admin: First posted on 2016 11 09
Five years ago, I wrote a post on the excommunication of the tritone by the catholic church. The tritone is an interval of six semitones (or three tones). The church excommunicated the tritone a long time ago. Presumably, they were hearing it as it used to sound then – with a tuning that was different than the tuning we use today. Today, we tune instruments so that the 12 notes on the chromatic scale split an octave evenly (i.e., the chromatic scale is equally tempered). In the past, tuning tried to get better use of harmonics (for example, the Pythogorean tuning).
I tried to replicate what the church might have heard in the past, but failed. I was using Orinj and built a MIDI file, in which the pitch of the tritone notes was slightly shifted to reflect old style tuning.
Pitch shifting for the old tritone
In the old post, I started with A = 440 Hz and added Eb. The tritone is the interval between A and Eb. In the contemporary, equal tempered tuning, Eb = 440 * 2^6/12 = 622.25 Hz. In Pythagorean tuning, Eb = 440 * ((2/3)^6) * 8 = 618.05 Hz. The difference is: Eb Pythagorean – Eb modern = 1200 * log2(618.05 / 622.25) = -11.73 cents (100 cents is a semitone).
I used the MIDI pitch bend control in Orinj (the MIDI pitch bend message). The MIDI pitch bend message tells a MIDI device to change the pitch of a MIDI channel. I took a standard A and pitch shifted Eb down by about 0.12 semitones. To make sure that only Eb was pitch shifted and A was not, I put A on MIDI channel 0 and Eb on MIDI channel 1. A MIDI pitch bend message pitch shifts the whole MIDI channel.
Nothing much came out of this experiment. Initially, I thought that there was something wrong with Orinj. There were some recent fixes to the MIDI pitch bend with Orinj version 2.6.4. These fixes, however, made no difference.
As it turns out, the changes in the pitch between the two types of tunings is just too small. Most people will notice a change in the pitch if it is larger than about 25 cents. Only a well-trained musical ear may notice a change of 12 cents.
Sound clips with the tritone
The following are some examples of the tritone that use contemporary and Pythagorean tunings. These are MIDI clips and so, I suppose, they may sound different on different computers. MIDI tells a device what to play, but the device is technically not required to implement every piece of the MIDI protocol. It may choose to ignore something or it may choose to interpret the MIDI pitch bend message differently than is usual.
The first clip plays the notes A and Eb sequentially and then together. This pattern is repeated twice. The first time the pattern uses the equal tempered scale. The second time the Eb in the pattern is shifted down by 12 cents. The difference between the two pattern repetitions is, in my opinion, unnoticeable.
Click Play to hear the tritone.
The second clip plays only the note Eb. It plays it twice – once before and once after the pitch shift. Even here, the difference is virtually inaudible.
Click Play to hear Eb under different tunings.
The third clip plays the note Eb only once, but changes pitch in the middle of the note. Even here, the difference is barely audible.
Click Play to hear the Eb.