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PDX OPERAbeat | A Company Blog is the blog for all things Portland Opera, featuring a variety of guest contributors who will provide insider's tidbits on all we do to celebrate the beauty and breadth of opera.

Temperamental Rinaldo


Highlights from Rinaldo rehearsal notes


Please ADD a practical ghost light.

Argante has 1 min. 45 seconds to remove the robe and the feathers from his turban.

Could we get the 2 rolling bakery racks in rehearsal?

The set has suffered its first damage -- a piece of the gold trim on the SL side of the door, near the bottom of the star, was pulled off by a skirt.

We used a piece of dragon fabric as the Rinaldo blindfold -- it worked great.

The music stand is falling over on the rake.


A little bit about temperament

Okay, first, the kind of temperament we're talking about isn't the one that describes one's natural disposition! Temperament, in musical terms, is the adjustment of intervals on the keyboard away from pure to make the intervals fit a particular system.


… Got it?


Me neither. Temperament is very mathematical in nature and, in my opinion, super complicated! Instrumentalists who mostly play modern music don't think so much about temperament, especially those of us who aren't keyboardists. It's difficult to explain not only to the layperson, but even to the practiced musician.


Okay, so. First let's talk about pure tones. A pure tone sounds ONLY at the fundamental frequency or pitch. So, 300 Hz, or 650 Hz, etc. Here is a great website where you can hear pure tones.


Musical tones are much more complex. They sound both at the fundamental pitch and at higher frequencies simultaneously. The higher frequencies are often called overtones. The first five harmonics (overtones) of C are: octave, fifth, fourth, major third, minor third. So when you hear a C played, say, on the piano, in addition to hearing the pure tone C, you're also hearing the C an octave above, the G above that, the C above that, the E above that, and the G above that. Plus others, but you get the idea. These harmonics, and their aural presence, are what gives each instrument its particular timbre. The fundamental gives us the pitch, the harmonics tell us what instrument the pitch is coming from.


Just intonation is a tuning system where the frequencies of all the notes in the system are members of the same harmonic series. There is a lot of math involved in this, and frankly, it's too much for one short blog post! But essentially, in just intonation, the intervals between notes are mathematically pure, related to each other in small ratios (3:2, 5:4, etc). Because the frequencies of pitches in just intonation are harmonically related, the aural result of playing them together is one of restfulness. They sound very calm.


But the trouble with just intonation, particularly on an instrument like a keyboard whose pitches are fixed in performance, is that the instrument can only sound 'in tune' in one key. As a musician modulates, more and more of the intervals within the new key sound off and are unusable. This is where temperament comes in. Tempering an instrument brings certain intervals slightly away from their pure tones in order to open up more harmonic possibilities. In Meantone temperament, for example, the perfect fifth is narrowed slightly in order to make the thirds sound better. Different temperaments fiddle with the intervals of the scale in different ways, but the universal problem with most temperaments used before 1700 is that they made some intervals better and some intervals worse, or unusable. (These are called wolf intervals). So for each of these temperaments, some key signatures work and some don't.


The rise of well tempering meant that the 12 notes of the octave were tuned in a way that made it possible to play in most major and minor keys without any of them sounding terribly out of tune. Although in well tempering, no key has extremely impure intervals, the fifths are generally of slightly different sizes, which meant that each key has a different 'character.' Bach's Well-Tempered Clavier makes use of this system; the 24 pairs of preludes & fugues progress chromatically upward in key, from C major to B minor. In earlier temperaments some of these pieces would have sounded really bad!


In equal temperament, which is what most of us know today, each of the steps of the octave is divided equally, with an equal frequency ratio between each successive note. Modern Western music typically uses 12-tone equal temperament, but other divisions (such as 15, 19, 24, 31, etc) exist. Just as settling on A440 (or 415, etc) makes it possible for instruments to universally play together, so does equal temperament. But equal temperament compromises the purity of tone for the sake of universality. Basically, every interval (save the octave) is slightly out of tune. It no longer sounds that way to most of our ears, though, because we're so used to hearing it.


By the way, one of the earliest proponents of twelve-tone equal temperament was Vincenzo Galilei, Galileo's father! THROWBACK


To bring it back to us, for Rinaldo we are using Young 1800 temperament, a well temperament designed by a man named Thomas Young so that the most frequently used keys were in tune. Young's main goal was to improve the major thirds in the most commonly used keys, which he did partially by making the fifths a little flat. By the way, Thomas Young was a fascinating guy.


To hear the difference in sonorities between just intonation and equal temperament, check out the just intonation wikipedia page.

A much more in-depth look at Young 1800 temperament

An extremely detailed and mathematical guide to tuning and temperament