Fwd: 12note Tuning Table Algorithms for 53tet.

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:

53tet is an ancient and much respected solution to the tuning problem.
More info at:

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

Beginners who don't know very much about this temperament can use the
following musical algorithms to instantly produce 53tet music. A sound
device like the Kurzweil K2xxx series (or similar) together with a
midi
interface and software that plays midi files is sufficient to achieve
good results.

Here is an algorithm where x = any interval in 53tet
and C = 22.64cents (or the 53tet comma):

C = zero cents
G = x
D = 2x
A = 3x
E = 4x-C
B = 5x-C
F# = 6x-C
C# = 7x-C
Ab = 8x-2C
Eb = 9x-2C
Bb = 10x-2c
F = 11x-2C

Multiples of 1200 are subtracted to bring all the results back to one
octave.

EXAMPLE: When x=702cents (actually 701.89) the tuning table becomes:

C = zero cents
G = 702
D = 204
A = 906
E = 385
B = 1087
F# = 589
C# = 91
Ab = 770
Eb = 272
Bb = 974
F = 475

A variation on this musical algorithm is to add +C and +2C rather than
subtract them.

--- End forwarded message ---

Hi Robert,
Thanks.
53tet is the only equal temperament I like :)

May I add that the resulting scale will give:
B 1/1
C 16/15
C# 9/8
D 6/5
D# 5/4
E 4/3
F 45/32
F# 3/2
G 8/5
G# 5/3
A 16/9
A# 15/8
B 2/1

Marcel

On Thu, Jan 29, 2009 at 6:03 PM, robert thomas martin <
robertthomasmartin@...> wrote:

> --- In MicroMadeEasy@yahoogroups.com <MicroMadeEasy%40yahoogroups.com>,
> "robert thomas martin"
> <robertthomasmartin@...> wrote:
>
> 53tet is an ancient and much respected solution to the tuning problem.
> More info at:
>
> http://en.wikipedia.org/wiki/53_equal_temperament
>
> Beginners who don't know very much about this temperament can use the
> following musical algorithms to instantly produce 53tet music. A sound
> device like the Kurzweil K2xxx series (or similar) together with a
> midi
> interface and software that plays midi files is sufficient to achieve
> good results.
>
> Here is an algorithm where x = any interval in 53tet
> and C = 22.64cents (or the 53tet comma):
>
> C = zero cents
> G = x
> D = 2x
> A = 3x
> E = 4x-C
> B = 5x-C
> F# = 6x-C
> C# = 7x-C
> Ab = 8x-2C
> Eb = 9x-2C
> Bb = 10x-2c
> F = 11x-2C
>
> Multiples of 1200 are subtracted to bring all the results back to one
> octave.
>
> EXAMPLE: When x=702cents (actually 701.89) the tuning table becomes:
>
> C = zero cents
> G = 702
> D = 204
> A = 906
> E = 385
> B = 1087
> F# = 589
> C# = 91
> Ab = 770
> Eb = 272
> Bb = 974
> F = 475
>
> A variation on this musical algorithm is to add +C and +2C rather than
> subtract them.
>
> --- End forwarded message ---
>
>
>

[Non-text portions of this message have been removed]

Oops..That should be A = 9/5 offcourse. Not 16/9.

Marcel

On Thu, Jan 29, 2009 at 7:21 PM, Marcel de Velde <m.develde@...>wrote:

> Hi Robert,
> Thanks.
> 53tet is the only equal temperament I like :)
>
> May I add that the resulting scale will give:
> B 1/1
> C 16/15
> C# 9/8
> D 6/5
> D# 5/4
> E 4/3
> F 45/32
> F# 3/2
> G 8/5
> G# 5/3
> A 16/9
> A# 15/8
> B 2/1
>
> Marcel
>
> On Thu, Jan 29, 2009 at 6:03 PM, robert thomas martin <
> robertthomasmartin@...> wrote:
>
>> --- In MicroMadeEasy@yahoogroups.com <MicroMadeEasy%40yahoogroups.com>,
>> "robert thomas martin"
>> <robertthomasmartin@...> wrote:
>>
>> 53tet is an ancient and much respected solution to the tuning problem.
>> More info at:
>>
>> http://en.wikipedia.org/wiki/53_equal_temperament
>>
>> Beginners who don't know very much about this temperament can use the
>> following musical algorithms to instantly produce 53tet music. A sound
>> device like the Kurzweil K2xxx series (or similar) together with a
>> midi
>> interface and software that plays midi files is sufficient to achieve
>> good results.
>>
>> Here is an algorithm where x = any interval in 53tet
>> and C = 22.64cents (or the 53tet comma):
>>
>> C = zero cents
>> G = x
>> D = 2x
>> A = 3x
>> E = 4x-C
>> B = 5x-C
>> F# = 6x-C
>> C# = 7x-C
>> Ab = 8x-2C
>> Eb = 9x-2C
>> Bb = 10x-2c
>> F = 11x-2C
>>
>> Multiples of 1200 are subtracted to bring all the results back to one
>> octave.
>>
>> EXAMPLE: When x=702cents (actually 701.89) the tuning table becomes:
>>
>> C = zero cents
>> G = 702
>> D = 204
>> A = 906
>> E = 385
>> B = 1087
>> F# = 589
>> C# = 91
>> Ab = 770
>> Eb = 272
>> Bb = 974
>> F = 475
>>
>> A variation on this musical algorithm is to add +C and +2C rather than
>> subtract them.
>>
>> --- End forwarded message ---
>>
>>
>>
>
>

[Non-text portions of this message have been removed]

--- In MakeMicroMusic@yahoogroups.com, Marcel de Velde
<m.develde@...> wrote:
>
> Oops..That should be A = 9/5 offcourse. Not 16/9.
>
> Marcel
>
> On Thu, Jan 29, 2009 at 7:21 PM, Marcel de Velde
<m.develde@...>wrote:
>
> > Hi Robert,
> > Thanks.
> > 53tet is the only equal temperament I like :)
> >
> > May I add that the resulting scale will give:
> > B 1/1
> > C 16/15
> > C# 9/8
> > D 6/5
> > D# 5/4
> > E 4/3
> > F 45/32
> > F# 3/2
> > G 8/5
> > G# 5/3
> > A 16/9
> > A# 15/8
> > B 2/1
> >
> > Marcel
> >
> > On Thu, Jan 29, 2009 at 6:03 PM, robert thomas martin <
> > robertthomasmartin@...> wrote:
> >
> >> --- In MicroMadeEasy@yahoogroups.com <MicroMadeEasy%
40yahoogroups.com>,
> >> "robert thomas martin"
> >> <robertthomasmartin@> wrote:
> >>
> >> 53tet is an ancient and much respected solution to the tuning
problem.
> >> More info at:
> >>
> >> http://en.wikipedia.org/wiki/53_equal_temperament
> >>
> >> Beginners who don't know very much about this temperament can
use the
> >> following musical algorithms to instantly produce 53tet music. A
sound
> >> device like the Kurzweil K2xxx series (or similar) together with
a
> >> midi
> >> interface and software that plays midi files is sufficient to
achieve
> >> good results.
> >>
> >> Here is an algorithm where x = any interval in 53tet
> >> and C = 22.64cents (or the 53tet comma):
> >>
> >> C = zero cents
> >> G = x
> >> D = 2x
> >> A = 3x
> >> E = 4x-C
> >> B = 5x-C
> >> F# = 6x-C
> >> C# = 7x-C
> >> Ab = 8x-2C
> >> Eb = 9x-2C
> >> Bb = 10x-2c
> >> F = 11x-2C
> >>
> >> Multiples of 1200 are subtracted to bring all the results back
to one
> >> octave.
> >>
> >> EXAMPLE: When x=702cents (actually 701.89) the tuning table
becomes:
> >>
> >> C = zero cents
> >> G = 702
> >> D = 204
> >> A = 906
> >> E = 385
> >> B = 1087
> >> F# = 589
> >> C# = 91
> >> Ab = 770
> >> Eb = 272
> >> Bb = 974
> >> F = 475
> >>
> >> A variation on this musical algorithm is to add +C and +2C
rather than
> >> subtract them.
> >>
> >> --- End forwarded message ---
> >>
> >>
> >>
> >
> >
>
>
> [Non-text portions of this message have been removed]
>
From Robert. Thankyou for your response. 53tet is very elegant from
a mathematical point of view but from a practical point of view I
prefer 22tet and from a scientific/experimental point of view I
prefer 100tet. But I am able to adapt my ideas to all sorts of
microtonal systems because I have carried out thousands of sound
harmonic experiments. Who knows what the majority of people will
finally decide? Evolution marches inexorably on!