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Rational-rounded PHI tuning: clean-up of JI ratios: I took forum advice

🔗djtrancendance <djtrancendance@...>

4/1/2009 11:15:45 PM

A good few of you complained in my last tuning about my efforts to round my PHI scale to low numbered ratios' sounding too much like straight-forward JI.
.....Turns out you all were very very right!..........

I found out that some of the ratios, namely 5/4 and 7/5...were not as close to the PHI scale as they should be (they were around 12 or so cents off...5/4 being the furthest off).
So, naturally, I went through tons of ratio combinations and eventually managed to replace them. :-)

What I came up with was the following scale:
********************************************************
18/17 (Arabic lute index finger)
9/8 (major whole tone: PHI tuning yields 1.122 in comparison)
19/16 (19th harmonic)
19/15 (un-devicesimal semitone)
4/3 (yes...the PHI tuning in fact yields 1.33203, basically the same)
10/7 (Euler's Tri-tone)
20/13 (Tri-Decimal semi-augmented fifth)
21/13 (estimate of PHI...used as the period IE start of interval repetition)
*****************************************************

Furthermore, the look at the gaps between the notes

Note---gap between this note and the last
18/17---18/170
9/8-----17/160
19/16---19/18X
19/15---16/150
4/3-----20/19X
10/7----15/140
20/13---14/130
21/13---21/20X

Apparently the series with X's represent a harmonic series (which sounds "major key") and the series of 0's represents a reversed harmonic series (which sounds "minor key"). So the difference tones actually form "difference tone harmonic series". Any comments on this odd occurrence?

I also noticed that making a scale of ONLY notes in the
"difference-tone harmonic series" IE 18/17,9/8,19/15,10/7,20/13...creates a much more consonant scale.
*********************************************************

Still I'm ITCHING to find a way to slip more notes into the scale and get advice. Particularly on the below issues/problems with my scale:

A) The 4/3 is probably the worst sounding interval in this scale so any ideas for changing it would be appreciated.
B) I found myself having to drop one note from my old "rational PHI" scale to make this work smoothly: that note was around the PHI tuning value 1.46808. Do any of you all have ideas what rational fractions would work well within this scale that evaluate to about 1.46808?