Pianotech

  • 1.  Roshan Kakiya's Stretched Young I

    Posted 10-13-2019 20:41
    Roshan Kakiya's Stretched Young I

    Cents

    C 0.00
    C# 96.40
    D 197.74
    D# 299.07
    E 395.47
    F 500.51
    F# 595.68
    G 699.49
    G# 798.35
    A 897.22
    A# 1001.03
    B 1096.19
    C 1201.23


    Offsets in Cents from Pure Octave Equal Temperament

    C 0.00
    C# −3.60
    D −2.26
    D# −0.93
    E −4.53
    F +0.51
    F# −4.32
    G −0.51
    G# −1.65
    A −2.78
    A# +1.03
    B −3.81
    C +1.23


    Offsets in Cents from Pure 12th Equal Temperament

    C 0.00
    C# −3.70
    D −2.47
    D# −1.23
    E −4.94
    F 0.00
    F# −4.94
    G −1.23
    G# −2.47
    A −3.70
    A# 0.00
    B −4.94
    C 0.00


    Frequencies in Hz

    A0 27.42
    A#0 29.12
    B0 30.76
    C1 32.69
    C#1 34.56
    D1 36.64
    D#1 38.85
    E1 41.07
    F1 43.64
    F#1 46.11
    G1 48.96
    G#1 51.84
    A1 54.88
    A#1 58.27
    B1 61.57
    C2 65.42
    C#2 69.16
    D2 73.33
    D#2 77.75
    E2 82.21
    F2 87.35
    F#2 92.28
    G2 97.99
    G#2 103.75
    A2 109.84
    A#2 116.63
    B2 123.22
    C3 130.93
    C#3 138.43
    D3 146.77
    D#3 155.62
    E3 164.53
    F3 174.82
    F#3 184.70
    G3 196.11
    G#3 207.64
    A3 219.84
    A#3 233.43
    B3 246.62
    C4 262.05
    C#4 277.05
    D4 293.75
    D#4 311.46
    E4 329.29
    F4 349.89
    F#4 369.66
    G4 392.51
    G#4 415.58
    A4 440.00
    A#4 467.19
    B4 493.59
    C5 524.47
    C#5 554.50
    D5 587.92
    D#5 623.36
    E5 659.06
    F5 700.29
    F#5 739.86
    G5 785.58
    G#5 831.75
    A5 880.63
    A#5 935.05
    B5 987.88
    C6 1049.68
    C#6 1109.79
    D6 1176.69
    D#6 1247.62
    E6 1319.06
    F6 1401.57
    F#6 1480.77
    G6 1572.27
    G#6 1664.68
    A6 1762.51
    A#6 1871.43
    B6 1977.18
    C7 2100.86
    C#7 2221.15
    D7 2355.05
    D#7 2497.02
    E7 2640.00
    F7 2805.14
    F#7 2963.65
    G7 3146.79
    G#7 3331.73
    A7 3527.54
    A#7 3745.53
    B7 3957.18
    C8 4204.71


    Mathematical Structure

    Pythagorean comma = −1.

    12/19 Pythagorean comma = 12/19 × −1 = − 12/19.

    a = The amount of the Pythagorean comma by which C-G, G-D, D-A and A-E are each narrower than Just.

    b = The amount of the Pythagorean comma by which E-B, B-F#, A#-F and F-C are each narrower than Just.

    c = The amount of the Pythagorean comma by which F#-C#, C#-G#, G#-D# and D#-A# are each narrower than Just.


    a = 2b.

    c = 0.


    4a + 4b + 4c = − 12/19.

    4a + 4b + 4 × 0 = − 12/19.

    4a + 4b = − 12/19.

    4 × 2b + 4b = − 12/19.

    8b + 4b = − 12/19.

    12b = − 12/19.

    b = − 12/19 × 1/12.

    b = − 1/19.


    a = 2 × (− 1/19).

    a = − 2/19.


    Features

    Arrangement of the Fifths:

    Pure Fifth narrowed by 2/19 Pythagorean comma: C-G, G-D, D-A and A-E.

    Pure Fifth narrowed by 1/19 Pythagorean comma: E-B, B-F#, A#-F and F-C.

    Pure Fifth: F#-C#, C#-G#, G#-D# and D#-A#.


    Retained elements of Young I:

    The Major Thirds are symmetrical on either side of F# around the Circle of Fifths.

    The Major Third C-E is closest to Just and the Major Third F#-A# is furthest from Just.

    The Fifths F#-C#, C#-G#, G#-D# and D#-A# are the same.


    Retained elements of Pure 12th Equal Temperament:

    The Fifth and the Octave will beat at the same rate within the Twelfths E-B, B-F#, A#-F and F-C.

    The Fifths and the Twelfths E-B, B-F#, A#-F and F-C are the same. 

    Every Octave is the same.

    The Major Thirds A-C# and D#-G are the same.

    ------------------------------
    Roshan Kakiya
    ------------------------------

    Attachment(s)

    zip
    Roshan Kakiya's Stretched Young I - Scale.zip   377 B 1 version
    xlsx
    Roshan Kakiya's Stretched Young I - Cents and Frequencies...xlsx   16 KB 1 version


  • 2.  RE: Roshan Kakiya's Stretched Young I

    Posted 10-14-2019 02:04
    Stretching of its own is not beautiful and so I don't understand the purpose of these mathematics. Stretching makes thirds more out of tune, disharmonious, disresonant and destroys the advantage of an unequal temperament rather than the equal(ly out of tune).

    Recently I read a quote that writing about music is like dancing about architecture. It has to be heard, experienced, as does tuning. Mathematiking about temperament without access to its aural effect on the piano is likewise. Organ tuning is another matter perhaps - but there's no stretching there.

    Possibly I'm not the only member of the forum who might urge you to get a tuning hammer in your hands and listen to an instrument as you tune it. Only then can you know what you're listening for. 

    Mathematics is a tool in an analogue world, not a definition. The trouble with the digital age is that people have become illusioned into thinking that precision is more valuable than the slide rule.

    Best wishes

    David P

    ------------------------------
    David Pinnegar BSc ARCS
    Curator and House Tuner - Hammerwood Park, East Grinstead, Sussex UK
    antespam@gmail.com

    Seminar 6th May 2019 - http://hammerwood.mistral.co.uk/tuning-seminar.pdf "The Importance of Tuning for Better Performance"
    ------------------------------

    Original Message


  • 3.  RE: Roshan Kakiya's Stretched Young I

    Posted 10-14-2019 05:00
    David,

    The traditional theoretical models of unequal temperament contain Pure Octaves which means that they do not account for inharmonicity at all.

    My Stretched Young I has been designed to account for inharmonicity whilst adhering to the overall design of Young I.

    I have achieved this by breaking the tradition of treating the Pure Octave as sacrosanct and by preserving the overall structure of Young I so that C-E is the Major Third that is closest to Just, F#-C# is the Major Third that is furthest from Just and all the Major Thirds are symmetrical on either side of F# around the Circle of Fifths. My Stretched Young I does not contain any Pythagorean Major Thirds.

    My Stretched Young I is a theoretical stretched framework.


    Roshan Kakiya's Stretched Young I: Major Thirds (Values in Cents)

    C-E 395.47
    G-B 396.71
    D-F# 397.94
    A-C# 400.41
    E-G# 402.88
    B-D# 404.12
    F#-A# 405.35
    C#-F 404.12
    G#-C 402.88
    D#-G 400.41
    A#-D 397.94
    F-A 396.71
    C-E 395.47

    ------------------------------
    Roshan Kakiya
    ------------------------------

    Original Message


  • 4.  RE: Roshan Kakiya's Stretched Young I

    Posted 10-14-2019 06:01

    But inharmonicity varies from instrument to instrument and is variable. It's not predictable and the skilled tuner decides which inharmonic to tune to which. And it does not work to harmonic advantage of unequal temperament.

    Please just tune a real instrument and then you'll start to hear.

    As organ builder Martin Renshaw says, tuning is a process not a formula.

    Best wishes

    David P

    On 14 Oct 2019 10:00 a.m., "Roshan Kakiya via Piano Technicians Guild" <Mail@connectedcommunity.org> wrote:
    David, My Stretched Young I has been designed to account for inharmonicity whilst adhering to the overall design of Young I. I have achieved... -posted to the "Pianotech" community
    Please do not forward this message due to Auto Login.

    Pianotech

      Post New Message
    Re: Roshan Kakiya's Stretched Young I
    Reply to Group Reply to Sender
    Oct 14, 2019 5:00 AM
    Roshan Kakiya
    David,

    My Stretched Young I has been designed to account for inharmonicity whilst adhering to the overall design of Young I.

    I have achieved this by breaking the tradition of treating the Pure Octave as sacrosanct and by preserving the overall structure of Young I so that C-E is the Major Third that is closest to Just and F#-C# is the Major Third that is furthest from Just.

    The traditional theoretical models of unequal temperament contain Pure Octaves which means that they do not account for inharmonicity at all.

    My Stretched Young I provides a theoretical stretched framework for Young I.

    ------------------------------
    Roshan Kakiya
    ------------------------------
      Reply to Group Online   View Thread   Recommend   Forward   Mark as Inappropriate  
    ------------------------------
    Original Message



     
    To change your subscriptions, go to My Subscriptions. To unsubscribe from this community discussion, go to Unsubscribe.



    Original Message------

    David,

    My Stretched Young I has been designed to account for inharmonicity whilst adhering to the overall design of Young I.

    I have achieved this by breaking the tradition of treating the Pure Octave as sacrosanct and by preserving the overall structure of Young I so that C-E is the Major Third that is closest to Just and F#-C# is the Major Third that is furthest from Just. My Stretched Young I does not contain any Pythagorean Major Thirds.

    The traditional theoretical models of unequal temperament contain Pure Octaves which means that they do not account for inharmonicity at all.

    My Stretched Young I provides a theoretical stretched framework for Young I.

    ------------------------------
    Roshan Kakiya
    ------------------------------

    Original Message:
    Sent: 10-14-2019 02:04
    From: David Pinnegar
    Subject: Roshan Kakiya's Stretched Young I

    Stretching of its own is not beautiful and so I don't understand the purpose of these mathematics. Stretching makes thirds more out of tune, disharmonious, disresonant and destroys the advantage of an unequal temperament rather than the equal(ly out of tune).

    Recently I read a quote that writing about music is like dancing about architecture. It has to be heard, experienced, as does tuning. Mathematiking about temperament without access to its aural effect on the piano is likewise. Organ tuning is another matter perhaps - but there's no stretching there.

    Possibly I'm not the only member of the forum who might urge you to get a tuning hammer in your hands and listen to an instrument as you tune it. Only then can you know what you're listening for.

    Mathematics is a tool in an analogue world, not a definition. The trouble with the digital age is that people have become illusioned into thinking that precision is more valuable than the slide rule.

    Best wishes

    David P

    ------------------------------
    David Pinnegar BSc ARCS
    Curator and House Tuner - Hammerwood Park, East Grinstead, Sussex UK
    antespam@gmail.com

    Seminar 6th May 2019 - http://hammerwood.mistral.co.uk/tuning-seminar.pdf "The Importance of Tuning for Better Performance"


  • 5.  RE: Roshan Kakiya's Stretched Young I

    Posted 10-16-2019 07:45
    David,

    Accounting for inharmonicity to some extent in the mathematical models of unequal temperament, as I have done, is better than not accounting for it at all.

    ------------------------------
    Roshan Kakiya
    ------------------------------

    Original Message


  • 6.  RE: Roshan Kakiya's Stretched Young I

    Posted 10-16-2019 08:13
    Well actually not.

    One can predict what is meant to resonate with what in straight unstretched mathematics. Then one has to listen for those effects in tuning and see the extent to which stretch needs to be applied. Using some of the ETD softwares one can see that different harmonics are inharmonic to different extents so any stretch applied becomes appropriate to which of the harmonics one is choosing.

    The array of notes on a piano is an analogue to the solution of tuning harmoniously. The digital of mathematics cannot match the sophistication of the analogue. Tuning a piano is not just about tuning strings.

    Best wishes

    David P

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



    Original Message