User:BudjarnLambeth/5- to 10-tone scales in 47zpi

The Riemann Siegel Z function has a local maximum close to 15.0535. One way to interpret this is to say that "15.0535edo" is the zeta stretched version of 15edo. This gives us a tuning very similar to 15edo, but with closer approximations of most just intervals, especially 3/2.

This article lists some 5- to 10-note scales in 15.0535edo. The tuning of each scale degree is given in cents.

Atoll (this is the original/default tuning)

• 79.716
• 398.578
• 478.294
• 717.441
• 956.588
• 1195.735

Aurora (approximated from Hexany 1728)

• 159.431
• 398.578
• 717.441
• 956.588
• 1195.735

Augmented[6] MOS

• 318.863
• 398.578
• 717.441
• 797.157
• 1116.020
• 1195.735

Equipentatonic (Approximated from 5edo)

• 239.147
• 478.294
• 717.441
• 956.5881
• 1195.735

Firedance (this is the original/default tuning)

• 239.147
• 558.010
• 717.441
• 956.588
• 1195.735

Monsoon (this is the original/default tuning)

• 239.147
• 478.294
• 717.441
• 1036.304
• 1195.735

Porcupine[6] MOS

• 398.578
• 558.010
• 717.441
• 876.872
• 1036.304
• 1195.735

Rockpool (this is the original/default tuning)

• 398.578
• 478.294
• 717.441
• 956.588
• 1195.735

In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:

• 79.716
• 159.431
• 239.147
• 318.863
• 398.578
• 478.294
• 558.010
• 637.725
• 717.441
• 797.157
• 876.872
• 956.588
• 1036.304
• 1116.020
• 1195.735

See also

• The Riemann Zeta Function and Tuning

• Augmented
• Blackwood
• Porcupine

• 5- to 10-tone scales in 30edo
• 5- to 10-tone scales in 60edo
• 5- to 10-tone scales in 84edo
• 5- to 10-tone scales in 91edo
• 5- to 10-tone scales in 96edo

• 5- to 10-tone scales from the modes of the harmonic series
• 5- to 10-tone scales from the modes of the subharmonic series