re: Ives' quartertones

Dan, you wrote:

"nice"

You bet. This is the first time I've heard these works, and I really
enjoyed them-- especially the Allegro. Did Ives write any other
quarter-tone works?

I've been experimenting with equal-tempered quarter-tones again lately,
and am trying a nine-tone scale made entirely of semitones and neutral
seconds (100 c. and 150 c. respectively):

s - n - s - n - n - s - n - n - n

If anyone has some experience with this scale and tuning, I'm open to
comments and advice. I'm still looking for its strong and weak points --
melodically it seems to work well, but harmony is still a booger.

Gene (or anyone), how would a Pythagorean quarter-tone scale be
constructed? That is, by using only fourths, fifths and all the
resulting ratios -- and tuning entirely by ear -- how could one
generate a quarter-tone scale? (The "quarter-tones" would be somewhere
between 40 c. and 55 c. sharp/flat of the "naturals".)

J. Smith wrote:

> Gene (or anyone), how would a Pythagorean quarter-tone scale be
> constructed? That is, by using only fourths, fifths and all the
> resulting ratios -- and tuning entirely by ear -- how could one
> generate a quarter-tone scale? (The "quarter-tones" would be somewhere
> between 40 c. and 55 c. sharp/flat of the "naturals".)

Well, of course if you want to use only fourths and fifths, you'll have a hell of a time getting an octave. But, considering that a 3/2 fifth is about 2 cents sharp of a 12tet fifth, that is to say 702 cents, (3/2)^25th would be about 750 cents (give or take, with rounding).

So, you could make a passable Pythagorean quarter-tone scale using the following powers of 3/2:

0 24 2 26 4 28 6 30 8 32 10 34 1 25 3 27 5 29 7 31 9 33 11 35

Does this make sense?

-jim

Hi Jon and Jim,

--- In MakeMicroMusic@yahoogroups.com, jim altieri <jim@...> wrote:
>
> J. Smith wrote:
>
> > Gene (or anyone), how would a Pythagorean quarter-tone
> > scale be constructed? That is, by using only fourths,
> > fifths and all the resulting ratios -- and tuning entirely
> > by ear -- how could one generate a quarter-tone scale?
> > (The "quarter-tones" would be somewhere between 40 c.
> > and 55 c. sharp/flat of the "naturals".)
>
> Well, of course if you want to use only fourths and fifths,
> you'll have a hell of a time getting an octave. But,
> considering that a 3/2 fifth is about 2 cents sharp of a
> 12tet fifth, that is to say 702 cents, (3/2)^25th would
> be about 750 cents (give or take, with rounding).
>
> So, you could make a passable Pythagorean quarter-tone
> scale using the following powers of 3/2:
>
> 0 24 2 26 4 28 6 30 8 32 10 34 1 25 3 27 5 29 7 31 9 33 11 35
>
> Does this make sense?

It's interesting to me that this question came up, because
i've looked into it myself in the past.

Here's my version, basically the same idea as Jim's, except
that it's entirely symmetrical on the negative and positive
sides from 1/1, in terms of generator 3/2 5ths and 4/3 4ths.
The table is arranged in descending order of pitch.

(click on "Option | Use Fixed Width Font" to see it
correctly if viewing this on the stupid Yahoo web interface)

1/4-tone . (3/2)^x . ~cents error

... 0 ....... 0 ....... 0
... 1 ...... 24 ...... -3.08
... 2 ...... -5 ...... -9.78
... 3 ..... -22 ...... +6.99
... 4 ....... 2 ...... +3.91
... 5 ...... 26 ...... +0.83
... 6 ...... -3 ...... -5.87
... 7 ...... 21 ...... -8.94
... 8 ....... 4 ...... +7.82
... 9 ..... -25 ...... +1.12
.. 10 ...... -1 ...... -1.96
.. 11 ...... 23 ...... -5.03
.. 12 ....... 6 ..... +11.73
.. 13 ..... -23 ...... +5.03
.. 14 ....... 1 ...... +1.96
.. 15 ...... 25 ...... -1.12
.. 16 ...... -4 ...... -7.82
.. 17 ..... -21 ...... +8.94
.. 18 ....... 3 ...... +5.87
.. 19 ..... -26 ...... -0.83
.. 20 ...... -2 ...... -3.91
.. 21 ...... 22 ...... -6.99
.. 22 ....... 5 ...... +9.78
.. 23 ..... -24 ...... +3.08
. (24).... (2/1) ...... 0

Arranged in order by generator number, the tuning goes
like this:

-26, -25, -24, -23, -22, -21, -5, -4, -3, -2, -1,
0, 1, 2, 3, 4, 5, 6, 21, 22, 23, 24, 25, 26

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi all

Referring to My mail: /tuning/topicId_68776.html#68840 and
Monzo : /tuning/topicId_68776.html#68824
Gene : /tuning/topicId_68776.html#68814
………...

1-if considering "grad" as (23.46/12)or 12th root of pyth.comma , we can
consider something like "semigrad" as (23.46/24)or 24th root of pyth.comma.
2-Considering chains of (3/2)^(1/2) we can have this result:

...........................Cent ..............After temp.
Degree in chain ........0 .............. 0
-23 .............. 33.382 .............. 50
7 .............. 56.842 .............. 50
-22 .............. 90.2249 .............. 100
14 .............. 113.685 .............. 100
-21 .............. 147.0675.............. 150
21 .............. 170.5275.............. 150
-20 .............. 180.45 .............. 200
4 .............. 203.91 .............. 200
-19 .............. 237.2925.............. 250
11 .............. 260.7525.............. 250
-18 .............. 294.135 .............. 300
18 .............. 317.595 .............. 300
-17 .............. 327.5175.............. 350
1 .............. 350.9775.............. 350
-16 .............. 384.36 ............. 400
8 .............. 407.82 .............. 400
-15 .............. 441.2025.............. 450
15 .............. 464.6625.............. 450
-14 .............. 498.045 .............. 500
22 .............. 521.505 .............. 500
-13 .............. 531.4275.............. 550
5 .............. 554.8875.............. 550
-12 .............. 588.27 .............. 600
12 .............. 611.73 .............. 600
-11 .............. 645.1125.............. 650
19 .............. 668.5725.............. 650
-10 .............. 678.495 .............. 700
2 .............. 701.955 .............. 700
-9 .............. 735.3375.............. 750
9 .............. 758.7975.............. 750
-8 .............. 792.18 .............. 800
16 .............. 815.64 .............. 800
-7 .............. 849.0225.............. 850
23 .............. 872.4825.............. 850
-6 .............. 882.405 .............. 900
6 .............. 905.865 .............. 900
-5 .............. 939.2475.............. 950
13 .............. 962.7075.............. 950
-4 .............. 996.09 .............. 1000
20 .............. 1019.55 .............. 1000
-3 .............. 1029.4725.............. 1050
3 .............. 1052.9325.............. 1050
-2 .............. 1086.315.............. 1100
10 .............. 1109.775.............. 1100
-1 .............. 1143.1575.............. 1150
17 .............. 1166.6175.............. 1150
24 .............. 1223.46 .............. 1200

So we see that in this result we have all intervals in chain of 3/2 and two size
for quarter tones , (like lima and appotom).
We have also here "schisma of philolaus".and this (3/2)^(1/2) is not a new thing
, in http://198.66.217.172/monzo/aristoxenus/318tet.htm we have " mese -
hemiolic chromatic lichanos" as "3 semitones + enharmonic diesis" measured
350.978 cent or :
(3/4)*(256/243)*((2187/2048)^(1/2)) 0.816497 ~-350.978 hemiolic
chromatic lichanos

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web siteوب سايت شاهين مهاجري <http://240edo.googlepages.com/>

My farsi page in Harmonytalk صفحه اختصاصي در هارموني تاك <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia شاهين مهاجري دردائره المعارف ويكي پديا <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

[Non-text portions of this message have been removed]

Gee, after all this time, you guys still don't realize that the Universe
Symphony by Charles Ives contains quartertones, in diverse places throughout.

Johnny Reinhard

************************************** See what's free at http://www.aol.com.

[Non-text portions of this message have been removed]

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:

> Here's my version, basically the same idea as Jim's, except
> that it's entirely symmetrical on the negative and positive
> sides from 1/1, in terms of generator 3/2 5ths and 4/3 4ths.
> The table is arranged in descending order of pitch.

Oops, my bad ... of course the table is listed in *ascending*
order of pitch, as in the Scala format.

(I guess it was habit: i usually do list pitches in
descending order. It makes sense to me to see the highest
pitch at the top of the list and the lowest at the bottom.
Alas, no one else seems to agree with me ...)

Anyway, since i mentioned Scala, i thought i might as
well make a .scl file of it:

-------------------------------------------------------
! monzo_pyth-quartertone.scl
!

24
!
46.92002
90.22500
156.98998
203.91000
250.83002
294.13500
341.05502
407.82000
451.12498
498.04500
544.96502
611.73001
655.03498
701.95500
748.87502
792.18000
858.94498
905.86500
949.16998
996.09000
1043.01002
1109.77500
1153.07998
2/1
---------------------------------------------------------

-monz
http://tonalsoft.com
Tonescape microtonal music software

Thanks, Dan and Daniel;\\

Dan, you might try 2 pianos 60 cents apart, as opposed to 50 cents (the
strict quartertone). In our new recording, Pianist Joshua Pierce, the duo of
Pierce and Jonas play on pianos 60 cents apart. Both the harmony and the melody
is improved.

The piece gets a real boost from the 13th harmonic relationship over the
11th harmonic relationship. The harmonies are richer (aka, more consonant), and
the melodies more angular with a closer/further relationship that beats the
identical equalness of 50 cent quartertones.

What's more is there is evidence in Memos that Ives had an experience with
this tuning and really loved it.

Johnny

************************************** See what's free at http://www.aol.com.

[Non-text portions of this message have been removed]

Hi Dan,

I was going to write something about Ives's 4th Symphony,
but kept putting it off ... but now that you've said this,
it's finally time for me to chime in. I agree totally --
the best word i can think of for the ending of this
symphony is the one you used: "transcendent". It blew
my mind the first time i heard it, on the Leopold Stokowski
(conducting the American Symphony Orchestra) recording on
vinyl, back at the Manhattan School of Music library.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@...> wrote:
>
> the end of the 4th symphony. It's like a talisman for me in times of
> existential trouble.....really, i think it's one of the most
> transcendent musics i know
>
> --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@> wrote:
> >
> > At 06:29 PM 5/7/2007, you wrote:
> > >that's it really, those two; though the quartertone piano in the 4th
> > >is pretty submerged in the overall texture of the piece. BTW, the
> > >finale in the 4th IS my all-time favorite piece of music!
> >
> > There are four of these? Or are you talking about the 4th
> > symphony?
> >
> > -Carl
> >
>

At 12:51 PM 5/8/2007, you wrote:
>Thanks, Dan and Daniel;\\
>
>Dan, you might try 2 pianos 60 cents apart, as opposed to 50 cents (the
>strict quartertone). In our new recording, Pianist Joshua Pierce, the
>duo of Pierce and Jonas play on pianos 60 cents apart. Both the harmony
>and the melody is improved.

It's closer to 4 secors, for one thing.

-Carl