Ritsu and ryo scales

Ritsu scale with secondary tones in brackets. Play^ⓘ E, F♯, (G,) A, B, C♯, (D,) ^[1][2]

Ryo scale with secondary tones in brackets D, E, F♯, (G/G♯), A, B, (C/C♯). Play^ⓘ[3][4]

The ritsu and ryo scales are anhemitonic pentatonic scales -- five-note scales without semitones -- used in a type of Japanese Buddhist chant called shōmyō. The ritsu scale is built up by intervals of major second, minor third, major second, major second, minor third, while the ryo scale is major second, major second, minor third, major second, minor third.^[5] A third scale called Hanryo hanritsu is created by combining the ritsu and ryo scales however there is no agreed way to combine the two.^[6]

The ritsu scales do not fit exactly into the equal temperament prominent in Western classical music but ritsu is transposable to E and B, Ryo is transposable to D and G, and Hanryo hanritsu to A.^[7] The Ritsu scale is one of the six scales (along with the major and minor scales, the common pentatonic scale, and the common "blues" scale) that provide more consonant harmonic intervals than any other possible scales that can be drawn from the 12 semitones of equally tempered pitch.^[8]

Esoteric significance

The ritsu scale is the voice of the male phoenix, yang, being, the voice that ascends from above and is inhaled breath, emerging from the ki while the ryo scale is the voice of the female phoenix, yin, nothingness, the voice that ascends from below and is exhaled breath, emerging from the breath; probably indicating that ritsu is vertical and ryo is horizontal.^[9]

Sources

1. Gillan gives just the five note scale: C, D, F, G, A. Gillan, Matt (2012). Songs from the Edge of Japan, p.40. ISBN 9781409424048.
2. Malm and Asai give the scale with two additional secondary tones D, E, (F), G, A, B, (C). Malm, William P. (2000). Traditional Japanese Music and Musical Instruments, p.68. ISBN 9784770023957, and Asai, Susan Miyo (1999). Nōmai Dance Drama, p.159. ISBN 9780313306983.
3. Malm, William P. (2000). Traditional Japanese Music and Musical Instruments
4. Asai, Susan Miyo (1999). Nōmai Dance Drama
5. Malm, William P. (2000). Traditional Japanese Music and Musical Instruments
6. Malm, William P. (2000). Traditional Japanese Music and Musical Instruments
7. Malm, William P. (2000). Traditional Japanese Music and Musical Instruments p.69.
8. David Huron Music Perception, Vol. 11, No. 3 (1994) pp. 289-305.
9. Zeami, Motoyiko (2011). Zeami, p.121. ISBN 9780231139595.