Topic: re: Ives' quartertones
1 scales
| File | Description | Notes | Period (¢) |
|---|---|---|---|
| monzo_pyth-quartertone | 24 | 1200.0 |
Thread (9 messages)
From: J.Smith (2007-05-08) Subject: 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".)
From: jim altieri (2007-05-08) Subject: Re: [MMM] re: Ives' quartertones 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
From: monz (2007-05-08) Subject: pythagorean approximation to quartertones (was: Ives' quartertones) Hi Jon and Jim, --- In [email protected], 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
From: Mohajeri Shahin (2007-05-08) Subject: Re:pythagorean approximation to quartertones (was: Ives' quartertones) Hi all Referring to My mail: http://launch.groups.yahoo.com/group/tuning/message/68840 and Monzo : http://launch.groups.yahoo.com/group/tuning/message/68824 Gene : http://launch.groups.yahoo.com/group/tuning/message/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]
From: [email protected] (2007-05-08) Subject: Re: Ives' quartertones 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]
From: monz (2007-05-08) Subject: Re: pythagorean approximation to quartertones (was: Ives' quartertones) --- In [email protected], "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
From: [email protected] (2007-05-08) Subject: Re: Ives' quartertones 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]
From: monz (2007-05-08) Subject: Re: Ives' quartertones 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 [email protected], "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 [email protected], 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 > > >
From: Carl Lumma (2007-05-09) Subject: Re: [MMM] Re: Ives' quartertones 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