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