Aphorisms on JI Scale Variants
Aphorisms on JI Scale Variants
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
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
qui jure suo utitur neminem laedit
aphorism 1
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.
Last edited by talasiga on Thu Jan 06, 2011 6:47 pm, edited 1 time in total.
III
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".
Last edited by talasiga on Thu Jan 06, 2011 8:12 pm, edited 1 time in total.
V
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.)
MMmMmMM and mMMMMMm
(EDIT NOTE: non aphoristic intrusion which demonstrated non enlightened status of author deleted by author.)
Last edited by talasiga on Thu Jan 06, 2011 5:48 pm, edited 2 times in total.
Aphorism VI
With this sootra let us suffer ideational surrender and start a scale based entirely on the perfect fith measure by a process of fifths
qui jure suo utitur neminem laedit
VII
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.
VIII
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.
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.
IX
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.
Re: Aphorisms on JI Scale Variants
oh dear! look at the time! naptial time!
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Re: Aphorisms on JI Scale Variants
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Re: Aphorisms on JI Scale Variants
but less comprehensible than this.
http://www.youtube.com/watch?v=zVAKRcv6WYo
http://www.youtube.com/watch?v=zVAKRcv6WYo
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Re: Aphorisms on JI Scale Variants
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.
And now there was no doubt that the trees were really moving - moving in and out through one another as if in a complicated country dance. ('And I suppose,' thought Lucy, 'when trees dance, it must be a very, very country dance indeed.')
C.S. Lewis
C.S. Lewis