Otis Murphy’s Theory of Quadrants: A Guide to Bis and Side B-flat Saxophone Fingerings

Recently, I was teaching my rules for Bb fingerings to a high school student. On this occasion I was correcting her habit of sliding between A# and B on her major scales. I stopped myself before I gave my advice and thought, “Is it really forbidden to slide from Bis A-sharp to B-natural?”

Sliding from Bis to B-natural may not be news to some of you, but it was completely foreign to me. I was raised in the Larry Teal tradition. He taught to primarily use Side Bb, and to only sprinkle in Bis, 1+4, or 1+5 in certain scenarios. Here’s an excerpt from his book The Art of Saxophone Playing:

1. The Side. This position should be considered the basic fingering for beginners…Adeptness in the use of this key is a fundamental requirement of adequate technique. It is a must in the chromatic scale, and the best available in the Bb-C shift.

2. The “bis.”…It is advantageous when the G-Bb or A-Bb interval is used, provided Bb is not followed or preceded by a C or B-natural. Avoid sliding from Bb to B-natural (or vice versa) with this fingering.

The first seeds of Side Bb doubt were planted when I arrived at university. My college teacher, Frederick Hemke, used Bis primarily. Nathan Nabb, my lesson partner in college, used Bis for just about everything, even his chromatic scale. My world of clean shifts from Side A# to B was crumbling beneath me. Why would someone willingly choose to slip and slide around their saxophone keys?


The French Connection

Hemke studied with Marcel Mule from 1955 to 1956. Hemke relayed to me only recently that he picked up his preference for Bis from Mule. He told me that Mule used Bis, and slid between Bis and B-natural. He added that he preferred Bis because it kept all of the technique in one hand instead of having to coordinate two hands for Side.

All this information started marinating in my mind. Why would the father of French saxophone use Bis so often? Wait, what does Bis mean anyway? Could the etymology of Bis explain French players’ preference? After some deep research, I discovered that “Bis” is used in France to describe two adjacent apartments that share the same address number (i.e. apartment 29 and 29A). To the French, Bis is simply the key adjacent to the B and A keys.

In French nomenclature Side Bb is “TA,” literally “trill A.” This contrasts with the American “Side Bb” or “RSK” (shoutouts to Rousseau), which simply describes the key’s location. There is no allusion to its function as a trill key. Therefore, Side Bb seems like a reasonable option to any teacher or student unfamiliar with its connotations to trilling in French nomenclature. Furthermore, Side Bb probably sounds better to freedom-loving, American ears when compared to the pretentious, exotic-sounding Bis (how do you pronounce that anyway?).

Side note for American saxophonists: the “P” above the B-flats and A-sharps found in Londeix’s “Les Gammes” means plateau (think tray, plate, or flat in English), and is the shorthand for Bis in France. (Thanks, Valentine Michaud, for teaching me that!)

Otis Murphy Saves the Day

Last year I was fortunate enough to see Otis Murphy, another saxophonist with French lineage, perform recitals and give masterclasses in Ohio. Not only did Otis sound great, but his masterclasses were compelling and informative, too. In one masterclass he unveiled his Theory of Quadrants (Quadrantic Theory?). He told us to imagine a large square divided into quadrants, and then to number each quadrant one through four. He then asked someone to randomly assign each quadrant with either Bis Bb or Side Bb. For example: 1) Bis Bb, 2) Bis Bb, 3) Side Bb, 4) Side Bb. Murphy then played a full-range F Major scale and played these fingerings in order (Bis Bb on the way up, and Side Bb on the way down).

At this point everyone caught on to the concept, so when Murphy asked someone else to randomly assign the quadrants they threw him a curveball: 1) Bis, 2) Side, 3) Bis, 4) Side. Murphy nodded, and proceeded to rip through these quadrants not in F Major, but in F# Major! After that display we were all convinced. Murphy made the point that everyone should have the flexibility to use either Bis or Side, and that today’s repertoire demands it.

From the article “Otis Murphy’s Theory of Quadrants: A Guide to Bis and Side B-flat Saxophone Fingerings”: “He told us to imagine a large square divided into quadrants, and then to number each quadrant one through four. He then asked someone to randomly assign each quadrant with either Bis Bb or Side Bb. For example: 1) Bis, 2) Bis 3) Side, 4) Side. Murphy then played a full-range F major scale and played these fingerlings in order (Bis on the way up and side on the way down). At this point everyone caught on to the concept, so when Murphy asked someone else to assign the quadrants they threw him a curveball: Bis, Side, Bis, Side. Murphy nodded and proceeded to rip through these quadrants not in F Major, but F# major! After that display we were all convinced.” So here’s my (much slower) recreation of that demonstration from Otis Murphy. Link will soon be in my bio @daddariowoodwinds @vandorenusa @yamahamusicusa @yamaha.bandandorchestra #scales #bis #sax #saxophone #saxophoneplayer#musiceducation #musiceducation #transcribeeverything #nowmyeducationbegins #saxophone #selmerparis #yamahasaxophone #woodwinds #jazz #jazzlite #jazzscrub

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He also shared a drill to develop dexterity between Bis A# and B. He trilled in quarter notes between A# and B, then in eighth notes, and finally in sixteenth notes.

Another trick I picked up from sliders is to bend the bis key or shave off some of the pearl to make it easier to roll your finger between Bis and B. And it should really be called a “roll” rather than a “slide”.

If you’re still not convinced, remember that sliding is pretty common in the woodwind world. Oboists slide their first finger to activate the upper octave. Clarinetists slide their first finger to navigate the break between the chalumeau and clarion register. This is unrelated but flutists have to press the Eb key with their pinky all the time, which is super hard. And don’t even get me started on bassoonists…Suffice it to say that sliding between A# and B on the saxophone is not that difficult in comparison.


What should you do with all this information? I suggest shoring up your weaknesses whether they be Bis or Side Bb. I’ve tried to implement the following guidelines:

  1. Use Bis 90% of the time, learn to “roll” the first finger from Bis to B
  2. Use Side Bb on the chromatic scale, trills, and passages where it sounds better
  3. 1+4 and 1+5 is for degenerates, and should only be used for tuning major thirds in quartet…err and maybe the last note in the second movement of the Creston Sonata.

Having experimented with this for a while now I don’t believe “sliding” to be such a saxo-faux pas (nailed it). However, I’m not ready to give up Side Bb/TA/RSK altogether. At very least I hope Marcel Mule, Frederick Hemke, and Otis Murphy have convinced you to incorporate both fingerings into your technique.

What are your thoughts? Are you a slider? Please leave a comment below!

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  1. I’m a slider, and a side key user. I have general “rules” that bis is a really great fingering when Bb/A# is approached by skip, and Side Bb/A# is generally best when approached by stepwise motion. I break these rules constantly, thus the quotes.

    1. Thanks for your comment, Jason. I generally agree with you, and I think we’re each a special little snowflake so I make no judgements about people’s Bb-technique as long as it sounds good.

  2. The comment by the author that clarinetists slide to the “A” key is incorrect. A rolling motion is essential, and technical exercises are employed to train the index finger in this way.

    1. Thanks for your comment, Dan! You are correct that rolling is essential. I used “sliding” here to keep the terminology consistent.

  3. Sean, as a GMus90 student of Dr. Hemke’s, I remember vividly the lesson he called me out on my overuse of side Bb. I rarely used Bis Bb before then. He explained to me his reasoning (one hand vs two) and I balked about sliding from A#/Bb to B. I challenged him to demonstrate his Bis technique in the 3rd mvt of the Dubois Concerto that I was working on in the lesson that day. He didn’t have his horn ready to play, so he stood behind me, put his fingers on my saxophone keys and told me to blow. Needless to say, his technique was flawless and I could feel the smoothness of the passages as I blew through my horn. He made his point!

    27 years later, I mostly use Bis Bb with the side Bb for trilling.

    Thanks for the post, it brought back some great memories for me!

    1. Susan, this is a wonderful story! I love hearing stories about our teacher. Thank you so much for sharing and keep up the Bis-tradition.

  4. Thanks for this article! I studied with Dr. Murphy at IU Bloomington some 15 years ago (while he was working on his DM), and I came to him as a regular Bis roller – though whether I picked it up from prior instruction or my own experimentation, I can’t say for sure. He encouraged me facility and flexibility with Bis and side Bb even then. For me, the side Bb tends to be very flat, so I try to only use it for smooth transitions in faster passages.

    I’m glad other comments covered the clarinet rolling (vs. sliding) to chalumeau keys, and I would add that the near-constant use of the right pinky on the flute quickly becomes second nature, as it helps keep the instrument stable. I also agree that what bassoonists must often do with their thumbs likely involves necromancy or voodoo though most of what I’ve played on bassoon has been composed by someone kind enough not to force too much of that on the players.

  5. I studied with Dr. Hemke in 1994 and 1995 for my MM and Certificate. Jonathan Helton was the TA. They both demanded smooth technique.

    I used 1 and 4 in the 1st movement of the Larsen. And have I used it since? Probably once or twice.

    I agree with using side keys for chromatic work and bis for diatonic. But I find myself cheating with Bis often (we have a secret thing).

    After 20 years, I went back to school at Northern Colorado to study with Dr. Dahlke. He also demanded smooth technique and intonation. So I have to agree with the Otis approach. Be prepared. Although, I’m firmly in the bis camp.

    I’m sure that Dr. Hemke probably influenced me to the bis side.

    Tuning is also a thing with my side C, so I only use it in faster notes. But that’s another article.

    Thanks for writing this, Sean!


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