A Tale of Two Temperings

2011Symposium_1_2In our well-tempered musical culture, all musical keys tend to sound the same, except for being higher or lower. Yet throughout the eighteenth and nineteenth centuries, composers enjoyed the rich and expressive variety in the way different keys sounded. Rousseau described D major as being suited for “gaiety or brilliance,” Schumann spoke of C major as “simple, unadorned, while Schubert, describing Bb minor, said “preparation for suicide sounds in this key.” The San Francisco Symphony has a wonderful demonstration of how different keys have different qualities when played on a piano as it would have been tuned in Beethoven’s day.

When you listen to the difference in tone quality and color between the keys outside of equal temperament, you realize that all tonics and other functions within a diatonic scale are not equal. The tonic in D major sounds quite different than the tonic in Eb major, apart form the difference in pitch. It is easy to forget, or perhaps never discover, that these differences exist, because equal tempering causes the notes that establish a tonic to be sterile duplications from one key to another. One of the things I like about fixed do solfege is that calling tonic notes by different names in different keys forces us to think of each tonic as a unique entity, related intervallically and harmonically to the other diatonic tones, but not to tones in other keys Tones that are called by the same name ought to sound the same.

Why don’t all keys sound the same outside of equal temperament? To answer this question, we will look at how pianos are tuned. Today, pianos are generally tuned with equal temperament, meaning the distance between every half step is exactly the same. This eliminates the differences between keys described by many of the classical composers. Well temperament was used by Bach and nineteenth century composers. Well temperament allowed the piano to be played in tune in all keys, but preserved the different character of each key by avoiding equal temperament. Pianos tuned with well temperament, which is not the same thing as equal temperament, are tuned with slower “beats” compared to equal temperament. “Beats” are the oscillations heard when shared overtones between two tones are not perfectly in tune. Slower beats are produced by notes that are less tempered. Tempering is the change from pure tuning. Well tempering creates a tuning where different keys will take on different characters and colors, but will still be useable in all keys. The tuning standard for well temperament is C. With the addition of each additional sharp or flat, more dissonance is introduced. That is why C major is the purest sounding key, and sharp keys are often described as more colorful; they simply have more dissonance built into them.

When a soloist plays with a pianist using an equal tempered instrument, the music can easily sound outWTC of tune because the soloist, if he or she is well trained, will avoid equal temperament as part of his or her collection of expressive performance devices. These notes clash against the equally tempered notes of the piano. This is also why singers and non-keyboard instrumentalists should not learn tuning from a piano. Matching pitch with a piano is destructive to good intonation for a singer or instrumentalist. While equal tempering is necessary for highly chromatic, frequently modulating, and atonal music, it is not necessary for performing music of the standard orchestral repertoire. A more authentic and expressive experience would result from using well tempering for these performances. Ear training in our music conservatories would also be improved with the use of well tempering, and the steady and historical rise in the tuning standard of 440 cycles per second for the tuning note “A” might be stopped or even reversed were well tempering employed, because the richer pallet of timbres musicians seek by playing on the sharp side would be readily apparent from the affects of the tempering. For music teachers, an awareness of the advantages of well tempering, and making use of them in their teaching is certainly worthwhile.

What is a Convenient Shorthand for Music Notation Within Word Processing Software?

2011Symposium_1_2When writing lesson plans, I frequently have wished that I had a way of writing melodies quickly and easily on my computer within my word processing software. After attempting to use available symbols on the computer keyboard to contrive stick notation, and then line up solfege syllables I found all of this too time consuming and inconvenient. Some time later, I finally thought of a system that, with practice reading it, would serve my purpose well. I may not be the first to use this system for notating music within word processing software, but I don’t recall being informed of it from any other source.


For many years, I have used Finale music notation software. In the speedy C-Major-Scaleentry mode, entering notes without a midi instrument, numbers are used for note values, and pitches are indicated with the click of the mouse on the desired line or space of the musical staff. In my music notation for word processing, I adapted the numbers, combining them with solfege syllables. Dotted notes have a period following the number, and rests are a dash followed by a number. Time signatures are indicated with a fraction, and key signatures are indicated with linearly placed bs or #s. Tied notes have a number for the second note of the tie, and the tied notes are connected by an underscore.  I will demonstrate the system with the well-known horn solo from the movement “andante cantabile” from Tchaikovsky’s fifth symphony.

Figure 1

Andante cantabile from symphony no. 5 by Tchaikovsky

bbb 12/8 mi4 re4 do4| mi5. re6. ti4 do4 re4| fa5. mi6. mi4 fa4 so4| la5. la5 la4 la5._5 la4| la5. so5.—5 –4 mi4 re4 do4| etc.

the three bs indicate three flats in the key signature. 12/8 is the time signature. The first note is mi4. Mi in fixed do solfege is E, and because of the key signature, it is E-flat. Solfege syllables continue in the same way. Measure lines are given with a vertical line

( | ). In the fourth measure, there are two A-flats that are tied; a dotted quarter note tied to a quarter note. These tied notes look like this: la5._5 with la5. being the dotted quarter note A-flat, the underscore being the tie, 5 being the tied quarter note. I am able to type all of those notes quickly, and with practice, can read the solfege for pitches and the number for rhythms, just as I read note heads for pitches and stems and connectors for pitches and rhythms respectively in standard music notation. Using this system also has the advantage of keeping me from seeing standard music notation, just as my students are unable to view it, as I sing to them in solfege, and then have them repeat what I sang. It reminds me of the position I place them in, and it also gives me extra practice using solfege in a purely aural/oral way. If you are working on your fixed do solfege, as I have been this year, writing out and then singing melodies using this system is good practice. For those times when I need to remind myself of a melody I will be teaching, this short-hand system works quite well.


Going Beyond the Lesson Plan for Quality Teaching

2011Symposium_1_2The first grade class came in and took their seats. I called for them to S.L.A.N.T. and they quickly did so. S.L.A.N.T. is an acronym for sit up, listen, ask & answer, nod when you understand, and track the speaker. I learned it from the book Teach Like A Champion. I then started the song “I Am Standing in the Shoes of John” and they sang it through, but many were out of tune, especially on the highest notes. This is a very high achieving class, and they are used to getting compliments from me, so when I told them their singing was awful, they were surprised. “Yes,” I explained, “it was out of tune. Sing “shoes of John” and I sang the occurrence that falls on re, ti, la in fixed do. They repeated it. We did this several times, and then they all sang it again. It was better, not good enough yet.

Without saying another word, I asked five students who had sung it well to stand and sing the song. I then called on another five who had sung reasonably well to stand and join the first group. They did, and rose to the level of the first group, so that now these 10 sounded excellent. Another four, and then the remaining students. By the time they were all standing, they were all singing in tune, and with the nice clear tone of the first group.

That is what we did to start this music class. Here is what it said in my lesson plan: Review the song, “Shoes of John.” There is a lot of potential packed into that word, “review.” I review to reinforce prior learning, and to informally check for what learning has taken place. When a soft spot in learning is revealed, such as singing a previously learned song out of tune, the review goes deeper, solving problems, correcting errors, and getting the material in the shape I had hoped it would be in when I last finished teaching it. There is a dynamic quality about the process of reviewing that is not adequately represented in the lesson plan entry. It is a changing and developing relationship between my students and me from which a better understanding and higher achievement is built. When that new level is reached, I can go back into the lesson plan, and resume.

Next in the plan was to add a rhythm ostinato, then to add pitches to the singing-kidsostinato sung with solfege, and then to transfer that ostinato to barred instruments. The students quickly were able to sing so re re — in fixed do solfege. Half then sang the ostinato, while the rest sang the song, now in tune. The 2-part harmony was satisfying. We then switched parts with equally satisfying results. Interestingly, when switching to instruments, two of the students dropped the rest on beat 4, though they had sung it correctly. Playing the part on instruments demands more independence than singing with the class, so this error presented the opportunity to develop more independence in these children. Reminding them of the rest, which they had already experienced through singing sufficed to correct the problem. They were able to relate what they did singing to what they were trying to do playing, once the connection was made for them. The song could now be performed with in-tune singing and an accurate instrumental ostinato.

I completed the lesson by teaching them a new song– the Creole lullaby “Crabe Dans Calalou.” First I sang it through using fixed do solfege, then sang short sections and had the children repeat them. The sections they repeated gradually were made longer, until they could sing the whole song. They have had plenty of experience singing fixed do solfege, so this was just another opportunity for them to do so. Because the lyrics are in French, I told them what the song was about, and then taught them the French lyrics. It was easy to connect the French words with English equivalents because many of the words, like papa, maman, crabe, and riviere, are similar in both languages. The first half of the first two phrases are identical both in words and music, and one of the children observed that the music was an ostinato. I acknowledged that it was a repeated pattern, and was glad they had noticed the repetition. Because the song is partly about a father, some of the children were excited to sing it for their fathers on father’s day, which is this Sunday as of the writing of this post. For the lesson plan, I had merely written, “Introduce the song, “Crabe Dans Calalou.” It is teaching that makes the plan come alive. When the plan is solid while still allowing for the flexibility of students shaping and directing the learning within the framework of the plan, learning takes place that is relevant and exciting for the children. That is, I think, the hallmark of quality teaching.