User:M-yac/Neutral Intervals and the FJS: Difference between revisions

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<div style="margin: 20px 10px">[[File:Fjs regions.png|1000px|FJS regions of the octave]]</div>

You can generate an interactive version of this image with my [https://www.yacavone.net/fjs-explorer Custom FJS Explorer].

If we mark where 5/4 lies on this picture, we immediately know its associated Pythagorean interval has `g = 4`, since it falls inside the region marked with "M3 (+4)". In the picture below, 5/4 and a few other octave-reduced prime harmonics are marked.

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An advantage of the NFJS is that its RoT and fifth sequence result in a cleaner division of the octave compare to the FJS. In fact, the NFJS' division of the octave is almost exactly the same as that in Margo Schulter's [https://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum] - they're within ±5 cents! In the image below, the regions on the top are exactly those defined in Schulter's article, and the regions on the bottom are exactly those defined by the NFJS.

<div style="margin: 20px 10px">[[File:Schulter vs NFJS regions.png|1000px]]</div>

<div style="margin: 20px 10px">[[File:Schulter vs NFJS regions.png|1000px|Schulter vs. NFJS regions of the octave]]</div>

Below is a table (hidden by default) of this same comparison.

@@ Line 127: / Line 127: @@
 <div style="margin: 20px 10px">[[File:Fjs regions.png|1000px|FJS regions of the octave]]</div>
+You can generate an interactive version of this image with my [https://www.yacavone.net/fjs-explorer Custom FJS Explorer].
 If we mark where 5/4 lies on this picture, we immediately know its associated Pythagorean interval has `g = 4`, since it falls inside the region marked with "M3 (+4)". In the picture below, 5/4 and a few other octave-reduced prime harmonics are marked.
@@ Line 193: / Line 195: @@
 An advantage of the NFJS is that its RoT and fifth sequence result in a cleaner division of the octave compare to the FJS. In fact, the NFJS' division of the octave is almost exactly the same as that in Margo Schulter's [https://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum] - they're within ±5 cents! In the image below, the regions on the top are exactly those defined in Schulter's article, and the regions on the bottom are exactly those defined by the NFJS.
-<div style="margin: 20px 10px">[[File:Schulter vs NFJS regions.png|1000px]]</div>
+<div style="margin: 20px 10px">[[File:Schulter vs NFJS regions.png|1000px|Schulter vs. NFJS regions of the octave]]</div>
 Below is a table (hidden by default) of this same comparison.