Topic: Re: A 17-ish tuning
1 scales
| File | Description | Notes | Period (ยข) | Limit |
|---|---|---|---|---|
| ri17isha | Rational intonation (RI) scale with some "17-ish" features (24 notes) | 24 | 1200.0 | 31 |
Thread (3 messages)
From: M. Schulter (2001-03-16) Subject: Re: A 17-ish tuning Hello, there, everyone, and in view of some recent discussions, here is a somewhat "17-ish" scale for people to consider, with special salutations to Robert Walker. There are some ratios of 17, although the definition of "17-ness" may rest largely in the eye of the beholder, or the ears of the listener. This 24-note tuning is designed for two 12-note manuals, with alternating notes placed on the two manuals. I give a Scala file, then Scala's output showing the value of each ratio in cents. There is also a tempered version of this scale which I have devised, and will post after giving people a chance to consider this rational version. Here I might comment that one feature of a tuning proposed by Kirnberger in 1766 plays a role by analogy in this scale, and also that on looking through the Scala archives, I found that Manuel Op de Coul had designed a scale with a certain conceptual affinity on some level which actually shares one ratio in common placed in a corresponding position. My special thanks go also to Jacky Ligon and Dave Keenan, who in sharing their often very different philosophies concerning rational and/or just intonation systems, and providing most illustrative examples, have both played a vital role in this creative process. Here I present first a Scala file of the tuning showing only the integer ratios, and suitable for import into the free Scala program created by Manuel Op de Coul; and then output from Scala showing the value of these ratios in cents. --------------- Scala file starts on next line of text ------------- ! ri17isha.scl ! Rational intonation (RI) scale with some "17-ish" features (24 notes) 24 ! 32/31 243/224 243/217 26/23 7/6 20/17 17/14 23/18 368/279 11160261/8388608 11160261/8126464 13/9 416/279 16777216/11160261 26040609/16777216 31/19 32/19 17/10 561/320 23/13 736/403 48/25 119/60 2/1 ------------- Scala output showing value of ratios in cents ---------- | Rational intonation (RI) scale with some "17-ish" features (24 notes) 0: 1/1 0.000000 unison, perfect prime 1: 32/31 54.96445 Greek enharmonic 1/4-tone 2: 243/224 140.9491 3: 243/217 195.9136 4: 26/23 212.2534 5: 7/6 266.8710 septimal minor third 6: 20/17 281.3584 7: 17/14 336.1296 supraminor third 8: 23/18 424.3645 9: 368/279 479.3289 10: 11160261/8388608 494.2411 11: 11160261/8126464 549.2055 12: 13/9 636.6179 13: 416/279 691.5823 14: 16777216/11160261 705.7594 15: 26040609/16777216 761.1121 16: 31/19 847.5230 17: 32/19 902.4874 19th subharmonic 18: 17/10 918.6421 19: 561/320 971.9151 20: 23/13 987.7471 21: 736/403 1042.711 22: 48/25 1129.328 classic diminished octave 23: 119/60 1185.513 24: 2/1 1200.000 octave Most respectfully, Margo Schulter [email protected]
From: shreeswifty (2001-03-16) Subject: Re: [tuning] Re: A 17-ish tuning Margo can you explain the "manuals" i am not familiar so much with the Kirnberger scale as i have been hard @ work with the Pagano/Beardsley 17 limit scale. can you post a brief history of the scale? Pat Pagano, Director South East Just Intonation Society http://indians.australians.com/meherbaba/ http://www.screwmusicforever.com/SHREESWIFT/ ----- Original Message ----- From: M. Schulter <[email protected]> To: <[email protected]> Sent: Thursday, March 15, 2001 11:49 PM Subject: [tuning] Re: A 17-ish tuning > Hello, there, everyone, and in view of some recent discussions, here > is a somewhat "17-ish" scale for people to consider, with special > salutations to Robert Walker. > > There are some ratios of 17, although the definition of "17-ness" may > rest largely in the eye of the beholder, or the ears of the listener. > > This 24-note tuning is designed for two 12-note manuals, with > alternating notes placed on the two manuals. I give a Scala file, then > Scala's output showing the value of each ratio in cents. > > There is also a tempered version of this scale which I have devised, > and will post after giving people a chance to consider this rational > version. > > Here I might comment that one feature of a tuning proposed by > Kirnberger in 1766 plays a role by analogy in this scale, and also > that on looking through the Scala archives, I found that Manuel Op de > Coul had designed a scale with a certain conceptual affinity on some > level which actually shares one ratio in common placed in a > corresponding position. > > My special thanks go also to Jacky Ligon and Dave Keenan, who in > sharing their often very different philosophies concerning rational > and/or just intonation systems, and providing most illustrative > examples, have both played a vital role in this creative process. > > Here I present first a Scala file of the tuning showing only the > integer ratios, and suitable for import into the free Scala program > created by Manuel Op de Coul; and then output from Scala showing the > value of these ratios in cents. > > > --------------- Scala file starts on next line of text ------------- > > ! ri17isha.scl > ! > Rational intonation (RI) scale with some "17-ish" features (24 notes) > 24 > ! > 32/31 > 243/224 > 243/217 > 26/23 > 7/6 > 20/17 > 17/14 > 23/18 > 368/279 > 11160261/8388608 > 11160261/8126464 > 13/9 > 416/279 > 16777216/11160261 > 26040609/16777216 > 31/19 > 32/19 > 17/10 > 561/320 > 23/13 > 736/403 > 48/25 > 119/60 > 2/1 > > > ------------- Scala output showing value of ratios in cents ---------- > > | > Rational intonation (RI) scale with some "17-ish" features (24 notes) > 0: 1/1 0.000000 unison, perfect prime > 1: 32/31 54.96445 Greek enharmonic 1/4-tone > 2: 243/224 140.9491 > 3: 243/217 195.9136 > 4: 26/23 212.2534 > 5: 7/6 266.8710 septimal minor third > 6: 20/17 281.3584 > 7: 17/14 336.1296 supraminor third > 8: 23/18 424.3645 > 9: 368/279 479.3289 > 10: 11160261/8388608 494.2411 > 11: 11160261/8126464 549.2055 > 12: 13/9 636.6179 > 13: 416/279 691.5823 > 14: 16777216/11160261 705.7594 > 15: 26040609/16777216 761.1121 > 16: 31/19 847.5230 > 17: 32/19 902.4874 19th subharmonic > 18: 17/10 918.6421 > 19: 561/320 971.9151 > 20: 23/13 987.7471 > 21: 736/403 1042.711 > 22: 48/25 1129.328 classic diminished octave > 23: 119/60 1185.513 > 24: 2/1 1200.000 octave > > > Most respectfully, > > Margo Schulter > [email protected] > > > > > > > > You do not need web access to participate. You may subscribe through > email. Send an empty email to one of these addresses: > [email protected] - join the tuning group. > [email protected] - unsubscribe from the tuning group. > [email protected] - put your email message delivery on hold for the tuning group. > [email protected] - change your subscription to daily digest mode. > [email protected] - change your subscription to individual emails. > [email protected] - receive general help information. > > > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ > > >
From: [email protected] (2001-03-16)
Subject: Re: A 17-ish tuning
--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and in view of some recent discussions, here
> is a somewhat "17-ish" scale for people to consider, with special
> salutations to Robert Walker.
>
> There are some ratios of 17, although the definition of "17-ness"
may
> rest largely in the eye of the beholder, or the ears of the
listener.
>
> This 24-note tuning is designed for two 12-note manuals, with
> alternating notes placed on the two manuals. I give a Scala file,
then
> Scala's output showing the value of each ratio in cents.
>
> There is also a tempered version of this scale which I have devised,
> and will post after giving people a chance to consider this rational
> version.
>
> Here I might comment that one feature of a tuning proposed by
> Kirnberger in 1766 plays a role by analogy in this scale, and also
> that on looking through the Scala archives, I found that Manuel Op
de
> Coul had designed a scale with a certain conceptual affinity on some
> level which actually shares one ratio in common placed in a
> corresponding position.
>
> My special thanks go also to Jacky Ligon and Dave Keenan, who in
> sharing their often very different philosophies concerning rational
> and/or just intonation systems, and providing most illustrative
> examples, have both played a vital role in this creative process.
>
> Here I present first a Scala file of the tuning showing only the
> integer ratios, and suitable for import into the free Scala program
> created by Manuel Op de Coul; and then output from Scala showing the
> value of these ratios in cents.
>
Margo,
Hello!
I've did a little deconstruction of your scale to view the inner
symmetries, and it is very compelling to look inside!
Let's look at the rounded cents values for the consecutive intervals:
Degree Ratio Rounded Consecutive
0: 1/1 0
1: 32/31 55
2: 243/224 86
3: 243/217 55
4: 26/23 16
5: 7/6 55
6: 20/17 14
7: 17/14 55
8: 23/18 88
9: 368/279 55
10: 11160261/8388608 15
11: 11160261/8126464 55
12: 13/9 87
13: 416/279 55
14: 16777216/11160261 14
15: 26040609/16777216 55
16: 31/19 86
17: 32/19 55
18: 17/10 16
19: 561/320 53
20: 23/13 16
21: 736/403 55
22: 48/25 87
23: 119/60 56
24: 2/1 14
And by considering the consecutive intervals (a somewhat melodic
consideration for me) we find:
1. Seven @ and average of 15 cents.
2. Twelve @ an average of 55 cents.
3. Five @ an average of 87 cents.
Now, I'm supposing that the odd scale degrees are for the lower
manual, which has the following structure:
Degree Ratio Cents Rounded Consecutive
0: 1/1 0
1: 32/31 54.96445 55
3: 243/217 195.9136 141
5: 7/6 266.871 71
7: 17/14 336.1296 69
9: 368/279 479.3289 143
11: 11160261/8126464 549.2055 70
13: 416/279 691.5823 142
15: 26040609/16777216 761.1121 70
17: 32/19 902.4874 141
19: 561/320 971.9151 69
21: 736/403 1042.711 71
23: 119/60 1185.513 143
24: 2/1 1200 14
And the even degrees giving:
Degree Ratio Cents Rounded Consecutive
1/1 0 0
2: 243/224 140.9491 141
4: 26/23 212.2534 71
6: 20/17 281.3584 69
8: 23/18 424.3645 143
10: 11160261/8388608 494.2411 70
12: 13/9 636.6179 142
14: 16777216/11160261 705.7594 69
16: 31/19 847.523 142
18: 17/10 918.6421 71
20: 23/13 987.7471 69
22: 48/25 1129.328 142
24: 2/1 1200 71
A "near MOS" for this manual.
Looking at the scale broken this way onto the two manuals, reveals
other interesting properties as we can see above:
1. One @ 14 cents.
2. Thirteen @ an average of 70 cents
3. Ten @ an average of 142 cents.
With this exploded view of the consecutive intervals, we can see how
the 15 cents commas, play into the real-time "adaptive" ability of
this scale for two manuals.
32/31 is it's most common interval, and has the remarkable property
of having 29 fifths @ an average of 702.293 - and is a constant
structure (I favor constant structures too).
A lovely structure Margo, and thanks for sharing. Please let us know
when the tempered version is available - I'll be eargerly awaiting
this.
In gratitude,
Jacky Ligon
P.S. Please let me know if I've missed anything special here.
> ------------- Scala output showing value of ratios in cents --------
--
>
> |
> Rational intonation (RI) scale with some "17-ish" features (24
notes)
> 0: 1/1 0.000000 unison, perfect prime
> 1: 32/31 54.96445 Greek enharmonic 1/4-tone
> 2: 243/224 140.9491
> 3: 243/217 195.9136
> 4: 26/23 212.2534
> 5: 7/6 266.8710 septimal minor third
> 6: 20/17 281.3584
> 7: 17/14 336.1296 supraminor third
> 8: 23/18 424.3645
> 9: 368/279 479.3289
> 10: 11160261/8388608 494.2411
> 11: 11160261/8126464 549.2055
> 12: 13/9 636.6179
> 13: 416/279 691.5823
> 14: 16777216/11160261 705.7594
> 15: 26040609/16777216 761.1121
> 16: 31/19 847.5230
> 17: 32/19 902.4874 19th subharmonic
> 18: 17/10 918.6421
> 19: 561/320 971.9151
> 20: 23/13 987.7471
> 21: 736/403 1042.711
> 22: 48/25 1129.328 classic diminished octave
> 23: 119/60 1185.513
> 24: 2/1 1200.000 octave
>
>
> Most respectfully,
>
> Margo Schulter
> mschulter@v...