128 notes per octave on the saxophone: How I did it and why!

Category: Classical Jazz Saxophone | Date posted: 21 October 2015

Author: Philipp Gerschlauer

Saxophonist Philipp Gerschlauer on how he went about devising a 128-note per octave fingering chart

The last couple of months have brought some of the most intensive practicing of my live so far. I tend to say this every time I finish a big project but I have reasons to believe that this time I am right. Because this time it was my quest to enter an undeveloped area of my instrument and take it into unchartered territory. The preliminary result was a division of 128 notes per octave based on the eighth octave of the overtone series and a microtonal fingering chart for alto saxophone which contains around 650 fingerings. But let’s take one thing at a time.

My interest in microtonality started when I was 22 and started to study jazz saxophone. When I listened to Hayden Chisholm for the first time on a recording of trombonist Nils Wogram called Fahrvergnügen (clips available here), I knew I had to check out quarter tones as well! So I found fingerings which would produce one note in between two half notes. The result was 24 notes per octave over almost the whole range of the saxophone.

I composed music with it and used this system in my band called Besaxung. Soon we became a microtonal jazz band which would improvise over quarter tone tunes with piano, drums and bass. We made two recordings with my songs and enjoyed the new sound possibilities which microtonality gave us.

This went on for a couple of years. My quarter tone playing improved because I composed more and more tunes based on quarter tones. Writing songs established a deep emotional connection to the melodies and harmonies and helped me to use my melodies in other contexts.

Eventually, I felt it was time to use more notes than just (!) 24 per octave so I was wondering if I could do 48 notes. I looked around for fingerings and found help in Hello! Mr. Sax by Jean-Marie Londeix and The Techniques of Saxophone Playing by Marcus Weiss and Giorgio Netti.

Using these pitches in a band would make the piano sound 'out of tune'. I had many situations when I listened to recordings of mine and could hear that a strong microtonal melody could indeed blend in well with regular harmony. The clashes between the piano and the saxophone were great. However, I started to wonder if there was an alternative to this sound.

After I graduated in Berlin with my bachelor’s degree in Jazz Saxophone in 2012, Bass player Greg Cohen suggested I should use a microtonal piano instead of a regular piano. I thought about it and came to the conclusion it was time to replace the regular piano with a microtonal keyboard.

One experience which changed my life in a second was when I listened to Gerard Grisey’s Partiels (1975). Any note on an instrument is made of many different overtones, which combine to produce a specific pitch and give that instrument its unique timbre. Listening to the chords that result from doubling parts of the overtone structure from a bass and trombone was the most beautiful sound I had ever listened to!

From this moment on I knew that an equally divided octave - no matter if 24 or even 48 notes - would never be able to produce such a rich, colourful and strong sound like the overtones of a strong fundamental note (Martin Vogel, in his book On The Relation Of Tone, suggests tuning system 171-EDO as a substitution for transposable Just Intonation. Martin Vogel: Lehre von den Tonbeziehungen“, p. 335 et seqq). So I knew I would have to leave the world of equally divided octaves and switch over to tuning systems which are closer to the overtone structure of a fundamental tone.

Using a microtonal keyboard was the right tool for doing so. But how would you be able to program a keyboard like that? I knew I wanted to have a regular keyboard surface so that the pianist wouldn’t have to learn a different instrument (back then I didn’t know about my friend Aaron Andrew Hunt who solved this problem elegantly with his Tonal Plexus keyboard).

I saw a documentary about Harry Partch in which John Schneider demonstrates the 43-tone Partch organ. I figured out this instrument was physically built so I wouldn’t be able to detune it for my purposes (Later I found out about the group Syzygyz who use this organ and play pop music). I wanted to be able to program every key of the keyboard individually and be able to produce all kinds of pitches and compose with them. To cut a long story short, it took me uncounted emails and phone calls, but after one year I found a solution which would sort of work. Thanks a lot to Jonathan Hoffmann from Cologne and Felix Roßkopf who did the programming! I was now able to play Harry Partch’s 43-tone scale or any other scale in the audible area.

I composed and played with these new sounds and brought them to my band. I tried to find fingerings which would work for whatever I had thought of and programmed. The result for me as a saxophonist is that I would end up with compositions which only used alternate fingerings - no regular ones. Whenever I played a regular fingering it sounded wrong! Of course it was still important to tune the saxophone first. But then I would exclusively use fingerings chosen specifically for the pitches in my composition. That was in New York already during my master’s studies in Jazz Saxophone at the New York University with drummer Tony Moreno, Vibraphonist Stefon Harris and Saxophonist Chris Potter.

At this point I was wondering if the number of possible fingerings for microtones would be limited - and then I met bassoon player Johnny Reinhard! Johnny Reinhard is the head of the American Festival of Microtonal Music in New York. This festival presents microtonal music and has done so every year since 1981. He introduced me to a concept which he developed in 2011. It’s called 'eighth octave overtone tuning'.

Every tone has, due to his physics, an infinite number of higher partials that define the colour of its sound. This is called the „Overtone Row“. Its characteristics are that the number of tones from root to root doubles with every octave. The first octave above the root only has two notes, the second octave 4, the third 8, the fifth 16, the sixth 32 and the seventh 64. The eighth octave of the overtone series divides the octave into 128 notes per octave. So we are talking about the 128th until the 256th overtone. As Johnny Reinhard states this system collects all even and uneven numbers including primes from the 1st to the 128th overtone. Plus all uneven overtones from the 128th to the 256th overtone. Johnny refers to high and uneven partials as „embellishment notes“. These notes only appear once in the eighth octave.

 Nick Gideo created a chart of the
first 256 overtones in the harmonic series,
all compressed into the space of a single octave. The “x” axis represents the Harmonic number, and the “y” represents the "Prominence Factor," or how many times the harmonic has recurred throughout the natural harmonic series. Johnny Reinhard © 2011

When I heard Johnny talking about his concept for the first time I thought: „You are kidding! That’s impossible!“. It sounded unreal to divide the octave on the bassoon into 128 notes per octave. Those intervals seemed to be too narrow to be expressed accurately by fingerings. When he demonstrated it I couldn’t believe my ears. Johnny encouraged me to use this system as well. I told him I could do 48 notes per octave but there might be some more possible fingerings…

I wanted to be in a situation where small changes of pitch could be made without changing the embouchure. Only this way would it be possible to play pitches accurately. Whenever you want to modulate within Just Intonation you basically need to be able to play any possible pitch situation on your instrument accurately (e.g. imagining an octave as a continuum rather than as divided into discrete notes). Once I would be able to play '128 Eighth Octave Overtone Tuning' the adjustments I would need to make with my embouchure would be 3.5 to 6.5 Cents. And that’s absolutely possible and within the range of what needs to be adjusted anyway in any musical situation.

So I finally started work on a project I’d been considering for a while: I tried to define a complete microtonal fingering chart for the alto saxophone. The way I was doing it was actually pretty simple. From the studies of 48 notes per octave I knew that below A1 there was not too much microtonal possibility on the alto. Quarter tones would work and a couple of eighth tones maybe but such a defined concept like '128' would have to start on the A1. So I tuned my instrument (first to 440 Hz, later to 442/443 Hz) and played the A. Then I switched to the next higher fingering from 48 notes per octave without changing my embouchure. I knew that I would have to stick to certain rules in order to make this fingering chart work. The first rule was that the embouchure needed to remain in a 'regular' position (you find a detailed instruction in the preface of my workbook).

When I played the next higher fingering after the A and switched back to the A. I followed my intuition in finding a fingering which would produce a sound 'in between'. When I found it, I tried to find a fingering which would fit in between again and so on. Like that I tried to fit as many fingerings as possible in between one half note (a half note meant from one regular fingering to the next one).

It occurred to me early on that certain regular fingerings would sound too high or too low. We all know this from practicing. So I had to find a compromise sometimes for notating regular fingerings as fingerings for microtonal pitches (e.g. the regular 'D2' appears to be too high when not being corrected with the embouchure or low B key in a regular context). 

Eventually I felt I was ready to start practising to divide the octave into 128 notes per octave. The first thing I did was to create a play along. Thanks to the microtonal keyboard I had an accurate play along in no time! I chose a steady sound with no vibrato. A sine wave would work well but instead I chose a sound close to an organ. Every note on this play along would last exactly one second. This was important because as I would practice this scale it would have gotten impossible to keep track of where I was. So I created a play along of over three minutes which would accompany me for almost a whole year.

At first I practiced second 0 until 1. I looped it and reduced the speed - sometimes up to 20 % of the original speed. I looked into my fingering chart and tried to find the fingering which would match to the play along best. A problem was the different temperature of the instrument and the tuning pitch of the saxophone. It took me a while to settle down all the variables and find a solution. I think those were just the kind of problems which occur every time you practice something new.

So I found fingering after fingering until I reached the next half tone. At the beginning of the eighth octave of the overtone series from A to Bb there are 8 pitches. On the top of the octave from G# to A there are 14 (keep in mind that the overtone series gets smaller the more you go up. Starting with intervals of around 13 cents the top of the eighth octave of the overtone series only has 7 cent steps!). Later I was able to practice precisely different parts of the scale e.g. second 76 - 88 knowing always which pitches I wanted to express.

I climbed up the overtone series finding more and more fingerings. Sometimes I had to go back and dismiss fingerings I had found before. Everything would change a lot. Sometimes a fingering combination would be uncomfortable to play or would sound poorly. I realized how my ears got better during the process at hearing small intervals. The more my ears developed the more possibilities I found. Fingerings that would sound too close to each other to be noticeable would half a year later appear to be individual pitches with their own characteristic in pitch and sound quality. An interesting result of my analysis was also that almost every fingering I used for quarter tones when I started to play microtonal saxophone proved to be inaccurate and sometimes not even close to quarter tones. For me this shows that for the ear it’s harder to recognize equally spaced distances than distances more closely related to overtones.

So the fingering chart improved and playing 128 per octave just became a side effect of what’s possible with this fingering chart. It was not hard to find the fingerings at all because there were so many alternatives the chart would offer me. I counted them in between. In August 2014 I had 115 fingerings in the first octave from A1 - A2. In September it was already 172 fingerings. In July when I refocused on finding more fingerings there were 223. The final version of my workbook from September 2015 contains 318 fingerings in the first octave from A1 - A2.

I started to look for fingerings starting on A1 on the alto but where should I stop? I thought high E would be good. But my workbook contains a couple of more fingerings higher than E3. When I was done I figured out that there were even more possibilities for fingerings between the perfect fifth of the high A2 - E3. I ended up splitting 7 half notes into 323 fingerings!

I play a regular Selmer Super Balanced Action Alto Saxophone from 1951. This means it doesn’t have a high 'F# / C5' key. I am sure that with this key even more microtones would be possible! I didn’t adjust anything on the instrument except for the interval between G and G#: If you close the regular F key you realize that two connected screws next to it move with it. Turn the higher one about a quarter anti-clockwise and it will enable the G#-key to slightly open when pressing G# and closing the lower key.

I was testing the fingerings with a Jupiter 769, a student’s model from the 1990s and a little bit with a Selmer Reference alto Saxophone. I also tested the fingerings on my students - with surprisingly good results! They were able to produce the same pitches and get similar results.

Finally I can say that practicing '128' plus developing a fingering chart opened up my saxophone skills, improved my ears, trained my intuition on the instrument and taught me a lot about how the instrument works. In addition it enabled me to play any pitch and to deal with microtonal music of any kind. Modulation inside Just Intonation or inside different scales of equal divisions of the octave is not a problem anymore. I just have to use my chart.

I also benefit when I play in uncomfortable tuning situations. Some organs are tuned in 450 Hz (in the summer). Some use lower in Baroque tuning. I would just use a different fingering from my chart and would be able to play in tune!

Whoever is interested in practicing this method is invited to purchase my workbook. It contains around 650 fingerings plus a detailed instruction of how to practice and to play these pitches. You get a personalized copy plus my play along with 128 notes per octave via email. The price, including shipping, is 55.50. Please send an email to mail@gerschlauermusic.com.

What’s up next? I am teaching workshops at different universities about microtonal music and microtonal saxophone. I just got an invitation from the Berklee College of Boston to teach a clinic there. I am playing in Germany and the USA, preferably New York. I will compose new music and there is a major recording about to come next year. I am thinking about a version for Tenor and the Soprano saxophone but this takes time…

Hopefully I will be able to host a big festival of microtonal music in Berlin in February 2016. Cooperations with the Berklee College of Music, the American festival of microtonal music, turkish guitar player Tolgahan Çogulu already exist. So come to Berlin if you find time and check my website for latest news!

If you want to see a demonstration of my results please watch the video in which I present the '128 eighth octave overtone tuning' on the saxophone. You can find it here.

An introduction video to my music can be found here.

Please visit my website: www.gerschlauermusic.com for more information about me.

Berlin, October 2015 Philipp Gerschlauer

About Philipp Gerschlauer

At age 16, Philipp Gerschlauer entered the Music university in Frankfurt to study classical saxophone as a youth student. Short after he became a member of the Youth Jazz Orchestra of the federal district of Hessen. As a founding member of the band »Besaxung« he won the German national youth jazz competition 2009 and also collected a special Soloist price. He also won the Jazzprice in Heidelberg. In 2010, the German national radio station (Deutschlandfunk) appointed him to be a part of the "European Jazz Orchestra". Philipp Gerschlauer toured in more than eighteen countries in the world. In the year 2012 he graduated at the Jazzinstitut Berlin where he studied with Peter Weniger, Claudio Puntin, Greg Cohen and Kurt Rosenwinkel. Thanks to grants of the German National Academic Foundation, the German Student Exchange Service (DAAD) and the New York University he moved to New York City. Since 2014 he is holding a master’s degree in Jazz Saxophone from the NYU where he studied with drummer Tony Moreno, Saxophonists Chris Potter and Billy Drews and Vibraphonist Stefon Harris. He plays all saxophones, clarinet, bass clarinet and flute. In his music Philipp Gerschlauer deals with conceptual and improvisational potential of microtonal harmonies and scales. He is dividing the octave into 128 notes based on the eighth octave of the overtone series. He developed a fingering chart for Saxophone which includes around 650 microtonal fingerings. He is teaching clinics for microtonal Saxophone at Universities such as the Berklee College of Music in Boston. Philipp Gerschlauer is considered to be one of the leading microtonal Saxophonists in the world. www.gerschlauermusic.com

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The Clarinet and Saxophone Society of Great Britain is a company limited by guarantee registered in England No. 3010228, whose registered office is at Flat 51, Parkview Apartments, 122 Chrisp Street, London, E14 6ET. Email: membership(@) cassgb.org. Tel: 01642 769 558

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