## Carl Kasell: diabolus in musica?

Inspired by "Trumpchant in B flat", Joel Roston sent me a link to his 1/22/2014 post "How's Carl this time?", where he proposes that

As the excitement builds over the course of each hour-long Wait Wait…Don’t Tell Me! episode, Carl Kasell’s exclamation of the last two syllables of the word “Chicago,” commensurately, rises in pitch.

This is an example of Carl Kasel's performance of  the word "Chicago", in the context of the obligatory periodic station identification in the cited show:

And here are the 30 instances of "…cago" that Joel investigated — six station breaks from each of five shows:

Joel found the analysis somewhat difficult, because Carl is speaking rather than singing:

I then isolated the six “[chi]CA-GO”s from each, and made a note of:

1. The starting pitch of each “CA”
2. The distance, intervallically speaking, from that pitch down to the “GO”

As you can imagine, the analysis was difficult due to some of the “GO”s being super wavery/slidy (the “CA”s are surprisingly solid). That said, I just ear-balled it the best I could and, generally, tried to measure from the “CA” to the very end of the “GO” — like, wherever it ended up after Carl’s micro-Tarzan-ing.

So one simple approach to investigating the distribution of Carl's "-cago" intervals, which sidesteps the micro-Tarzan-ing problem.

I pitchtracked the whole sequence — the first four (of 30) instances look like this:

Then I looked at the within-"-cago" dipole statistics  — that is, the joint distribution of time differences (in seconds) and f0 differences (in semitones). Across the 30 repetitions, at 200 f0 estimates per second, there are more than 3,000 f0 differences at each time lag.

The result looks like this:

The bimodal distribution of time-pitch differences, corresponding to the prosodic characteristics of the two-syllable pattern studied, is clear. And the modal pitch difference seems to be about 6 semitones, corresponding to the interval of a tritone.

This interval is half of a tempered octave — but to the great disappoint of pythagoreans across the ages, does not correspond to any ratio of small integers. Wikipedia explains darkly why some theorists called it "diabolical", and banned it from counterpoint:

The tritone is a restless interval, classed as a dissonance in Western music from the early Middle Ages through to the end of the common practice period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with the development of Guido of Arezzo's hexachordal system, who suggested that rather than make B♭ a diatonic note, the hexachord be moved and based on C to avoid the F-B tritone altogether. Later theorists such as Ugolino d'Orvieto and Tinctoris advocated for the inclusion of B♭. From then until the end of the Renaissance the tritone was regarded as an unstable interval and rejected as a consonance by most theorists.

The name diabolus in musica ("the Devil in music") has been applied to the interval from at least the early 18th century […]

The dipole plot doesn't take account of the interesting token-to-token differences in overall level and in interval width that Joel discusses. But analysis of those will have to wait for another day.

1. ### S Frankel said,

November 5, 2016 @ 12:02 pm

Not sure that the Early Middle Ages is a good gauge for later periods, since thirds were also classified as dissonances then.

2. ### AntC said,

November 5, 2016 @ 2:15 pm

This interest in Chicago is because of the rugby fest, right?

New Zealand All Blacks are about to play Ireland at Soldier Field. (And the Maori All Blacks played the USA Eagles yesterday.)

3. ### Bill Benzon said,

November 5, 2016 @ 6:55 pm

The tritone appeared in bebop as the flatted-fifth, or sharp eleven, depending on how you think about it. John Coltrane built the chord structure to "Giant Steps" around the so-called tritone substitution.

4. ### rootlesscosmo said,

November 5, 2016 @ 11:01 pm

The first two notes of "Maria," in "West Side Story," are a tritone.

5. ### maidhc said,

November 6, 2016 @ 1:22 am

I think every song in "West Side Story" starts with a different interval. It's very useful when practicing ear training.

6. ### Ryan said,

November 6, 2016 @ 4:44 am

@Bill Benzon:
John Coltrane's Giant Steps is built around major thirds, not the tritone substitution.

In any case, the three notes making up "Chicago" could possibly define a dominant seventh chord, an unstable chord used for setting up the tonic, i.e. the "anchor" of a melody.

7. ### Robert Coren said,

November 6, 2016 @ 10:50 am

The tritone — in fact the sequence C-F#-G — is a frequent motif in West Side Story, most notably in the song "Cool" (which song, incidentally, contradicts @maidhc's claim that each song begins with a different interval).

The existence of hexachords with both B and B flat led, in arcane ways, to the convention by which German-speakers call those two pitches H and B respectively.

8. ### January First-of-May said,

November 6, 2016 @ 7:04 pm

Half a tempered octave is, of course, the square root of two, which indeed would be almost as far from being approximable by rational numbers as it could possibly get.

[(myl) From Wikipedia:

The unstable character of the tritone sets it apart, as discussed in [28] [Paul Hindemith. The Craft of Musical Composition, Book I. Associated Music Publishers, New York, 1945]. It can be expressed as a ratio by compounding suitable superparticular ratios. Whether it is assigned the ratio 64/45 or 45/32, depending on the musical context, or indeed some other ratio, it is not superparticular, which is in keeping with its unique role in music.

]

I wonder what an interval corresponding to the golden section (the actual "worst" case) would sound like – and whether anyone had ever built a musical piece on it (and I won't be surprised if someone did and it actually sounded half decent).

[(myl) The golden-section ratio is about 8 and a third tempered semitones:

12*log2((1+sqrt(5))/2) = 8.330903

or a bit more than a minor sixth. And musical tuning based on this ratio? Of course it's been done.]