Alternate Diatonics

Recently, I discovered the following diatonic as part of my studies to my article in PNM:

19ET scale:

0,2,4,5,7,9,11,12,14,16,18,0. The 'Fifth' is 442 cents wide and the 'Major Third' is is 253 cents wide, making a triad of 0,4,7 = 0,253,442. Transposing this by 7 steps up we get:
7,9,11,12,14,16,18,0,2,4,6: So 5 is replaced by 6. I am currently experimenting with this scale in MIDI, but would like, if anyone would care to try, other opinions on this scale (which can also be notated 22122212221).
M

In-Reply-To: <E16Y7qC-0000JB-00@smtp.argonet.co.uk>
Mark Gould wrote:

> 19ET scale:
>
> 0,2,4,5,7,9,11,12,14,16,18,0. The 'Fifth' is 442 cents wide and the
> 'Major Third' is is 253 cents wide, making a triad of 0,4,7 =
> 0,253,442. Transposing this by 7 steps up we get:
> 7,9,11,12,14,16,18,0,2,4,6: So 5 is replaced by 6. I am currently
> experimenting with this scale in MIDI, but would like, if anyone would
> care to try, other opinions on this scale (which can also be notated
> 22122212221).

I don't have a keyboard to hand, but anybody who does could try these
variations

0.0
131.3
262.5
312.5
443.8
575.0
706.3
756.2
887.5
1018.8
1150.0
1200.0

0.0
128.8
257.5
314.2
442.9
571.7
700.5
757.1
885.8
1014.6
1143.4
1200.0

Graham

--- In tuning@y..., mark.gould@a... wrote:
> Recently, I discovered the following diatonic as part of my studies
to my article in PNM:
>
> 19ET scale:
>
> 0,2,4,5,7,9,11,12,14,16,18,0.

i believe this scale came up on tuning-math a while back . . . it's
an MOS generated by the 7/19 oct. interval. graham may have been
eluding to two optimal tunings for scales with generators in this
vicinity.

>The 'Fifth' is 442 cents wide and >the 'Major Third' is is 253 cents
>wide, making a triad of 0,4,7 = >0,253,442.

/tuning/files/perlich/wavs/gould.wav

you asked for opinions, so here goes . . . i think the central pitch
processor in the brain, which is what allows us to hear a
single 'timbre' and 'pitch' when a musical instrument plays a note,
would be a bit confused by this chord. i decided to try it out for
myself, and since the human voice, brass, reed, and bowed string
instrument timbres consist of partials in an exact harmonic series, i
used such a timbre. i hear it as the 7th, 8th, and 9th of an implied
root -- try looping the .wav and humming the root you hear -- i think
you might agree. the 'first inversion' of this chord would thus sound
more 'rooted' and 'final'. thus music composed 'on paper' with this
system might not work out quite as intended 'in the ear'.

i'm tempted to fill in the big hole in the chord, especially if voice
leading is a consideration, and the scale unfortunately provides for
this endeavor, at least not for the 'tonic' chord in this instance. i
tried playing the triad along with all the additional notes from 19-
equal, and the ones that fit by far the best (the effect is really
striking) are not in the scale above. you should try this yourself.
as you can infer from my paper, i like my tonal analogues to the
diatonic scale to act rather differently from this.

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, February 05, 2002 7:26 PM
> Subject: [tuning] Re: Alternate Diatonics
>
>
> --- In tuning@y..., mark.gould@a... wrote:
> > Recently, I discovered the following diatonic as part
> > of my studies to my article in PNM:
> >
> > 19ET scale:
> >
> > 0,2,4,5,7,9,11,12,14,16,18,0.
> >
> > The 'Fifth' is 442 cents wide and >the 'Major Third'
> > is is 253 cents wide, making a triad of 0,4,7 = >0,253,442.
>
> /tuning/files/perlich/wavs/gould.wav
>
> ... i hear it as the 7th, 8th, and 9th of an implied
> root -- try looping the .wav and humming the root you hear
> -- i think you might agree.

i totally agree. this was exactly the same perception
i had, before i read what Paul wrote.

sounds to me like a cluster of "2nds" which comes from
a JI "dominant 9th" chord featuring the 7th harmonic:
7:8:9 harmonics. the "9th-chord" feeling is overpowering
to my ears.

-monz

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> From: mark.gould@argonet.co.uk
> Subject: Alternate Diatonics
>
> Recently, I discovered the following diatonic as part of
> my studies to my article in PNM:
>
> 19ET scale:
>
> 0,2,4,5,7,9,11,12,14,16,18,0. The 'Fifth' is 442 cents
> wide and the 'Major Third' is is 253 cents wide, making
> a triad of 0,4,7 = 0,253,442. Transposing this by 7
> steps up we get:
> 7,9,11,12,14,16,18,0,2,4,6: So 5 is replaced by 6.
> I am currently experimenting with this scale in MIDI,
> but would like, if anyone would care to try, other
> opinions on this scale (which can also be notated 22122212221).
> M
>

I've been exploring lots of these scales (mostly on paper)
which I have refered to as "transposable systems" and is
more officially refered to as MOS.

The one you show is very similar to one that I have improvised
with (probably in 31, though 31's "11.3" [my notation meaning
"11 notes, 3 chunks"] doesn't include this particular
MOS). Another naming convention for MOS would call it [3.8]
meaning "three small and eight large".

My take on it was to treat it as a "rootless" scale with
"in tune" fifths and thirds. On this scale would be...

1 2 2 1 2 2 2 1 2 2 1
10 11 13 15 16 18 1 3 4 6 8 10
[0]

...where the point of repose is the major (or minor) sixth
embracing, but not including, the note I marked at [0]. There
are good sixths on other degrees as well, leading tones above
and below the missing [0], and its transposable in a
strict sense (single alteration results in rotation). Theres
a whole tonal system sitting which can wander to unexpected
crevices, but is incapable of saying its own name.

Bob Valentine

In-Reply-To: <200202060729.JAA100930@ius578.iil.intel.com>
Mark G:

> > 0,2,4,5,7,9,11,12,14,16,18,0. The 'Fifth' is 442 cents
> > wide and the 'Major Third' is is 253 cents wide, making
> > a triad of 0,4,7 = 0,253,442. Transposing this by 7
> > steps up we get:
> > 7,9,11,12,14,16,18,0,2,4,6: So 5 is replaced by 6.
> > I am currently experimenting with this scale in MIDI,
> > but would like, if anyone would care to try, other
> > opinions on this scale (which can also be notated 22122212221).

Bob V:

> The one you show is very similar to one that I have improvised
> with (probably in 31, though 31's "11.3" [my notation meaning
> "11 notes, 3 chunks"] doesn't include this particular
> MOS). Another naming convention for MOS would call it [3.8]
> meaning "three small and eight large".

That'll be 11*2+3*3. So the pattern of large and small steps is reversed
from Mark's scale, which makes it qualitatively different.

> My take on it was to treat it as a "rootless" scale with
> "in tune" fifths and thirds. On this scale would be...
>
> 1 2 2 1 2 2 2 1 2 2 1
> 10 11 13 15 16 18 1 3 4 6 8 10
> [0]
>
> ...where the point of repose is the major (or minor) sixth
> embracing, but not including, the note I marked at [0]. There
> are good sixths on other degrees as well, leading tones above
> and below the missing [0], and its transposable in a
> strict sense (single alteration results in rotation). Theres
> a whole tonal system sitting which can wander to unexpected
> crevices, but is incapable of saying its own name.

Have you tried my alternative tunings? I actually found a good sense of
tonic around the first note in 19-equal. I don't know if that's by
design. As it's preceded by a small step, maybe.

I thought my retuning made a big improvement to the sound, which makes me
suspicious. It may have been the timbres changing on reload. The
consonances definitely got better, but maybe the tonalness was weakened.

I don't know if this is anything special as MOS scales go, but it is at
least half-magic.

Graham

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <200202060729.JAA100930@i...>
> Mark G:
> > > I am currently experimenting with this scale in MIDI,
> > > but would like, if anyone would care to try, other
> > > opinions on this scale (which can also be notated 22122212221).
>
> Bob V:
>
> > The one you show is very similar to one that I have improvised
> > with (probably in 31, though 31's "11.3" [my notation meaning
> > "11 notes, 3 chunks"] doesn't include this particular
> > MOS). Another naming convention for MOS would call it [3.8]
> > meaning "three small and eight large".
>
> That'll be 11*2+3*3. So the pattern of large and small steps is reversed
> from Mark's scale, which makes it qualitatively different.

Yes, thats why I said that particular MOS didn't occur. What I call
"11.3" occurs but as [8.3] in what I think was Dans notation for these
things.

Bob

>
> Graham

I have been familiar with the 8-tone MOS of the supermajor third in 19-TET for a while now,but i still don�t have a name for it.

It only has one perfect fifth,though there are four in the 11-note form that was discussed here;which i in fact used in my piece for the trumpet concert in London.

I wouldn�t call it diatonic though,but on the point of"alternate diatonics",the 16-TET"Goldsmith"and 20-TET"Balzano/Zweifel/Stearns"system are in fact true diatonics-the generator is a fifth.

I�ve been particularly interested in 16-TET lately,as the scale contains 5 each of major and minor triads.But it doesn�t sound so good without some spectral tempering,which i�m not equipped for at the moment.

/�ljare
(digging Klarth)

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In-Reply-To: <LAW2-F1118vz0iU6ltA0001e5e5@hotmail.com>
Mats �ljare wrote:

> It only has one perfect fifth,though there are four in the 11-note form
> that was discussed here;which i in fact used in my piece for the
> trumpet concert in London.

You had a piece performed in London! Why wasn't I informed?

Graham