13/8 & spirituality etc.

Hello,

I spoke with Dave Canright over the weekend and he reminds us that 13:8
is a member of the Fibernacci (sp?) series and may share the
"uniqueness" found in other intervals of this special class.

Could it's Fibernacci connection contribute to its added appeal over 11?

On Fri, 12 Mar 1999 10:07:12 -0800
Kraig Grady said: All of these chords are in Helmholtz books. Let me
state one again, I don't like the 6/5 as a minor, I never use it!

This sentence caused me a double take. Sends shock waves to these ears.

I just finished a piece featuring just this interval as I found it a key
towards exploring the 72ET with these +17� notes. My previous
explorations centered on exclusively flat 12ET notes and the -83� notes
seemed the outer edge of this interpretation of the 72ET universe and
were consequently less utilized.

Looking at my score right now regarding my use of 11:8, I was wrong. It
was actually a 13 derived harmony I used to climax a piece for
orchestra. The piece is in d minor and the P5th enters alone very high,
in the harmonic range, followed by the 13th an octave lower. After
allowing the ear to acclimate to the 13th, the rest of the tonic chord
follows in force minus the 3rd. The effect is tense, perhaps, but not
too frightening.

I'm having trouble documenting my "spiritual" equation with just
intonation. Suffice it to say, the more just the music, the more higher
harmonics are in the air. And triggering these "hidden" notes has
seemed to me a worthy goal.

- * -

The following is quoted from Arthus H. Thornhill III, Six Circles, One
Dewdrop, Princeton University Press, Princeton, NJ, 1993

[p177] . . . Nanko then illustrates the proper attitude [re:
"spirituality" in music] by alluding to two koans in the Pi-yen lu:

Ho Shan imparted some words saying, "Cultivating study is called
'learning.' Cutting off study is called 'nearness.' Going beyond these
two is to be considered real going beyond."
A monk came forward and asked, "What is 'real going beyond'?" Shan
said, "Knowing how to beat the drum." [Translated by Thomas and J. C.
Cleary, The Blue Cliff Record (Boulder: Shambala, 1977), 2:312]

Surely, in this context the implication is that true music transcends
the dichotomy of careful study and total spontaneity. Nanko then
alludes to dance by mentioned Chin Niu, who appears in case 74:

Every day at mealtime, Master Chin Niu would personally take the rice
pail and do a dance in front of the monks' hall: laughing, out loud he
would say, "Bodhisattvas, come eat!"
Hs�eh Tou said, "Though he acted like this, Chin Niu was not
good-hearted."
A monk asked Ch'ang Ch'ing, "When the man of old said, 'Bodhisattvas,
come eat!" what was his meaning?" Chi-ing said, "Much like joyful
praise on the occasion of a meal." [Ibid., 3:490]

This incident highlights the tension felt by monks who endeavor to be
free of desire, like pure bodhisattvas, yet at mealtime they cannot
ignore the pangs of appetite. Chin Niu dances in delight at this
paradox, the inseparability of purity and desire in the human realm.
Nanko's reference mocks those who suggest that art is devoid of
emotional attachment.
Nanko then remarks that an overtly "spiritual" attitude toward
sarugaku, as exemplified by the rokurin ichiro system, destroys the
vitality of song and dance. He prefers simply to enjoy Zenchiku's
performances, rather than daring to augment the erudite comments of
Shigyoku and Kaneyoshi. Thus the Zen spokesman gets the last word, and
the last laugh, negating Zenchiku's reified, rigid symbols that destroy
the subtle life of noh, just as cooking ruins the delicate flavor of the
Ai family's pears.

RT

Rick Tagawa <ricktagawa@earthlink.net> wrote:

>I spoke with Dave Canright over the weekend and he reminds us that 13:8
>is a member of the Fibernacci (sp?) series and may share the
>"uniqueness" found in other intervals of this special class.
>
>Could it's Fibernacci connection contribute to its added appeal over 11?

I think the suggestion that Fibonacci ratios (1:1, 2:1, 3:2, 5:3, 8:5,
13:8, 21:13, 34:21, 55:34, ....) or the golden mean (which these approach,
approx 1.618) have anything special going for them with regard to
consonance, is pure numerology.

The slightly lower dissonance of 13:8 than 11:8 (for harmonic timbres)
despite its slightly higher COMPLEXITY, can be explained by a combination
of TOLERANCE and SPAN. Regarding TOLERANCE: 13:8 is between 5:3 and 8:5 (27
cents from 8:5, 54 cents from 5:3) while 11:8 is between 5:4 and 7:5 (31
cents from 7:5, 53 cents from 5:4). Regarding SPAN: 13:8 (841 cents) is
significantly wider than 11:8 (551 cents).

I love Zen koans. Thanks.

Regards,
-- Dave Keenan
http://dkeenan.com

Rick Tagawa wrote,

>Hello,

>I spoke with Dave Canright over the weekend and he reminds us that 13:8
>is a member of the Fibernacci (sp?) series and may share the
>"uniqueness" found in other intervals of this special class.

>Could it's Fibernacci connection contribute to its added appeal over
11?

Yes -- I made the same point in my off-list reply to Dante Rosati on
13:8. It is very close to the Golden Ratio, and the golden ratio has
fewer coinciding partials than any other ratio (for any given tolerance
for what "coinciding" means, you have to go higher up in the partials of
the Golden Ratio to find that degree of coincidence than you do for any
other ratio).

Paul Erlich wrote:

>Rick Tagawa wrote,
>>Could it's Fibonacci connection contribute to its added appeal over
>>11?
>
>Yes -- I made the same point in my off-list reply to Dante Rosati on
>13:8. It is very close to the Golden Ratio, and the golden ratio has
>fewer coinciding partials than any other ratio (for any given tolerance
>for what "coinciding" means, you have to go higher up in the partials of
>the Golden Ratio to find that degree of coincidence than you do for any
>other ratio).

Hey, this is neat, and not numerology (I take that back), but doesn't this
mean it should be a dissonance *maximum*. How does this explain why 13:8 is
slightly *less* dissonant than 11:8? There is certainly a *local*
dissonance maximum around the Golden ratio, but there are several higher,
including the one around 1.36 (near 11:8).

Regards,
-- Dave Keenan
http://dkeenan.com

Dave Keenan wrote:

> From: Dave Keenan <d.keenan@uq.net.au>
>
> Rick Tagawa <ricktagawa@earthlink.net> wrote:
>
> >I spoke with Dave Canright over the weekend and he reminds us that 13:8
> >is a member of the Fibernacci (sp?) series and may share the
> >"uniqueness" found in other intervals of this special class.
> >
> >Could it's Fibernacci connection contribute to its added appeal over 11?
>
> I think the suggestion that Fibonacci ratios (1:1, 2:1, 3:2, 5:3, 8:5,
> 13:8, 21:13, 34:21, 55:34, ....) or the golden mean (which these approach,
> approx 1.618) have anything special going for them with regard to
> consonance, is pure numerology.

Walter O'Connell started to explore this area back in the seventies. In one
experiment he had a drone and another voice going up in small microtonal
intervals. He ask the class to raise their hand at the octave. When he got to
the golden Mean of the octave just about everyone raised their hand. You Can't
always judge a tuning by its Mathematical cover. Walter was La Monte's Physic
teacher , much later mine. He also had Articles in DIE REIHE

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

>>Yes -- I made the same point in my off-list reply to Dante Rosati on
>>13:8. It is very close to the Golden Ratio, and the golden ratio has
>>fewer coinciding partials than any other ratio (for any given
tolerance
>>for what "coinciding" means, you have to go higher up in the partials
of
>>the Golden Ratio to find that degree of coincidence than you do for
any
>>other ratio).

Dabe Keenan wrote

>Hey, this is neat, and not numerology (I take that back), but doesn't
this
>mean it should be a dissonance *maximum*. How does this explain why
13:8 is
>slightly *less* dissonant than 11:8? There is certainly a *local*
>dissonance maximum around the Golden ratio, but there are several
higher,
>including the one around 1.36 (near 11:8).

I shouldn't have used the word "coinciding." How about "conflicting?" So
with fewer partials conflicting at any degree of tolerance, that means
less critical-band roughness than any other ratio without partials that
really do coincide (or nearly so). In other words, the two notes making
up a golden ratio maintain their separate identities better than two
notes at any other interval (assuming harmonic spectra). This might also
be an example of what I just e-mailed you about, the possibility that
the brain could hear two notes and interpret them as separate
fundamentals rather than partials of a single one, which would require a
modification of the whole harmonic entropy formulation. If that happens
at all, it happens at the golden ratio. Note that octave equivalents of
the golden ratio wouldn't work at all for this! However, as a first
approximation for getting some results out of harmonic entropy I'll
assume it doesn't happen at all.

P.S. Why does your TOLERANCE function explain why 13:8 is more consonant
than 11:8?

> In one experiment he had a drone and another
> voice going up in small microtonal intervals.
> He ask the class to raise their hand at the octave.
> When he got to the golden Mean of the octave just
> about everyone raised their hand. You Can't
> always judge a tuning by its Mathematical cover.

I don't have the references right now, but in
an experiment I know about, the most commonly
picked interval for the "octave" was one of
1215 cents.

In fact, all the intervals perceived as the
"most consonant" were actually a bit sharper
than the simple integer ratios we would expect
them to be.

The smallest-integer ratio of 1215 cents is 113:56.
There is a 5-limit interval which comes somewhat
close: an octave + syntonic comma, 81/40 = 1222 cents.
interesting . . .

- Monzo
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