I've been off line for a few days and was surprised to see the
interval-discussion still going on.
Below is a link to the "materials" page of my music theory course web
site. There you can find charts and explanations pertaining to the
rudiments of music theory (intervals etc.).
http://www.wm.edu/CAS/music/gutwein/mus201/201mater.htm
Here is the link to the table of contents of the on-line textbook for the
above course.
http://www.wm.edu/CAS/music/theorybk/text/tabofcnt.htm
Regarding the potential for theoretical knowledge to pollute your
music-making, I generally tell my students that I've known many performers
who have given uninspired performances who knew very little music theory,
and I've also known performers who deeply understood theoretical issues and
gave inspiring and passionate performances. I usually tell students who
have this concern, "To blame a knowledge of theory for a poor performance
is similar to blaming bad sex on a knowledge of reproductive biology." The
failure to be body-aware and connected to the physical and emotional
experience is most likely to be caused by a deeper problem than the
possession of theoretical knowledge.
Regarding the concern that intervals imply a harmonic basis to a music that
does not have one, one must remember that an "interval'' is merely the
distance between two melodic or simultaneous tones. An interval can be
defined in any of three different ways (1) by measuring the distance
between two tones using fixed values like cents (1/100th of an equally
tempered half step), or more simply half-steps, (2) by the 5-line staff
notation of contextual relationship between the two tones (i.e. the "sound
of" 5 half steps may be notated as a Perfect 4 [c to f], or an Augmented
3rd [c to e-sharp] depending on the musical context, and (3) in a "fuzzy"
way by referring to the distance between to tones as being approximately
(give or take a quarter-tone) "a Perfect 4th". To scientifically measure
distances between tones using any language, one has to use a fixed standard
of measurement and that requires a tuning system (such as equal temperament
or mean-tone). As I understand it (and that ain't saying much), shakuhachi
music doesn't use fixed common units of measurement such as these, and I'm
unaware of a tuning "system" used in the making of shakuhachies; therefore,
any attempt to discuss distances between shakuhachi tones in scientifically
graduated terms would be a misrepresentation of the way in which the
tradition conceives of the music. That is why I prefer the "fuzzy" way of
speaking about intervals. It allows us to make analogies between
traditions when and if such an analogy can be useful. For transcription or
estimating instrument length on a CD it may be useful, but for learning to
play RE to U properly, in the traditional manner, it may not be useful.
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