http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_12tet. seq (set scale to 12tet in Scala before rendering)

Marcel

🔗Marcel de Velde <m.develde@...>

For those who have trouble playing pitch-bent MIDI files I've recorded my
soundcards MIDI output to mp3:
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Harmonic-JI.mp3
/tuning/files/Marcel/Harmonic-JI_test1/woo30_Classic-JI.mp3
/tuning/files/Marcel/Harmonic-JI_test1/woo30_12tet.mp3

Also wish to explain a bit more about my new system.
The example scale I gave is for instance a chromatic scale when you play 12
tones from for instance C3 to C4.
When you do this you do NOT have the fundamental bass constantly on C.
The fundamental bass changes.
For for instance F 4/3 when you play it together with C 1/1 the fundamental
bass is actually 4/3, no longer 1/1.
The example scale I gave arises from playing the tones from C to C an octave
higher with a certain simple "cadence" or progression of the true
fundamental bass.
To play truly from the fundamental C keeping the true fundamental on C 1/1
would give a scale something like:
1/1 17/16 9/8 19/16 5/4 21/16 45/32 3/2 51/32 27/16 57/32 15/8 2/1
Here we're only connecting 2 harmonic segements. You could say that even
here the fundamental changes halfway to 3/2, though it doesn't have to.

Some thought on how to construct scales inside this system that are
different from common practice western music:
Smaller division of the harmonic series.
For instance 30:31:32:33:34:35:36:37:38:39:40 could give:
1/1 33/32 17/16 35/32 9/8 37/32 19/16 39/32 5/4 31/24 11/8 17/12 35/24 3/2
99/64 51/32 105/64 27/16 111/64 57/32 117/64 15/8 31/16 2/1
Seen from a different scale degree:
1/1 33/32 17/16 35/32 9/8 37/32 19/16 39/32 5/4 31/24 4/3 11/8 17/12 35/24
3/2 37/24 19/12 13/8 5/3 31/18 11/6 17/9 35/18 2/1

Or taking a different harmonic segment but still building the scale on
repetition of this segment and simple fundamental bass progression.
For instance 24:25:26:27:28:29:30:31:32
Could give:
1/1 25/24 13/12 9/8 75/64 39/32 81/64 21/16 87/64 45/32 93/64 3/2 25/16
13/8 27/16 7/4 29/16 15/8 31/16 2/1
Seen from a different scale degree:
1/1 25/24 13/12 9/8 7/6 29/24 5/4 31/24 4/3 25/18 13/9 3/2 25/16 13/8 27/16
7/4 29/16 15/8 31/16 2/1

There's a lot of research to be done should this be the right direction
(which it seems it is).
But it seems like there's no real limit to what can be done with it :)
(though perhaps limits on the progression of the fundamental bass)

Marcel

🔗Marcel de Velde <m.develde@...>

Hi Michael,

Thanks for listening.

For the record, I like your version a bit better than 12TET this time
> around (much better than the last time). However only certain chords sound
> significantly better than "classic JI" and it seems a toss-up between your
> JI and "classic JI" as to which is the best.
>
> For example (taking examples of the chord that creep near the edge
> between what I consider consonant and dissonant):
> A) The chords hit at about 25 and 28 seconds sound clearer in your JI
> B) The chords at 14 and 15 seconds sound better in your JI
> C) The chords at 1 and 17 seconds sounds better in classic JI
> D) The chords at 33 and 38 seconds sounds better in classic JI
>

Oef I must disagree here.
I dislike the sound of the 1/1 3/2 2/1 12/5 chord in the beginning (and
every time it comes around) very much.
It has struck me as beeing too high from the beginning I started working on
this piece (you can read my mention of it a few weeks back on this list)
There are many other things I don't like about the classic JI version, the
way the high melody goes etc. This is why I had so much trouble with the
piece.

So they seem virtually neck and neck just....different.
> You might want to look into the JI constructions for the chords that sound
> better in classic JI and tweak those in your own scale...then you might have
> a winner.
> Also...if I were you I might try more fractions in x/3, x/6, x/12 and
> even x/24 format...and not just those that can be expressed in x/32, x/16,
> x/8, x/4, x/2...format. I have found using such a "second harmonic series"
> can help you find tones that fit "close enough to perfect" to more chords in
> more ways so far as JI goes. I realize, of course, this just my
> opinion...and realize this technique bares little 'respect' for odd-limits
> in JI scales (IE 27/24 in the form x/24 would be something like
> 23-limit...far north of 11-odd-limit!)...however, my ears still like the
> result of the above technique.
>

Well my new theory isn't really about trying out different intervals.
Either it's the way I've made it or the theory is wrong (though there is
some room for interpretation in some parts it is not in the way you suggest.
(for instance the melody in measure 4 could be seen as allready belonging to
the fundamental bass of measure 4 which would cause it to drop a bit in
pitch, though I like the version I posted better))

Marcel

🔗Marcel de Velde <m.develde@...>

Hi Petr,

if you have a copy of Manuel's "Scale Archive" handy, maybe these scales
> could be interesting to you:
> ganassi.scl
> parizek_jiweltmp.scl
> parizek_jiwt2.scl
> parizek_jiwt3.scl
>

Ah yes thank you!
I was looking for the Ganassi one but somehow read straight over it in your
message.

Sylvestro Ganassi's temperament (1543)
|
1/1 20/19 10/9 20/17 5/4 4/3 24/17 3/2 30/19 5/3 30/17 15/8 2/1
scale steps:
20/19 19/18 18/17 17/16 16/15 18/17 17/16 20/19 19/18 18/17 17/16 16/15

He built woodwinds and made some very pretty music, have to look it up
again.

These are the ones I found 2 years ago. Ganassi, Simpleton and Chalmers.
But they all seem to be ment as fixed scales (like I was thinking back then)
and are subsets of the thing I'm proposing.
To make music with the above fixed scales would be tempering and is
something completely different.

Marcel

🔗Marcel de Velde <m.develde@...>

Changed one note in the Harmonic-JI version.Updated the .mid .seq and .mp3

Doesn't give a very audible change (so no need to listen again)
Made a sloppy error in analysing the fundamental bass in one part and though
wrong about the diminished chord.
The change is on measure 7 where i changed 17/12 into 45/32.
1/1 3/2 2/1 19/8 (fundamental bass = 1/1)
1/1 45/32 2/1 19/8 (fundamental bass stays 1/1, wrongly put 17/12 here)
3/2 3/2 15/8 9/4 (fundamental bass becomes 3/2)
Btw the diminished 7th chord is 1/1 19/16 45/32 27/16 (fundamental bass 1/1)
and all of its inversions, and it mosts want to go to 3/2 15/8 9/4 major or
3/2 57/32 9/4 minor (fundamental bass 3/2)

To make another point clear, I think all harmony is the harmonic series
above the true fundamental bass.
So no 4/3 above the fundamental bass etc. only */1 */2 */4 etc
For the 15:16:17:18:19:20 harmonic segment and my Harmonic-JI theory it
gives the following simplest intervals for all 12 tones of western music:
1/1 17/16 9/8 19/16 5/4 171/128 45/32 3/2 51/32 27/16 57/32 15/8 2/1
This is for the fundamental bass of 1/1.
I have yet to find a harmony that can't be explained in this.

Btw I find it surprising there's no response other than the one from Michael
to the audio examples.
To my ears the Harmonic-JI sounds so much better than the Classic-JI
version.
And after hearing the Harmonic-JI version, for intstance the 1/1 4/3 8/5
opening chord of the Classic-JI version sounds so out of tune it hurts my
ears.
Nobody else hearing this?

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Michael Sheiman <djtrancendance@...>

It does sound better than the last version.
The first chord style is growing on me...meaning, I think you're right: the "classic" JI version actually does sound flat...now that I am getting used to this.

I'll write more once I get to play this on a computer with a decent midi card...the piece itself admittedly seems a bit crowded with the trumpets used in the mp3 version.

-Michael

--- On Thu, 4/23/09, Marcel de Velde <m.develde@...> wrote:

From: Marcel de Velde <m.develde@...>
Subject: Re: [tuning] harmonic series as the basis for harmony and scales
To: tuning@yahoogroups.com
Date: Thursday, April 23, 2009, 8:15 PM

Finished the entire piece in Harmonic-JI.Not saying it's perfect because I don't know yet.It's hard to analyse. But it sounds like I must have gotten it atleast mostly right.In my opinion by far the best sounding version so far.

MIDI:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_andante_ Harmonic- JI.mid

http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_andante_ 12tet.mid

MP3:http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_andante_ Harmonic- JI.mp3

http://launch. groups.yahoo. com/group/ tuning/files/ Marcel/Harmonic- JI_test1/ woo30_andante_ 12tet.mp3

Sorry for the low audio quality of the mp3s, simply recorded my soundcards midi output.
Marcel

🔗Marcel de Velde <m.develde@...>

Hi Michael,

It does sound better than the last version.
> The first chord style is growing on me...meaning, I think you're right:
> the "classic" JI version actually does sound flat...now that I am getting
> used to this.

Thanks :)
Yes I agree on the classic-ji version sounding off a bit.
Most evident to me in the chords between 30 and 40 seconds.

Btw this version is slightly different from the previous one in that here I
did see the melody on measure 3 etc as belonging allready to the fundamental
bass of measure 4. So the free melody allready drops in pitch before the
chord.
Found it bit hard to accept at first but sounds natural to me now.

I'll write more once I get to play this on a computer with a decent midi
> card...the piece itself admittedly seems a bit crowded with the trumpets
> used in the mp3 version.

Ok thanks.
Btw you may want to redownload both mp3 and midi as I changed 1 single note
in a chord that bothered me in measure 39 (result of analysing the
fundamental bass as beeing 3/2 lower, was allready in doubt)
Don't worry I won't change it again comming days as I'll be out of the house
;-)

Marcel

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Finished the entire piece in Harmonic-JI.Not saying it's perfect because I
> don't know yet.
> It's hard to analyse. But it sounds like I must have gotten it atleast
> mostly right.
> In my opinion by far the best sounding version so far.
>
> MIDI:
> /tuning/files/Marcel/Harmonic-JI_test1/woo30_andante_Harmonic-JI.mid
> /tuning/files/Marcel/Harmonic-JI_test1/woo30_andante_12tet.mid
>
> MP3:
> /tuning/files/Marcel/Harmonic-JI_test1/woo30_andante_Harmonic-JI.mp3
> /tuning/files/Marcel/Harmonic-JI_test1/woo30_andante_12tet.mp3
>
> Sorry for the low audio quality of the mp3s, simply recorded my soundcards
> midi output.
>
> Marcel
>
Hi Marcel,

Don't know what you did but it sounds much nicer now.

-Rick

🔗Marcel de Velde <m.develde@...>

Hi Rick,

Hi Marcel,
>
> Don't know what you did but it sounds much nicer now.
>
> -Rick
>

Thanks :)
If you're referencing to an older rendering of the full piece then what I
did this time was everything completely different.
Threw out my old theory and did this one based on a completely new one
(partially explained in the beginning of this thread)
I don't think it's perfect yet overall, still some parts that bug me and
still some doubt about some things, but for the most part it works out like
magic with the new theory.
I'll leave this one for a while and work on a few simpler pieces that have
basic comma shift problems and things like that.
After I get those perfect I may get a better idear at how this drei equali
piece works and perhaps do it perfectly.

Marcel

🔗Marcel de Velde <m.develde@...>

Throwing the Harmonic-JI theory in the trash again allready :)
Have been working on a Bach piece when I noticed it made more sense in
another way than Harmonic-JI.
It gives results very close (almost inaudibly) to Harmonic-JI with the
harmonics I was using.
I actually saw this option before when working on the Drei Equali but
dismissed it as it didn't seem logical to me at that time.
Now it does seem logical to me. Infact it's the simplest solution of all
solutions I've ever tried.
And came across it several times earlyer the past 2-3 years. Everytime
choosing the wrong direction into more complexity.

Still working it out but till then here's the first part of the Drei Equali
in the new theory:

/tuning/files/Marcel/woo30_MJI.mid

And here the Scala sequence file for the interested:
/tuning/files/Marcel/woo30_MJI.seq

One can see it as a scale of 3/2 repeated, with a 5/4 on every 3/2 (only one
5/4 above, not below and no repetitions of 5/4), though I came to it by a
different route the resulting scale is thesame.

As I said the difference between this and the Harmonic-JI version is very
small in cents.
Though this version is 5-limit.
I like the sound of this one a lot, and think it's perfect. It's completely
stable to my ears.
Will finish the full piece soon.

Marcel

🔗Andy <a_sparschuh@...>

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

> if you have a copy of Manuel's "Scale Archive" handy, maybe these
scales
> > ganassi.scl

> Sylvestro Ganassi's temperament (1543)
> |
> 1/1 20/19 10/9 20/17 5/4 4/3 24/17 3/2 30/19 5/3 30/17 15/8 2/1
> scale steps:
> 20/19 19/18 18/17 17/16 16/15 18/17 17/16 20/19 19/18 18/17 17/16
16/15

Hi Marcel,
there exists an similar successoer of Ganassi's concept, see:
http://groenewald-berlin.de/text/text_T030.html
"
(h) 15/8 x 16/15 = 2/1 (c)
(b) 85/48 x 18/17 = 15/8 (h)
(a) 5/3 x 17/16 = 85/48 (b)
(gis) 19/12 x 20/19 = 5/3 (a)
(g) 3/2 x 19/18 = 19/12 (gis)
(fis) 17/12 x 18/17 = 3/2 (g)
(f) 4/3 x 17/16 = 17/12 (fis)
(e) 5/4 x 16/15 = 4/3 (f)
(dis) 19/16 x 20/19 = 5/4 (e)
(d) 9/8 x 19/18 = 19/16 (dis)
(cis) 17/16 x 18/17 = 9/8 (d)
(c) 1/1 x 17/16 = 17/16 (cis)

or as chain of a dozen 5ths

(f) 4/3 x 3/2 : 2 = 1/1 (c)
(b) 85/48 x 3/2 x 256/255 : 2 = 4/3 (f)
(es) 19/16 x 3/2 : 171/170 = 85/48 (b)
(gis) 19/12 x 3/2 : 2 = 19/16 (es)
(cis) 17/16 x 3/2 : 153/152 = 19/12 (gis)
(fis) 17/12 x 3/2 : 2 = 17/16 (cis)
(h) 15/8 x 3/2 x 136/135 : 2 = 17/12 (fis)
(e) 5/4 x 3/2 = 15/8 (h)
(a) 5/3 x 3/2 : 2 = 5/4 (e)
(d) 9/8 x 3/2 : 81/80 = 5/3 (a)
(g) 3/2 x 3/2 : 2 = 9/8 (d)
(c) 1/1 x 3/2 = 3/2 (g)

! AlexMalcom1721.scl
Alexander Malcoms's ~[1721] tuning, compiled by A . Sparschuh
!Attend the construction from : C:C#:D:Eb:E = 16:17:18:19:20
12
!
17/16 ! C#
9/8 ! D
19/16 ! Eb
5/4 ! E
4/3 ! F
17/12 ! F#
3/2 ! G
19/12 ! G#
5/3 ! A
85/48 ! Bb
15/8 ! B
2/1
!
![eof]

bye
Andy