Fingering Positions and Pitch

Playing/Techniques
#1

I am trying to interpret the fingering position chart (page 112 of Shamisen of Japan, 3rd Edition) in terms of pitch intervals. Since the position numbers omit some of the semitones in the western chromatic scale, I’m not certain what pitch I should expect to hear, especially on the upper notes.

The lower (i.e. closer to the kamigoma) fingering positions are fairly easy to figure out by ear. At the upper end, the positions get pretty close together. Position four (at the outer neck splice) corresponds to a perfect fourth interval. Somewhere else I read that position 10 (39.84 cm) represents the octave, which suggests that the chart represents an open string length of 79.68 cm. Given that frequency is inversely proportional to the vibrating string length, the second octave position should be 59.76 cm from the kamigoma. On the chart, that lands between position 20 (58.73 cm) and 21 (60 cm).

Following this thought, I translated the fingering distances in the chart into frequencies (for a given string pitch, e.g. “C”), and compared them to an “equal tempered” scale. The results were rather inconsistent; some intervals were higher, and some were lower. This would be expected if the positions represented a temperament other than “equal”, but the variations were not consistent between the lower and upper octaves. For example, the fifth interval was high in the lower octave (position 6), and low in the upper octave (position 16). Also, while positions # and 4 correspond reasonably well to a major third and a perfect fourth, position 14 falls halfway between the two intervals. And, as noted above, is the second octave supposed to be position 20 or 21?

So, my question is, does this chart represent non-Western intervals, a non-equal temperament, or are the locations simply incorrect?

#2

Hi Dan,

I have the second edition and they are wrong there. Kyle said that he fixed it in a later edition but I don’t know which one.

Also, there are different sized tsugaru shamisens so the exact measurements are only valid for one length. For example Anne’s shamisen that she bought from Masahiro was shorter than mine. It’s like with a Gibson compared to a Fender.

As for comparing with the Western intervals, there are no other tones used than the same frequencies as our 12 tones. It is only the marking of them that is different. If the book seems to indicate otherwise it is wrong.

#3

Kyle - please add the revised chart to the errata page:
http://shamisenofjapan.com/corrections

#4

Here’s information to easily calculate your own (equal temperament) fingering positions .

Definitions:

  • The scale is the open string length, measured between the kamigoma (nut) and koma (bridge).
  • A semitone is a half-step pitch interval (1/12th of an octave).
  • Interval refers to the relative pitch in the musical scale.
  • Position refers to the Shamisen bunkafu fingering number.
  • Location is the distance from the kamigoma to the fingering position.
The ratio of Location to Scale can be found by:
Location/Scale = 1 - 2(-N/12)
where N is the number of the semitone.

The exact position locations corresponding to the scale of your instrument can easily be calculated using a spreadsheet. To be precise, you can compensate for the higher pitch that results from pressing the string down to the fingerboard by subtracting several millimeters from the measured string length. On the other hand, your fingering is probably not that accurate!

                            Location  for 80cm
  N   Interval        Pos.   /Scale    Scale
                                  
  0   unison (open)     0    0.0000     0.00
  1   minor second      1    0.0561     4.49
  2   major second      2    0.1091     8.73
  3   minor third       3    0.1591    12.73
  4   major third       #    0.2063    16.50
  5   perfect fourth    4    0.2508    20.07
  6   aug. fourth       5    0.2929    23.43
  7   perfect fifth     6    0.3326    26.61
  8   minor sixth       7    0.3700    29.60
  9   major sixth       8    0.4054    32.43
 10   minor seventh     9    0.4388    35.10
 11   major seventh    NA    0.4703    37.62
 12   octave           10    0.5000    40.00
 13   minor second     11    0.5281    42.25
 14   major second     12    0.5546    44.36
 15   minor third      13    0.5796    46.36
 16   major third      NA    0.6031    48.25
 17   perfect fourth   14    0.6254    50.03
 18   aug.fourth       15    0.6464    51.72
 19   perfect fifth    16    0.6663    53.30
 20   minor sixth      17    0.6850    54.80
 21   major sixth      18    0.7027    56.22
 22   minor seventh    19    0.7194    57.55
 23   major seventh    NA    0.7351    58.81
 24   octave           20    0.7500    60.00
#5

Kyle - please add the revised chart to the errata page:
http://shamisenofjapan.com/corrections

Oh snap! I didn’t know that website still existed (the front page redirects to Bachido. I’ll do it one better and make a special page in the learning center for the position mark distance.

I should mention to all that Dan was a major help in finding many errors in the earlier edition. Especially for the mitsuori instructions. Much appreciation goes out to him, so it’s an honor that he’s now part of Bachido. :slight_smile:

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