Harmonic Interference

There are a number of things one can explore using the spreadsheet macro buttons. I have use the Bb scale at the basis for the study because of my familiarity with the Trombone. If we look at the synchronization of the chords pressing "Harmonic" button first, we see that Bb, Bb7, Eb, Ebm and F chords all look very tidy and all in perfect tune. This is apparent because the patterns are all symmetrical. However, when we check out the F7 chord, for some reason the seventh note, Eb, is way too sharp. Well, I had a hard time selecting its harmonic ratio but concluded it should be 1/4 x 4/3 x 16/21 of the first Eb harmonic encountered on the trombone at 1,232 Hz. This is really high and is the "F" above the trumpet "high C", but the adjusted pitch is compatible with the Eb and Ebm patterns. Now, when we select the F7 harmonic pattern, the Eb is way too sharp. I created a correction button to alter that Eb ratio to 1/4 and this flattens the 7th pitch for perfect compatibility. But now the other chords don't work. Of course Bach acquiesced and went with the tempered scale.

Anyway the following examples of the Eb patterns show the first 7th chord with the sharp 7th tone, and the second example shows how it was corrected:

This is the F7 Chord but with a very sharp 7th Tone causing the Asymmetric Pattern

Now, the F7 Chord has been corrected by Flattening the 7th Tone and Showing a Symmetrical Pattern

Now, you can experiment with the harmonic and tempered chords. I have included two-tone combinations also. You can alter the Time range on the chart by selecting the factors from .00001 to .001. Also, you will see the chord correction factors if you navigate to the left using your back arrow. I used these for the above example. The spreadsheet, with all its macros, does not operate well from the server. So, I have created a downloadable zip file containing the Excel Workspace (.xlw), Spreadsheet (.xls), Chart (.xlc), and Macro (.xlm) files.

Put your cursor on the zip file designation below, right click, select "save target as", and save the file to a new folder. Then extract the zip file on your computer. If you execute the .xlw file, everything will open up and you can start studying the problem of chord pitch.

Harmonic Interference/PITCH.zip

I hope you enjoy seeing chords for the first time. I had thought it will be very instructive to add the sound to the program, but I never got that far. All I know is that the natural harmonic 7th pitch always sounds too flat on the horn. However, when played with brass instruments, it fits right in for a rich . . . "fat" chord.

Good Luck and Happy Chording . . .

Harmonic Interference
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