Yahoo Tuning Groups Ultimate Backup tuning Hi

I have just found this group, as a consequence of a search on Albert
von Thimus (about whom I know next to nothing having just encountered
the name in McClain's book 'Myth of Invariance'). There is no way I
am going to catch up on 49000 messages! I just hope to hook into what
is going on and that I can contribute something meaningful to the
proceedings.

I am the author of a piece of software which demonstrates that the
particular vibration ratios of just intonation maximize
correspondences to the defining set, between notes other than the
tonic and octave. This software, which runs under Windows and which
comes with full help, can be downloaded from
http://www.odeion.org/atlantis/natural2.html

I refer to these correspondences as correlative intervals. I have
created some music where melodic steps are constrained to the
correlative intervals. You can find this music under the
heading 'Natural Aesthetics', among some of my other compositions, at
http://www.odeion.org/music

🔗Carl Lumma <ekin@lumma.org>

>I have just found this group, as a consequence of a search on Albert
>von Thimus (about whom I know next to nothing having just encountered
>the name in McClain's book 'Myth of Invariance'). There is no way I
>am going to catch up on 49000 messages! I just hope to hook into what
>is going on and that I can contribute something meaningful to the
>proceedings.

Welcome aboard!

>I am the author of a piece of software which demonstrates that the
>particular vibration ratios of just intonation maximize
>correspondences to the defining set, between notes other than the
>tonic and octave. This software, which runs under Windows and which
>comes with full help, can be downloaded from
>http://www.odeion.org/atlantis/natural2.html

Interesting...

>I refer to these correspondences as correlative intervals. I have
>created some music where melodic steps are constrained to the
>correlative intervals. You can find this music under the
>heading 'Natural Aesthetics', among some of my other compositions, at
>http://www.odeion.org/music

I particularly liked your Interlude No. 1, and I thought
Odeion Natural No. 1-003 was pretty impressive for a completely
algorithmic piece. I'd like to know more about The Rule of
The Natural Aesthetic.

-Carl

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

>
> Welcome aboard!
>

Thankyou kindly sir.

> I'd like to know more about The Rule of
> The Natural Aesthetic.
>
> -Carl

The rule is that melodic steps comprise only intervals which
correspond to one of the defining set. The defining set is that from
pitch class 0 (the tonic) to the other pitches of the full
dodekaphonic scale. For example, the interval from pitch 0 to pitch 4
is defined by the vibration ratio 4:5 and that from pitch 0 to pitch
7 by the ratio 2:3. This means that the vibration ratio of the
interval from pitch 4 to pitch 7 is equal to 2:3 divided by 4:5.

2:3 / 4:5 = 2:3 x 5:4 = 10:12 = 5:6

Now 5:6 is indeed the defining vibration ratio of the interval from
pitch 0 to pitch 3 - a minor 3rd. Thus a melodic step from pitch 4 to
pitch 7 or vice versa is allowable. The combination of pitches 4 and
7 in a chord is also allowable under the rule.

On the other hand, the vibration ratio of the interval from pitch 7
to pitch 10 is

9:16 / 2:3 = 9:16 x 3:2 = 27:32

which is is not equal to the defining ratio of 5:6 for a minor 3rd.
Thus a melodic step between (or chordal combination of) pitches 7 and
10 is not allowed under the rule.

In the piece of music named Natural No.1-003, this constraint is
applied to alternate notes as well as adjacent notes, laterally along
both melodic lines and vertically between the lines. Natural No.1-003
is also constrained to the notes of Mode V, also known as the
Phrygian Dominant Scale, of the Harmonic Minor Scale. There are a few
other constraints, such as maximum melodic step size (interval class
7 in this case) and compass. Tempo and rhythmic constraints should
need no further explanation.

The parameter set Natural No.1 causes the algorithm to auto-modulate
to a new tonic on pitch 5 whenever pitch 5 is the first note of a
bar. One of the lines (the bass in this particular case) is defined
as a 'canto firmo' for this purpose, to which the other line is
slaved.

This system works only in dodekaphony and is the basis of my thesis
that dodekaphony is a product of nature - it's all in the numbers.

🔗Carl Lumma <ekin@lumma.org>

>> I'd like to know more about The Rule of
>> The Natural Aesthetic.
>
>The rule is that melodic steps comprise only intervals which
>correspond to one of the defining set.//

Ah, now I've got it, thanks.

>In the piece of music named Natural No.1-003, this constraint is
>applied to alternate notes as well as adjacent notes,

I understand adjacent as, in Mary Had A Little Lamb, E-D-C,
E and D are adjacent but not E and C. Is that right?

What do you mean by alternate?

>The parameter set Natural No.1 causes the algorithm to auto-modulate
>to a new tonic on pitch 5 whenever pitch 5 is the first note of a
>bar. One of the lines (the bass in this particular case) is defined
>as a 'canto firmo' for this purpose, to which the other line is
>slaved.
>
>This system works only in dodekaphony and is the basis of my thesis
>that dodekaphony is a product of nature - it's all in the numbers.

I'm not yet convinced that this wouldn't work with a different
number of tones, but I do like the result you got!

-Carl

🔗hstraub64 <hstraub64@telesonique.net>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

>
> >In the piece of music named Natural No.1-003, this constraint is
> >applied to alternate notes as well as adjacent notes,
>
> I understand adjacent as, in Mary Had A Little Lamb, E-D-C,
> E and D are adjacent but not E and C. Is that right?
>

No. Adjacent notes of a melody line, not in the scale. I.e. for any
given note of a melody, the immediately preceding and immediately
following notes.

> What do you mean by alternate?
>

As in 'adjacent', +/- unity. I.e. The note immediately before the
preceding adjacent note and the note immediately after the following
adjacent note.

> I'm not yet convinced that this wouldn't work with a different
> number of tones, but I do like the result you got!
>
> -Carl

Even with dodekaphony the system sometimes gives rise to 'gridlock' -
i.e. a melody line sometimes reaches a dead-end because no note
satisfies the conditions and the melody cannot prodeed any further.

It only works with dodekaphony I promise you. Only dodekaphony,
provides enough internal relationships which correspond to the
defining set. Don't forget that I am talking about natural tunings
(in the case of dodekaphony, Just Intonation) where the vibration
coefficients of the intervals are defined by ratios of whole numbers.

Justly intoned dodekaphony provides 44 correlative intervals out of a
total of 66 relative intervals. If any ratio is changed that number
falls, for example by using a tone of 9:10 instead of 8:9. Only a few
need to be replaced by others to result in zero degrees of freedom.

And please note - I am English. Usage of the words 'note' and 'tone'
is different here, where a 'note' is any pitched sound and a 'tone'
is a major step = 2 x semitones. To further confuse the issue, 'note'
means 'written mark upon a score' in both American and British
terminology and 'tone' has the same meaning in both when used in the
context of acoustic science, as in 'difference tone'.

Please don't get the idea that I think that alternate divisions of
the octave are invalid per se. Anything that produces a sweet sound
is ok by me.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Can Akkoc <can193849@yahoo.com>

Peter,

Are you implying some form of short term "memory" in melody lines when it comes to the mathematical patterns in interval sequences making up the melody line?

Can Akkoc

Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

No. Adjacent notes of a melody line, not in the scale. I.e. for any
given note of a melody, the immediately preceding and immediately
following notes.

> What do you mean by alternate?
>

As in 'adjacent', +/- unity. I.e. The note immediately before the
preceding adjacent note and the note immediately after the following
adjacent note.

> I'm not yet convinced that this wouldn't work with a different
> number of tones, but I do like the result you got!
>
> -Carl

Please don't get the idea that I think that alternate divisions of
the octave are invalid per se. Anything that produces a sweet sound
is ok by me.

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🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > It only works with dodekaphony I promise you.
>
> I never believe such promises without first seeing enough
definitions
> so I know what I've been promised. Can you start by giving the
> (presumably 12) notes of the (presumptive) dodekaphonic scale? I'm
> envisioning something like the Ellis scale, but I could be all wet.

Hi Gene - dodekaphony is the division of the octave into 12
intermediate intervals. In ET the steps are all of equal size. In
Just Intonation they vary slightly because of the impossibility of
expressing the 12th root of two as a ratio of two whole numbers. But
really you knew that all along, didn't you? The entire humanly
performable repertoire is dodekaphonic. All standard western musical
instruments are dodekaphonic. I am of the opinion that our very souls
are dodekaphonic though I realize that may be a contentious statement.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> Hi Gene - dodekaphony is the division of the octave into 12
> intermediate intervals. In ET the steps are all of equal size. In
> Just Intonation they vary slightly because of the impossibility of
> expressing the 12th root of two as a ratio of two whole numbers.
But
> really you knew that all along, didn't you? The entire humanly
> performable repertoire is dodekaphonic.

I very much doubt Johnny Reinhard would agree.

All standard western musical
> instruments are dodekaphonic.

Not true. What's dodekaphonic about a violin, for example?

I am of the opinion that our very souls
> are dodekaphonic though I realize that may be a contentious
statement.

Given that it seems to imply that e.g. Turks (one of whom at least is
on this list) aren't human, I'd have to agree.

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

> > The entire humanly
> > performable repertoire is dodekaphonic.
>
> I very much doubt Johnny Reinhard would agree.
>

Who else apart from Johnny Reinhard can perform Johnny Reinhard's
music?

> All standard western musical
> > instruments are dodekaphonic.
>
> Not true. What's dodekaphonic about a violin, for example?
>

Inherently nothing, which is precisely why violin training can be so
very painful upon the ears.

> Given that it seems to imply that e.g. Turks (one of whom at least
is
> on this list) aren't human, I'd have to agree.

I take it Turks are not dodekaphonically inclined. Neither are (were)
Australian Aboriginals but they did at least manage to keep going for
some 50,000 years before Europeans upset their honeypot. I hope only
to finish scratching my slate (all essential research now being
complete) before Armageddon arrives on my doorstep, as it surely will
as I am quite literally surrounded by USAF bases within a few miles
of my home.

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗monz <monz@attglobal.net>

Friday afternoon on NPR (National Public Radio)
there was a feature on "Sacred Harp Singing",
a type of 5-limit just-intonation "fa-sol-la"
singing using Baptist Christian hymns as texts.

the occassion prompting the NPR segment was a
national convention held at Mt. Pleasant Home
Primitive Baptist Church (what a great name)
located in Fultondale, Jefferson County, Alabama,
the last week in November.

"Sacred Harp" singing (which BTW is entirely
_a capella_ and never contains any harps) is
interesting as a JI style because, in contrast
to the mellow soothing sound that is usually a
feature of JI music, "Sacred Harp" emphasizes
the resonance of JI and can be characterized as
rugged, powerful, loud, and perhaps even somewhat
crude.

"Sacred Harp" singers will themselves admit this
crude quality and are actually proud of it and
have no desire to change it.

unfortunately, i was listening to this on the
radio in the car between lessons this afternoon
and only heard about 15 minutes of the program.

one of the most amusing segments was where the
main "Sacred Harp" singer they were interviewing
told a story about how his church allowed another
religious group to have Sunday School at their church,
and they brought in a piano for use during the hours
of their Sunday School. the piano was only used
the first week it was installed, and all the church
regulars (who were all "Sacred Harp"-ers) hated
having the piano there. the following Sunday,
it was gone. :)

a few years ago there was a fantastic website
that gave a detailed explanation of shape-note
and Sacred Harp singing, but unfortunately it
either moved without a forwarding address or
disappeared about a year ago. here are some
other links relevant to my post:

http://www.rootsworld.com/rw/feature/sacred-harp.html
http://www.cduniverse.com/productinfo.asp?PID=1002913&frm=sh_google
http://www.mcsr.olemiss.edu/~mudws/regional.html
http://tinyurl.com/xzlo

-monz

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> >
> > > It only works with dodekaphony I promise you.
> >
> > I never believe such promises without first seeing
> > enough definitions so I know what I've been promised.
> > Can you start by giving the (presumably 12) notes of
> > the (presumptive) dodekaphonic scale? I'm envisioning
> > something like the Ellis scale, but I could be all wet.
>
> Hi Gene - dodekaphony is the division of the octave into
> 12 intermediate intervals. In ET the steps are all of
> equal size. In Just Intonation they vary slightly because
> of the impossibility of expressing the 12th root of two
> as a ratio of two whole numbers. But really you knew that
> all along, didn't you?

Peter, Gene knows just about all there is to know about
the mathematics of tuning. take a look at the archives
on the tuning-math list.

> The entire humanly performable repertoire is dodekaphonic.

sorry, not true. one contrary example is Mozart's
orchestral music, which was written with the intention
of being played in a 19 or 20-tone subset of 55edo. see:
http://sonic-arts.org/monzo/55edo/55edo.htm

> All standard western musical instruments are dodekaphonic.

sorry again, also not true. do you know how the violin,
viola, cello, contrabass, and trombone work? they can
produce any conceivable pitch within the limits of their
ranges.

> I am of the opinion that our very souls are dodekaphonic
> though I realize that may be a contentious statement.

hmmm ... maybe you should post more about that.
sounds intriguing, altho my instinct is to argue with you.

;-)

-monz

🔗Dante Rosati <dante@interport.net>

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>

/tuning/topicId_49031.html#49130

> >
> > All the ensebles who have played it -- the performance of
> the 'Cosmic
> > Rays' string quartet was extremely impressive, for example. But
of
> > course at least as relevant is all the music of others that
Johnny
> > has played or presented in his concerts.
>
> Have you got an MP3 I can listen to?

***Hello Peter!

Johnny's mp3s are here:

http://www.stereosociety.com/cdaudio.html

However, the string quartet doesn't seem to be here. All the other
pieces are also microtonal, though.

best,

Joseph Pehrson

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...>
> > > wrote:
> > >
> > > > It only works with dodekaphony I promise you.
> > >
> > > I never believe such promises without first seeing
> > > enough definitions so I know what I've been promised.
> > > Can you start by giving the (presumably 12) notes of
> > > the (presumptive) dodekaphonic scale? I'm envisioning
> > > something like the Ellis scale, but I could be all wet.
> >
> > Hi Gene - dodekaphony is the division of the octave into
> > 12 intermediate intervals. In ET the steps are all of
> > equal size. In Just Intonation they vary slightly because
> > of the impossibility of expressing the 12th root of two
> > as a ratio of two whole numbers. But really you knew that
> > all along, didn't you?
>
>
> Peter, Gene knows just about all there is to know about
> the mathematics of tuning. take a look at the archives
> on the tuning-math list.
>
>
>
> > The entire humanly performable repertoire is dodekaphonic.
>
>
> sorry, not true. one contrary example is Mozart's
> orchestral music, which was written with the intention
> of being played in a 19 or 20-tone subset of 55edo. see:
> http://sonic-arts.org/monzo/55edo/55edo.htm
>
>

Ok I looked at it. I find it utterly opaque. And that's a very large
claim you're making. I think I'll stick to ET dodekaphonic Mozart.
Perhaps that's just my enculturated personal taste - or perhaps it's
not. Who can say?

>
> > All standard western musical instruments are dodekaphonic.
>
>
> sorry again, also not true. do you know how the violin,
> viola, cello, contrabass, and trombone work? they can
> produce any conceivable pitch within the limits of their
> ranges.
>
>

I already answered that one. Please let me know who plays his violin
non-dodekaphonically so I can avoid it. Actually, my young niece does
a pretty good imitation of a cat hung by its tail.

>
> > I am of the opinion that our very souls are dodekaphonic
> > though I realize that may be a contentious statement.
>
>
> hmmm ... maybe you should post more about that.
> sounds intriguing, altho my instinct is to argue with you.
>
> ;-)
>
>

Spoke like a true sophist, sir. I salute you.

>
>
> -monz

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Dante Rosati <dante@interport.net>

The chromatic sequences you mention can always be understood in a diatonic
context, at least until late romanticism. Dodekaphony has nothing to do with
"rows" and everything to do with actually using all 12 notes without
hierarchy. Outside of Schoenberg et al., nowhere else on earth (that I know
of) does anyone use 12 notes equally without any kind of hierarchy. In north
India they have alot more than 12 notes, but they dont use them all at the
same time. So my point is that what is important is not how many pitches and
inflected intervals (chromatic inflections) you may have at your disposal,
but how many are actually used, and in what way. So, the world is tonal (and
so Paul doesn't jump on me- I'll say I include modal music within the rubric
"tonal"), and mostly pentatonic or septatonic. 12 just allows for
transposition and modulation- and other, larger # edos do the same, and much
better too- but for whatever historical reasons were too unwieldy to catch
on.

If you look at a consonance graph like Helmholtz:

http://users.rcn.com/dante.interport//helmholtz.html

its pretty clear why most of the world's scales are the way they are.

Dante

> -----Original Message-----
> From: Peter Wakefield Sault [mailto:sault@cyberware.co.uk]
> Sent: Monday, December 08, 2003 1:09 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Hi Dante Rosati
>
>
> --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> > > > I am of the opinion that our very souls are dodekaphonic
> > > > though I realize that may be a contentious statement.
> >
> > Only Schoenberg and Boulez would agree with you. The rest of the
> world is
> > penta- and septatonic for the most part.
> >
> > Dante
>
> You misunderstand me, sir. I am not suggesting that the only music is
> Schoenberg-style tone-row composition by any manner of means.
> Pentantonic and heptatonic (and octatonic and what have you) scales
> are subsets of dodekaphony. Many composers, from Bach onwards, have
> used chromatic sequences of 3 of 4 notes during modulation and in the
> preparation and resolution of the extended harmonies (7ths, 9ths
> etc.).
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> Ok I looked at it. I find it utterly opaque. And that's a very
large
> claim you're making. I think I'll stick to ET dodekaphonic Mozart.
> Perhaps that's just my enculturated personal taste - or perhaps
it's
> not. Who can say?

I'm cooking up a version of Mozart'a piano concerto #22 in a
circulating temperament I call "bifrost" at the moment. I guarantee
it isn't precisely the tuning Mozart had in mind, but I am quite sure
he would have found it a lot more acceptable than 12-et, and I very
much doubt he would have found it objectionable in any way, given the
nature of his music and the fact that I can transpose the scale
according to key (E flat in this case) in question. Mozart to me
really does not work very well in equal temperament, and since his
harmony never requires such a thing, it strikes me that it amounts to
a lazy solution to the problem of tuning Mozart.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> The chromatic sequences you mention can always be understood in a
diatonic
> context, at least until late romanticism. Dodekaphony has nothing
to do with
> "rows" and everything to do with actually using all 12 notes without
> hierarchy.

There I must disagree with you. My usage of the word 'dodekaphony'
describes the system not the music created out of that system which,
as you rightly point out, generally only uses subsets such as the
various pentatonic and heptatonic scales.

>Outside of Schoenberg et al., nowhere else on earth (that I know
> of) does anyone use 12 notes equally without any kind of hierarchy.
In north
> India they have alot more than 12 notes, but they dont use them all
at the
> same time. So my point is that what is important is not how many
pitches and
> inflected intervals (chromatic inflections) you may have at your
disposal,
> but how many are actually used, and in what way. So, the world is
tonal (and
> so Paul doesn't jump on me- I'll say I include modal music within
the rubric
> "tonal"), and mostly pentatonic or septatonic. 12 just allows for
> transposition and modulation- and other, larger # edos do the same,
and much
> better too- but for whatever historical reasons were too unwieldy
to catch
> on.
>
> If you look at a consonance graph like Helmholtz:
>
> http://users.rcn.com/dante.interport//helmholtz.html
>
> its pretty clear why most of the world's scales are the way they
are.
>
>
>
> Dante
>
> > -----Original Message-----
> > From: Peter Wakefield Sault [mailto:sault@c...]
> > Sent: Monday, December 08, 2003 1:09 AM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Re: Hi Dante Rosati
> >
> >
> > --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> > > > > I am of the opinion that our very souls are dodekaphonic
> > > > > though I realize that may be a contentious statement.
> > >
> > > Only Schoenberg and Boulez would agree with you. The rest of the
> > world is
> > > penta- and septatonic for the most part.
> > >
> > > Dante
> >
> > You misunderstand me, sir. I am not suggesting that the only
music is
> > Schoenberg-style tone-row composition by any manner of means.
> > Pentantonic and heptatonic (and octatonic and what have you)
scales
> > are subsets of dodekaphony. Many composers, from Bach onwards,
have
> > used chromatic sequences of 3 of 4 notes during modulation and in
the
> > preparation and resolution of the extended harmonies (7ths, 9ths
> > etc.).
> >
> >
> >
> > You do not need web access to participate. You may subscribe
through
> > email. Send an empty email to one of these addresses:
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - unsubscribe from the
tuning group.
> > tuning-nomail@yahoogroups.com - put your email message delivery
> > on hold for the tuning group.
> > tuning-digest@yahoogroups.com - change your subscription to
> > daily digest mode.
> > tuning-normal@yahoogroups.com - change your subscription to
> > individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> >
> > Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
> >
> >

🔗monz <monz@attglobal.net>

hi Haresh,

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > Friday afternoon on NPR (National Public Radio)
> > there was a feature on "Sacred Harp Singing",
> > a type of 5-limit just-intonation "fa-sol-la"
> > singing using Baptist Christian hymns as texts.
>
>
> Hello Monz, how does 5-limit JI "Sacred Harp Singing"
> temperament compare with the Indian gamut?

first, please note that "Sacred Harp Singing" is *not*
any kind of temperament! it's _a capella_ vocal music,
and entirely in JI.

as far as a comparison with Indian tuning ... well,
i would really have to devote some time to a study of
"Sacred Harp" to learn more about it than i do.

but i can pretty confidently state that it *does* have a
relationship to the traditional Indian gamut which has
pairs of notes a syntonic-comma apart, since the whole
objective of using the different shapes for noteheads
in the "shape-note" notation used in Sacred Harp is to
secure small-integer JI ratios in the vertical harmonies
and melodic progressions, which inevitably will result
in the need for pairs of notes tuned a comma apart.

-monz

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> > >
> > > The entire humanly performable repertoire is dodekaphonic.
> >
> >
> > sorry, not true. one contrary example is Mozart's
> > orchestral music, which was written with the intention
> > of being played in a 19 or 20-tone subset of 55edo. see:
> > http://sonic-arts.org/monzo/55edo/55edo.htm
> >
> >
>
> Ok I looked at it. I find it utterly opaque.

i admit that the page can use some editing. but please
read it again carefully from beginning to end and i think
you'll see what i'm saying.

essentially it boils down to this: during the baroque and
early "classical" era, the standard tuning for keyboards
was some form of a 12-tone circulating well-temperament,
while the standard tuning that was taught for the playing
of orchestral music was a meantone in which the "whole-tone"
was divided into two different-sized "semitones" which
varied in size by one "comma": the "diatonic semitone" from
one letter-name to another (one of which may have a sharp
or flat) which contained 5 commas, and the "chromatic semitone"
which always involved two notes with the same letter-name
but a change of natural/sharp or natural/flat which contained
4 commas, and the "whole-tone" thus containing 9 commas.
the only tuning which solves this equation is 55-tone
equal-temperament.

> And that's a very large claim you're making.

yes, i know it is ... but i've fully substantiated it.
it's in Mozart's own handwriting.

> I think I'll stick to ET dodekaphonic Mozart.
> Perhaps that's just my enculturated personal taste - or
> perhaps it's not. Who can say?

well, whatever it is, it's *not* what Mozart intended,
which is all i'm trying to get to.

he clearly intended his orchestral music to be played
in a 19- or 20-tone subset of 55edo ... so regardless of
the tuning, it is most emphatically *not dodekaphonic*.

> > > All standard western musical instruments are dodekaphonic.
> >
> >
> > sorry again, also not true. do you know how the violin,
> > viola, cello, contrabass, and trombone work? they can
> > produce any conceivable pitch within the limits of their
> > ranges.
> >
> >
>
> I already answered that one. Please let me know who plays
> his violin non-dodekaphonically so I can avoid it. Actually,
> my young niece does a pretty good imitation of a cat hung by
> its tail.

almost all string quartets play in a tuning which is not 12edo.
the tuning of the open strings is Pythagorean, and to my ears
the playing of the stopped (fingered) notes has elements of
both JI and the Pythagorean-based "expressive intonation"
which came into vogue around the time of Mozart's death.

Schoenberg himself had to laboriously coach his own ensemble
(the Kolisch quartet) from the piano to get them to play
his quartets in strict 12edo.

> > > I am of the opinion that our very souls are dodekaphonic
> > > though I realize that may be a contentious statement.
> >
> >
> > hmmm ... maybe you should post more about that.
> > sounds intriguing, altho my instinct is to argue with you.
> >
> > ;-)
> >
> >
>
> Spoke like a true sophist, sir. I salute you.

if you've taken a look at my "Sumerian tuning" webpages,
you've seen that i am indeed interested in aspects of
tuning which go far beyond "mere" music and sound.
i was serious when i asked you to post more about
your ideas.

-monz

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...>
> > > wrote:
> > > >
> > > > The entire humanly performable repertoire is dodekaphonic.
> > >
> > >
> > > sorry, not true. one contrary example is Mozart's
> > > orchestral music, which was written with the intention
> > > of being played in a 19 or 20-tone subset of 55edo. see:
> > > http://sonic-arts.org/monzo/55edo/55edo.htm
> > >
> > >
> >
> > Ok I looked at it. I find it utterly opaque.
>
>
> i admit that the page can use some editing. but please
> read it again carefully from beginning to end and i think
> you'll see what i'm saying.
>

Ok. Will do. Prepare yourself for a mountain of questions.

> essentially it boils down to this: during the baroque and
> early "classical" era, the standard tuning for keyboards
> was some form of a 12-tone circulating well-temperament,
> while the standard tuning that was taught for the playing
> of orchestral music was a meantone in which the "whole-tone"
> was divided into two different-sized "semitones" which
> varied in size by one "comma": the "diatonic semitone" from
> one letter-name to another (one of which may have a sharp
> or flat) which contained 5 commas, and the "chromatic semitone"
> which always involved two notes with the same letter-name
> but a change of natural/sharp or natural/flat which contained
> 4 commas, and the "whole-tone" thus containing 9 commas.
> the only tuning which solves this equation is 55-tone
> equal-temperament.
>
>
> > And that's a very large claim you're making.
>
>
> yes, i know it is ... but i've fully substantiated it.
> it's in Mozart's own handwriting.
>

That must be a pretty valuable piece of paper you've got there.

>
>
> > I think I'll stick to ET dodekaphonic Mozart.
> > Perhaps that's just my enculturated personal taste - or
> > perhaps it's not. Who can say?
>
>
> well, whatever it is, it's *not* what Mozart intended,
> which is all i'm trying to get to.
>
> he clearly intended his orchestral music to be played
> in a 19- or 20-tone subset of 55edo ... so regardless of
> the tuning, it is most emphatically *not dodekaphonic*.
>

I see. So the horns and stuff would provide the frequencies for the
strings to lock onto. Is that right? With regard to your example on
the webpage, I am afraid you will have to recreate the whole symphony
and not just add a harmonium on top. It could be done with MIDI. I
MIDIfied the 1st movement Mendelssohn's 4th so I could study it more
closely. I should put that on my webpage, as it is vastly better than
most modern recordings which omit the codas to shorten it and which
are always much too fast, turning it into a race between the wind and
the strings.

>
> > > > All standard western musical instruments are dodekaphonic.
> > >
> > >
> > > sorry again, also not true. do you know how the violin,
> > > viola, cello, contrabass, and trombone work? they can
> > > produce any conceivable pitch within the limits of their
> > > ranges.
> > >
> > >
> >
> > I already answered that one. Please let me know who plays
> > his violin non-dodekaphonically so I can avoid it. Actually,
> > my young niece does a pretty good imitation of a cat hung by
> > its tail.
>
>
> almost all string quartets play in a tuning which is not 12edo.
> the tuning of the open strings is Pythagorean, and to my ears
> the playing of the stopped (fingered) notes has elements of
> both JI and the Pythagorean-based "expressive intonation"
> which came into vogue around the time of Mozart's death.
>

Yes I understand the tendency to naturalize ET intervals. Singers are
the worst offenders.

> Schoenberg himself had to laboriously coach his own ensemble
> (the Kolisch quartet) from the piano to get them to play
> his quartets in strict 12edo.
>
>
>
> > > > I am of the opinion that our very souls are dodekaphonic
> > > > though I realize that may be a contentious statement.
> > >
> > >
> > > hmmm ... maybe you should post more about that.
> > > sounds intriguing, altho my instinct is to argue with you.
> > >
> > > ;-)
> > >
> > >
> >
> > Spoke like a true sophist, sir. I salute you.
>
>
> if you've taken a look at my "Sumerian tuning" webpages,
> you've seen that i am indeed interested in aspects of
> tuning which go far beyond "mere" music and sound.
> i was serious when i asked you to post more about
> your ideas.
>

Yes I want to read more of that too. Please can you arrange for me to
have an extra 12 hours in every day?

>
>
> -monz

🔗Paul Erlich <paul@stretch-music.com>

🔗Afmmjr@aol.com

🔗Dante Rosati <dante@interport.net>

Paul-

You mean there are no 5 and 7 note scales that use what we would call
fifths, fourths, thirds, sixths, etc. in all of the Middle East, Africa,
Indonesia...?

Dante

> -----Original Message-----
> From: Paul Erlich [mailto:paul@stretch-music.com]
> Sent: Monday, December 08, 2003 11:08 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Hi Dante Rosati
>
>
> --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
>
> > If you look at a consonance graph like Helmholtz:
> >
> > http://users.rcn.com/dante.interport//helmholtz.html
> >
> > its pretty clear why most of the world's scales are the way they
> are.
> >
> >
> >
> > Dante
>
> Except for Arabic, Indonesian, African . . . still wanna say "most"??
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery
> on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to
> daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
> individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

🔗Paul Erlich <paul@stretch-music.com>

No, I just mean you'd be hard pressed to derive the interval sizes
used there from Helmholtz's curve -- for example, 670-cent fifths
(pelog), 350-cent thirds (arabic, thai), 250-cent whatises (slendro,
central africa). It was a direct reply to your post.

--- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> Paul-
>
> You mean there are no 5 and 7 note scales that use what we would
call
> fifths, fourths, thirds, sixths, etc. in all of the Middle East,
Africa,
> Indonesia...?
>
> Dante
>
> > -----Original Message-----
> > From: Paul Erlich [mailto:paul@s...]
> > Sent: Monday, December 08, 2003 11:08 AM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Re: Hi Dante Rosati
> >
> >
> > --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> >
> > > If you look at a consonance graph like Helmholtz:
> > >
> > > http://users.rcn.com/dante.interport//helmholtz.html
> > >
> > > its pretty clear why most of the world's scales are the way they
> > are.
> > >
> > >
> > >
> > > Dante
> >
> > Except for Arabic, Indonesian, African . . . still wanna
say "most"??
> >
> >
> >
> > You do not need web access to participate. You may subscribe
through
> > email. Send an empty email to one of these addresses:
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - unsubscribe from the
tuning group.
> > tuning-nomail@yahoogroups.com - put your email message delivery
> > on hold for the tuning group.
> > tuning-digest@yahoogroups.com - change your subscription to
> > daily digest mode.
> > tuning-normal@yahoogroups.com - change your subscription to
> > individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> >
> > Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
> >
> >

🔗Dante Rosati <dante@interport.net>

Paul-

Just as in the West we have many tempered approximations of the simple ratio
intervals, why cant these intervals be considered the same way? Notice how
you still call 670cents a "fifth". Anyway, my point was not so much the
exact tuning of the scale steps but rather their number- I was pointing out
that 5 or 7 notes to an octave is common, whereas 12 notes to an octave is
not. I believe the common 5 or 7 notes come from the valleys in the
consonance graphs, regardless of whether they are spot on or within a
temperament band around the valleys. I'd be interested to know if there is
any music from any culture at any time the used dodecaphony (in the sense of
using all twelve equally at once, rather than various diatonic subsets
thereof) before Arnie the S. thot it up.

Dante

> -----Original Message-----
> From: Paul Erlich [mailto:paul@stretch-music.com]
> Sent: Monday, December 08, 2003 2:16 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Hi Dante Rosati
>
>
> No, I just mean you'd be hard pressed to derive the interval sizes
> used there from Helmholtz's curve -- for example, 670-cent fifths
> (pelog), 350-cent thirds (arabic, thai), 250-cent whatises (slendro,
> central africa). It was a direct reply to your post.
>
> --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> > Paul-
> >
> > You mean there are no 5 and 7 note scales that use what we would
> call
> > fifths, fourths, thirds, sixths, etc. in all of the Middle East,
> Africa,
> > Indonesia...?
> >
> > Dante
> >
> > > -----Original Message-----
> > > From: Paul Erlich [mailto:paul@s...]
> > > Sent: Monday, December 08, 2003 11:08 AM
> > > To: tuning@yahoogroups.com
> > > Subject: [tuning] Re: Hi Dante Rosati
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> > >
> > > > If you look at a consonance graph like Helmholtz:
> > > >
> > > > http://users.rcn.com/dante.interport//helmholtz.html
> > > >
> > > > its pretty clear why most of the world's scales are the way they
> > > are.
> > > >
> > > >
> > > >
> > > > Dante
> > >
> > > Except for Arabic, Indonesian, African . . . still wanna
> say "most"??
> > >
> > >
> > >
> > > You do not need web access to participate. You may subscribe
> through
> > > email. Send an empty email to one of these addresses:
> > > tuning-subscribe@yahoogroups.com - join the tuning group.
> > > tuning-unsubscribe@yahoogroups.com - unsubscribe from the
> tuning group.
> > > tuning-nomail@yahoogroups.com - put your email message delivery
> > > on hold for the tuning group.
> > > tuning-digest@yahoogroups.com - change your subscription to
> > > daily digest mode.
> > > tuning-normal@yahoogroups.com - change your subscription to
> > > individual emails.
> > > tuning-help@yahoogroups.com - receive general help information.
> > >
> > >
> > > Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
> > >
> > >
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery
> on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to
> daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
> individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:

> I believe the common 5 or 7 notes come from the valleys in the
> consonance graphs, regardless of whether they are spot on or within
a
> temperament band around the valleys.

I'm assuming you mean "whether they are spot on or within a
temperament band around the valleys, or not" -- since clearly even
the thirds in Arabic or Thai scales fail to be within any sort of
temperament band around valleys of discordance graphs.

Anyway, perhaps there's a grain of truth to what you're saying, but I
don't believe the scales come *directly* from the valleys of
*intervallic* discordance, translated into pitch ratios -- you don't
really see any such scales *anywhere*, West or East. For example, the
*seconds* or consecutive intervals of these scales, whether 116, 133,
150, 171, 194, or 240 cents, do not correspond to such valleys in any
way. Instead, the derivation of 5 and 7 tone scales from these
consonances occurs, I believe, through *chains* or *lattices* of
tuned (or mistuned) consonances, continued until intervals considered
too small occur. Hence periodicity blocks:

http://sonic-arts.org/td/erlich/intropblock1.htm

So the most basic, 3-limit, pentatonic scale would be

16/9 - 4/3 - 1/1 - 3/2 - 9/8

or any mode (rotation) thereof. Though the pitches in any given mode
won't all fall near consonance valleys, the scale can be derived
entirely as a chain of such consonances, extended as far as possible
without creating 90 cent or smaller intervals. Continue through the
links linked to from above and you'll see 7- and 12-note scales
derived. Other periodicity blocks include 5-note Japanese scales,
like 1/1-16/15-4/3-3/2-8/5, which can be derived from unison vectors
135:128 and 10:9. Temper out the 135:128 (so that '16/15' goes up
enough, and '3/2' goes down enough, so that the interval between the
two forms some vague approximation to 3:4), and you're awfully close
to pelog scales. Etc.

The only place you'd expect a scale to resemble the valleys in a
consonance graph is if you have a persistent *drone* played at the
pitch labeled '1/1' and all other notes are simply played one at a
time against this 1/1 -- then, and only then, do the valleys in the
consonance graph correspond to theoretically 'preferred' scale
pitches -- but even so, such scales are rare, to say the least, even
in 'dronal' music cultures.

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > ... but i've fully substantiated it.
> > it's in Mozart's own handwriting.
> >
>
> That must be a pretty valuable piece of paper you've got there.

not at all. Thomas Attwood was a student who studied
with Mozart, and kept good notes and his notebooks have
been published. i'm just very good at doing interlibrary loan.
:)

> > > I think I'll stick to ET dodekaphonic Mozart.
> > > Perhaps that's just my enculturated personal taste - or
> > > perhaps it's not. Who can say?
> >
> >
> > well, whatever it is, it's *not* what Mozart intended,
> > which is all i'm trying to get to.
> >
> > he clearly intended his orchestral music to be played
> > in a 19- or 20-tone subset of 55edo ... so regardless of
> > the tuning, it is most emphatically *not dodekaphonic*.
> >
>
> I see. So the horns and stuff would provide the frequencies
> for the strings to lock onto. Is that right?

i imagine that you're thinking that the "natural" (i.e., JI)
tones of the horns are the "target" pitches to which the
other instruments gravitate. not at all. meantone is
entirely different from JI, and Mozart's tuning (~55edo)
was clearly meantone.

> With regard to your example on the webpage, I am afraid
> you will have to recreate the whole symphony and not just
> add a harmonium on top. It could be done with MIDI.

huh? i don't know what you mean. the example on my page
is the first part of the first movement of Mozart's 40th Symphony
done in MIDI, which full MIDI orchestra.

> > almost all string quartets play in a tuning which is not 12edo.
> > the tuning of the open strings is Pythagorean, and to my ears
> > the playing of the stopped (fingered) notes has elements of
> > both JI and the Pythagorean-based "expressive intonation"
> > which came into vogue around the time of Mozart's death.
> >
>
> Yes I understand the tendency to naturalize ET intervals.
> Singers are the worst offenders.

oh boy ... you're asking for trouble around here with a
response like that.

singers and string players *do* tend to make the intonation
of what they sing/play fit a JI paradigm, but i don't see
why you would call them "the worst offenders". most people
find _a capella_ vocal music or string quartet music to
be among the most resonant and "consonant", whatever that
might mean. ;-)

> Yes I want to read more of that too. Please can you
> arrange for me to have an extra 12 hours in every day?

if i could figure out how to put any more hours in a day,
i'd do it for myself first before giving them to anyone else.
;-)

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_49031.html#49378

> --- In tuning@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
>
> > I believe the common 5 or 7 notes come from the valleys in the
> > consonance graphs, regardless of whether they are spot on or
within
> a
> > temperament band around the valleys.
>
> I'm assuming you mean "whether they are spot on or within a
> temperament band around the valleys, or not" -- since clearly even
> the thirds in Arabic or Thai scales fail to be within any sort of
> temperament band around valleys of discordance graphs.
>
> Anyway, perhaps there's a grain of truth to what you're saying, but
I
> don't believe the scales come *directly* from the valleys of
> *intervallic* discordance, translated into pitch ratios -- you
don't
> really see any such scales *anywhere*, West or East. For example,
the
> *seconds* or consecutive intervals of these scales, whether 116,
133,
> 150, 171, 194, or 240 cents, do not correspond to such valleys in
any
> way. Instead, the derivation of 5 and 7 tone scales from these
> consonances occurs, I believe, through *chains* or *lattices* of
> tuned (or mistuned) consonances, continued until intervals
considered
> too small occur. Hence periodicity blocks:
>
> http://sonic-arts.org/td/erlich/intropblock1.htm
>
> So the most basic, 3-limit, pentatonic scale would be
>
> 16/9 - 4/3 - 1/1 - 3/2 - 9/8
>
> or any mode (rotation) thereof. Though the pitches in any given
mode
> won't all fall near consonance valleys, the scale can be derived
> entirely as a chain of such consonances, extended as far as
possible
> without creating 90 cent or smaller intervals. Continue through the
> links linked to from above and you'll see 7- and 12-note scales
> derived. Other periodicity blocks include 5-note Japanese scales,
> like 1/1-16/15-4/3-3/2-8/5, which can be derived from unison
vectors
> 135:128 and 10:9. Temper out the 135:128 (so that '16/15' goes up
> enough, and '3/2' goes down enough, so that the interval between
the
> two forms some vague approximation to 3:4), and you're awfully
close
> to pelog scales. Etc.
>
> The only place you'd expect a scale to resemble the valleys in a
> consonance graph is if you have a persistent *drone* played at the
> pitch labeled '1/1' and all other notes are simply played one at a
> time against this 1/1 -- then, and only then, do the valleys in the
> consonance graph correspond to theoretically 'preferred' scale
> pitches -- but even so, such scales are rare, to say the least,
even
> in 'dronal' music cultures.

***I find this really interesting. So the "reality" of scale
construction among various cultures is more *complex* and
maybe "arbitrary" than just plotting consonances from Helmholtz and
believing most scales would fit those. I think this is something
that Kraig Grady was talking about at one time -- how the "reality"
is not always consistent with consonances...as much a *cultural*
derivation as an acoustical one in many ways...

J. Pehrson