Is there a Relative Pitch Clef?

Question

To start out: I am more-or-less familiar with all the standard musical clef notations, including F, C, and G clefs; as well as the fact that clefs can be movable (tenor clef, french violin clef...) and have octave displacements (8va/8vb). I'm also aware of the unpitched percussion clef. With the exception of the later, these are all ways to map staff positions to absolute pitches. (I should also mention that in the case of transposing instruments, like Clarinets or Horns, this absolute pitch may not be the pitch it first appears to be.)

My question is whether anyone has ever seen a clef that maps staff positions to relative pitches (i.e. scale degrees) rather than absolute pitches. I realize this would be of limited use, especially for performers, who need to know which note on their instrument to play. But I could see such a system being useful in certain harmonic or analytical contexts, where the absolute pitch is unimportant (for example, notating chord progressions, or melodic motifs, irrespective of key). I could also see it being used for initial steps of transcriptions done by-ear, where the key isn't immediately important.

The "work around" is just to pick some specific key (which may or may not be correct, and which may often end up being 'C'), and just notate in that key. That works fine, I suppose, but it makes an explicit statement about key which may not be accurate or relevant. Of course, there are also numbers and solfege symbols which can be used, but these use alphanumeric characters, rather than standard music notes, and thus lose rhythmic information. One similar thing I've seen is shape-notes, in which the shape of note heads indicate scale degree. But this is non-standard notation practice (thankfully!), and it still uses normal clefs to indicate absolute pitches. I suppose transposing instruments are probably closest to what I'm looking for, if they were notated without a specific transposition in mind.

I have not been able to find any information on Google about the existence of such a clef, so I presume it doesn't exist, but I might not be using the right keywords, or it might be very obscure, so I'm wondering if anyone else has ever come across something like this? I'd be mildly surprised if no music theoretician anywhere has ever proposed some such system.

Answer 1

In western staff notation every clef represent fixed set of notes so the what is written can easily be conveyed to any musician without much knowledge of the theory behind the notes just the knowledge of this is X note. Also note the key signatures themselves are set in a fixed pattern to simplify the reading for musicians. Even in the more loosely defined percussion (or neutral) clef, there is an understanding that the first space is for bass drum, the third space is for snare, and the space above the staff is for some kind of cymbal. The notation is meant for precision and not for theory and relativity.

There are analysis techniques that can reduce harmony (chords) into relative ideas. The most widely used analysis is Roman Numeral Analysis and it's modern form the Nashville number system. These are extremely useful for chords and making them relative to any key, but it's not for melodies.

There is a numbered musical notation popular in Asian countries. The basic idea is that the key is given and the notes are all numbers based on the scale degree. There is no clef because we are dealing with numbers instead notes on a staff. Here is the Wikipedia entry for the kind of notation.

Answer 2

I encountered the same question when I started playing the jammer (in the form of the Hexiano Android app). Due to its isomorphic keyboard layout (and thus ease of transposition), this instrument lends itself very well to a relative-pitch notation.

Eventually, I developed my own system of jammer tablature. Of course, it suffers from a lack of musical scores written in it, and for that reason may not be a suitable answer for your question. But just in case anyone here is curious, here's what it looks like.

Pitch Notation

Notes are written on a vertical staff consisting of 4 lines and 3 spaces. The spaces correspond to the “root row” (do-re-mi) on the jammer keyboard, and the lines correspond to the “dominant row” (fa-so-la-ti) above.

  do
fa  so  la  ti
  do  re  mi

Notes of the major scale

│ │
├─┼─┬─┐
│●│ │ │ do
│ │●│ │ re
│ │ │●│ mi
● │ │ │ fa
│ ● │ │ so
│ │ ● │ la
│ │ │ ● ti
│▲│ │ │ do
└─┴─┴─┘

Notes of the minor scale

Uses the same root and dominant rows of the relative major, but starts on “la” of the row below.

    │
┌─┬─┼─┐
│ │ ▼ │ la
│ │ │ ▼ ti
│●│ │ │ do
│ │●│ │ re
│ │ │●│ mi
● │ │ │ fa
│ ● │ │ so
│ │ ● │ la
└─┴─┴─┘

Chromatic notes

continue the same jammer keyboard-based arrangement.

  C♭  D♭  E♭  F   G   A   B   C♯  D♯  E♯
F♭  G♭  A♭  B♭  C   D   E   F♯  G♯  A♯  B♯
  C♭  D♭  E♭  F   G   A   B   C♯  D♯  E♯
F♭  G♭  A♭  B♭  C   D   E   F♯  G♯  A♯  B♯
  C♭  D♭  E♭  F   G   A   B   C♯  D♯  E♯
F♭  G♭  A♭  B♭  C   D   E   F♯  G♯  A♯  B♯

Ledger lines are added as necessary.

Here's an ascending melodic minor scale:

    │
┌─┬─┼─┐
│ │ ▼ │     la
│ │ │ ▼     ti
│●│ │ │     do
│ │●│ │     re
│ │ │●│     mi
│ │ │ │●    fi
│ │ │ │ │●  si
│ │ ● │     la
└─┴─┴─┘

Octaves

The “main” octave uses circular (●) noteheads. The octave above it uses upward-pointing triangles (▲), and the octave below it uses downward-pointing triangles (▼). Pieces that span 3 or more octaves need to use “8va” notation.

Chords

Multiple notes played together are written in the same horizontal row. Here are the triads within the major scale:

┌─┬─┬─┐
│●● │●│ I
● │●● │ ii
│ ● │●● iii
●▲│ ● │ IV
│ ●▲│ ● V
│▲│ ●▲│ vi
▲ │▲│ ● vii°
└─┴─┴─┘

Key signatures

Because jammer tablature is a relative-pitch notation, these are optional!

Major key

Above the staff, write the tonic (“do”) on the first space.

 C
│ │
├─┼─┬─┐
│●│ │ │
│ │●│ │
│ │ │●│
...

Minor key

Above the staff, write the tonic (“la”) on the third line.

    A
    │
┌─┬─┼─┐
│ │ ▼ │
│ │ │ ▼
│●│ │ │
...

Note length

Notehead colors

• ▽ ○ △ = whole note (4 beats unless otherwise specified)
• ▽ ∅ △ = half note (2 beats)
• ▼ ● ▲ = quarter note
• X = quarter rest (longer rests are written as a sequence of multiple X's)

Length modifiers

Placed to the right of the note, chord, or rest.

• / = multiply by 1/2 (thus ●/ = 8th note, ●// = 16th note, etc.)
• 3 = multiply by 1/3
• · = multiply by 3/2

Example

The melody to “Frère Jacques”

│ │
├─┼─┬─┐
│●│ │ │
│ │●│ │
│ │ │●│
│●│ │ │
├─┼─┼─┤
│●│ │ │
│ │●│ │
│ │ │●│
│●│ │ │
├─┼─┼─┤
│ │ │●│
● │ │ │
│ ∅ │ │
├─┼─┼─┤
│ │ │●│
● │ │ │
│ ∅ │ │
├─┼─┼─┤
│ ●/│ │
│ │ ●/│
│ ●/│ │
●/│ │ │
│ │ │●│
│●│ │ │
├─┼─┼─┤
│ ●/│ │
│ │ ●/│
│ ●/│ │
●/│ │ │
│ │ │●│
│●│ │ │
├─┼─┼─┤
│●│ │ │
│ ▼ │ │
│∅│ │ │
├─┼─┼─┤
│●│ │ │
│ ▼ │ │
│∅│ │ │
└─┴─┴─┘

Answer 3

All of the clefs used in Gregorian chant notation represent relative pitch only. A Gregorian C or F clef only tells you the position of the half steps, but the absolute pitch is up to the people singing.

The very earliest chant notation is "adiastematic"--not on a staff, which hadn't been invented yet, and not showing specific intervals. The symbols indicate only relative up and down movements. The problem is that you can only sing from this notation if you already know how the melody goes. This is why the staff and clefs were invented---not to indicate absolute pitch, but to clarify the position of the half steps and the exact intervals between notes.

Also before the eighteenth century, pitch varied so widely from place to place, and local customs varied for how to interpret clefs, so written clefs did not correspond to modern pitches.

Answer 4

Check out the chromatic staff -- looks similar to standard notation but the interval from one line to the next space (and vice verse) is always a semi-tone, and thus doesn't imply any particular key.

Answer 5

It's possible that some of Schoenberg's Sprechstimme notation is close to what you are looking at. In works such as A Survivor from Warsaw or the Ode to Napoleon, he used a single line without a clef, with ledger lines above and below the "staff", and even with accidentals, although these are bit "impressionistic" without an idea of where Do is, and might be too imprecise for what you're looking at.

He also came up with a chromatic notation system that might serve well without clefs - it's fairly extensible, accommodates standard rhythmic notation well. Musicnotation.org (Dave's link) has a bit about it, but the real detail is to be found in his book Style and Idea.

Answer 6

Clefs and related symbols "are all ways to map staff positions to absolute pitches"

Yes and no. A clef's function is only to fix one specific pitch on the staff. The staff itself denotes relative pitches. That is, for example, an adjacent line and space always form a second; adjacent lines (or adjacent spaces) always form a third; and so forth.

The problem is ...

... that while the staff denotes the magnitude of intervals, it does not consistently denote the quality of the interval. Adjacent lines and spaces are always seconds, but whether they are major or minor seconds is dependent on the specific clef — similarly so for thirds, fourths, etc.

Regarding the chromatic staff

User Dave points out the chromatic staff. This works after a fashion, but it removes enharmonic distinctions between intervals. An augmented second and minor third, for example, are indistinguishable, which is fine in non-tonal music, but is problematic for Tonality. In the chromatic staff, for example, modulation is effectively hidden — or rather, can be recognized only by looking at large enough swaths of notes to realize they fall into the pattern of a new key. (A new key might also be recognized by ear.)

A proposal

I suggest that the "best" way to achieve the desired goal is not a new clef (or staff) but rather to simply "notate" intervallically. The starting "pitch" is arbitrary, followed by a "list" of M2^ m6v m2^, where ^ and v indicate up and down. Duration could be notated with standard symbols below (or above) the interval designations. This also has the potential advantage (for example, with transcription) of allowing for pitch and rhythm to be dealt with separately — notate all the intervals, say, first, then go back and fill in the rhythm.