This topic intends to honour some pre naptial ideas that float up to my dizzy brain from time to time for no good reason that I can see as yet because I am neither an instrument maker (able to test this out) and nor do I have the mathematical proclivity to spell this out in technical formulae.
JI in the title refers to Just Intoned and the adjective is used loosely.
For fun, initial expressions of these ideas will be aphoristic in the
sootra tradition
For this thread the primary building block of any scale shall be the measure of a particular note to be called “1” to its just intoned perfect fifth note to be called “5” where, and only where, such a measure is naturally evident in the timbre of note 1.
To make note 4 one takes the primary JI measure and subtracts it from the octave
Thus notes 1, 4 and 5 are made.
The difference between notes 4 and 5 is the measure of a major interval and by building other notes of the scale by as many as these that can fit in between 1 to 4 and 5 to octave we get the notes of the major scale, such a scale resulting in five intervals each of which we can call “major” or “M” and two lesser intervals each of which we can call “minor” or “m”.
After about 75% of the the next aphorism we depart from the paradigmatic terrain covered or implied by Pythagoras.
The arrangement of the 5M and 2m in sequences different to the initial one results in eight other scales, only six of which may be viewed as scales relative to the original one with the non relative ones with these sequences from note 1:
MMmMmMM and mMMMMMm
(EDIT NOTE: non aphoristic intrusion which demonstrated non enlightened status of author deleted by author.)
With this sootra let us suffer ideational surrender and start a scale based entirely on the perfect fith measure by a process of fifths
By a cycle of JI fifths one proceeds from notes 1 to 5, then 5 to 2, then 2 to 6, then 6 to 3, then 3 to 7, then 7 to an augmented 4 (#4), then #4 to flatted 2 (b2), then b2 to b6, then b6 to b3, then b3 to b7, then b7 to the penultimate 4 and finally 4 to octave, but an octave neither as mean as Pythagoras’ nor as ill tempered as the moderns find convenience in.
Noting that the measure of an octave so formed will not be mathematically “consonant”,
note 1 and its octave played together may be either audibly dissonant or the deviation between them not perceived at all
and, therefore, in the former case, such a scale may be rejected excepting that the audible dissonance shall be a measure of a JI derived microtone and retained for posterity, and, in the case of no dissonance perceived, the scale may be retained as a fruitful product of a simplistic JI cycle of fifths.
A shorter and, yet, less simplistic way to arrive at a less contestable octave is to apply the mediant (note 3) in the timbre of the tonic so that one proceeds only from such 3 to 7 to #4 to b2 to b6 to b3 to b7 to 4 to octave with the shortfall of notes 5, 2 and 6 being taken from the spelling in the first part of the predceding simplistic process.
oh dear! look at the time! naptial time!
As sootra VIII is to VII so this X is to IX.
but less comprehensible than this.
http://www.youtube.com/watch?v=zVAKRcv6WYo
I’m loving the thought of ‘pre-naptual’ as the state of being of - either - an overtired two-year-old, or of me, at about 3:45 pm, most work days.
in my case, perhaps, a post nappietial overaged two-year-old …
Naptial? Oh yeah! Party time fur the rest of us! http://www.youtube.com/watch?v=-6lNuNI7uQM&feature=related
Oh. Oh. Now you gone and done it good. You’re going to get a PM from the Tallyman.
What I want to know is, isn’t “do, re, me, fa, so” one of those variants, and, if so, what is all the fuss about?
Thus far, 40 interval variants are potentially derived by application of a natural JI perfect 5th interval in various ways to make a sequence of notes, namely
*the M and m of the purportedly Pythagorean terrain
*the further 12 semitone and 6 whole tone variants effected by the sootra VII procedure
*the microtone remnant of the octave of sootra VII
*the further 12 semitone and 6 whole tone variants effected by the sootra IX procedure
*the microtone remnant of the octave of sootra IX