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3 Minute Introduction

Five Degree Calculation Line

String Numbering Order

Cipher Demonstrations

Pattern of Unisons and Octaves

Fretboard Note Spellers

Musical number formula translation tables

Free PDFs -- Grids, Spellers, Cipher Formula


The Cipher for Ukulele


[Tenor and Baritone directly]



Before reading this be forewarned that I use Commonsense String Numbers for Ukulele in all explanations.

Also note; all that follows here (of The Cipher for Ukulele) uses the guitar-like all-ascending tuning pattern and the all-ascending Five Degree Calculation Line (of guitar-like tenor and baritone ukulele). Explanations are below.

Index of The Cipher for Ukulele:

The Cipher System’s Five-Degree (Perfect Fourth) Calculation Line used for plotting musical materials on the guitar fretboard also works for  tenor and baritone Ukulele (directly) — and indirectly for re-entrant tunned soprano, concert, and tenor ukulele. See the special note following.

Special note; There are four sizes of ukulele’s, being from smallest to largest: soprano, concert, tenor, and baritone. To start, the two smallest and two largest in the family can be grouped together conceptually by the way they are tuned:

Guitar tuning:
The two bigger ukulele’s, tenor and baritone, can be conceptualized as guitars — without the guitar’s two lowest pitched strings and still having an all-ascending tuning pattern. [But see re-entrant tenor ukulele tuning next.]

Re-entrant tuning:
concert, (and also Tenor) ukulele’s however, are slightly different birds. They all use a slightly different tuning where the 1st string (using common sense string numbers) is actually higher in pitch than the 2nd string! This is known as re-entrant tuning.
In the following table, compare the standard “C” ukulele tuning G C E A between a guitar-like tuned tenor and tenor/soprano/concert ukuleles in re-entrant tuning. Pitches are given in Hertz or CPS (cycles per second). You should already be familiar with  A=440 (4th string). But look at the G strings (1st string):
Guitar-like Tenor G = 196 cps,
Re-entrant Tenor/Soprano/Concert G = 392 cps.
That later G note is actually higher in pitch than the instruments 2nd string (C note). And that G note is one octave higher than the G on the guitar-tuned tenor ukulele.
Tenor ukulele players use either of these tuning schemes. Re-entrant gives the quintessential Hawaiian sound. Guitar-like tenor is preferred for “slack-key” or finger-picked ukulele, at least.
In the end, from a practical perspective and the perspective of music theory and chord construction generally, these two tuning-pattern variations in the ukulele family really don’t change the results very much. For example, ukulele’s are used primarily for chording and chordal accompaniment. The chord voicings generated by these two different  tunings (two different octaves of G string) will sound slightly different, but they still use the same chord names, same notes and numbers (in standard chord analysis), same fingering patterns (diamonds and dots on the fretboard), same letters on a spelled fretboard chart, and the same (or essentially the same) pattern of unisons and octaves, etc.
The one thing that would change however is the calculation line (and possibly the string numbering order) in the Cipher System. The calculation line for re-entrant tuned ukulele’s is not uniform ascending fourths. In fact, it would be difficult to use a calculation line at all with this tuning — being mixed descending and  ascending! But then, even in standard procedure this is a difficult tuning to get your head around and conceptualize generally, and to conceptualize from the perspective of standard chord construction and standard string instrument chord voicing theory and practice.
For anyone who really wants to understand and conceptualize how (any/all) ukulele fretboards work though, I would (still) probably suggest they start by studying the guitar-like tenor ukulele tuning with the all-ascending fourths Five Degree Calculation Line,  and the resulting fretboard patterns and chord voicings. After all, historically, I’m quite sure that’s how it happened in the first place. The guitar-like tuning must have come first, and only later did folks decided to use the octave G string. In other words, the first ukulele players were conceptualizing and playing “guitar” essentially, and they were benefiting from their knowledge of guitar and the relative conceptual ease of an all-ascending tuning pattern. So I don’t think it wouldn’t be “cheating” or incorrect if you did the same thing, followed the same evolutionary progression of string tuning pattern, fretboard logic, learning, conceptualizing, playing, and finally modifying (by tuning the G string up one octave). This makes the most sense to me, but it’s up to you.
At any rate, all that follows here (of The Cipher for Ukulele) uses the guitar-like all-ascending tuning pattern and the all-ascending Five Degree Calculation Line (of guitar-like tenor and baritone ukulele theory).
P.S. But don’t forget to return your Uke to re-entrant tuning when you’re done studying some theory. You’ll miss half the fun and half the beauty of Ukulele unless you do.


Soprano, Concert, and Tenor ukulele tuning oddity
[ Re-entrant octave G’s ]

Strings   low to high





Tenor (guitar-like)





Soprano / Concert / Tenor







For application to guitar-like tenor and baritone ukulele (only); drop the two pattern points of the guitar’s Five Degree Calculation Line that correspond to it’s two lowest pitched strings. The tenor and baritone ukulele version of the Five Degree Calculation Line is discussed in on it’s own page.

The tenor and baritone ukulele version of the Five Degree Calculation Line is made entirely of uniform Perfect-4th intervals,  just like on guitar. It  also exhibits a pattern shift just like on guitar. The pattern shift is a one fret down offset in the otherwise straight-line pattern. On guitar, it occurs at the fifth string. On ukulele it comes at the third string.

As usual, Commonsense String Numbering Order is also used here — the lowest pitched string “G” is String-One (Figure 1)

A Pattern of Unisons and Octaves specific to the four string ukulele is also needed (Figure 2).




The Cipher for 4-string Ukulele (tenor and baritone only):

  • A four string Five Degree (Perfect-Fourth) Calculation Line is used [this is the same as the pattern on the guitar’s four highest pitched strings]
  • The same Cipher number formula (for intervals, scales, and chords) used for guitar are used for ukulele as well. The formula are simply plotted relative to the 4-string version of the Five Degree Calculation Line and it’s resulting counting grids. Again, these patterns and counting grids are natural to the ukulele fretboard. This is how it truly works (in it’s standard tuning).




Figure 1






Figure 2






Figure 3








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© Copyright 2002   Roger Edward Blumberg


All  text, images, system components, devices, key terminology* and logos, on this web site are copyrighted [physically at the U.S. Library of Congress]. Reproduction in any form without written permission from the author and creator is prohibited.

[*including but not limited to: The Cipher System, The Cipher, Music Theory Cipher, The Guitarist’s Music Theory Cipher, Blumberg’s Music Theory Cipher for Guitar, Cipher Formula, The Five Degree Calculation Line, Perfect-fourth Calculation Line, The Seven Degree Calculation Line, Perfect-fifth Calculation Line, Fretboard Navigator, Counting Grids, The Pattern of Unisons and Octaves, Rooting-Center, The Fifth String Pattern Shift, The Third String Pattern Shift, Commonsense String Numbering Order.]

Thank you.

© Copyright 2002   Roger E. Blumberg












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