Re: A "17-ish" tuning

Hello, there, Jacky Ligon, Pat Pagano, and everyone. In response to
some questions about the layout of the manuals, maybe I might
helpfully provide a keyboard diagram, since Scala files may not always
clarify exact intentions here.

Pat, please let me explain that I'll discuss the Kirnberger connection
in a coming post, but might want first to offer some other clues as to
the concept and structure of this tuning. Maybe it's a bit like Paul
Erlich's "well-temperament" riddle of last summer, but I promise that
I will provide a full explanation within the week (if someone else
doesn't first). For now, let's just say that the Kirnberger allusion has
to do with schismas.

Jacky -- and congratulations on your nonoctave tunings! -- your analysis
of the intervals is fascinating, and reveals at least one property of
which I wasn't aware. Maybe a clearer chart of the manuals might give you
a firmer basis for pursuing your already very perspicacious investigation
further, although I would add that my note names and the like also impose
a certain viewpoint which is not necessarily inherent in the tuning
itself, more in my own overview. A vital feature of tunings is that they
are _not_ restricted to the intentions of the person who first presents
them, or maybe first "rediscovers" them in a given forum, so please take
this diagram with due caution that it is only _one_ view of the tuning
itself.

243:217 17:14 416:279 32:19 736:403
195.91 336.13 691.58 902.49 1042.71
C#*4 Eb*4/D#4 F#*4 G#*4 Bb*4/A#4
_140.9|71.0_69.3|143.2_ _142.4|69.5_141.4|69.5_70.8|142.8_
C*4 D*4 E*4 F*4 G*4 A*4 B*4 C*5
32:31 7:6 368:279 11160261: 26040609: 561:320 119:60 64:31
8126464 16777216
54.96 266.87 479.33 549.21 761.11 971.92 1185.51 1254.96
211.91 212.46 70.88 211.90 210.81 213.59 69.45
------------------------------------------------------------------------
243:224 20:17 13:9 31:19 23:13
140.95 281.36 636.62 847.52 987.75
C#4 Eb4 F#4 G#4 Bb4
_140.9|71.3_69.1|143.0_ _142.4|69.1_141.8|71.1_69.1|141.6_
C4 D4 E4 F4 G4 A4 B4 C5
1:1 26:23 23:18 11160261: 16777216: 17:10 48:25 2:1
8388608 11160261
0 212.25 424.36 494.24 705.76 918.64 1129.33 1200
212.25 212.11 70.88 211.52 212.88 210.69 70.67

Note that in my keyboard scheme for this tuning, the lower manual
takes the even-numbered notes of the Scala output (repeated below),
and the upper manual the odd-numbered notes. Incidentally, in case of
any divergence between the Scala output and the above diagram, I would
say that the Scala output should be taken as correct (proofreading
errors have been known to occur in my keyboard diagrams).

|
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 appreciatively,

Margo Schulter
mschulter@value.net