Pythagoras was wrong: there are no universal musical harmonies, study finds
The tone and tuning of musical instruments has the power to manipulate our appreciation of harmony, new research shows. The findings challenge centuries of
..harmony..
- Thread starter losthobos
- Start date
Rosie C
Well-known member
Interesting, but there is something beautiful about Pythagoras' work.
Interesting and worth a second read.
As if we didn't have enough problems. Add in how we replaced C# and D♭ with (C# + D♭)/2 (or thereabouts) and that guitars are so far out they really need a compensated bridge - things only get worse.
The English concertina was designed to include the sharps and flats (eg C# and D♭)
Bring back the fretless banjo I say.
Thinking about it, Blues players are (were?) happy to sing a nearly flat B while strumming a G major chord.
Edited to add:
Re "something beautiful about Pythagoras' work."
There was never anything ugly about being nearly right.
As if we didn't have enough problems. Add in how we replaced C# and D♭ with (C# + D♭)/2 (or thereabouts) and that guitars are so far out they really need a compensated bridge - things only get worse.
The English concertina was designed to include the sharps and flats (eg C# and D♭)
Bring back the fretless banjo I say.
Thinking about it, Blues players are (were?) happy to sing a nearly flat B while strumming a G major chord.
Edited to add:
Re "something beautiful about Pythagoras' work."
There was never anything ugly about being nearly right.
Rosie C
Well-known member
My smaller recorders do exactly that. But my great bass (about 4' long) has different fingering for the sharps and flats!
Not much use if you're playing with a keyboard in equal temperament though.
Siegmund
Well-known member
I have a feeling that this is one of those things that is discovered and re-discovered with considerable frequency.
Re timbre affecting perceived dissonance, it certainly does: I remember trying out pure sine waves against each other to try to pin down what I thought was dissonant, soon after I had my first computer, and being surprised how un-dissonant they sounded; most of the tension came from the interaction of the overtones not the pure sine waves.
There's a fascinating book (with online audio samples) called Tuning, Timbre, Spectrum, Scale by Bill Sethares --- about 20 years old now --- that opens with examples of carefully constructed sounds, where a 1:2 ratio sounds terrible and a 1:2.1 ratio sounds good. That is an illusion I can't recreate myself - but it was startling to hear it demonstrated.
As for the all-encompassing claim that we prefer our intervals slightly out of tune to pure, I am not 100% sure I am swallowing that... I do think we took a lot of color out of music by going to 12-tone equal temperament.
Re timbre affecting perceived dissonance, it certainly does: I remember trying out pure sine waves against each other to try to pin down what I thought was dissonant, soon after I had my first computer, and being surprised how un-dissonant they sounded; most of the tension came from the interaction of the overtones not the pure sine waves.
There's a fascinating book (with online audio samples) called Tuning, Timbre, Spectrum, Scale by Bill Sethares --- about 20 years old now --- that opens with examples of carefully constructed sounds, where a 1:2 ratio sounds terrible and a 1:2.1 ratio sounds good. That is an illusion I can't recreate myself - but it was startling to hear it demonstrated.
As for the all-encompassing claim that we prefer our intervals slightly out of tune to pure, I am not 100% sure I am swallowing that... I do think we took a lot of color out of music by going to 12-tone equal temperament.
If you want to play with sound, try connecting a microphone to an oscilloscope. You can sing, whistle, hum, play a note, use tuning fork etc and watch the sound waves on the monitor. Almost all notes from the voice and musical instruments are loaded with overtones; to see a pure sine wave you almost need an frequency generator.
I used to do short science programs in elementary school classes - things with electricity, gasses, telescopes, etc. One of the favorites was the microphone on the oscilloscope - kids would line up to sing or talk into microphone and watch the changing patterns!
I've got several, but the new digital scopes are relatively inexpensive. I got a 2-channel 100mhz digital storage scope for less than $400. Invaluable if you are into debugging electronics.
JKJ
For a generous definition of "pure sine wave", and frequencies are in rational relations to "A" rather than the irrational factors from equal temperament.
In acoustic instruments, recorders are comparatively pure, and ocarinas even more so.
