Saturday, September 14, 2019

Bohlen-Pierce Scale

from Wikipedia:
The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics,[1] specifically the equal tempered diatonic scale.

The interval 3:1 (often called by a new name, tritave) serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent.

The BP scale divides the tritave into 13 steps, either equal tempered (the most popular form), or in a justly tuned version. Compared with octave-repeating scales, the BP scale's intervals are more consonant with certain types of acoustic spectra.

The scale was independently described by Heinz Bohlen,[2] Kees van Prooijen[3] and John R. Pierce. Pierce, who, with Max Mathews and others, published his discovery in 1984,[4] renamed the Pierce 3579b scale and its chromatic variant the Bohlen–Pierce scale after learning of Bohlen's earlier publication. Bohlen had proposed the same scale based on consideration of the influence of combination tones on the Gestalt impression of intervals and chords.[5]

The intervals between BP scale pitch classes are based on odd integer frequency ratios, in contrast with the intervals in diatonic scales, which employ both odd and even ratios found in the harmonic series. Specifically, the BP scale steps are based on ratios of integers whose factors are 3, 5, and 7. Thus the scale contains consonant harmonies based on the odd harmonic overtones 3:5:7:9 (play (help·info)). The chord formed by the ratio 3:5:7 (play (help·info)) serves much the same role as the 4:5:6 chord (a major triad play (help·info)) does in diatonic scales (3:5:7 = 1:1 & 2/3:2 & 1/3 and 4:5:6 = 2:2 & 1/2:3 = 1:1 & 1/4:1 & 1/2).

10 comments:

(((Thought Criminal))) said...

Imaging hand coding CD audio data at the level of being able to synthesize the sound of an entire song, singer included, with no actual instruments playing or singer singing.

(((Thought Criminal))) said...

Tritave scaling allows you to find the beat in the sound of a dentist's drill lol

-FJ said...

It is different...

(((Thought Criminal))) said...

Beauty in dissonance.

jez said...

I thought the idea was that it's less dissonant than the 12-tet octave?

(((Thought Criminal))) said...

To me it seems like it is trying to mathematically correct the intervals between notes. A metric system for music I guess.

1609344000000 nanometers by any other name would still be a mile.

jez said...

"trying to mathematically correct the intervals between notes" is a genuinely hard technical / artistic problem. We in the west are accustomed to the 12-tet equal-temperament, but it contains some ugly intervals that an un-corrupted ear would reject; and though few of us would put our finger on it, even westerners tend to respond warmly to nicely intonated harmonies (a capella voices, string quartets, "open tuning" on guitars etc.).
As for this scale, it contains genuinely different notes, and it's hard to think of anything more radical than abandoning the octave-equivalence assumption. I don't think this is mere semantics.

(((Thought Criminal))) said...

Well I'm many subjects and about 30 years separated from my scant musical training but I'm always curious about "impossible" music (usually computer generated, such as bass lines no human bass player could play because there's either not enough strings or the human hand isn't big enough to be on all the spots on the fretboard at the same time to produce those notes. Maybe this new scale is something like that.

(((Thought Criminal))) said...

I mentioned "wabi sabi" - acceptance of imperfection - maybe the traditional scales and mathematically asymmetrical intervals are the gold we stitched the broken pottery back together with. Yeah, it's a busted vase glued back together with gold, but it's a beautiful busted vase. There's going to be those that resist trying to "fix" the vase with something else.

FJ check out the new Tool album!

jez said...

Lest this seem like a theoretical cul-de-sac, let me assert the practical imporance of this tuning business, even to unsophisticated musicians -- I first ran into it back in the '90s when I was adding instruments to some vocal harmonies which I'd recorded first. I found that, although my voices were nicely in tune with themselves, the top line especially was horribly out of tune with the instruments I was adding. I now know that, with no instruments to fix me to the standard scale, I'd sung my harmonies with just-intonated intervals, and they were interfering most unpleasantly with the equal-temperament instruments; but this confused me for years!
I always saw it as a problem, but better musicians are exploiting it -- young jazz wizard Jacob Collier has used it to modulate seemlessly from a standard key into an in-between key for example. But I think even non-nerd artists have been reaching intuitively for sweeter intervals for decades/centuries, eg. the mircrotonal "blue notes" (listen to muddy waters, and count how many different notes he can fit between adjacent semitones!!), or the minute manipulation of sample tuning in hip-hop, or the deliberately flattened major thirds on pop guitar records etc...