The δ scale is a non-octave repeating musical scale

Musical scale

In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...

. It may be regarded as the beta scale

Beta scale

The β scale is a non-octave-repeating musical scale which splits the perfect fourth into two equal parts, or eight equal parts of approximately 64 cents each . This totals approximately 18.75 steps per octave...

's reciprocal since it is, "as far 'down' the (0 3 6 9

Diminished seventh chord

A diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh above the root. Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically...

) circle from α

Alpha scale

The α scale is a non-octave-repeating musical scale which splits the minor third into two equal parts, or four equal parts of approximately 78 cents each . This totals approximately 15.39 steps per octave...

 as β is 'up.'" As such it would split the minor second into eight equal parts of approximately 14 cents each . This would total approximately 85.7 steps per octave.

The Bohlen-Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad

Triad (music)

In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...

  and the 9:7:5 "narrow" triad (rather than the conventional 4:5:6 triad). Notes include:

1:1

Unison

In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...

 

25:21

Bohlen-Pierce scale

The Bohlen–Pierce scale is a musical scale that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the diatonic scale. Compared with octave-repeating scales, its intervals are more consonant with certain types of acoustic spectra. It was...

 

9:7

Septimal major third

In music, the septimal major third , also called the supermajor third and sometimes Bohlen–Pierce third is the musical interval exactly or approximately equal to a just 9:7 ratio of frequencies, or alternately 14:11. It is equal to 435 cents, sharper than a just major third by the septimal...

 

75:49

Bohlen-Pierce scale

The Bohlen–Pierce scale is a musical scale that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the diatonic scale. Compared with octave-repeating scales, its intervals are more consonant with certain types of acoustic spectra. It was...

 

5:3 

9:5 

15:7 

7:3

Septimal minor third

In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...

 

25:9 

3:1

Further reading

• Bohlen, Heinz: "13 Tonstufen in der Duodezime", Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76 - 86.