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RE: Irrational time signature and tuplets


From: Mark Stephen Mrotek
Subject: RE: Irrational time signature and tuplets
Date: Thu, 12 Jun 2014 13:30:18 -0700

Hans,

(1+sqrt 5)/2 = 1.618... is the golden ratio, phi. 
http://en.wikipedia.org/wiki/Golden_ratio

Do you know of other instances of this ratio in music?

Mark

-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of Hans Aberg
Sent: Thursday, June 12, 2014 12:33 PM
To: Malte Meyn
Cc: address@hidden
Subject: Re: Irrational time signature and tuplets

On 12 Jun 2014, at 13:21, Malte Meyn <address@hidden> wrote:

> This can be done in LilyPond without using LaTeX:

I have made an example incorporating your code; it looks pretty neat. For the 
midi, I wrote out the ornaments in a separate version using the 5/3 ratio, so 
as to be closer to the (1+sqrt 5)/2 = 1.618...; so this is 19 = 5+3+3+5+3, 
instead of the traditional 12 = 3+2+2+3+2, the latter which is used as a base 
for the engraving. It is from a common tune, Egejki Majki, played by the Boys 
from Bouf/Buf in the videos [1-2]. If someone wants to make snippet, please go 
ahead!

1. https://www.youtube.com/watch?v=NCDe41TtV-Y
2. https://www.youtube.com/watch?v=OfyZZ8OFvvs


---- IrrationalMeter.ly ----

\version "2.19.6"

\header{
  title = "Exampel of irrational meter"
  subtitle = "Egejki Majki, original meter 12 = 3+2+2+3+2"
  composer = "Traditional (Macedonia)"
  copyright = "© Hans Åberg"
  tagline = ##f  % Removing "Music engraving by LilyPond (version)"
}


above = { \once \override Script #'script-priority = #-100 } below = { \once 
\override TextScript #'script-priority = #-100 }


irrtuplet = \once \override TupletNumber.text =  \markup \concat {
   "1:1+"
   \tiny "√"
   \hspace #-0.15
   \override #'(offset . -16)
   \override #'(thickness . 1.6)
   \underline "5"
 }


music = << \new Staff {
  \tempo 4 = 176
  \key d \minor

  \time 12/8
  \set beatStructure = #'(3 2 2 3 2)

  \override Staff.TimeSignature.stencil = #ly:text-interface::print
  \override Staff.TimeSignature.text =
  \markup \override #'(baseline-skip . 0) \center-column \number {
    \concat {
      "8+2"
      \tiny "√"
      \hspace #-0.2
      \override #'(offset . -25)
      \override #'(thickness . 1.6)
      \underline "5"
    }
    "8"
  }


  \override TupletNumber.text = #tuplet-number::calc-fraction-text

  \relative c' {
   \repeat volta 2 {
      \once \override TextScript #'padding = #1.0
      \set Staff.midiInstrument = "church organ"
      \irrtuplet \tuplet 2/3 {f16 g a d,}  a'8\prall d,  a'8\prall d
        \irrtuplet \tuplet 2/3 {c16 bes a g}  a8\prall g |
      \irrtuplet \tuplet 2/3 {f16 g a c,}  a'8\prall c,  a'8\prall d
        \irrtuplet \tuplet 2/3 {c16 bes a g}  a8\prall r8 |
      \irrtuplet \tuplet 2/3 {b16 c d d}  d8 d
        \above d8\trill^\markup{\flat}~d16 c
        \irrtuplet \tuplet 2/3 {c16 d c bes}  a8\prall g |
      \irrtuplet \tuplet 2/3 {f16 g e g}  f8\prall e  \times 2/3 {d8 e c}
        \irrtuplet \tuplet 2/3 {d16 e f g}  a8\prall g |
      \irrtuplet \tuplet 2/3 {f16 g e g}  f8\prall e  \times 2/3 {d8 e c}
        \irrtuplet \tuplet 2/3 {\above d8\trill^\markup{\flat}~d16 a}  d8-. r8 |
      }
    }
  }
>>

\score {
  \music
        \layout {}
}


musicmidi = << \new Staff {
  \tempo 4. = 186
  \key d \minor

  \time 19/8
  \set beatStructure = #'(5 3 3 5 3)

  \override TupletNumber.text = #tuplet-number::calc-fraction-text

  \relative c' {
    \repeat volta 2 {
      \once \override TextScript #'padding = #1.0
      \set Staff.midiInstrument = "church organ"
        \once \override TupletNumber.text = 
          #(tuplet-number::fraction-with-notes "4" "4.")
      \tuplet 2/5 {f16 g a d,}  \tuplet 2/3 {a'32 bes32 a16 d,8}  \tuplet 2/3 
{a'32 bes32 a16 d8}
        \once \override TupletNumber.text = 
          #(tuplet-number::fraction-with-notes "4" "4.")
        \tuplet 2/5 {c16 bes a g}  \tuplet 2/3 {a32 bes32 a16 g8} |
      \tuplet 2/5 {f16 g a c,}  \tuplet 2/3 {a'32 bes32 a16 c,8}  \tuplet 2/3 
{a'32 bes32 a16 d8}
        \tuplet 2/5 {c16 bes a g}  \tuplet 2/3 {a32 bes32 a16 r8} |
      \tuplet 2/5 {b16 c d d}  \tuplet 2/3 {d8 d}
        \tuplet 2/3 {d32 es d es d16 c}
        \tuplet 2/5 {c16 d c bes}  \tuplet 2/3 {a32 bes32 a16  g8} |
      \tuplet 2/5 {f16 g e g}  \tuplet 2/3 {f32 g f16 e8}  {d8 e c}
        \tuplet 2/5 {d16 e f g}  \tuplet 2/3 {a32 bes32 a16 g8} |
      \tuplet 2/5 {f16 g e g}  \tuplet 2/3 {f32 g f16 e8}  {d8 e c}
        \tuplet 2/5 {d32 es d es d16 a}  \tuplet 2/3 {d8-. r8} |
      }
    }
  }
>>


\score {
  \unfoldRepeats
    \musicmidi
        \midi {}
}

----


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