question about the harmonic series and 72-tET

OK... at the end of Vyshnegradski's article about quartertones he has
an interesting chart that shows the closest quartertones to the
harmonic series, as deviations from 12-tET.

Now, let's say we are to take this a level beyond this, into 72-tET,
so that we have available the 12th tones and 6th tones.

Basing upon 12-tET and starting on C, I know the following are
obviously closely emulated:

5th partial on E with 12th tone low

7th partial on Bb with 6th tone low

11th partial on F natural with quartertone high...

Are there any other ones that are closely and accurately emulated by
72-tET??

If so, could I please have the starting 12-tET pitch and the 72-tET
deviation??

Thanks so much!!!

Joseph

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>

> Are there any other ones that are closely and accurately emulated by
> 72-tET??
>
> If so, could I please have the starting 12-tET pitch and the 72-tET
> deviation??

37th harmonic, 252 cents.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> OK... at the end of Vyshnegradski's article about quartertones he
has
> an interesting chart that shows the closest quartertones to the
> harmonic series, as deviations from 12-tET.
>
> Now, let's say we are to take this a level beyond this, into 72-
tET,
> so that we have available the 12th tones and 6th tones.
>
> Basing upon 12-tET and starting on C, I know the following are
> obviously closely emulated:
>
> 5th partial on E with 12th tone low
>
> 7th partial on Bb with 6th tone low
>
> 11th partial on F natural with quartertone high...
>
> Are there any other ones that are closely and accurately emulated
by
> 72-tET??

well, since 72-equal is steps of 16 2/3 cents, no interval can
possibly have an error greater than 8 1/3 cents . . .

these harmonics are also within 4 cents of just:

3rd partial -- G

9th partial -- D

19th partial -- Eb

21st partial -- F sixthtone low

29th partial -- Bb sixthtone high

33rd partial -- C quartertone high

72-equal uniquely articulates the 11-limit and is consistent through
the 17-limit.

but joseph, i thought you had trouble hearing any consonance even in
the 11-limit? so why would you care about anything beyond that?

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_38174.html#38176

>
> well, since 72-equal is steps of 16 2/3 cents, no interval can
> possibly have an error greater than 8 1/3 cents . . .
>

***That's funny, because it makes such obvious sense. I wish I'd
thought of it myself... :)

> these harmonics are also within 4 cents of just:
>
> 3rd partial -- G
>
> 9th partial -- D
>
> 19th partial -- Eb
>

***Well, so obviously 12-tET realizes these same partials to the
same, and quite good, degree of accuracy...

> 21st partial -- F sixthtone low
>
> 29th partial -- Bb sixthtone high
>
> 33rd partial -- C quartertone high
>
> 72-equal uniquely articulates the 11-limit and is consistent
through the 17-limit.
>

***I can't believe I'm going to need *review* of this. Call the
Alzheimers lab techs...

So *unique* means that there is only *one* interval that describes
*each* 11-limit ratio, correct??

And *consistent* means... whoaboy... I guess it means that it
*describes* all the possible 17-limit ratios, but not necessarily
with only *one* interval? What a guess.

> but joseph, i thought you had trouble hearing any consonance even
in the 11-limit? so why would you care about anything beyond that?

***It's true that the 11-limit "consonances" didn't even seem
especially *consonant* to me...

However, might it not be possible that I would want to compose with
the quasi-dissonances of the overtone series even if I didn't hear
them as *consonant??*

As a method of composition, rather than just *scattershot* "addition
of pitches" or serializing the 72 degrees, or whatever??

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> > 72-equal uniquely articulates the 11-limit and is consistent
> through the 17-limit.
> >
>
> ***I can't believe I'm going to need *review* of this. Call the
> Alzheimers lab techs...
>
> So *unique* means that there is only *one* interval that describes
> *each* 11-limit ratio, correct??

umm . . . it means that each 72-equal interval approximates either
zero, or only one, 11-(odd-)limit ratio. this isn't true for 31, for
example -- in 31, the major second approximates *both* 10:9 *and*
9:8. please see my chart, _the intervallic continuum_, again, to see
all the 11-odd-limit ratios, and how they're approximated in 72-equal.

> And *consistent* means... whoaboy... I guess it means that it
> *describes* all the possible 17-limit ratios, but not necessarily
> with only *one* interval? What a guess.

it means you won't run into the problems i demonstrated the other day
with rick tagawa's post of david canright's list of 72-equal's just
approximations, using the chord 8:13:19. remember that? well, that
won't happen in the 17-limit or under, with 72-equal.

> > but joseph, i thought you had trouble hearing any consonance even
> in the 11-limit? so why would you care about anything beyond that?
>
>
> ***It's true that the 11-limit "consonances" didn't even seem
> especially *consonant* to me...
>
> However, might it not be possible that I would want to compose with
> the quasi-dissonances of the overtone series even if I didn't hear
> them as *consonant??*
>
> As a method of composition, rather than just
*scattershot* "addition
> of pitches" or serializing the 72 degrees, or whatever??

well, there are a lot of intervals and chords in the 11-limit! 29
intervals in the 11-odd-limit alone! in fact, you can derive *ANY*
interval in 72-equal by combining no more than *TWO* 11-odd-limit
ratios!

so why derive your compositional materials from something you can't
even hear? you'd be better off just going by pure creative instinct,
or transcribing speech, or whatever . . .

Hello Paul!
This and your other comments i totally agree . In fact i can't remember a day where i have
been in so much agreement. It must be one of the planetary alignments or all the carrot juice and
wheatgrass i had today.

emotionaljourney22 wrote:

>
> so why derive your compositional materials from something you can't
> even hear? you'd be better off just going by pure creative instinct,
> or transcribing speech, or whatever . . .

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Hello Paul!
> This and your other comments i totally agree . In fact i can't
remember a day where i have
> been in so much agreement. It must be one of the planetary
alignments or all the carrot juice and
> wheatgrass i had today.

mmm . . . when i'm feeling disaligned, i go for a large carrot-
spinach-pineapple-ginger juice with a shot of wheatgrass.

now, it appears from daniel wolf's comments (quoted by joel) that
someone named lourie may have advocated 72-equal before novaro.
anyone know who lourie is?

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > Hello Paul!
> > This and your other comments i totally agree . In fact i can't
> remember a day where i have
> > been in so much agreement. It must be one of the planetary
> alignments or all the carrot juice and
> > wheatgrass i had today.
>
> mmm . . . when i'm feeling disaligned, i go for a large carrot-
> spinach-pineapple-ginger juice with a shot of wheatgrass.

Well, here I am in Lotus-land without any wheatgrass juice to speak of. But at least I gave a copy of Mary Beth Ackerly's CD to a practicing healing artist today! And yet the purpose of this is to say, just like Kraig, I feel Paul and I are aligned today...

...but I have to jump over to metatuning for the finale.

Cheers,
Jon (who likes serendipity, synchronicity, and ginger beer)

Hello Paul!

emotionaljourney22 wrote:

> someone named lourie may have advocated 72-equal before novaro.
> anyone know who lourie is?
>

or if Lourie knew how well it mapped the harmonic hexad. (or octoad). i will investigate

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Mary's work seems to attract fine things that i will have to wait till the inquisition over to expose about!
But as Paul implied alot to be said about going with the intuition. It explains why Feldman might be one of 12 ET last great sunset-possibly rainbow

jonszanto wrote:

> Well, here I am in Lotus-land without any wheatgrass juice to speak of. But at least I gave a copy of Mary Beth Ackerly's CD to a practicing healing artist today! And yet the purpose of this is to say, just like Kraig, I feel Paul and I are aligned today...
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_38174.html#38184

please see my chart, _the intervallic continuum_, again, to see
> all the 11-odd-limit ratios, and how they're approximated in 72-
equal.

***This is an *incredibly* beautiful chart, and I have two different
copies of it on two different walls, so one might think that I would
look at it from time to time! Good suggestion!

>
> > And *consistent* means... whoaboy... I guess it means that it
> > *describes* all the possible 17-limit ratios, but not necessarily
> > with only *one* interval? What a guess.
>
> it means you won't run into the problems i demonstrated the other
day with rick tagawa's post of david canright's list of 72-equal's
just approximations, using the chord 8:13:19. remember that? well,
that won't happen in the 17-limit or under, with 72-equal.
>

***Oh, sure. That was the one where, literally, "the whole was not
equal to the sum of its parts...etc..."

>
> well, there are a lot of intervals and chords in the 11-limit! 29
> intervals in the 11-odd-limit alone! in fact, you can derive *ANY*
> interval in 72-equal by combining no more than *TWO* 11-odd-limit
> ratios!
>
> so why derive your compositional materials from something you can't
> even hear? you'd be better off just going by pure creative
instinct, or transcribing speech, or whatever . . .

***Hmmm. I can't make a very good case for writing music with
materials I can't hear... I'll let *other* composers do that... :)

Guess the thing to do is to concentrate more on _The Intervallic
Continuum_ chart in my 72-tET work. There's sure plenty to work with
here!

Joseph