Yahoo Tuning Groups Ultimate Backup tuning the ultimate proportional beating well-temperament

Carl, thank you for this wondorous solution by Kalle Aho. To tell you
the truth, I have had extreme difficulty in attempting to discern the
differences between Kalle's ultimate and my own ultimate WT. I didn't
notice much (if any) difference between them. A brief evaluation of
the Pros and Cons of these two competitors are as follows:

Kalle's Ultimate Proportional Beating WT
|
PROS

1. Seven limit beat ratios at every tonality; extremely clean-looking.
2. Simple pitch ratios.
3. No harmonic waste; no wider-than-pure fifths.

CONS

1. Too many pure fifths invalidating the proportionality of triadic
beat ratios (at 12 keys).
2. Cannot be tuned by ear, complex beat frequencies.
3. One too narrow fifth that deviates from pure by nearly 7 cents.
4. Not too successful at approximating 5-limit JI at common keys; not
enough key-colour.

______________________________________

And now, Dr. Oz.'s Ultimate Proportional Beating WT
|
PROS

1. Simple integer beat frequencies at concert pitch.
2. Tunable by ear by just counting the beating (once or twice per
sec.) of the fifths from pure.
3. Simple pitch ratios.
4. Successful at completing the circle of fifths with no more than 5 cents maximum absolute deviation.
5. Only 6 keys where the pure fifth spoils the proportionality of
triadic beat ratios.
6. Wide fifths only as wide as 2 cents from pure.
7. Clean approach to simulating 5-limit JI at common keys; good key-
contrast.
8. High prime brats in only 8 keys.

CONS

1. 19-limit brats not so simple; remainder numbers (m3/M3) not
following a clean pattern in 3 keys.
2. Harmonic waste, however small.
3. Two common keys where 6:5 and 5:4 yield about a Pythagorean comma
error.

So, what say?
Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 11, 2010, at 8:15 PM, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> Inspired by George Secor's pursuit for synchronous beating 12-tone
>> Temperaments, here is my "Ultimate Well-Temperament" that is
>> synchronous in all major and minor triads:
>>
>> 12-tone Ultimate Well Temperament by Oz.
>> |
>> 1/1
>> 277/262
>> 147/131
>> 156/131
>> 329/262
>> 175/131
>> 185/131
>> 196/131
>> 208/131
>> 220/131
>> 234/131
>> 247/131
>> 2/1
>
> A subset of the 262nd mode of the harmonic series.
> Because some 5ths are larger than pure, this has
> "harmonic waste".
>
> Kalle Aho showed it's possible to find a similar
> temperament in the 155th mode of the harmonic series,
> with no harmonic waste. See what you think:
>
> !
> Kalle Aho's 12-tone rational well temperament.
> 12
> !
> 164/155 !..164
> 174/155 !..174
> 184/155 !..184
> 39/31 !..195
> 207/155 !..207
> 219/155 !..219
> 232/155 !..232
> 246/155 !..246
> 52/31 !..260
> 276/155 !..276
> 292/155 !..292
> 2/1 !..310
> !
>
> -Carl
>
>

🔗Carl Lumma <carl@...>

🔗Ozan Yarman <ozanyarman@...>

🔗Carl Lumma <carl@...>

🔗Ozan Yarman <ozanyarman@...>

🔗genewardsmith <genewardsmith@...>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> |
> 1/1
> 277/262
> 147/131
> 156/131
> 329/262
> 175/131
> 185/131
> 196/131
> 208/131
> 220/131
> 234/131
> 247/131
> 2/1
>
Hi Oz,
that old idea agrees almost with Werckmeister's 'septenarian'
string-lenghts in reverse order:
http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings
"
C 196 1/1 0
Câ¯ 186 98/93 91
D 176(175) 49/44(28/25) 186(196)
Dâ¯ 165 196/165 298
E 156 49/39 395
F 147 4/3 498
Fâ¯ 139 196/139 595
G 131 196/131 698
Gâ¯ 124 49/31 793
A 117 196/117 893
Bâ 110 98/55 1000
B 104 49/26 1097

simply read here the stringlengths upwards
as absolute-pitch-frequncies from the bottom to the top,
as already Johann Heinrich Scheibler [~1820] did,
when he defined A4:=440Hz in reference to Werckmeister.
See also my earlier corresponding meassage:

/tuning/topicId_69724.html#71269

My actual refiend version was dicussed
recently in the clavichord yahoo-group, please see and confirm:

/clavichord/topicId_unknown.html#9914

!SpEqBeat440Hz
Sparschuh's Equal-Beating @ A4=440Hz
!
! 1/1 ! C_1 32.8 Hz 'contra-octve' Pedal-C1
173/164 ! C#1 32.8
46/41 ! D_1 34.6
389/328 ! Eb1 38.9
411/323 ! E_1 44.1
219/164 ! F_1 43.8
231/164 ! F#1 46.2
3/2 ! G_1 49.2
519/328 ! G#1 51.9
275/164 ! A_1 55
73/41 ! Bb1 58.4
77/41 ! B_0 61.6
2/1
!
![eof]

[In order to read here the intended spaceings properly without]
[the defacement by yahoo, please click and view under the option]
[{'Show-Meassage-Info'} then on the button for
{"Use-Fixed-Width-Font"}]

here comes a precise determination of what could mean
Martin's "~(6-7)" beats per second more precisely.
Consider the sequential circle
of a dozen 5ths in Werckmeister's 'equal-beating' manner,
when refined by one decimal-place
more resolution than in W's original 'spetenarian'-scheme,
that todays mathematicans call as an:
http://en.wikipedia.org/wiki/Collatz_sequence

Note-names: below A0 : in first-piano-octave : above or equal A1=55Hz
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A:(13.7E0_/3 27.4E1_/3 <) 27.5A_0 55A1 110A2 220A3 440Hz := A4
E: 41.1E_1 := 3*13.7
B: 7.7B-2 15.4B-1 30.8B_0 61.6B0 123.2B1 (<123.3:=E1*3)
F#: 3*B-2 =: 23.1F#0 46.2F#1 := 3*B-1
C#: 17.3C#0 34.6C#1 69.2C#2 ( <69.3:= 23.1F#0 * 3)
G#: 51.9G#1 := 3*C#0
D#: 38.9D#1 79.8D#2 155.6D#3(<155.7=3*G#1)
Bb: 7.3Bb-2 14.6Bb-1 29.2Bb0 58.4Bb1 166.8Bb2(>166.7=3*D#1)
F: 3*Bb-2 =: 21.9F0 43.8F_1 := 3*Bb-1
C: 4.1C-2 8.2C-1 16.4C0 32.8C_0 65.6C1 ( < 65.7 := 3*21.9F0 )
G: 3*C-2:= 12.3G-1 24.6G0 49.2G_1 := 3*C0
D:2.3Hz 4.6 9.2D-1 18.4D0 36.8D_1 ( < 36.9 := 3*12.3G-1) [M]=138
A: 27.5A_0 ( < 27.6 := 3*9.2D-1 )

that "Collatz-Sequence" procedere yields as beating-plan for the 3rds
in units of Hertzians and beats-per-minute=[bpm] on the Metronome [M]

lowest piano octave..3rds beatings from 220A3 to 440A4 in Hz and bpm's
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
27.5 A_0 .. A_3 220.0 [*5/4 =: c#4 275 <] 276.8 C#4 @ 1.8Hz M 108bpm
29.2 Bb0 .. Bb3 233.6 [*5/4 =: d_4 292 <] 294.4 D_4 @ 2.4Hz M 144bpm
30.8 B_0 .. B_3 246.4 [*5/4 =: d#4 308 <] 311.2 D#4 @ 3.2Hz M 192bpm
32.8 C_1 .. C_4 262.4 [*5/4 =: e_4 328 <] 328.8 E_4 @ 0.8Hz M _48bpm
34.6 C#1 .. C#4 276.8 [*5/4 =: f_4 346 <] 350.4 F_4 @ 4.4Hz M 264bpm
36.8 D_1 .. D_4 294.4 [*5/4 =: f#4 368 <] 374.3 F#4 @ 6.3Hz M 378bpm
38.9 D#1 .. D#4 311.2 [*5/4 =: g_4 389 <] 393.6 G_4 @ 4.6Hz M 276bpm
41.1 E_1 .. E_4 328.8 [*5/4 =: g#4 411 <] 415.2 G#4 @ 4.2Hz M 252bpm
43.8 F_1 .. F_4 350.4 [*5/4 =: a_4 438 <] 440.0 A_4 @ 2.0Hz M 120bpm
46.2 F#1 .. F#4 374.3 [*5/4 =: bb4 462 <] 467.2 Bb4 @ 5.2Hz M 312bpm
49.2 G_1 .. G_4 393.6 [*5/4 =: b_4 492 <] 492.8 B_4 @ 0.8Hz M _48bpm
51.9 G#1 .. G#4 415.2 [*5/4 =: c_5 519 <] 524.8 C_5 @ 5.8Hz M 348bpm
55.0 A_1 .. A_4 440.0 [*5/4 =: c#5 550 <] 553.6 C#5 @ 3.6Hz M 216bpm

Simply try out to apply that absolute-pitchs on yours own keyboard-instrument.
So, you can judge yourself how well such synchrone-beats
can really sound in the sense of A.Werckmeister's "equal-beating" concept.

That beatings turn out to be much simpler even than "ultimate" ;-)

bye
A.S.

🔗a_sparschuh <a_sparschuh@...>

🔗Michael <djtrancendance@...>

🔗Ozan Yarman <ozanyarman@...>

Dear Andreas,

A pitch by pitch comparison between Werckmeister's Septenarius
according to Tom Dent (2006) and my UWT is below:

1: 1: 25676/25761 -5.721757 0.9127 Hertz, 54.7603
cycles/min.
2: 2: 524/525 -3.300733 0.5592 Hertz, 33.5520
cycles/min.
3: 3: 6419/6435 -4.309904 0.7746 Hertz, 46.4789
cycles/min.
4: 4: 1834/1833 0.944223 0.1792 Hertz, 10.7538
cycles/min.
5: 5: 524/525 -3.300733 0.6657 Hertz, 39.9428
cycles/min.
6: 6: 25676/25715 -2.627625 0.5603 Hertz, 33.6209
cycles/min.
7: 7: 1/1 0.000000 0.0000 Hertz, 0.0000
cycles/min.
8: 8: 6419/6448 -7.803819 1.8683 Hertz, 112.0976
cycles/min.
9: 9: 6419/6435 -4.309904 1.0925 Hertz, 65.5472
cycles/min.
10: 10: 6419/6435 -4.309904 1.1620 Hertz, 69.7184
cycles/min.
11: 11: 6419/6422 -0.808924 0.2304 Hertz, 13.8264
cycles/min.
12: 12: 1/1 0.000000 0.0000 Hertz, 0.0000
cycles/min.
Mode: 1 1 1 1 1 1 1 1 1 1 1 1 Twelve-tone Chromatic
Total absolute difference : 37.4375 cents
Average absolute difference: 3.1198 cents
Root mean square difference: 3.8687 cents
Highest absolute difference: 7.8038 cents
Number of notes different: 10

You see, there is one instance of 8 cents maximum deviation and
another of 6 cents deviation. They resemble each other, but are not
that much alike.

As for your equal beating tuning, you should make the correction for
411/328 (you misspelled 328 as 323). Otherwise, it looks very neat!
But still not feasible to tune by ear compared to my UWT. Besides,
there are two brats which are 29-limit and there are two fifths
deviating from pure by more than 6 cents. However, I tried this in
Logic Pro 8 using a evp88 Suitcase MkI with tremolos nullified, and I
attest to its success and beauty in common keys. It truly sings!

Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 12, 2010, at 8:03 PM, a_sparschuh wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> |
>> 1/1
>> 277/262
>> 147/131
>> 156/131
>> 329/262
>> 175/131
>> 185/131
>> 196/131
>> 208/131
>> 220/131
>> 234/131
>> 247/131
>> 2/1
>>
> Hi Oz,
> that old idea agrees almost with Werckmeister's 'septenarian'
> string-lenghts in reverse order:
> http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29
> :_the_Septenarius_tunings
> "
> C 196 1/1 0
> Câ™¯ 186 98/93 91
> D 176(175) 49/44(28/25) 186(196)
> Dâ™¯ 165 196/165 298
> E 156 49/39 395
> F 147 4/3 498
> Fâ™¯ 139 196/139 595
> G 131 196/131 698
> Gâ™¯ 124 49/31 793
> A 117 196/117 893
> Bâ™ 110 98/55 1000
> B 104 49/26 1097
>
>
> simply read here the stringlengths upwards
> as absolute-pitch-frequncies from the bottom to the top,
> as already Johann Heinrich Scheibler [~1820] did,
> when he defined A4:=440Hz in reference to Werckmeister.
> See also my earlier corresponding meassage:
>
> /tuning/topicId_69724.html#71269
>
> My actual refiend version was dicussed
> recently in the clavichord yahoo-group, please see and confirm:
>
> /clavichord/topicId_unknown.html#9914
>
> !SpEqBeat440Hz
> Sparschuh's Equal-Beating @ A4=440Hz
> !
> ! 1/1 ! C_1 32.8 Hz 'contra-octve' Pedal-C1
> 173/164 ! C#1 32.8
> 46/41 ! D_1 34.6
> 389/328 ! Eb1 38.9
> 411/323 ! E_1 44.1
> 219/164 ! F_1 43.8
> 231/164 ! F#1 46.2
> 3/2 ! G_1 49.2
> 519/328 ! G#1 51.9
> 275/164 ! A_1 55
> 73/41 ! Bb1 58.4
> 77/41 ! B_0 61.6
> 2/1
> !
> ![eof]
>
>
> [In order to read here the intended spaceings properly without]
> [the defacement by yahoo, please click and view under the option]
> [{'Show-Meassage-Info'} then on the button for
> {"Use-Fixed-Width-Font"}]
>
> here comes a precise determination of what could mean
> Martin's "~(6-7)" beats per second more precisely.
> Consider the sequential circle
> of a dozen 5ths in Werckmeister's 'equal-beating' manner,
> when refined by one decimal-place
> more resolution than in W's original 'spetenarian'-scheme,
> that todays mathematicans call as an:
> http://en.wikipedia.org/wiki/Collatz_sequence
>
> Note-names: below A0 : in first-piano-octave : above or equal A1=55Hz
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> A:(13.7E0_/3 27.4E1_/3 <) 27.5A_0 55A1 110A2 220A3 440Hz := A4
> E: 41.1E_1 := 3*13.7
> B: 7.7B-2 15.4B-1 30.8B_0 61.6B0 123.2B1 (<123.3:=E1*3)
> F#: 3*B-2 =: 23.1F#0 46.2F#1 := 3*B-1
> C#: 17.3C#0 34.6C#1 69.2C#2 ( <69.3:= 23.1F#0 * 3)
> G#: 51.9G#1 := 3*C#0
> D#: 38.9D#1 79.8D#2 155.6D#3(<155.7=3*G#1)
> Bb: 7.3Bb-2 14.6Bb-1 29.2Bb0 58.4Bb1 166.8Bb2(>166.7=3*D#1)
> F: 3*Bb-2 =: 21.9F0 43.8F_1 := 3*Bb-1
> C: 4.1C-2 8.2C-1 16.4C0 32.8C_0 65.6C1 ( < 65.7 := 3*21.9F0 )
> G: 3*C-2:= 12.3G-1 24.6G0 49.2G_1 := 3*C0
> D:2.3Hz 4.6 9.2D-1 18.4D0 36.8D_1 ( < 36.9 := 3*12.3G-1) [M]=138
> A: 27.5A_0 ( < 27.6 := 3*9.2D-1 )
>
> that "Collatz-Sequence" procedere yields as beating-plan for the 3rds
> in units of Hertzians and beats-per-minute=[bpm] on the Metronome [M]
>
> lowest piano octave..3rds beatings from 220A3 to 440A4 in Hz and bpm's
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 27.5 A_0 .. A_3 220.0 [*5/4 =: c#4 275 <] 276.8 C#4 @ 1.8Hz M 108bpm
> 29.2 Bb0 .. Bb3 233.6 [*5/4 =: d_4 292 <] 294.4 D_4 @ 2.4Hz M 144bpm
> 30.8 B_0 .. B_3 246.4 [*5/4 =: d#4 308 <] 311.2 D#4 @ 3.2Hz M 192bpm
> 32.8 C_1 .. C_4 262.4 [*5/4 =: e_4 328 <] 328.8 E_4 @ 0.8Hz M _48bpm
> 34.6 C#1 .. C#4 276.8 [*5/4 =: f_4 346 <] 350.4 F_4 @ 4.4Hz M 264bpm
> 36.8 D_1 .. D_4 294.4 [*5/4 =: f#4 368 <] 374.3 F#4 @ 6.3Hz M 378bpm
> 38.9 D#1 .. D#4 311.2 [*5/4 =: g_4 389 <] 393.6 G_4 @ 4.6Hz M 276bpm
> 41.1 E_1 .. E_4 328.8 [*5/4 =: g#4 411 <] 415.2 G#4 @ 4.2Hz M 252bpm
> 43.8 F_1 .. F_4 350.4 [*5/4 =: a_4 438 <] 440.0 A_4 @ 2.0Hz M 120bpm
> 46.2 F#1 .. F#4 374.3 [*5/4 =: bb4 462 <] 467.2 Bb4 @ 5.2Hz M 312bpm
> 49.2 G_1 .. G_4 393.6 [*5/4 =: b_4 492 <] 492.8 B_4 @ 0.8Hz M _48bpm
> 51.9 G#1 .. G#4 415.2 [*5/4 =: c_5 519 <] 524.8 C_5 @ 5.8Hz M 348bpm
> 55.0 A_1 .. A_4 440.0 [*5/4 =: c#5 550 <] 553.6 C#5 @ 3.6Hz M 216bpm
>
> Simply try out to apply that absolute-pitchs on yours own keyboard-
> instrument.
> So, you can judge yourself how well such synchrone-beats
> can really sound in the sense of A.Werckmeister's "equal-beating"
> concept.
>
> That beatings turn out to be much simpler even than "ultimate" ;-)
>
> bye
> A.S.
>
>

🔗Ozan Yarman <ozanyarman@...>

Dear Andreas,

Please trust my word when I say that I did not know of your usage of
the 524th harmonic series utilizing many ratios with a common 131
denominator similar to my UWT. I swear by Allah that I had as basis tomy proposal not your version of Werckmeister's Septenarius dated April
2007, but a curious 12-tone scale I saved in my personal archive of
Scala tunings dated 2/28/2009 during my tabula rasa trials. Hence, I
arrived at a very similar solution through an altogether different path.

I underline this information to clear any doubts that might lead to
thoughts of plagiarism.

Having settled that issue, let me say that your approach involving 13-
limit brats and no harmonic waste, which can be tuned by ear via
simply listening to the beats per sec. of fifths from pure is a
fabulous solution! But then, there is the issue of closer proximity to
12-equal and loss of key-contrast.

A simple comparison between our versions involving ratios with 131 as
denominator shows that we have chosen a different ratio for E and C# -
with the result that your pitches are 5 and 3 cents higher
respectively. Thus, yours might not be the practical WT approach for better approximation of regular 5-limit harmony at some tonalities.

I shall labour further to reduce the brats to 7-limit, making sure to
credit your pioneering approach.

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 12, 2010, at 10:48 PM, a_sparschuh wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> 12-tone Ultimate Well Temperament by Oz.
>> |
>> 1/1
>> 277/262
>> 147/131
>> 156/131
>> 329/262
>> 175/131
>> 185/131
>> 196/131
>> 208/131
>> 220/131
>> 234/131
>> 247/131
>> 2/1
> Congratulation Oz, see from "Tue Apr 17, 2007 8:49 pm" in:
> /tuning/topicId_69724.html#71269
> there:
> !septenarius_GG49Hz.scl
> sparschuh's version @ middle-c'=262Hz or a'=440Hz
> 12
> !absolute pitches relativ to c=131 Hz
> 555/524 ! c# 138.75 Hz
> 147/131 ! d
> 156/131 ! eb
> 165/131 ! e
> 175/131 ! f
> 185/131 ! f#
> 196/131 ! g
> 208/131 ! g#
> 220/131 ! a 440Hz/2
> 234/131 ! bb
> 247/131 ! b
> 2/1
>
> that they nearly contain almost the same ratios ;-)
>
> bye
> A.S.
>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:

>... the 524th harmonic series utilizing many ratios
>... with a common 131 denominator similar to my UWT....

Dear Oz,
it is always again amazing how completely different
ansatzes do lead later to similar solutions.
Hence, please understand my "congratulation" exclusively
as an sober-minded compliment.

> Having settled that issue,
> let me say that your approach involving 13-
> limit brats and no harmonic waste, which can be tuned by ear via
> simply listening to the beats per sec. of fifths from pure is a
> fabulous solution!
You are in deed the first person,
who reckognized that hidden integral-feature,
how it works.

> But then, there is the issue of closer proximity to
> 12-equal and loss of key-contrast.
I.m.h.o:
There will never be any well compomise,
within the restriction of barely 12 different pitches per octave.

> A simple comparison between our versions
> involving ratios with 131
> as denominator shows that we have chosen a different ratio
> for E > and C# -
> with the result that your pitches are 5 and 3 cents higher
> respectively.

Would you agree:
Whatever you try to do within 12-tones when subdividing the PC
into however sized subparts, there will always appear some
drawbacks within the 'key-characteristics',
especially in the remote keys among the accidential-notes.

Hence I do agree with Issac Newton,
that it is about time for a change from 12 towards 53:
http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif

as you can also study im my many other contributions to that group.

> Thus, yours might not be the practical WT approach for
> better approximation of regular 5-limit harmony at some tonalities.
> I shall labour further to reduce the brats to 7-limit,

For seven-limit I use mostly 171 tones per octave.

>making sure to credit your pioneering approach.
That's also valid for yours really remarkable results.

Yours Sincerely
A.S.

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
> A pitch by pitch comparison between Werckmeister's Septenarius
> according to Tom Dent (2006) and my UWT is below:
>
> 1: 1: 25676/25761 -5.721757 0.9127 Hertz, 54.7603
> cycles/min.
> 2: 2: 524/525 -3.300733 0.5592 Hertz, 33.5520
> cycles/min.
> 3: 3: 6419/6435 -4.309904 0.7746 Hertz, 46.4789
> cycles/min.
> 4: 4: 1834/1833 0.944223 0.1792 Hertz, 10.7538
> cycles/min.
> 5: 5: 524/525 -3.300733 0.6657 Hertz, 39.9428
> cycles/min.
> 6: 6: 25676/25715 -2.627625 0.5603 Hertz, 33.6209
> cycles/min.
> 7: 7: 1/1 0.000000 0.0000 Hertz, 0.0000
> cycles/min.
> 8: 8: 6419/6448 -7.803819 1.8683 Hertz, 112.0976
> cycles/min.
> 9: 9: 6419/6435 -4.309904 1.0925 Hertz, 65.5472
> cycles/min.
> 10: 10: 6419/6435 -4.309904 1.1620 Hertz, 69.7184
> cycles/min.
> 11: 11: 6419/6422 -0.808924 0.2304 Hertz, 13.8264
> cycles/min.
> 12: 12: 1/1 0.000000 0.0000 Hertz, 0.0000

Dear Oz,
by mischange unfortunatley that's not Werckmeister's intened original scheme of his "Musikalische-Temperatur,Quedlinburg [1691]

For Werckmeisters s primordial numbers see:
http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings
or my own:
/tuning/topicId_77364.html#77872
there:

! septenarius.scl
! Werckmeister's #6 in string-lenghts on the monochord
!
C196 C#186 D176 D#165 E156 F147 F#139 G131 G#124 A117 B110 H104...
!
12
!
98/93 ! := 196/186 = C/C#
196/176 ! = C/D
196/165 ! = C/D#
49/39 ! := 196/156 = C/E = (5/4)*(196/195)
4/3 ! := 196/147 = C/F
196/139 ! = C/F#
196/131 ! = C/G = (3/2)*(392/393)
49/31 ! :=196/124 = C/G#
196/117 ! = C/A
98/55 ! =196/110 = C/B
49/26 ! =196/104 = C/H
2/1
!
!(eof]

Here please attend, in order to pervent interlanguage confusion,
that the German note-name called "H" means in English "B" and
the German "B" corresponds zo "Bb"
in the Anglo-Saxon nomenclauture of labeling pitches respectively.

Again consider W's aboriginal calculation,
in terms of an dozen consecutive 4ths
as an "Collatz-Sequence":

C: 49 := 7*7 98 C=196
F: F=147 := C*3
B:(German) 55 B=110 220 440 (<441:=F*3) English: "Bb"
Eb: Eb=165 := B*3
G#: 31 62 G#=124 := Eb*3
C#: 93 C#=186 := G#*3
F#: F#=139 278 (<279 := C#*3)
H: 13 26 52 H=104 208 416 (< 417 := F#*3) Engl.:"B"
E: 39 78 E=156 := H*3
A: A=117 := E*3
D: 11 22 44 88 D=176 352(> 351 := A*3) or ???"175"???
G: G=131 (132 := D44 * 3)
C: C=196 392 (< 393 := G*3)

Everything else than that ratios are later modifications.

Hope that age-old -but-still-relevant- folk stuff,
helps in order to clarify, from where Johann Heinrich Scheibler overtook his innovative 440Hz creation for the C-major scale:

1 : 9/8 : 5/4 : 4/3 : 3/2 : 5/3 : 15/8 : 2/1

when concret realized in absolute-pitch, by his classical defintion:

264C4 : 297D4 : 330E4 : 352F4 : 392G4 : 440A4 : 495B4 : 528C5

later he changed from that to:
http://www.mmdigest.com/Tech/jorgensen.html
"133. Tuning equal temperament by using Johann Heinrich Scheibler's metronome method of [1836] introduced to the British before 1853 133. Tuning equal temperament by using Johann Heinrich Scheibler's metronome method of [1836] introduced to the British before 1853...
"

So far my little report on the historical priority,
about the two real originator fahters,
to clear the quest about the priority:
Where did the modern A4=440Hz pitch-convention came from?
presumably "ultimate" for all times maybe,
but valid at least for another while....

References:
http://en.wikipedia.org/wiki/A440
http://en.wikipedia.org/wiki/History_of_pitch_standards_in_Western_music

Official authoritative paper:
http://www.iso.org/iso/catalogue_detail.htm?csnumber=3601
"
Abstract:
Specifies the frequency for the note A in the treble stave and shall be 440 Hz. Tuning and retuning shall be effected by instruments producing it within an accuracy of 0,5 Hz.
"

🔗George Sanders <georgesanders11111@...>

Michael,

why are you searching for originality on this list? If some tuning idea has already been tried, that's a fact you wish away or declare null and void.

Now one can throw up one's hands and declare that originality doesn't exist, as Mr. Sparshuh apparently does, but that is making the opposite mistake. One could define "originality" as having absolutely no precedents in whole or part, in which case it is obvious that nothing is original. But this manoeuvre--commonly used by postmodernists--is conceptually vacuous because it is based on a false definition (in fact, a form of vicious circle).

"Original" originally meant the source or cause from which something arises, as in a document from which copies are made, or the birth of an idea or an artistic movement (also, a person of great invention or, formerly, a unique [read: eccentric] person). None of these standard definitions requires that an "original" have absolutely no precedents.

It seems that the main purpose of this list is to share information about tunings. Following the standard definition, you can't force your ideas to be original, or force others to accept them as original. However, it seems that your main focus is really one reaching a mass audience with your microtonal music. If you can achieve this, more power to you--if your music comes to serve as a model and creates an new artistic movement, your achievement will be original. It seems that you really should be directing most of your efforts to this end.

best

Franklin

--- On Fri, 5/14/10, a_sparschuh <a_sparschuh@...> wrote:

From: a_sparschuh <a_sparschuh@...>
Subject: [tuning] Re: the ultimate proportional beating well-temperament
To: tuning@yahoogroups.com
Date: Friday, May 14, 2010, 10:58 AM

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> The quest for originality on this list is futile,...

Fully agreed.

> ... anything you can say will be references to some bizarre....

Just yesterday a highly-decorated big-headed academy-member

explained me with arrogance: Everyting that would deviate from 12-EDO as generally "bizarre" and hence by the way, when argueing so,

as well all other subcribers of that list to have the same "strange" status to his mind...&ct...pp...

> .... (and often ancient)...

In the most cases.

>...micro-tonal theory you didn't know about.

That's why I'm here.

bye

A.S.

🔗George Sanders <georgesanders11111@...>

🔗Michael <djtrancendance@...>

Geroge>"why are you searching for originality on this list? If some tuning
idea has already been tried, that's a fact you wish away or declare
null and void. "

Examples? I beg to differ. For example right after when I ran into Ptolemy's Homalon scale I asked Jacques directly if my ratios matched an existing scale and he found that match. And, of course, I never claimed that one scale I ran into was original by me since.
When I created my 7-tone or so PHI Sections scale generated by (1/PHI)^x + 1 there was no scale it fell under but a PHI tuning well over 20 tones...equating those would be like saying the diatonic scale and 12TET are the same because one fits within the other (IE not very reasonable). Same situation though...after I made the scale I asked people if they knew an exact copy immediately...but no one did, they only knew much larger tunings generated by completely different methods which just happened to A) use PHI B) include my scale among tons of other notes (some of them even included infinite numbers of notes generating a huge loop).

>"It seems that the main purpose of this list is to share information about tunings."
Right, so where's the part where you supposedly can't
A) Share your own tuning
B) Check it with experts on this list against existing material
C) Regardless of whether it does/doesn't exist, share more about it...for example even though I ran into Ptolemy's tuning system I explained "what I like about Ptolemy's tuning system which made me run into it".

You know I actually at one point suggested this group be split into a historical and modern/"about new scales or at least trying to find new scales" group. The main reason I even bothered was because of the amount of anger and at times ignorance.
Toward not just myself, but also people like Jacques, Jacky Ligon, or just about anyone interested in either new tunings OR existing tunings focusing on new theories such as difference tones (Jacques) or mirroring (Cameron). Even in which case they ALSO discovered something truly new I often saw people smack down their ideas as "historical" even before they bothered to try and prove it. And I REALLY REALLY don't see how that sort of closed mind-ness could help the tuning world grow...

>"Following the standard definition, you can't force your ideas to be original, or force others to accept them as original."
The idea is not to say "haha, I'm the first, now give me power", but rather to indicate "maybe others should help study these relationships in my tuning and improve upon them, turning them into something new and great that appeals somewhat across the board".

>"However, it seems that your main focus is really one reaching a mass
audience with your micro-tonal music."
Right, and I think a huge part of this is offering something both audibly different than 12TET and with a similar or better balance toward consonance. I figure I certain need to convince people it's a somewhat revolutionary change, and not just a "historic optimization", before they are willing to buy new instruments to play micro-tonal music. Someone, say, would doubtfully buy a 19-tone guitar just to play 12TET intervals with a "few new chords".

>"If you can achieve this, more
power to you--if your music comes to serve as a model and creates an
new artistic movement, your achievement will be original. It seems
that you really should be directing most of your efforts to this end."

Already am. Have one release for the Split Notes micro-tonal music net-label down and another one coming. It's called "Smack My Pitch Up" (Cameron's name idea) and you're sure to hear about it in the near future.

Realize it's a tough struggle: Jacky Ligon (a fantastic musician) who also made original/new scales and culminated his efforts in incredibly good original/new sounding music apparently gave up forums and albums supposedly due to their blatant ignorance toward completely new tunings (good job guys?!). :-(
Meanwhile I don't just sit around and say my scales are "done", I constantly tweak them, measure them with various psycho-acoustic and mathematical/computer-program tests to optimize them. This is why only now I'm concentrating on music...because now I know my main tuning theory called "Infinity" finally has all notes within 10 cents of forming their ideal intervals with all other notes in the scale. And, I've learned through testing in composition...it finally for the most part nails the definition of "an incredibly easy to play 7-tone-or-more scale where it's impossible to hit a sour chord no matter how large or small".

Now both of Jacky Ligon and our *should be censored?* :-D original scales are on the album...and I'm confident you'll be pleasantly surprised by the odd combination of extra tonal flexibility and 12TET-or-better consonance (goals aimed toward public acceptance) achieved with both. :-)

Let's check back in on this after you hear the album. Then we'll re-convene about whether this quest for original scales and their role in popularizing micro-tonal music is such a bad idea. :-)

-Michael

🔗George Sanders <georgesanders11111@...>

Michael,
I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up. What I object to is your thin-skinned approach to criticism. Criticism is not necessarily an attack, and it is definitely not censorship. The people who criticize you turn into "big-headed academics" or "closed-minded" or worse. When you insult other people, how can you object to whatever comes back at you?
If you look carefully at everything I've written to you, you'll see that I am criticizing incorrect statements that you have made, or suggesting that you spend less time arguing and more time writing the music you want to write. That is not an attack. Franklin

--- On Sat, 5/15/10, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@yahoo.com>
Subject: Re: [tuning] Re: the ultimate proportional beating well-temperament
To: tuning@yahoogroups.com
Date: Saturday, May 15, 2010, 3:26 PM

Geroge>"why are you searching for originality on this list? If some tuning
idea has already been tried, that's a fact you wish away or declare
null and void. "

Examples? I beg to differ. For example right after when I ran into Ptolemy's Homalon scale I asked Jacques directly if my ratios matched an existing scale and he found that match. And, of course, I never claimed that one scale I ran into was original by me since.
When I created my 7-tone or so PHI Sections scale generated by (1/PHI)^x + 1 there was no scale it fell under but a PHI tuning well over 20 tones...equating those would be like saying the diatonic scale and 12TET are the same because one fits within the other (IE not very reasonable). Same situation though...after I made the scale I asked people if they knew an exact copy immediately. ..but no one did, they only knew much larger tunings generated by completely different methods which just happened to A) use PHI B) include my scale among tons of other notes (some of them even included infinite numbers of notes
generating a huge loop).

You know I actually at one point suggested this group be split into a historical and modern/"about new scales or at least trying to find new scales" group. The main reason I even bothered was because of the amount of anger and at times ignorance.
Toward not just myself, but also people like Jacques, Jacky Ligon, or just about anyone interested in either new tunings OR existing tunings focusing on new theories such as
difference tones (Jacques) or mirroring (Cameron). Even in which case they ALSO discovered something truly new I often saw people smack down their ideas as "historical" even before they bothered to try and prove it. And I REALLY REALLY don't see how that sort of closed mind-ness could help the tuning world grow...

>"However, it seems that your main focus is really one reaching a mass
audience with your micro-tonal music."
Right, and I think a huge part of this is offering something both audibly different than 12TET and with a similar or better balance toward consonance. I figure I certain need to convince people it's a somewhat revolutionary change, and not just a "historic optimization" , before they are willing to buy new instruments to play micro-tonal music. Someone, say, would doubtfully buy a 19-tone guitar just to play 12TET intervals with a "few new chords".

Realize it's a tough struggle: Jacky Ligon (a fantastic musician) who also made original/new scales and culminated his efforts in incredibly good original/new sounding music apparently gave up forums and albums supposedly due to their blatant ignorance toward completely new tunings (good job guys?!). :-(
Meanwhile I don't just sit around and say my scales are "done", I constantly tweak them, measure them with various psycho-acoustic and mathematical/ computer- program tests to optimize them. This is why only now I'm concentrating on music...because now I know my main tuning
theory called "Infinity" finally has all notes within 10 cents of forming their ideal intervals with all other notes in the scale. And, I've learned through testing in composition. ..it finally for the most part nails the definition of "an incredibly easy to play 7-tone-or-more scale where it's impossible to hit a sour chord no matter how large or small".

Let's check back in on this after you hear the album. Then we'll re-convene about whether this quest for original scales and their role in popularizing micro-tonal music is such a bad idea. :-)

-Michael

🔗Michael <djtrancendance@...>

>"I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up."
But you see, there is no conflict of terms here that would indicate direct hypocrisy. The two go together...most of the attack I've seen on here, not just toward myself but others, that annoy me involve censorship. Many of them follow the lines of "the rules are already there, now learn and follow them" whenever something new comes up.
I don't see why I'm a hypocrit for "attacking/censoring censorship"...I don't consider myself at all personally attacked but, rather, am annoyed by the concept of music (in micro-tonal form) boiling down to who is more proper than who, who's written more papers, etc. ...reserving the right to call shots in theories EVEN that they don't know about. Specifically new ones that they almost impulsively label according to old ones. The nasty response to Jacky's 12/11 9/8 12/11 tuning being slapped the label "Mojira" (sp?) on being yet another classic example of this problem.

________________________________
From: George Sanders <georgesanders11111@...>
To: tuning@yahoogroups.com
Sent: Sat, May 15, 2010 11:03:44 AM
Subject: Re: [tuning] Re: the ultimate proportional beating well-temperament

Michael,

I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up. What I object to is your thin-skinned approach to criticism. Criticism is not necessarily an attack, and it is definitely not censorship. The people who criticize you turn into "big-headed academics" or "closed-minded" or worse. When you insult other people, how can you object to whatever comes back at you?

If you look carefully at everything I've written to you, you'll see that I am criticizing incorrect statements that you have made, or suggesting that you spend less time arguing and more time writing the music you want to write. That is not an attack.

Franklin

--- On Sat, 5/15/10, Michael <djtrancendance@ yahoo.com> wrote:

>From: Michael <djtrancendance@ yahoo.com>
>Subject: Re: [tuning] Re: the ultimate proportional beating well-temperament
>To: tuning@yahoogroups. com
>Date: Saturday, May 15, 2010, 3:26 PM
>
>
>>
>
>
>
>
>
>
>
>
>
>
>
>
> >
>
>
>>
>
>Geroge>"why are you searching for originality on this list? If some tuning
>idea has already been tried, that's a fact you wish away or declare
>null and void. "
>
> Examples? I beg to differ. For example right after when I ran into Ptolemy's Homalon scale I asked Jacques directly if my ratios matched an existing scale and he found that match. And, of course, I never claimed that one scale I ran into was original by me since.
> When I created my 7-tone or so PHI Sections scale generated by (1/PHI)^x + 1 there was no scale it fell under but a PHI tuning well over 20 tones...equating those would be like saying the diatonic scale and 12TET are the same because one fits within the other (IE not very reasonable). Same situation though...after I made the scale I asked people if they knew an exact copy immediately. ..but no one did, they only knew much larger tunings generated by completely different methods which just happened to A) use PHI B) include my scale among tons of other notes (some of them even included infinite numbers of notes
> generating a huge loop).
>
>>"It seems that the main purpose of this list is to share information about tunings."
> Right, so where's the part where you supposedly can't
>A) Share your own tuning
>B) Check it with experts on this list against existing material
>C) Regardless of whether it does/doesn't exist, share more about it...for example even though I ran into Ptolemy's tuning system I explained "what I like about Ptolemy's tuning system which made me run into it".
>
> You know I actually at one point suggested this group be split into a historical and modern/"about new scales or at least trying to find new scales" group. The main reason I even bothered was because of the amount of anger and at times ignorance.
> Toward not just myself, but also people like Jacques, Jacky Ligon, or just about anyone interested in either new tunings OR existing tunings focusing on new theories such as
> difference tones (Jacques) or mirroring (Cameron). Even in which case they ALSO discovered something truly new I often saw people smack down their ideas as "historical" even before they bothered to try and prove it. And I REALLY REALLY don't see how that sort of closed mind-ness could help the tuning world grow...
>
>>"Following the standard definition, you can't force your ideas to be original, or force others to accept them as original."
> The idea is not to say "haha, I'm the first, now give me power", but rather to indicate "maybe others should help study these relationships in my tuning and improve upon them, turning them into something new and great that appeals somewhat across the board".
>
>>"However, it seems that your main focus is really one reaching a mass
>audience with your micro-tonal music."
> Right, and I think a huge part of this is offering something both audibly different than 12TET and with a similar or better balance toward consonance. I figure I certain need to convince people it's a somewhat revolutionary change, and not just a "historic optimization" , before they are willing to buy new instruments to play micro-tonal music. Someone, say, would doubtfully buy a 19-tone guitar just to play 12TET intervals with a "few new chords".
>
>>"If you can achieve this, more
>power to you--if your music comes to serve as a model and creates an
>new artistic movement, your achievement will be original. It seems
>that you really should be directing most of your efforts to this end."
>
> Already am. Have one release for the Split Notes micro-tonal music net-label down and another one coming. It's called "Smack My Pitch Up" (Cameron's name idea) and you're sure to hear about it in the near future.
>
> Realize it's a tough struggle: Jacky Ligon (a fantastic musician) who also made original/new scales and culminated his efforts in incredibly good original/new sounding music apparently gave up forums and albums supposedly due to their blatant ignorance toward completely new tunings (good job guys?!). :-(
> Meanwhile I don't just sit around and say my scales are "done", I constantly tweak them, measure them with various psycho-acoustic and mathematical/ computer- program tests to optimize them. This is why only now I'm concentrating on music...because now I know my main tuning
> theory called "Infinity" finally has all notes within 10 cents of forming their ideal intervals with all other notes in the scale. And, I've learned through testing in composition. ..it finally for the most part nails the definition of "an incredibly easy to play 7-tone-or-more scale where it's impossible to hit a sour chord no matter how large or small".
>
> Now both of Jacky Ligon and our *should be censored?* :-D original scales are on the album...and I'm confident you'll be pleasantly surprised by the odd combination of extra tonal flexibility and 12TET-or-better consonance (goals aimed toward public acceptance) achieved with both. :-)
>
> Let's check back in on this after you hear the album. Then we'll re-convene about whether this quest for original scales and their role in popularizing micro-tonal music is such a bad idea. :-)
>
>-Michael
>

🔗Michael <djtrancendance@...>

🔗George Sanders <georgesanders11111@...>

Michael,
At some point you should the rules of reasonable discussion. Nowhere did I claim that there was any "hypocrisy" involved; that is your invention, which you are attributing to me. I reject your claim.
Secondaly, censorship involves an organization preventing publication of material or redacting controversial passages. I haven't noticed anyone preventing you from expressing yourself--quite the opposite. And when people criticize a point you have made, they are not censoring you. This belongs to Language 101: learn how to use words.
Again, criticism isn't necessarily an attack. It seems to me that you are carrying a chip on your shoulder and waiting until someone knocks it off.
Franklin

--- On Sat, 5/15/10, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@...>
Subject: Re: [tuning] Re: the ultimate proportional beating well-temperament
To: tuning@yahoogroups.com
Date: Saturday, May 15, 2010, 9:07 PM

>"I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up."
But you see, there is no conflict of terms here that would indicate direct hypocrisy. The two go together...most of the attack I've seen on here, not just toward myself but others, that annoy me involve censorship. Many of them follow the lines of "the rules are already there, now learn and follow them" whenever something new comes up.
I don't see why I'm a hypocrit for "attacking/censorin g censorship". ..I don't consider myself at all personally attacked but, rather, am annoyed by the concept of music (in micro-tonal form) boiling down to who is more proper than who, who's written more papers, etc. ...reserving the right to call
shots in theories EVEN that they don't know about. Specifically new ones that they almost impulsively label according to old ones. The nasty response to Jacky's 12/11 9/8 12/11 tuning being slapped the label "Mojira" (sp?) on being yet another classic example of this problem.

From: George Sanders <georgesanders11111@ yahoo.com>
To: tuning@yahoogroups. com
Sent: Sat, May 15, 2010 11:03:44 AM
Subject: Re: [tuning] Re: the
ultimate proportional beating well-temperament

Michael,
I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up. What I object to is your thin-skinned approach to criticism. Criticism is not necessarily an attack, and it is definitely not censorship. The people who criticize you turn into "big-headed academics" or "closed-minded" or worse. When you insult other people, how can you object to whatever comes back at you?
If you look carefully at everything I've written to you, you'll see that I am criticizing incorrect statements that you have made, or suggesting that you spend less time arguing and more time writing the
music you want to write. That is not an attack. Franklin

--- On Sat, 5/15/10, Michael <djtrancendance@ yahoo.com>
wrote:

From: Michael <djtrancendance@ yahoo.com>
Subject: Re: [tuning] Re: the ultimate proportional beating well-temperament
To: tuning@yahoogroups. com
Date: Saturday, May 15, 2010, 3:26 PM

Geroge>"why are you searching for originality on this list? If some tuning
idea has already been tried, that's a fact you wish away or declare
null and void. "

Examples? I beg to differ. For example right after when I ran into Ptolemy's Homalon scale I asked Jacques directly if my ratios matched an existing scale and he found that match. And, of course, I never claimed that one scale I ran into was original by me since.
When I created my 7-tone or so PHI Sections scale generated by (1/PHI)^x + 1 there was no scale it fell under but a PHI tuning well over 20 tones...equating those would be like saying the diatonic scale and 12TET are the same because one fits within the other (IE not very reasonable). Same situation though...after I made the scale I asked people if they knew an exact copy immediately. ..but no one did, they only knew much larger tunings generated by completely different methods which just happened to A) use PHI B) include my scale among tons of other notes (some of them even included infinite numbers of notes
generating a huge loop).

You know I actually at one point suggested this group be split into a historical and modern/"about new scales or at least trying to find new scales" group. The main reason I even bothered was because of the amount of anger and at times ignorance.
Toward not just myself, but also people like Jacques, Jacky Ligon, or just about anyone interested in either new tunings OR existing tunings focusing on new theories such as
difference tones (Jacques) or mirroring (Cameron). Even in which case they ALSO discovered something truly new I often saw people smack down their ideas as "historical" even before they bothered to try and prove it. And I REALLY REALLY don't see how that sort of closed mind-ness could help the tuning world grow...

>"However, it seems that your main focus is really one reaching a mass
audience with your micro-tonal music."
Right, and I think a huge part of this is offering something both audibly different than 12TET and with a similar or better balance toward consonance. I figure I certain need to convince people it's a somewhat revolutionary change, and not just a "historic optimization" , before they are willing to buy new instruments to play micro-tonal music. Someone, say, would doubtfully buy a 19-tone guitar just to play 12TET intervals with a "few new chords".

Realize it's a tough struggle: Jacky Ligon (a fantastic musician) who also made original/new scales and culminated his efforts in incredibly good original/new sounding music apparently gave up forums and albums supposedly due to their blatant ignorance toward completely new tunings (good job guys?!). :-(
Meanwhile I don't just sit around and say my scales are "done", I constantly tweak them, measure them with various psycho-acoustic and mathematical/ computer- program tests to optimize them. This is why only now I'm concentrating on music...because now I know my main tuning
theory called "Infinity" finally has all notes within 10 cents of forming their ideal intervals with all other notes in the scale. And, I've learned through testing in composition. ..it finally for the most part nails the definition of "an incredibly easy to play 7-tone-or-more scale where it's impossible to hit a sour chord no matter how large or small".

Let's check back in on this after you hear the album. Then we'll re-convene about whether this quest for original scales and their role in popularizing micro-tonal music is such a bad idea. :-)

-Michael

🔗Michael <djtrancendance@...>

Me>"But
you see, there is no conflict of terms here that would indicate direct
hypocrisy. The two go together...most of the attack I've seen on here,
not just toward myself but others, that annoy me involve censorship.
Many of them follow the lines of "the rules are already there, now
learn and follow them" whenever something new comes up."

George (in response)>"At some point you should the rules of reasonable discussion. Nowhere did I claim that there was any "hypocrisy" involved; that is your invention, which you are attributing to me. I reject your claim."

Well before you had said...
George>"I've seen you claim to be attacked when people criticize you, and now the claim of censorship comes up."
Not quite sure what you were trying to say: your above statement does seem to say I'm labeling myself as being attacked and then "censored". I'm taking this back to the topic of tuning and saying this is >not< a problem of my being attacked, but an issue with a common attitude on the tuning list. When I said
Me>"The
nasty response to Jacky's 12/11 9/8 12/11 tuning being slapped the
label "Mojira" (sp?) on being yet another classic example of this
problem."
...I was trying to make it utterly clear that it seems your claim (and many other people's) is that those who try to make original scales are working toward a fairly pointless goal. Jacky isn't even on the list...and yet his scale was shot down...if that isn't an example of "non-personal" censorship than I don't know what could be more so a case of that.

George>"Secondaly, censorship involves an organization preventing publication of material or redacting controversial passages"

But surely, that has been done on this list...a lot.
Rick Ballan was blamed for "practicing pseudo-science" with his GCD theories and then had his theories restated as "simply another way to describe the commonly accepted theory of virtual pitch". He actually took himself off the list, much like Jacky did, citing the lack of people taking him seriously and mis-interpreting his theories as the reason. Only much later did a few people realize he really was working on something distinct from virtual pitch. And, IMVHO, having your theory labeled as invalid by many known experts in the field after publishing has much the same effect as its "not being allowed to be published". So how "correct" my use of the word "censorship" is...is not relevant since the overall effect is so similar.

George>"And when people criticize a point you have made, they are not censoring you."
At best, they are censoring the point. But, let me again state, the point started NOT with the issue of me but with the response to JACKY'S SCALE. And I am not Jacky, get it? The other thing is there's a huge rift between constructive criticism...which always indicates ways to improve the result without giving up. You appear to be implying simply giving up, and that is NOT constructive criticism.
In fact I'm under the impression you are taking this route of mis-labeling your attempt at invalidating the point of new/original scales as constructive criticism...because if you didn't add that lie to the equation your point wouldn't be strong enough to compete. To compete with the fact that Rick Ballan, Charles Lucy, Marcel, Jacky Ligon, and (even) Jacques Dudon have at many times had there theories "rounded to the nearest historical version", mis-interpreted, and then cast off as "invalid" without any hint of constructive criticism.
That, my friend, is not primarily if at all problem with my or anyone else who creates scales "chips on their shoulders"...but an issue that in many ways ensures any attempts to do anything highly original in the micro-tonal world are shot down rather than worked with and improved to the point of helping micro-tonality.

>>>>
The only chip on my shoulder I have...is that the community in general seems to have a tough time embracing change and perhaps realizing that not all the ideas you are taught in things like Doctorate-level education may be the only good answers.
<<<<<<

I just hope tuning, as an artistic community, becomes more welcoming and respecting of innovation in general.

_,_._,___

🔗Ozan Yarman <ozanyarman@...>

Dear Andreas,

✩ ✩ ✩
www.ozanyarman.com

On May 14, 2010, at 2:48 PM, a_sparschuh wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
>
>> ... the 524th harmonic series utilizing many ratios
>> ... with a common 131 denominator similar to my UWT....
>
> Dear Oz,
> it is always again amazing how completely different
> ansatzes do lead later to similar solutions.
> Hence, please understand my "congratulation" exclusively
> as an sober-minded compliment.
>

Many thanks for that.

>> Having settled that issue,
>> let me say that your approach involving 13-
>> limit brats and no harmonic waste, which can be tuned by ear via
>> simply listening to the beats per sec. of fifths from pure is a
>> fabulous solution!
> You are in deed the first person,
> who reckognized that hidden integral-feature,
> how it works.
>

Indeed? I'm surprised. One would think that's the obvious feature.

>
>> But then, there is the issue of closer proximity to
>> 12-equal and loss of key-contrast.
> I.m.h.o:
> There will never be any well compomise,
> within the restriction of barely 12 different pitches per octave.
>

A compromise at attaining decent approximations for 4:5:6s and
10:12:15 at every key? No. But a variety of meantonishness and
Pythagoreanism? Absolutely. That's the whole point to Temperament
Ordinaires and Well-Temperaments in my opinion. It is boring to hear
the same interval sizes everywhere. The flow of music needs coloration
with intervallic variety of no small change!

>
>> A simple comparison between our versions
>> involving ratios with 131
>> as denominator shows that we have chosen a different ratio
>> for E > and C# -
>> with the result that your pitches are 5 and 3 cents higher
>> respectively.
>
> Would you agree:
> Whatever you try to do within 12-tones when subdividing the PC
> into however sized subparts, there will always appear some
> drawbacks within the 'key-characteristics',
> especially in the remote keys among the accidential-notes.
>

I agree that the remote keys are expected to be more Pythagorean than
purish, as a requirement of the circle-of-fifths diatonic notation in
use. The more (enharmonically interchangable) sharps or flats a
tonality has, the more one can expect it not to conform to 5-limit
regular JI.

> Hence I do agree with Issac Newton,
> that it is about time for a change from 12 towards 53:
> http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif
>
> as you can also study im my many other contributions to that group.
>

53 is a meaningful solution not only for 5-limit regular JI chords and
decent 7-limit extensions, but also for approximating the middle
seconds peculiar to some maqams: Hence the tendency to describe Maqam
inflexionsby "commas".

>> Thus, yours might not be the practical WT approach for
>> better approximation of regular 5-limit harmony at some tonalities.
>> I shall labour further to reduce the brats to 7-limit,
>
> For seven-limit I use mostly 171 tones per octave.
>

I remember having suggested that as as master resolution for high
prime limit JI that has three decent perfect fifths by which cycles
can be formed.

>> making sure to credit your pioneering approach.
> That's also valid for yours really remarkable results.
>
> Yours Sincerely
> A.S.
>

What do you think of my UWT nr.3?

Cordially,
Oz.

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:

>
> A compromise at attaining decent approximations for 4:5:6s and
> 10:12:15 at every key? No. But a variety of meantonishness and
> Pythagoreanism? Absolutely.
> That's the whole point to Temperament
> Ordinaires and Well-Temperaments in my opinion.
> It is boring to hear
> the same interval sizes everywhere. The flow of music needs
> coloration with intervallic variety of no small change!
>
In deed Oz,
mostly yours views do agree with the research about that topic, as in
the reference:
http://openlibrary.org/works/OL664376W/A_history_of_key_characteristics_in_the_eighteenth_and_early_nineteenth_centuries
>
>
> I agree that the remote keys are expected
> to be more Pythagorean than
> purish, as a requirement
> of the circle-of-fifths diatonic notation in
> use. The more (enharmonically interchangable) sharps or flats a
> tonality has, the more one can expect it not to conform to 5-limit
> regular JI.
>
ok, keeping the remote accidetial keys almost Pythaogorean
was already applied in Werckmeister's most famous nr. W_III,
or in his own labeling the: "Quaternarius"
/tuning/topicId_68023.html#68047?var=0
"
nalog it's also possible to fit the corresponding four 5ths of his
#3(1691) the 'quaternarius' according in the same manner,
My actual interpretation sounds:

C 6560/6561 G 204/205 D 152/153 A>E>B 512/513 F#>C#>G#>Eb>Bb>F>C

expanded in absolute frequencies:

273.375 C ((17<)<)2187:= 3^7
410 G (17*3=51,102,204<)205. ;410; 820,1640,3280,6560(<6561:= 3^8)
306 D (19,38,76,152 < ) 153.:= 17*9
456 A 57:= 19*3 456.
342 E 171:= 19*9 342.
256.5 B (1,...,512 < ) 513.:= 19*27
384 F# 3
288 C# 9
432 G# 27
324 Eb 81
486 Bb 243
364.5 F 729:= 3^6
273.375 C 2187:= 3^7

that's in ascending pitch order

273.375 C 1 middle C
288 C# ! 256/243
306 D ! 272/243
324 Eb ! 32/27
342 E ! 304/243
364.5 F ! 4/3
384 F# ! 1024/729
410 G ! 3280/2187 coeval Cammer-tone ~410cps
432 G# ! 128/81
456 A ! 1216/729 coeval Choir-tone ~456cps
486 Bb ! 152/81
512.5 B ! 16/9
546.75 C' 2/1
"

Actually here comes my recently modified version of that:

-6: Ab 27 54 108 216 Ab4:=432.0Hz Mersenne's & Sauveur's "son-fixe"
-5: Eb 81 162 324.0=Eb4
-4: Bb 243 486.0=Bb4
-3: F (91 182 364 <) 364.5=F4 729F5 := 3^6
-2: C(34.1 136.4<)136.5 273.0=C4 middle_C4
-1: G 102.3 204.6 409.2=G4
00: D (19 38 76 152 304<) 305.5=D4 (< 306.9 := 3*G2)
+1: A 57 114 228 456.0=A4 ~Werckmeister's~"Choir-Thone"~
+2: E (3*A1=171 342 >) 341.5=E4 683 1366 [>1365:=5*C4]
+3: B 1 2 4 .... 256 512.0=B4 [1023:=10*G2 <]1024 2048(<2049)
+4: F# 3 6 12 ...192 384.0=F#4
+5: C# 9 18 36...144 288.0=C#4
+6: G# 27 54 108 216 432.0=G#4

or in chromatically ascending order in the tuner's octave A3->A4

228.0 A_3
243.0 Bb3
256.0 B_3
273.0 C_4 middle C
288.0 C#4
305.5 D_4
324.0 Eb4
341.5 E_4
364.5 F_4
384.0 F#4
409.2 G_4
432.0 G#4
456.0 A_4

!SpChoirTone456Hz.scl
Sparschuh's [2010] Choir-tone modification of Werckmeister #3
12
!
96/91 ! C#
47/42 ! D (10/9)*(141/140~+12.3...C) = (9/8)*(188/189~-9.2...C)
108/91 ! Eb
683/546 ! E (5/4)*(1366/1365 ~+1.2678389...Cents)
243/182 ! F (4/3)*(729/728 ~+2.3764369..Cents)
128/91 ! F#
682/455 ! G (3/2)*[1364/1365 ~-1.26876814...Cents]
144/91 ! G#
152/91 ! A = F*(5/4)*[1216/1215 ~+1.4242...C] Erasthostenes's Comma
162/91 ! Bb
512/273 ! B = G*(5/4)*[1024/1023 ~+1.691484...Cents]
2/1
!
![eof]

Attend the many exact Pythagorean 3-limit relations inbetween the remote keys: B-F#-C#-G#-Eb-Bb-F and strong the contrast especially
in the almost pure fusing 3rds F-A, C-E and G-B as already
Schlick [1511] had demanded almost 2 centuries before Werckmeister.

> 53 is a meaningful solution
> not only for 5-limit regular JI chords and
> decent 7-limit extensions, but also for approximating the middle
> seconds peculiar to some maqams:
> Hence the tendency to describe Maqam
> inflexionsby "commas".

http://en.wikipedia.org/wiki/53_equal_temperament

...that's more generally explained by considering the:
http://www.research.att.com/~njas/sequences/A060528
" 1, 2, 3, 5, 7, 12, 29, 41, 53, 200, 253, 306, 359, 665,...
A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of two tones of musical harmony: the perfect 4th, 4/3 and its complement the perfect 5th, 3/2. "

> > (A.S):For seven-limit I use mostly 171 tones per octave.
> I remember having suggested that as as master resolution for high
> prime limit JI that has three decent perfect fifths by which
> cycles can be formed.

Already my late friend
http://de.wikipedia.org/wiki/Martin_Vogel
preferred exact that 171 resolution instead of only 53-tones.
Meanwhile i have a completely
http://en.wikipedia.org/wiki/Dyadic_rational
version of 171 tones-per-octave in preparation.

>
> What do you think of my UWT nr.3?
Sorry, but that contains not yet enough contrast in Key-characteristics, especially
inbetween the F-C-G-D-A-E-B versus my purely Pythagorean
3-limit ratios among the remote keys B-F#-C#-G#-Eb-Bb-F
as in the above demonstrated case, of refineing Werckmeister #3,
at least in my ears, due to the inherent automatic schismatic transition from 3-limit to 5-limit, when having a consecutive
chain of 8 pure 5ths.

Yours Sincerely
A.S.

🔗genewardsmith <genewardsmith@...>

🔗George Sanders <georgesanders11111@...>

🔗Ozan Yarman <ozanyarman@...>

O Andreas, in between the lines:

✩ ✩ ✩
www.ozanyarman.com

On May 19, 2010, at 9:40 PM, a_sparschuh wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
>>
>> A compromise at attaining decent approximations for 4:5:6s and
>> 10:12:15 at every key? No. But a variety of meantonishness and
>> Pythagoreanism? Absolutely.
>> That's the whole point to Temperament
>> Ordinaires and Well-Temperaments in my opinion.
>> It is boring to hear
>> the same interval sizes everywhere. The flow of music needs
>> coloration with intervallic variety of no small change!
>>
> In deed Oz,
> mostly yours views do agree with the research about that topic, as in
> the reference:
> http://openlibrary.org/works/OL664376W/A_history_of_key_characteristics_in_the_eighteenth_and_early_nineteenth_centuries

Though I cannot download a copy from there, I'm glad my views have
been deliberated upon by some worthy researchers.

>>
>>
>> I agree that the remote keys are expected
>> to be more Pythagorean than
>> purish, as a requirement
>> of the circle-of-fifths diatonic notation in
>> use. The more (enharmonically interchangable) sharps or flats a
>> tonality has, the more one can expect it not to conform to 5-limit
>> regular JI.
>>
> ok, keeping the remote accidetial keys almost Pythaogorean
> was already applied in Werckmeister's most famous nr. W_III,
> or in his own labeling the: "Quaternarius"
> /tuning/topicId_68023.html#68047?var=0
> "
> nalog it's also possible to fit the corresponding four 5ths of his
> #3(1691) the 'quaternarius' according in the same manner,
> My actual interpretation sounds:
>
> C 6560/6561 G 204/205 D 152/153 A>E>B 512/513 F#>C#>G#>Eb>Bb>F>C
>
> expanded in absolute frequencies:
>
> 273.375 C ((17<)<)2187:= 3^7
> 410 G (17*3=51,102,204<)205. ;410; 820,1640,3280,6560(<6561:= 3^8)
> 306 D (19,38,76,152 < ) 153.:= 17*9
> 456 A 57:= 19*3 456.
> 342 E 171:= 19*9 342.
> 256.5 B (1,...,512 < ) 513.:= 19*27
> 384 F# 3
> 288 C# 9
> 432 G# 27
> 324 Eb 81
> 486 Bb 243
> 364.5 F 729:= 3^6
> 273.375 C 2187:= 3^7
>
> that's in ascending pitch order
>
> 273.375 C 1 middle C
> 288 C# ! 256/243
> 306 D ! 272/243
> 324 Eb ! 32/27
> 342 E ! 304/243
> 364.5 F ! 4/3
> 384 F# ! 1024/729
> 410 G ! 3280/2187 coeval Cammer-tone ~410cps
> 432 G# ! 128/81
> 456 A ! 1216/729 coeval Choir-tone ~456cps
> 486 Bb ! 152/81
> 512.5 B ! 16/9
> 546.75 C' 2/1
> "
>

Aie, there are incredibly low 690 and 693 cent fifths here.
Werckmeister would have approved of that? I suspect not. This, despite
the fact that it yields clean brats at many keys, Major or minor.

> Actually here comes my recently modified version of that:
>
> -6: Ab 27 54 108 216 Ab4:=432.0Hz Mersenne's & Sauveur's "son-fixe"
> -5: Eb 81 162 324.0=Eb4
> -4: Bb 243 486.0=Bb4
> -3: F (91 182 364 <) 364.5=F4 729F5 := 3^6
> -2: C(34.1 136.4<)136.5 273.0=C4 middle_C4
> -1: G 102.3 204.6 409.2=G4
> 00: D (19 38 76 152 304<) 305.5=D4 (< 306.9 := 3*G2)
> +1: A 57 114 228 456.0=A4 ~Werckmeister's~"Choir-Thone"~
> +2: E (3*A1=171 342 >) 341.5=E4 683 1366 [>1365:=5*C4]
> +3: B 1 2 4 .... 256 512.0=B4 [1023:=10*G2 <]1024 2048(<2049)
> +4: F# 3 6 12 ...192 384.0=F#4
> +5: C# 9 18 36...144 288.0=C#4
> +6: G# 27 54 108 216 432.0=G#4
>
> or in chromatically ascending order in the tuner's octave A3->A4
>
> 228.0 A_3
> 243.0 Bb3
> 256.0 B_3
> 273.0 C_4 middle C
> 288.0 C#4
> 305.5 D_4
> 324.0 Eb4
> 341.5 E_4
> 364.5 F_4
> 384.0 F#4
> 409.2 G_4
> 432.0 G#4
> 456.0 A_4
>
>

Again ay ay ay! Still 693 and 694 cent fifths in the cycle. I don't
see the purpose of suggesting such rational tunings. Is it to
demonstrate some Well-Temperament scheme? Certainly, these cannot be
acceptable from the Western common-practice point of view.

> !SpChoirTone456Hz.scl
> Sparschuh's [2010] Choir-tone modification of Werckmeister #3
> 12
> !
> 96/91 ! C#
> 47/42 ! D (10/9)*(141/140~+12.3...C) = (9/8)*(188/189~-9.2...C)
> 108/91 ! Eb
> 683/546 ! E (5/4)*(1366/1365 ~+1.2678389...Cents)
> 243/182 ! F (4/3)*(729/728 ~+2.3764369..Cents)
> 128/91 ! F#
> 682/455 ! G (3/2)*[1364/1365 ~-1.26876814...Cents]
> 144/91 ! G#
> 152/91 ! A = F*(5/4)*[1216/1215 ~+1.4242...C] Erasthostenes's Comma
> 162/91 ! Bb
> 512/273 ! B = G*(5/4)*[1024/1023 ~+1.691484...Cents]
> 2/1
> !
> ![eof]
>
> Attend the many exact Pythagorean 3-limit relations inbetween the
> remote keys: B-F#-C#-G#-Eb-Bb-F and strong the contrast especially
> in the almost pure fusing 3rds F-A, C-E and G-B as already
> Schlick [1511] had demanded almost 2 centuries before Werckmeister.
>

Schlick's suggested Orgelmacher under Organisten Temperament in 1511
according to Barbour has no wolf fifths as you have suggested Andreas.
Others have suggested some meantonish method with only one wolf where
it's supposed to be. And the purpose for procuring your tunings above
in this discussion eludes me.

>
>> 53 is a meaningful solution
>> not only for 5-limit regular JI chords and
>> decent 7-limit extensions, but also for approximating the middle
>> seconds peculiar to some maqams:
>> Hence the tendency to describe Maqam
>> inflexionsby "commas".
>
> http://en.wikipedia.org/wiki/53_equal_temperament
>
> ...that's more generally explained by considering the:
> http://www.research.att.com/~njas/sequences/A060528
> " 1, 2, 3, 5, 7, 12, 29, 41, 53, 200, 253, 306, 359, 665,...
> A list of equal temperaments (equal divisions of the octave) whose
> nearest scale steps are closer and closer approximations to the
> ratios of two tones of musical harmony: the perfect 4th, 4/3 and its
> complement the perfect 5th, 3/2. "

And what of 171?

>
>>> (A.S):For seven-limit I use mostly 171 tones per octave.
>> I remember having suggested that as as master resolution for high
>> prime limit JI that has three decent perfect fifths by which
>> cycles can be formed.
>
> Already my late friend
> http://de.wikipedia.org/wiki/Martin_Vogel
> preferred exact that 171 resolution instead of only 53-tones.
> Meanwhile i have a completely
> http://en.wikipedia.org/wiki/Dyadic_rational
> version of 171 tones-per-octave in preparation.
>

It is next to impossible to utilize all the tones of 171-equal on an
acoustical instrument altogether. So why bother with such a high
resolution impossible-to-set equal division aside from the brain
gymnastics at theoretical minutiae?

>>
>> What do you think of my UWT nr.3?
> Sorry, but that contains not yet enough contrast in Key-
> characteristics, especially
> inbetween the F-C-G-D-A-E-B versus my purely Pythagorean
> 3-limit ratios among the remote keys B-F#-C#-G#-Eb-Bb-F
> as in the above demonstrated case, of refineing Werckmeister #3,
> at least in my ears, due to the inherent automatic schismatic
> transition from 3-limit to 5-limit, when having a consecutive
> chain of 8 pure 5ths.
>

It has been demonstrated that your suggestions do not work as Well-
Temperaments due to brutishly low fifths in the cycles. More key-
contrast should not mean roughing up the modulation track. My
optimization on UWT nr.3 works superbly, and it's possible to tune by
ear in simple steps.

> Yours Sincerely
> A.S.
>

Cordially,
Oz.

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗George Sanders <georgesanders11111@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> ...In some ways they are like the integers except that 2 has been
> stricken from the roll of primes....

Hi Gene,
Boethius reports in his "De-musica"
http://www.mirroroftheworld.com.au/inspiration/manuscripts/de_musica.php
that
http://en.wikipedia.org/wiki/Philolaus

once had distributed arithmetically the the tone 8/9 into 9 subparts:

8/9 = 72/81 =: 72 : 73 : 74 : 75 : 76 : 77 : 78 : 79 : 80 : 81

also in the same way P. subdivided the limma 243/256 into 4 subparts:

243/256 = 972/1024 =: 972 : 985 : 998 : 1011 : 1024

[please enable before reading,
the option <button>: "use-fixed-wide-font"]

here an dyadic-rational !interpolation! that fits both presumptions

0 : C- 1 unison C-_4 = 256 middle_C-_4 ... !1024! := 2^10
1 : G- 3 ... G-_4 = 384
2 : D- 9 18 36 !72!... D-_4 = 288
3 : A- 27 ... A-_4 = 432
4 : E- !81! ... E-_4 = 324
5 : B- 243 B-_4 = 486 !972!:= 243*4
6 : GB 729=3^6 GB_4 = 364.5
7 : DB DB_4 = 273.5 547 1094 2188 (>2187 := 3^7)
8 : AB AB_4 = 410.5 821 1642 (> 1641 := 3*C#_5 )
9 : EB !77! 154 EB_4 = 308 616 1232 2464(>2463:=3*G#_5)
10: BB 231 BB_4 = 462 := 3*!77!
11: F\ F\_4 = 346.5 693 := 3*BB_3
12: C\ 65 130 C\_4 = 260 520 1040 2080(>2079:=3*F\_5)
13: G\ 195 G\_4 = 390
14: D\ !73! 146 D\_4 = 292
15: A\ 219 A\_4 = 438
16: E\ E\_4 = 328.5 657 := 3*A\_3
17: B\ B\_4 = 492.5 !985! 1970 (<1971:=3*E\_5)
18: Gb Gb_4 = 369.5 739 1478 2956(<2955:=3*B\_5)
19: Db Db_4 = 277 554 1108 2216(>2217:=3*Gb_5)
20: Ab 13 26 ... 208 Ab_4 = 416 832 (> 831 := 3*Db_4)
21: Eb 39 !78! 156 Eb_4 = 312
22: Bb 117 234 Bb_4 = 468
23: F. F._4 = 351
24: C. C._4 = 263.5 527 1054 (>1053 := 3*F._4)
25: G. G._4 = 395 790 1580 (<1581 := 3*C._5)
26: D. 37 !74! 148 D._4 = 296 592 1184 (<1185 := 3*G-_4)
27: A. 111 222 A._4 = 444
28: E. E._4 = 333
29: B. B._4 = 499 !998! (<999 := 3*E._4)
30: F# F#_4 = 374.5 749 1498 (>1497 :=3*B._4)
31: C# C#_4 = 281 562 1124 2248 (>2247:=3*F#_5)
32: G# G#_4 = 421.5 843 := 3*C#_4
33: D# !79! 158 D#_4 = 316 632 1264 2528 (>2529:=3*G#_5)
34: A# 237 A#_4 = 474
35: F/ F/_4 = 355.5 711 := 3*A#_3
36: C/ C/_4 = 266.5 533 1066 (<1599 := 3*F/_5)
37: G/ 25 50 100 200 G/_4 = 400 800 1600 (>1599 := 3*C/_5)
38: D/ !75! 150 D/_4 = 300
39: A/ 225 A/_4 = 450
40: E/ (337 <) E/_4 = 337.5 675 := 3*A/_3
41: B/ B/_4 = 505.5 !1011! := 3*337
42: F& F&_4 = 379 758 1516 3032 (> 3033:=3*B/_5)
43: C& C&_4 = 284.5 569 1138 (>1137 := 3*F&_4)
44: G& G&_4 = 426.5 853 1706 (>1707 := 3*C&_5)
45: D& 5 10...!80! 160 D&_4 = 320 640 1280 2560(<2559:=3*G&_5)
46: A& 15 30 60 ...240 A&_4 = 480
47: F+ 45 90 180 F+_4 = 360
48: C+ 135 C+_4 = 270
49: G+ G+_4 = 405
50: D+ 19 38 !76! 152 D+_4 = 304 608 1216(>1215) Erasthostenes
51: 57 ... A+_4 = 456
52: 171 F-_4 = E+_4 = 342
53: 1 2 ... C-_5 = B+_4 = 512 (< 513) Boethius' comma

or as 'scala'-file:

!SpDyadRat53.scl
Sparschuh's [2010] Dyadic-Rational 53 in Philolaos/Boethius style
53
!
65/64 ! 1: C\
527/512 ! 2: C.
533/512 ! 3: C/
135/128 ! 4: C+
547/512 ! 5: DB
277/256 ! 6: Db
281/256 ! 7: C#
569/512 ! 8: C&
9/8 ! 9: D- tone
73/64 ! 10: D\
37/32 ! 11: D.
75/64 ! 12: D/
19/16 ! 13: D+
77/64 ! 14: EB
39/32 ! 15: Eb
79/64 ! 16: D#
5/4 ! 17: D& the "just" 3rd
81/64 ! 18: E- Pythagorean "ditone"
657/512 ! 19: E\
333/256 ! 20: E.
675/512 ! 21: E/
171/128 ! 22: E+ = F- (4/3)*(513/512) an 4th of ratio 1.335,937,5
693/512 ! 23: F\
351/256 ! 24: F.
711/512 ! 25: F/
45/32 ! 26: F+ Syntonic 5-limit tritone
729/512 ! 27: GB Pythagorean 3-limit tritone
739/512 ! 28: Gb
749/512 ! 29: F#
379/256 ! 30: F&
3/2 ! 31: G- the JI 5th
195/128 ! 32: G\
395/256 ! 33: G.
25/16 ! 34: G/
405/256 ! 35: G+
821/512 ! 36: AB
13/8 ! 37: Ab the 13th partial overtone
843/512 ! 38: G#
853/512 ! 39: G&
27/16 ! 40: A- Pythagorean 6th
219/128 ! 41: A\
111/64 ! 42: A. absolute-pitch @ A4=444Hz
225/128 ! 43: A/ (7/4)*(225/224) ~natural~septime~
57/32 ! 44: A+
231/128 ! 45: BB
117/64 ! 46: Bb
237/128 ! 47: A#
15/8 ! 48: A& Syntonic 5-limit 7th
243/128 ! 49: B- Pythagoran 7th or octave/limma
985/512 ! 50: B\
499/256 ! 51: B.
253/128 ! 52: B/
2/1 ! 53: B+ = C-
!
![eof]

Sounds really somehow archaic,
but better than any 12-tone tuning.

Attend:
There are some wrong rumors about the history of 53-tone in WIKI:

http://en.wikipedia.org/wiki/Jing_Fang
Quote:
"
He was the first to notice how closely a succession of 53 just fifths approximates 31 octaves. This observation would much later lead to the discovery of 53 equal temperament in the seventeenth century.
"
Appearenty already Pihlolaos had mastered that 'discovery',
also did so very likely the ancient ~300BC indian
http://en.wikipedia.org/wiki/Bharata_Muni
in his famous tretaise:
http://en.wikipedia.org/wiki/Natya_Shastra_of_Bharata

Book:
http://books.google.de/books?id=3TKarwqJJP0C&pg=PA119&lpg=PA119&dq=bharata+muni+gosh&source=bl&ots=bjg2uA5y97&sig=gmotPf6gkneVVol5oJB9dcdk7hU&hl=de&ei=KUb1S-z6GI6QOMqlicYI&sa=X&oi=book_result&ct=result&resnum=2&ved=0CB8Q6AEwAQ#v=onepage&q&f=false

bye
A.S.

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, George Sanders <georgesanders11111@...> wrote:
>
>) Â Well, then, we agree that the word "originality" has some
> meaning in the real world.
Dear Franklin,
fully agreed, because even the entry for:
http://en.wikipedia.org/wiki/Originality
warns:
"
This article has multiple issues. Please help improve the article or discuss these issues on the talk page.

* It does not cite any references or sources. Please help improve it by citing reliable sources. Tagged since August 2007.
* It may be confusing or unclear for some readers.
"

Personally I would wish to read also such classifications
in the conventional standard-encyclopedias as for instance the "Britannica" and its mostly worser counterparts in other foreign languages respectively.

> Â I have a problem, though, when people define it in such a
> restrictive manner that it is impossible to find an example in the > world of anything original.

about an century ago there had been an patent-office clerk,
http://www.welt.de/print-welt/article537028/Einsteins_Uhren_gingen_anders.html
Quote:
"
...Viele Patente gingen über den Tisch eines jungen Beamten im Berner Patentamt namens Albert Einstein, dessen Vorgesetzter Friedrich Haller ihm einschärfte: "Wenn Sie einen Patentantrag in die Hand nehmen, gehen Sie davon aus, dass alles, was der Erfinder sagt, falsch ist." Eine praktische Maxime, die Einstein mit Gewinn auch auf die theoretische Physik anwandte...."

Tr:
'...Many patents went over the table, of a young official clerk in the Bern patent office named Albert Einstein, whose superior chief Friedrich Haller him inculcated: "If you take a patent application in the hand, you must assume that anything that says the inventor is wrong." A practical maxim that Einstein applied to his profit on his
own later work theoretical physics..."

> Â But this would be a vacuous definition. It would also negate the > history of the word as it has been used in history.

> However, I would maintain that Wikipedia is not a credible source;
Probably Haller and Einstein would agree with yours statement.

> I and many other professors forbid my students to use it as a
> reference.
It's up to my own students whatever source they want to consult,
as far as they do keep sceptical in critial distance against
the allegations, wild speculations and false pretences:
Otherwise I advise theirs fellow-students to roast them in my Seminar.

> Â A dictionary or encyclopedia is more reliable.
I dare to doubt about that bold presumption,
due to the many counter-examples,
when encyclopedias simply turn out to be faulty,
when examined under closer view
or often at second glance,
after having slept a night over it.

So far about Haller's criterion for Einstein,
that I have taken over into my own teaching.

Yours Sincerely
Andreas Sparschuh

🔗George Sanders <georgesanders11111@...>

A lot of this depends on which encyclopedia you check, how recent it is, and so forth; you need to do some scholarly legwork. I should have said "reliable encyclopedia" early on; just checking any encyclopedia of any year won't do; I would never allow a student to use the Encyclopedia Brittanica for a scholarly paper, because this is a general-interest encyclopedia, not a professional source. Textbooks are also not allowed for citations. The Grove's Encyclopedia in general is is (and the Grove's project has been improved owing to it's being extended to the web via Grove's online), as long as it is the most recent version of the encyclopedia and as long as further sources are cited.

I use Wikipedia regularly as a means of finding sources, which I then check myself. It does have advantages in that it can be revised swiftly in case mistaken information appears. But it is prey to partisan viewpoints, and usually the viewpoint of the most persistent contributor wins. There are numerous entries on contemporary music, for example, that are blatantly partisan and full of hogwash. People then cite these entries as sources, and the hogwash spreads throughout the internet.

I agree that some entries are more reliable than others, and it can be a useful tool for sharing information. But it is simply not a reliable source for information, largely because nobody's professional career is dependent on the reliability of anything that appears in it. There is a tremendous variability in the reliability of the entries.

Carl mentioned the Josquin birth date; this has been changed several times on Wikipedia. Now is it correct now? It depends on which source you are using. The scholarly consensus seems to be revolving around 1450-1455, but the scholarly consensus before was 1440. Scholars think the latter date is more accurate, and it's nice to see Wikipedia reflect that consensus.

But this article is only as good as the sources to which it refers. This is one of the better-cited articles, and most of the sources are recent. These are serious scholars, and it is their research that provides the reliable core to the Wikipedia entry.

best

Franklin

--- On Thu, 5/20/10, a_sparschuh <a_sparschuh@...> wrote:

From: a_sparschuh <a_sparschuh@...>
Subject: [tuning] Re: the ultimate proportional beating well-temperament
To: tuning@yahoogroups.com
Date: Thursday, May 20, 2010, 11:06 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> .... Andreas seems to have taken to this years ago ;).

Indeed Carl,

on the one hand:

in my view it is better to disprove faulty WIKI information,

and declare it as rubbish nonsene, or at least mark it as questionable, than to suffer complete lack of any information at all.

But also on the other hand, I'm afraid:

From my own usage of traditional standard enclopedias,

sadly I have conclude:

Just in the said reputable encyclopedia there occur

many serious errors. I observed: That faults got perpetuaded again and again from the early pig-leather bound editions to the extend of todays plastic-embedded editions: Unamended. In some cases that evil can be traced back even over centuries. Apparently, the conservative editors must have developed a certain kind of resistance against apt corrections in order to preserve their Reputation immune. Even if an Expert in the topic rubs them the just correction in the nose:

There is no cure for that ill.

Hence, so sceptically I always expect from my students to evaluate carefully the reliability of their sources of information may be assessed as true even or not, before overtakeing in theirs presentations.

Anyway:

I'm fully aware that WIKI delivers in some cases only "bollocks"

because: 'All too many cooks spoil the broth.'

Enjoy your mail!

A.S.

🔗Ozan Yarman <ozanyarman@...>

Enough with this wikipedia worship or derision. Please return to
tuning-related discussions under a thread which I opened.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 20, 2010, at 6:22 PM, George Sanders wrote:

>
>
> A lot of this depends on which encyclopedia you check, how recent it
> is, and so forth; you need to do some scholarly legwork. I should
> have said "reliable encyclopedia" early on; just checking any
> encyclopedia of any year won't do; I would never allow a student to
> use the Encyclopedia Brittanica for a scholarly paper, because this
> is a general-interest encyclopedia, not a professional source.
> Textbooks are also not allowed for citations. The Grove's
> Encyclopedia in general is is (and the Grove's project has been
> improved owing to it's being extended to the web via Grove's
> online), as long as it is the most recent version of the
> encyclopedia and as long as further sources are cited.
>
> I use Wikipedia regularly as a means of finding sources, which I
> then check myself. It does have advantages in that it can be
> revised swiftly in case mistaken information appears. But it is
> prey to partisan viewpoints, and usually the viewpoint of the most
> persistent contributor wins. There are numerous entries on
> contemporary music, for example, that are blatantly partisan and
> full of hogwash. People then cite these entries as sources, and the
> hogwash spreads throughout the internet.
>
> I agree that some entries are more reliable than others, and it can
> be a useful tool for sharing information. But it is simply not a
> reliable source for information, largely because nobody's
> professional career is dependent on the reliability of anything that
> appears in it. There is a tremendous variability in the reliability
> of the entries.
>
> Carl mentioned the Josquin birth date; this has been changed several
> times on Wikipedia. Now is it correct now? It depends on which
> source you are using. The scholarly consensus seems to be revolving
> around 1450-1455, but the scholarly consensus before was 1440.
> Scholars think the latter date is more accurate, and it's nice to
> see Wikipedia reflect that consensus.
>
> But this article is only as good as the sources to which it refers.
> This is one of the better-cited articles, and most of the sources
> are recent. These are serious scholars, and it is their research
> that provides the reliable core to the Wikipedia entry.
>
> best
>
> Franklin
>
>
>
>
> --- On Thu, 5/20/10, a_sparschuh <a_sparschuh@...> wrote:
>
> From: a_sparschuh <a_sparschuh@...>
> Subject: [tuning] Re: the ultimate proportional beating well-
> temperament
> To: tuning@yahoogroups.com
> Date: Thursday, May 20, 2010, 11:06 AM
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > .... Andreas seems to have taken to this years ago ;).
>
> Indeed Carl,
> on the one hand:
> in my view it is better to disprove faulty WIKI information,
> and declare it as rubbish nonsene, or at least mark it as
> questionable, than to suffer complete lack of any information at all.
>
> But also on the other hand, I'm afraid:
> From my own usage of traditional standard enclopedias,
> sadly I have conclude:
> Just in the said reputable encyclopedia there occur
> many serious errors. I observed: That faults got perpetuaded again
> and again from the early pig-leather bound editions to the extend of
> todays plastic-embedded editions: Unamended. In some cases that evil
> can be traced back even over centuries. Apparently, the conservative
> editors must have developed a certain kind of resistance against apt
> corrections in order to preserve their Reputation immune. Even if an
> Expert in the topic rubs them the just correction in the nose:
> There is no cure for that ill.
> Hence, so sceptically I always expect from my students to evaluate
> carefully the reliability of their sources of information may be
> assessed as true even or not, before overtakeing in theirs
> presentations.
>
> Anyway:
> I'm fully aware that WIKI delivers in some cases only "bollocks"
> because: 'All too many cooks spoil the broth.'
>
> Enjoy your mail!
> A.S.
>
>
>
>
>
>

🔗Michael <djtrancendance@...>

"An original work is one not received from others nor one copied based on the work of others." -http://en.wikipedia.org/wiki/Originality

I see how this article is up to easy misinterpretation. When it says "based on the work of others"...that could refer to either, for example, the work's actually being copied and/or based on other people's ideas.

The latter is definitely false...even the most new and novel ideas have some sort of historical pre-cursor...although some have far less than others. You can even say Henry Ford's Model T car was not original because it used wheels and an engine...both of which existed far before the Model T. Or that any piece of music is "not original" because it uses the same scale or chords as many other pieces. It's...indeed far too strict a qualification for being original.

I'd vouch to say something original must be significantly different and uniquely useful(or, at times, useless) in contrast to predecessors. For example, to gain a patent an idea has to pass a number of people's votes as to being significantly different from the most closely related ideas in existence.
Meanwhile so far as things such as musical works (in which subjectivity among listeners plays a huge role)...it seems fair to say music that's considered original achieves either moods or techniques recognized by many people as uniquely useful. For example, Debussy's use of transposition within verses creates a unique new sense of open-ness while maintaining a single-key sense of balanced resolve. If someone made a style of music which made people lose balance...it would still be original...just in a "uniquely useless" way. :-D

So being "original", I'd vouch...doesn't necessarily mean "well liked" either...it much more so means it does something that, in many ways, has not been done before.

For a scale to qualify as original one must ask, for example, what that scale can do (or what multiple things it can acheive simultaneously) that other tunings can't. And of course mathematically original and original "when played" are two different things as many people can't hear slight mathematical optimizations.
I'd actually say it's easy to make an original scale far as using different math and/or having a distinct combination of dyadic intervals...but hard to make one that's original in many ways at once and different enough from existing scales to be easily recognized audibly as different...and not just mathematically.

-Michael

🔗Chris Vaisvil <chrisvaisvil@...>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> ...In some ways they are like the integers except that 2 has been
> stricken from the roll of primes....
>
> 0 : C- 1 unison C-_4 = 256 middle_C-_4 ... !1024! := 2^10
> 1 : G- 3 ... G-_4 = 384
> 2 : D- 9 18 36 !72!... D-_4 = 288
> 3 : A- 27 ... A-_4 = 432
> 4 : E- !81! ... E-_4 = 324
> 5 : B- 243 B-_4 = 486 !972!:= 243*4
> 6 : GB 729=3^6 GB_4 = 364.5
> 7 : DB DB_4 = 273.5 547 1094 2188 (>2187 := 3^7)
> 8 : AB AB_4 = 410.5 821 1642 (> 1641 := 3*C#_5 )
> 9 : EB !77! 154 EB_4 = 308 616 1232 2464(>2463:=3*G#_5)
> 10: BB 231 BB_4 = 462 := 3*!77!
> 11: F\ F\_4 = 346.5 693 := 3*BB_3
> 12: C\ 65 130 C\_4 = 260 520 1040 2080(>2079:=3*F\_5)
> 13: G\ 195 G\_4 = 390
> 14: D\ !73! 146 D\_4 = 292
> 15: A\ 219 A\_4 = 438
> 16: E\ E\_4 = 328.5 657 := 3*A\_3
> 17: B\ B\_4 = 492.5 !985! 1970 (<1971:=3*E\_5)
> 18: Gb Gb_4 = 369.5 739 1478 2956(<2955:=3*B\_5)
> 19: Db Db_4 = 277 554 1108 2216(>2217:=3*Gb_5)
> 20: Ab 13 26 ... 208 Ab_4 = 416 832 (> 831 := 3*Db_4)
> 21: Eb 39 !78! 156 Eb_4 = 312
> 22: Bb 117 234 Bb_4 = 468
> 23: F. F._4 = 351
> 24: C. C._4 = 263.5 527 1054 (>1053 := 3*F._4)
> 25: G. G._4 = 395 790 1580 (<1581 := 3*C._5)
> 26: D. 37 !74! 148 D._4 = 296 592 1184 (<1185 := 3*G-_4)
> 27: A. 111 222 A._4 = 444
> 28: E. E._4 = 333
> 29: B. B._4 = 499 !998! (<999 := 3*E._4)
> 30: F# F#_4 = 374.5 749 1498 (>1497 :=3*B._4)
> 31: C# C#_4 = 281 562 1124 2248 (>2247:=3*F#_5)
> 32: G# G#_4 = 421.5 843 := 3*C#_4
> 33: D# !79! 158 D#_4 = 316 632 1264 2528 (>2529:=3*G#_5)
> 34: A# 237 A#_4 = 474
> 35: F/ F/_4 = 355.5 711 := 3*A#_3
> 36: C/ C/_4 = 266.5 533 1066 (<1599 := 3*F/_5)
> 37: G/ 25 50 100 200 G/_4 = 400 800 1600 (>1599 := 3*C/_5)
> 38: D/ !75! 150 D/_4 = 300
> 39: A/ 225 A/_4 = 450
> 40: E/ (337 <) E/_4 = 337.5 675 := 3*A/_3
> 41: B/ B/_4 = 505.5 !1011! := 3*337
> 42: F& F&_4 = 379 758 1516 3032 (> 3033:=3*B/_5)
> 43: C& C&_4 = 284.5 569 1138 (>1137 := 3*F&_4)
> 44: G& G&_4 = 426.5 853 1706 (>1707 := 3*C&_5)
> 45: D& 5 10...!80! 160 D&_4 = 320 640 1280 2560(<2559:=3*G&_5)
> 46: A& 15 30 60 ...240 A&_4 = 480
> 47: F+ 45 90 180 F+_4 = 360
> 48: C+ 135 C+_4 = 270
> 49: G+ G+_4 = 405
> 50: D+ 19 38 !76! 152 D+_4 = 304 608 1216(>1215) Erasthostenes
> 51: 57 ... A+_4 = 456
> 52: 171 F-_4 = E+_4 = 342
> 53: 1 2 ... C-_5 = B+_4 = 512 (< 513) Boethius' comma
>
or as 'scala'-file, now additional
with the absolute-pitch frequencies in the middle octave

!SpDyadRat53.scl
Sparschuh's [2010] Dyadic-Rational 53 in Philolaos/Boethius style
53
! 1/1 ! 0: C- 256 Hz middle_C-_4
65/64 ! 1: C\ 260
527/512 ! 2: C. 263.5
533/512 ! 3: C/ 266.5
135/128 ! 4: C+ 270
547/512 ! 5: DB 273.5
277/256 ! 6: Db 277
281/256 ! 7: C# 281
569/512 ! 8: C& 284.5
9/8 ! 9: D- 288 ! tone
73/64 ! 10: D\ 292
37/32 ! 11: D. 296
75/64 ! 12: D/ 300
19/16 ! 13: D+ 304
77/64 ! 14: EB 308
39/32 ! 15: Eb 312
79/64 ! 16: D# 316
5/4 ! 17: D& 320 ! the "just" 3rd
81/64 ! 18: E- 324 Pythagorean "ditone"
657/512 ! 19: E\ 328.5
333/256 ! 20: E. 333
675/512 ! 21: E/ 337.5
171/128 ! 22: E+ 342 = F- (4/3)*(513/512) an 4th: ratio 1.335,937,5
693/512 ! 23: F\ 346.5
351/256 ! 24: F. 351
711/512 ! 25: F/ 355.5
45/32 ! 26: F+ 360 ! Syntonic 5-limit tritone
729/512 ! 27: GB 364.5 ! Pythagorean 3-limit tritone
739/512 ! 28: Gb 369.5
749/512 ! 29: F# 374.5
379/256 ! 30: F& 379
3/2 ! 31: G- 384 ! the JI 5th
195/128 ! 32: G\ 390
395/256 ! 33: G. 395
25/16 ! 34: G/ 400 Hz ! Mersenne's "French-opera-tone"
405/256 ! 35: G+ 405
821/512 ! 36: AB 410.5
13/8 ! 37: Ab 416 ! the 13th partial overtone
843/512 ! 38: G# 421.5 ! ~Mozart's~Vienna-pitch
853/512 ! 39: G& 426.5
27/16 ! 40: A- 432 ! Sauveur's & Verdi's ; Pythagorean 6th
219/128 ! 41: A\ 438 ! Pavarotti's abs.-pitch
111/64 ! 42: A. 444 ! Herbert Karajan's "
225/128 ! 43: A/ 450 ! (7/4)*(225/224) ~natural~septime~
57/32 ! 44: A+ 456 ! Werckmeister's ~"Choir~Thon"~
231/128 ! 45: BB 462
117/64 ! 46: Bb 468
237/128 ! 47: A# 474
15/8 ! 48: A& 480 ! Syntonic 5-limit 7th
243/128 ! 49: B- 486 ! Pythagoran 7th or octave/limma
985/512 ! 50: B\ 492.5
499/256 ! 51: B. 499
1011/512 ! 52: B/ 505.5
2/1 ! 53: B+ 512 =C-! tenor_C-_5
!
![eof]

Her attend again the artihmetically equal steps inbetween

1.)#9:...:#18 = 72:73:74:74:75:76:77:78:79:80:81 and
2.)#49:#50:#51:#52:#53 = 972:985:998:1011:1024 = B-5:B\5:B.5:B/5:B+5
respectively with the constant step-wide of 13:= 256-243 = 2^8 - 3^5

due to the Philolaos's specification of construction.

Rehablitation:
Dont't belive any of the highly-decorated scholars in the encyclopedias, that labeled wrongly Phliolaos due to that genial method in an derogative way as:
"incompetenten Wirr-Kopf" ~~ 'incompetent muddle-head' :-(

It appears that particular case again:
An incompetent scholar once-more copied in turn by yet another even less incompetent, all both togehter without the slightest understanding of the matter and the two present themself as a self-proclaimed experts, by blowing and exchangeing barely
soap-bubbles, merely because theirs unverified nonsense was proudly brought to us readers per 'authoritative' encyclopaedia.

Conclusion:
Some outdated views are not even worth the paper on which it is printed. Paper is patient!

Yours Sincerely
Andreas Sparschuh

🔗genewardsmith <genewardsmith@...>

🔗George Sanders <georgesanders11111@...>

Michael,

agreed that the decision as to whether something is original or not requires some consideration. My main point was that the word does not mean "having no element that cannot be found in previous works." And, as you've pointed out, when one claims that something is original, one needs to say in which respect it is original.

I've changed the thread title so as not to irritate Ozan.

Franklin

--- On Thu, 5/20/10, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@...>
Subject: [tuning] Definition of originality and why tuning seems more "varied in levels of originallity" rather than either "original" or "aboriginal"
To: tuning@yahoogroups.com
Date: Thursday, May 20, 2010, 7:22 PM

"An original work is one not received from others nor one copied based on
the work of others." -
http://en.wikipedia .org/wiki/ Originality

The latter is definitely false...even the most new and novel ideas have some sort of historical pre-cursor.. .although some have far less than others. You can even say Henry Ford's Model T car was not original because it used wheels and an engine...both of which existed far before the Model T. Or that any piece of music is "not original" because it uses the same scale or chords as many other pieces. It's...indeed far too strict a qualification for being original.

I'd vouch to say something original must be significantly different and uniquely useful(or, at
times, useless) in contrast to predecessors. For example, to gain a patent an idea has to pass a number of people's votes as to being significantly different from the most closely related ideas in existence.
Meanwhile so far as things such as musical works (in which subjectivity among listeners plays a huge role)...it seems fair to say music that's considered original achieves either moods or techniques recognized by many people as uniquely useful. For example, Debussy's use of transposition within verses creates a unique new sense of open-ness while maintaining a single-key sense of balanced resolve. If someone made a style of music which made people lose balance...it would still be original...just in a "uniquely useless" way. :-D

So being "original", I'd vouch...doesn' t necessarily mean "well liked" either...it much more so means it does something that, in many ways, has not been done
before.

For a scale to qualify as original one must ask, for example, what that scale can do (or what multiple things it can acheive simultaneously) that other tunings can't. And of course mathematically original and original "when played" are two different things as many people can't hear slight mathematical optimizations.
I'd actually say it's easy to make an original scale far as using different math and/or having a distinct combination of dyadic intervals... but hard to make one that's original in many ways at once and different enough from existing scales to be easily recognized audibly as different... and not just mathematically.

-Michael

__._,

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-->

🔗Ozan Yarman <ozanyarman@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗a_sparschuh <a_sparschuh@...>

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

> And what of 171?

Hi Gene & Oz,
ok, you both asked me for an dyadic-rational 171-tone,
ok here you can get one:

Split the semitone 15/16 into 16 consecutive subparts by:

15/16 = 240/256 = 240:241:242: ... :255:256

that procedure contains the superparticular ratios sequence

for the subdivision of the Limma 243/256 into 13 parts

243/256 = 243:244: ... : 255:256

also the Syntonic-Comma SC=80/81 into 3 parts

80/81 = 240/243 = 240:241:242:243

and finally Archytas's 'septimal-comma' into 4 parts

63/64 = 252:253:254:255

then interpolate all that 16 absolute-pitches by 171 quintes
Recommendation, please read under: [Use <option> Fixed-Wide-Font ]

000:_________C- 1 unison ..... _!256Hz!_ initial-fit_______________
001: G- 3
002: D- 9
003: A- 27
004: E- 81
005:_________B- _!243!_ second-match coincides_____________________
006: GB 729
007: DB 2187 3^7*2=4374 {> 4375 = 7 * 5^4} the Ragisma
008:= 16-8 AB 205=41*5 ... 6560 (< 6561 := 3^8) -----------------
009: EB 615
010: BB 1845
011: F\ 2767 5534 (<5535 := 3*BB)
012: C\ 2075 4150 8300 (< 8301 := 3*2767)
013: G\ 389 ... 6224 (< 6225 := 3*C\ )
014: D\ 1167
015: A\ 875 = 7*5^3 1750 3500 (< 3501 := 3*D\ )
016: E\ 41 ... 2624 ( < 2625 )
017:_________B\ 123 _!246!________________________________________
018: Gb 369
019: Db 1107
020:= 28-8 Ab 415=83*5 ... 3320 (< 3321 )-----------------------
021: Eb 1245
022: Bb 1867 3734 (< 3735)
023: F. 175=7*5^2 350 700 1400 2800 5600 (<5601)
024: C. 525
025: G. 1575
026: D. 1181 ... 4724 (<4725)
027: A. 1771 ... 3542 (<3543)
028: E. 83 ... 5312 (< 5313)
029:_________B. _!243!___________________________________________
030: F# 747
031:= 39-8 C# 35=7*5 70 140 ... 2240 (<2241) ------------------
032: G# 105
033: D# 315
034: A# 59 118 ... 944 (<945)
035: F/ 177
036: C/ 571
037: G/ 1593
038: D/ 4779
039: A/ 7 ... 14436 (<14437) natural 7th partial overtone
040: E/ 21
041:_________B/ 63 126 _!252!___Archytas_'septimal-comma'________
042: F& 189
043: C& 567
044:= 52-8 G& 425=17*5^2 850 1700 (<1701)------------------------
045: D& 1275
046: A& 239 ... 3824 (<3825)
047: F+ 717
048: C+ 2151
049: G+ 1613 ... 6452 (<6453)
050: D+ 2419 2438 (<2439)
051: A+ 907 ... 7256 (<7257)
052: E+ = F-, 85 ... 2720 (<2721)
053:____B+ = C-, _!255!_____________________________________________
054: G-, 765
055: D-, 2295
056: A-, 1721 ... 6684 (<6685)
057: E-, 5163
058:_________B-, 121=11^2 __!242!___________________________________
059: GB, 363
060: DB, 1089
061: AB, 3267
062:=70-8 EB, 1225=245*5 2450 4900 9800 (<9801) the "Gauss-Comma"
063: BB, 1837 3674 (<3675)
064: F\, 2755=551*5 5510 (<5511)----------------------------
065: B-" C\, 1033
066: G\, 3099
067: D\, 581=83*7 ... 9296 (<9297)
068: A\, 1743
069: E\, 1307
070:_________B\, _!245!_ 490 .... 3920 (<3921)_____________________
071: Gb, 735 = 7^2*5*3
072: Db, 2205
073: Ab, 3307 6614 (<6615)
074:=82-8 Eb, 155=31*5 ... 9920 (<9921) ------------------------
075: Bb, 465
076: F., 1395
077: B\" C., 523 ... 4184 (<4185)
078: G., 49=7^2 ... 1568 (<1569 ) Werckmeister's choice
079: D., 147
080: A., 441 Hz Scheibler's choice 441Hz/440Hz
081: E., 1323
082:_________B., 31 62 124 _!248!_ 496 892 1784 3968 (<3969=49*81)
083: F#, 93
084: C#, 279
085: G#, 837
086:=94-8 D#, 1255=251*5 2510 (<2511)-----------------------------
087: B." A#, 941 ... 3764 (<3765)
088: F/, 2823
089: C/, 2177 ... 8468 (<8469)
090: G/, 3175 ... 6350 (<6351)
091: D/, 2381 ... 9524 (<9525)
092: A/, 3571 7142 (<7143)
093: E/, 1339 ... 10712 (<10713)
094:_________B/, _!251!_ 502 ... 4016 (<4017)_______________________
095: F&, 753
096: C&, 2259
097: G&, 847 ... 6776 (<6777)
098:=106-8 D&, 635=127*5 ... 1270 2540 (<2541)
099: B/" A&, 1905 = 381*5---------------------------------------
100: F/" F+, 2857 5714 (<5715)
101:=109-8 C+, 4285=857*5 C+,=C/" in '171' enharmonics
102: G/" G+, 6427 12854 (<12855)
103: D/" D+, 1205 ... 19280 (<19281)
104: A/" A+, 1807 3614 (<3615)
105: E/" E+, 1355 ... 5420 (<5421)
106:__B/"____B+, 127 _!254!_ 508 1016 2032 4064 (4065)______________
107: F&" 381
108: C&" 1143
109: G&" 857 1714 3428 (<3429)
110: D&" 2571
111:_________A&" _!241!_ 482 ... 7712 (<7713)________________________
112: F+" 723
113: C+" 2169
114: G+" 6507
115: D+" 305=61*5 ... 19520 (<19521)------------------------
116:=124-8 A+" 915 = 183*5 ---------------------------------------
117: F-' E+" 343 = 7^3 the 3rd power of the 7th-harmonics
118: B+" C-' 1029 B+" = C-' enharmonics
119: G-' 3087 = 7^3 * 3^2
120: D-' 2315 ... 9260 (<9261)
121: A-' 217 = 31*7 ... 6944 (<6945)
122: E-' 651
123:_________B-' 61 122 _!244!_ 488 976 1952 (<1953)________________
124: GB' 183
125: DB' 549
126: AB' 1647
127:=135-8 EB' 1235 = 247*5 --------------------------------------
128: BB' 463 ... 3704 (<3705)
129: F\' 1389
130: C\' 2083 4166 (<4167)
131: G\' 781 ... 6248 (<6249)
132: D\' 2343
133: A\' 1757 3514 7028 (<7029)
134: E\' 2635 ... 5270 (<5271)
135:_________B\' _!247!_ 7904 (<7905)_______________________________
136: Gb' 741
137: Db' 2223
138: Ab' 1667 ... 6668 (<6669)
139:=147-8 Eb' 625=5^4 ... 5000(<5001)the 4th power the 5th partial
140: Bb' 1875
141: F.' 703 ... 5624 (<5625)
142: C.' 527 ... 2108 (<2109)
143: G.' 1581
144: D.' 2371 4742 (<4742)
145: A.' 889 ... 7112 (<7113)
146: E.' 2667
147:_________B.' 125 _!250!_ 500 1000 2000 4000 8000 (<8001)__5^3__
148: F#' 375
149: C#' 1125
150: G#' 1687
151:=159-8 D#' 1265=253*5 ... 5060 (<5061)
152: A#' 1897 3794 (< 3795)
153: F/' 2845 = 569*5 ------------------------------------
154: C/' 4267 8534 (<8535)
155: G/' 25 50 100 ... 12800 (<12801)________5^2___________
156: D/' 75
157: A/' 225 (> 224 ... 7 = 039: A/)
158: E/' 675
159:_________B/' _!253!_ 506 1012 2024 (<2025)_____________________
160: F&' 759
161: C&' 569 1138 2276 (<2277)
162: G&' 1707
163. D&' 5 10 20 40 80 160 320 640 1280 2560 5120 (<5121)
164: A&' 15
165: F+' 45
166: C+' 135
167: G+' 405
168: D+' 1215
169: A+' 911 1822 3644 (<3645 := 3*D+')
170: F- = E+' 683 1366 2732 (<2733 := 3*A+') enharmonics F-=E+'
171: B+' = C- 1 2 4 8 16 32 64 128 _!256!_ 512 1024 2048(<2049)

.......to be continued later.....

A.S.

the ultimate proportional beating well-temperament

🔗Ozan Yarman <ozanyarman@...>

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