- --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>

wrote:>

I don't know abot others, here, Andreas, but I am not even gonna try

> --- In tuning@yahoogroups.com, Brad Lehman <bpl@> wrote:

>

to unravel what you might trying to say until you stop doing several

rediculous things:

(1) Peppering you posts with endless wiki links for really stupid

things, like middle C or piano keyboard frequencies.

(2) Start using just ONE clear and easy to understand method for

indicating temperaments. All that scala mismash and wierd stuff like

multiplying frequencies by 3 instead of 1,5 just makes it all not

worth the time.

Try being simple and clear for just once. Maybe you've really got

something to say, who knows? At the moment it just looks like the

ravings of a madman.

Ciao,

P --- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:

Hi Paul,

> Start using just ONE clear and easy to understand method for

> indicating temperaments.

Simply consider all given values there

as frequencies in Hz of absolute pitches,

that are subjects of 3 possible sequential operations:

Algorithm for synchroneous well-temperaments:

1. Step 19-times an octaves down, by halfing the pitch-frequency

2. Go 12 times to partial 3:1, by multipying with facor 3.

occasional

3. Decrement frequncy by -1Hz down, when intend tempering flattend.

but only if you insist in "wide-5ths" then allow also too:

(4. Increment by +1Hz upwards, for an sharper "French"-5th.)

Comeback condition:

Choose the chain of flow in the operation sequence

so that the circle of a dozen 5ths returns back to the initial

start after 12times 3:1 and 19times 1:2 while fitting the

decrements so, that they yield an distribution of the PC=3^12:2^19

into

http://en.wikipedia.org/wiki/Superparticular_ratio

s.

> All that scala mismash and wierd stuff like

> multiplying frequencies by 3 instead of 1,5 just makes it all not

> worth the time.

That ratio of 3/2 = 1.5 arises operationally from taking the

quotient of the 3rd partial (3:1) over an octve (2:1),

when realting that both overtones #2 and #3 to theirs fundamental

(1:1) base.

http://en.wikipedia.org/wiki/Harmonic_series_(music)

"...allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, etc. times of the

fundamental."

but on strings there never appear 2/3 = 1:(3/2) due to the lack of

http://en.wikipedia.org/wiki/Subharmonics

in pianos:

http://www.sfu.ca/sonic-studio/handbook/Subharmonic.html

"Subharmonics do not normally occur in natural sounds, although the

subharmonic f/2 may be generated by the cone of a LOUDSPEAKER."

That makes an 5th (3:2 = 1.5) less fundamental than the ratio

inbetween the overtones 3:1 and 2:1 within the harmonic series.

Hence an 5th is composed by an

division of an 12th (3:1) as nominator

over an octave (2:1) as denominator by the calculation

(3:2) := (3:1):(2:1)

In other words:

any 5th (3:2) consists terms of

http://en.wikipedia.org/wiki/Harmonic

as composed of the difference of an '12th'-'8th'.

"3 just perfect fifth P8 + P5 1902.0 702.0"

when both do refer to the same (1:1) base or

http://en.wikipedia.org/wiki/Fundamental_frequency

hope that helps,

why i do prefer the multiplication by the "harmoic" factor 3

in order to stay wihin the partial-series.

Even Brad understood that in his:

http://www-personal.umich.edu/~bpl/larips/bachtemps.html

"...in the line of fifths A-E-B-F#-C#-G#-D#-Bb-F-C-G-D-A to reduce the

next note by 1 Hz, i.e. introducing a beat rate of 1 per second

against the preceding fifth. The fifths F#-C#-G#-D# and D-A are kept

pure. The other eight are adjusted by different geometric amounts,

based on the superparticular ratios described in his algorithm.

(Arithmetically, it amounts to subtracting 1 Hz from the top of most

of the columns, in his chart, wherever there are values in

parentheses.)"...

Brad contiues or the experts:

"Sparschuh's mathematical algorithm resembles the classic unproven

"Collatz Conjecture" from 1937, except that Sparschuh's iterated

function uses (3n-1) rather than (3n+1). [And see Eric Roosendaal's

3x+1 web site, along with this page by Frits Beukers demonstrating and

comparing the numerical sequences....]"

Yours Sincerely

A.S.

Yours Sincerely

A.S.