Pianotech

  • 1.  Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Posted 05-29-2019 13:51

    Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)


    Note Cents
    C 0.00
    C# 100.00
    D 203.26
    D# 298.04
    E 403.91
    F 498.70
    F# 601.96
    G 701.96
    G# 798.70
    A 903.91
    A# 998.04
    B 1103.26
    C 1200.00



    Fifths


    Fifth Cents
    C-G 701.96
    G-D 701.30
    D-A 700.65
    A-E 700.00
    E-B 699.35
    B-F# 698.70
    F#-C# 698.04
    C#-G# 698.70
    G#-D# 699.35
    D#-A# 700.00
    A#-F 700.65
    F-C 701.30
    C-G 701.96



    Fourths


    Fourth Cents
    G-C 498.04
    D-G 498.70
    A-D 499.35
    E-A 500.00
    B-E 500.65
    F#-B 501.30
    C#-F# 501.96
    G#-C# 501.30
    D#-G# 500.65
    A#-D# 500.00
    F-A# 499.35
    C-F 498.70
    G-C 498.04



    Offsets in Cents from 12-TET


    Note Cents
    C 0.00
    C# 0.00
    D +3.26
    D# −1.96
    E +3.91
    F −1.30
    F# +1.96
    G +1.96
    G# −1.30
    A +3.91
    A# −1.96
    B +3.26
    C 0.00


    Symmetrical Beat Synchrony


    C-G is a Pure Fifth (701.96 cents).

    F#-C# is a Fifth reduced by 1/6 of the Pythagorean comma (698.04 cents).

    F#-A#-C# is directly opposite C-E-G in the Circle of Fifths.

    Each consecutive Fifth differs by the same amount (0.65 cents). 


    Beat synchrony will be the lowest for C-E-G, the Major Triad.

    Beat synchrony will increase smoothly for each consecutive Major Triad around the Circle of Fifths.

    Beat synchrony will be the highest for F#-A#-C#, the Major Triad, at the middle of the Circle of Fifths.

    Beat synchrony will decrease smoothly for each consecutive Major Triad around the Circle of Fifths.

    Beat synchrony will be the lowest for C-E-G, the Major Triad.


    In conclusion, symmetrical beat synchrony will occur from C-E-G, the Major Triad, to C-E-G, the Major Triad, around the Circle of Fifths.

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    Roshan Kakiya
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    Attachment(s)

    xlsx
    Roshan Kakiya's Final Temperament (Symmetrical Beat Synch...xlsx   11 KB 1 version
    zip
    Scala File - Roshan Kakiya's Final Temperament (Symmetric...zip   469 B 1 version


  • 2.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Posted 05-29-2019 17:40
      |   view attached


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    Roshan Kakiya
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    Original Message


  • 3.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Registered Piano Technician
    Posted 05-30-2019 16:40
    "Beat cancellation occurs because + 17.60 cents − 17.60 cents + 0.00 cents = 0.00 cents."

    No. Synchronous temperaments are associated with reinforced, prominent, clear beating, not beat masking. Beat synchrony is not necessarily a bad thing; it just doesn't cause beat cancelation.

    Think about it. Beats are fluctuations in amplitude. If the peaks and troughs of different coincident partial pairs sync up, then the beating will be reinforced.

    Beat masking is associated with asynchronous beat rates in which the peaks and troughs don't coincide with each other.





    Original Message


  • 4.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Posted 05-30-2019 19:38
    "Beat cancellation" was not the correct term to use.

    I should have used the words "overall deviation from Just Intonation" instead.


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    Roshan Kakiya
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    Original Message


  • 5.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Posted 05-30-2019 17:29
    With minimum third at E to G# this is the wrong way round, sorry to say. CE FA GB should be the comfortable thirds. BD# AbC F#Bb should be the most hideous.

    This going around the circle of fifths picking up a beat or two each time is putting my head in a spin 

    :-)

    ;-)

    Best wishes and all encouragement - without wishing you to go round and round reinventing the wheel on an endless journey,

    David P 

    --
    - - - - - - - - - - - - - - - - - - - - - - - -
    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594



    Original Message


  • 6.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Posted 05-30-2019 20:05
    This version of my Final Temperament is experimental because I have deliberately made the general trend of the beat synchrony symmetrical around the Circle of Fifths.

    It is actually quite difficult to reinvent the wheel in the world of tuning.

    For example, compare the following two images:

    http://rollingball.com/images/Kakiya-Symmetrical.gif

    http://rollingball.com/images/DeMorgan.gif

    After creating my Final Temperament, I discovered that it is almost exactly the same as De Morgan's temperament. Therefore, I deliberately shifted the Circle of Fifths of my Final Temperament to match De Morgan's temperament.


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    Roshan Kakiya
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    Original Message


  • 7.  RE: Roshan Kakiya's Final Temperament (Symmetrical Beat Synchrony Version)

    Registered Piano Technician
    Posted 05-30-2019 21:56
    It is actually quite difficult to reinvent the wheel in the world of tuning.

    I think many of us have been wondering when you were going to realize this. Virtually every combination and arrangement of the scale has already been tried over 300 years. Can't fault you for trying again though. 

    Pwg

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    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
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    Original Message