Re: [tuning] Re: J.S. Bach: Badinerie from Suite in B Minor (golden meantone)

Thanks, actually somebody else did the sequencing in 12-equal and I just re-tuned it with Scala and revoiced it, added harpsichord and made the file louder.

The timing is good, since I'm now working on a modified Boehm system for a 19-tone flute.

~DaW~
----- Original Message -----
From: John A. deLaubenfels
To: tuning@yahoogroups.com
Sent: Wednesday, October 24, 2001 1:05 PM
Subject: [tuning] Re: J.S. Bach: Badinerie from Suite in B Minor (golden meantone)

Danny Wier uploaded the MIDI file badinerie.mid this morning, and I
went and grabbed it. Sounds very nice! The harpsichord part is choppy
throughout much of the piece, but I'm becoming used to it.

For fun, I peeked at the tuning. Was very surprised to find the circle
of fifths going from C to E#! The piece is in B minor.

But Danny is right. I ran it thru my COFT analysis, and got the same
basic tuning (cents deviation from 12-tET):

Danny JdL's COFT
------ ----------
C 0.00 +14.22
G -3.78 +13.57
D -7.57 +11.42
A -11.35 +10.75
E -15.14 +2.39
B -18.92 -1.57
F# -22.71 -2.49
C# -26.49 -3.97
G# -30.27 -8.72
D# -34.06 -7.54
A# -37.87 -11.76
E# -41.65 -16.30

I haven't adjusted for the absolute differences, but the change in
tuning across the circle of fifths tells the story. His is even (.267
comma meantone); mine is of course jagged, reflecting the particular
intervals in the piece, and with a somewhat narrower overall range.
(what is the definition of "golden meantone" again?).

I show adaptive 5-limit pain as not much less than COFT pain (22534 vs.
29652), which is not much less than 1/4 comma meantone C to E# (36033).
So this is one of those pieces that is extremely well suited to
meantone, just as Danny has done it.

Thanks, Danny!

JdL

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And I got the original MIDI file from
http://www.midiworld.com/cmc/bach.html where there is a ton of Bach.

> (what is the definition of "golden meantone" again?).

I promise, this is my last P.S. to this post! Golden meantone is
based on a diatonic scale where the ratio of major seconds to minor
seconds are 1.6180:1.0000 -- the first number is called the golden
mean and is defined as 0.5 + half the square root of 5. That number
is the limit of the ratio of two adjacent numbers in the Fibonacci
sequence 1 1 2 3 5 8 13 21 34 55 89 144...

I actually came up with this temperament independently before I found
out who did it first. I nicknamed it "infinite-tone equal
temperament" since I wanted to have some idea of what equal
temperaments might sound like beyond 19 and 31 in that class (that
is, 50-tone, 81-tone, 131-tone, 212-tone etc.)

17-tone, 22-tone and 53-tone work differently by the way.

~DaW~