scale_util.R

semitone <- 2^(1/12)
middleC <- 440/(2^(9/12))

getRoots <- function(n,jump) accumulate(0:(n-1),~(.x+jump-1)%%n,.init=0)+1

# create a series 1, f0^1, f0^2, ... f0^n ,such that all terms lie within (1,2)
getFreqSeries <- function(n,f0)
  accumulate(1:n,
             ~{f<-.x*f0;if(f>2.01) f/2 else f},
             .init=1)

getScale <- function(root,notes,scaleIdx) {
  scale <- notes[(root+which(scaleIdx)[-8]-2)%%12+1]
  str_c(scale,collapse=",")
}

# these are extracting in the order they appear on the scale,
# not in the order sharps (or flats) are introduced by 5ths (or 4ths)
clean_chr0 <- function(s) if(length(s)==0) "" else s
getBasic <- function(s,regex) s %>%
  str_extract_all(regex)%>%
  map(clean_chr0)%>%
  map_chr(str_c,collapse=",")
getSharps <- function(s) s%>%getBasic(".#")
getFlats <- function(s) s%>%getBasic(".b")

### Draw fretboard

fretDist <- function(fretN) 1 / (2^(fretN/12))

draw_fretboard <- function(tones12,fw2=.1) {
  fretDists <- fretDist(0:24)
  stringYs <- seq(fw2,-fw2,-2*fw2/5)
  tibble(stringYs=stringYs) %>%
    ggplot() +
    # fretboard (light wood)
    geom_rect(xmin=0,xmax=1,
              ymin=-1.1*fw2,ymax=1.1*fw2,
              color="#663300",fill="#663300") +
    # bridge (dark wood)
    geom_rect(xmin=-.02,xmax=0.02,
              ymin=-1.2*fw2,ymax=1.2*fw2,
              color="#330000",fill="#330000") +
    # nut (motherpearl)
    geom_rect(xmin=1,xmax=1.02,
              ymin=-1.2*fw2,ymax=1.2*fw2,
              color="#888888",fill="#888888") +
    # frets (black)
    geom_segment(aes(x=fretDists,xend=fretDists,
                     y=-1.1*fw2,yend=1.1*fw2),
                 data=tibble(fretDists=fretDists)) +
    # marker dots (white)
    geom_point(aes(x=.5*(dotx+dotxN),y=0),
               data=tibble(dotx=fretDists[c(3,5,7,9)],
                           dotxN=fretDists[c(4,6,8,10)]),
               size=2,color="white") +
    geom_point(aes(x=dotx,y=doty),
               data=tibble(dotx=rep(.5*(fretDists[12]+fretDists[13]),2),
                           doty=c(-fw2/12,fw2/12)),
               size=2,color="white") +
    # strings
    geom_segment(aes(y=stringYs,yend=stringYs,
                     x=0,xend=1.02),color="grey") +
    # bridge pegs (blue)
    geom_point(aes(x=0,y=stringYs),size=4,color="blue") +
    coord_fixed(xlim=c(0,1.05),ylim=1.1*c(-fw2,fw2)) +
    labs(x="",y="",title="") +
    theme(axis.text=element_blank(),
          axis.ticks = element_blank(),
          panel.background = element_blank(),
          plot.margin=unit(c(0,0,0,0), "cm"),
          panel.spacing=unit(c(0,0,0,0), "cm"),
          panel.border = element_blank())
}

# draw_fretboard(tones12_5ths_and_4ths)

draw_naturals <- function(tones12,fw2=.1) {
  tuning6 <- c("E","A","D","G","B","E")
  # where in the notes vector
  tuning6idx <- map_int(tuning6,~match(.x,tones12$notes[-13]))
  naturalfretsCroot <- unlist(map((0:3)*12,~.x+which(tones12$majorIdx[-13])))-1
  
  naturalfingerPos <-
    map(tuning6idx-1,~as.integer(keep(naturalfretsCroot-.x,
                                      function(y)y>0&y<=24)))
  naturalfingerRel <-
    map2(tuning6idx,naturalfingerPos,~(.x+.y-1)%%12+1)
  naturalfingerNotes <- map(naturalfingerRel,~tones12$notes[.x])
  fretDists <- fretDist(0:24)
  stringYs <- seq(fw2,-fw2,-2*fw2/5)
  fretDistsMid <- map2_dbl(fretDists[-length(fretDists)],
                           fretDists[-1],~.5*(.x+.y))
  drawNotes <- function(p,s) {
    nfp <- naturalfingerPos[[s]]
    nfn <- naturalfingerNotes[[s]]
    df <- tibble(nfp=nfp,
                     x=fretDistsMid[nfp],
                     y=stringYs[s],
                     nfn=nfn)
    p+
      geom_point(aes(x=x,y=y),size=5,color="black",data=df) +
      geom_text(aes(x=x,y=y,label=nfn),color="white",
                size=3,data=df)
  }
  
  fretboard <- draw_fretboard(tones12,fw2)
  #open notes
  df0 <- tibble(x=1.05,y=stringYs,nfn=tuning6)
  # draw entire fretboard.
  # loop doesn't work because drawNotes requires previous plot
  reduce(1:6,~drawNotes(.x,.y),.init=fretboard) +
    geom_point(aes(x=x,y=y),size=5,color="grey",data=df0) +
    geom_text(aes(x=x,y=y,label=nfn),color="black",
              size=3,data=df0) +
    theme(axis.text=element_blank(),
          axis.ticks = element_blank(),
          panel.background = element_blank(),
          plot.margin=unit(c(0,0,0,0), "cm"),
          panel.spacing=unit(c(0,0,0,0), "cm"),
          panel.border = element_blank())
}