Topic: Ennealimmal[72] and Hemiennealimmal[72], strictly proper

2 scales

Thread (4 messages)

From: Gene Ward Smith (2007-02-17)
Subject: Ennealimmal[72] and Hemiennealimmal[72], strictly proper

Both of these are strictly proper, but are MOS in only the broad 
sense inclusive of fractional octave periods. I don't know if the 
repetion od the same pattern is bad or good from Ozan's point of 
view. Of course, both are wickedly accurate, and are loaded with 
effectively just 7-limit (ennealimmal) or 11-limit (hemiennealimmal) 
intervals.

Ennealimmal[72] does something which may be very nice for this 
business, which is to alternate just fifths with flat fifths of 694 
cents in the same interval class. From that point of view 
hemiennealimmal is disappointing; it doesn't really have any very 
flat or sharp fifths, and it alternates just fifths with slightly 
flat fifths of 698 cents in an interval class. I would guess 
ennealimmal might do for Ozan, but not hemiennealimmal. Anyway, here 
they both are.

! ennea72.scl
Ennealimmal[72] in 612-et tuning (strictly proper)
72
!
13.725490
35.294118
49.019608
62.745098
84.313725
98.039216
119.607843
133.333333
147.058824
168.627451
182.352941
196.078431
217.647059
231.372549
252.941176
266.666667
280.392157
301.960784
315.686275
329.411765
350.980392
364.705882
386.274510
400.000000
413.725490
435.294118
449.019608
462.745098
484.313725
498.039216
519.607843
533.333333
547.058824
568.627451
582.352941
596.078431
617.647059
631.372549
652.941176
666.666667
680.392157
701.960784
715.686275
729.411765
750.980392
764.705882
786.274510
800.000000
813.725490
835.294118
849.019608
862.745098
884.313725
898.039216
919.607843
933.333333
947.058824
968.627451
982.352941
996.078431
1017.647059
1031.372549
1052.941176
1066.666667
1080.392157
1101.960784
1115.686275
1129.411765
1150.980392
1164.705882
1186.274510
1200.000000


! hemienn82.scl
Hemiennealimmal[72] in 612-et tuning (strictly proper)
72
!
17.647059
31.372549
49.019608
66.666667
84.313725
98.039216
115.686275
133.333333
150.980392
164.705882
182.352941
200.000000
217.647059
231.372549
249.019608
266.666667
284.313725
298.039216
315.686275
333.333333
350.980392
364.705882
382.352941
400.000000
417.647059
431.372549
449.019608
466.666667
484.313725
498.039216
515.686275
533.333333
550.980392
564.705882
582.352941
600.000000
617.647059
631.372549
649.019608
666.666667
684.313725
698.039216
715.686275
733.333333
750.980392
764.705882
782.352941
800.000000
817.647059
831.372549
849.019608
866.666667
884.313725
898.039216
915.686275
933.333333
950.980392
964.705882
982.352941
1000.000000
1017.647059
1031.372549
1049.019608
1066.666667
1084.313725
1098.039216
1115.686275
1133.333333
1150.980392
1164.705882
1182.352941
1200.000000

From: Gene Ward Smith (2007-02-17)
Subject: Ennealimmal well-temperament

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> 
wrote:

> Ennealimmal[72] does something which may be very nice for this 
> business, which is to alternate just fifths with flat fifths of 694 
> cents in the same interval class. 

This produces a completely absurd well-temperament, ennealimmal well-
temperament. I call it absurd because all the major thirds are still 
400 cents exactly, whereas the minor thirds are messed with a bit 
compared to 12-et, but not in a way which makes things any better. It 
may be described as a circle of fifths, consisting of three pure fifths 
followed by one 1/3 of a Pythagorean comma flat.  

However, this business is not altogether idiocy, since this is a way of 
organizing Ennealimmal[72]: six ranks of 12-note scales, spaced 
slightly irregularly and each tuned to ennealimmal well-temperament 
with shifted C.

From: Ozan Yarman (2007-02-17)
Subject: Re: [tuning] Ennealimmal[72] and Hemiennealimmal[72], strictly proper

Why, even 72-equal is less troublesome. These won't do at all.

Oz.


----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 17 \ufffdubat 2007 Cumartesi 10:41
Subject: [tuning] Ennealimmal[72] and Hemiennealimmal[72], strictly proper


> Both of these are strictly proper, but are MOS in only the broad
> sense inclusive of fractional octave periods. I don't know if the
> repetion od the same pattern is bad or good from Ozan's point of
> view. Of course, both are wickedly accurate, and are loaded with
> effectively just 7-limit (ennealimmal) or 11-limit (hemiennealimmal)
> intervals.
>
> Ennealimmal[72] does something which may be very nice for this
> business, which is to alternate just fifths with flat fifths of 694
> cents in the same interval class. From that point of view
> hemiennealimmal is disappointing; it doesn't really have any very
> flat or sharp fifths, and it alternates just fifths with slightly
> flat fifths of 698 cents in an interval class. I would guess
> ennealimmal might do for Ozan, but not hemiennealimmal. Anyway, here
> they both are.
>
> ! ennea72.scl
> Ennealimmal[72] in 612-et tuning (strictly proper)
> 72
> !
> 13.725490
> 35.294118
> 49.019608
> 62.745098
> 84.313725
> 98.039216
> 119.607843
> 133.333333
> 147.058824
> 168.627451
> 182.352941
> 196.078431
> 217.647059
> 231.372549
> 252.941176
> 266.666667
> 280.392157
> 301.960784
> 315.686275
> 329.411765
> 350.980392
> 364.705882
> 386.274510
> 400.000000
> 413.725490
> 435.294118
> 449.019608
> 462.745098
> 484.313725
> 498.039216
> 519.607843
> 533.333333
> 547.058824
> 568.627451
> 582.352941
> 596.078431
> 617.647059
> 631.372549
> 652.941176
> 666.666667
> 680.392157
> 701.960784
> 715.686275
> 729.411765
> 750.980392
> 764.705882
> 786.274510
> 800.000000
> 813.725490
> 835.294118
> 849.019608
> 862.745098
> 884.313725
> 898.039216
> 919.607843
> 933.333333
> 947.058824
> 968.627451
> 982.352941
> 996.078431
> 1017.647059
> 1031.372549
> 1052.941176
> 1066.666667
> 1080.392157
> 1101.960784
> 1115.686275
> 1129.411765
> 1150.980392
> 1164.705882
> 1186.274510
> 1200.000000
>
>
> ! hemienn82.scl
> Hemiennealimmal[72] in 612-et tuning (strictly proper)
> 72
> !
> 17.647059
> 31.372549
> 49.019608
> 66.666667
> 84.313725
> 98.039216
> 115.686275
> 133.333333
> 150.980392
> 164.705882
> 182.352941
> 200.000000
> 217.647059
> 231.372549
> 249.019608
> 266.666667
> 284.313725
> 298.039216
> 315.686275
> 333.333333
> 350.980392
> 364.705882
> 382.352941
> 400.000000
> 417.647059
> 431.372549
> 449.019608
> 466.666667
> 484.313725
> 498.039216
> 515.686275
> 533.333333
> 550.980392
> 564.705882
> 582.352941
> 600.000000
> 617.647059
> 631.372549
> 649.019608
> 666.666667
> 684.313725
> 698.039216
> 715.686275
> 733.333333
> 750.980392
> 764.705882
> 782.352941
> 800.000000
> 817.647059
> 831.372549
> 849.019608
> 866.666667
> 884.313725
> 898.039216
> 915.686275
> 933.333333
> 950.980392
> 964.705882
> 982.352941
> 1000.000000
> 1017.647059
> 1031.372549
> 1049.019608
> 1066.666667
> 1084.313725
> 1098.039216
> 1115.686275
> 1133.333333
> 1150.980392
> 1164.705882
> 1182.352941
> 1200.000000
>
>

From: Gene Ward Smith (2007-02-17)
Subject: Re: Ennealimmal[72] and Hemiennealimmal[72], strictly proper

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Why, even 72-equal is less troublesome. These won't do at all.

It would help me understand what's going on if you'd say why--
especially in terms I can decipher.