Base-X Tunings for Instruments

I'm setting my electric violin with base-√3, because the frequency of base-3 is too high with the string of violin.

When I/you play the Glass Bead Game, the first generation exists in myself/yourself and in power the flooding (God) always.

It is unique and ubiquitous because of the first generation.

Now the common denominator of music and mathematics here from base-x; the norm.

Fig.1.0. the difference of base-2 and base-√3

The link of fig.1.1~1.3:I’ve planned 300 hours for the details of Wiles’ Proof of Fermat’s Last Theorem.

https://www.kiyomnishio.com/post/i-ve-planned-300-hours-for-the-details-of-wiles-proof-of-fermat-s-last-theorem

Fig.1.1. fig.10.0 of the linked article.

Fig.1.2. fig.10.11a of the linked article.

Fig.1.3. fig.10.11b of the linked article.

Fig.1.3. fig.10.11a right:

I've drawn each ψ in Galois field.

[0, 10, 100, ... , ∞]'s green means complement.

Below I used 信号発生器 (signal generator) for iPhone for the setting, I use MultiTone Generator PRO for iPhone for the programmed play. The both applications are excellent.

When it is calculated with C ≒ 261.3Hz, the base-√3 series is below as example.

Fig.2.0. base-√3's tone generation from C ≒ 261.3Hz. generated by 信号発生器 (signal generator) for iPhone.

Fig.2.1. base-√3's tone generation from C ≒ 261.3Hz. generated by Calculator for iPhone.

Fig.3.0. my electric violin.

When it is calculated from base-2 A ≒ 440Hz to base-√3 A ≒ 434.75 from base-2_G × (√3^(1/12)) as for Violin, the base-√3 series is below as example.

Fig.3.1. base-√3's tone generation from A ≒ 434.75. generated by Calculator for iPhone.

Fig.3.2. base-√3's tone generation from A ≒ 434.75. generated by Calculator for iPhone.

Any imaginary number exists between base-2 and base-x, because only 2 is a prime number with the Galois' imaginary number in itself.

I think a guitar that the frets have been removed is played with base-x.

Fig.4.0. base-2's tone generation from C ≒ 261.3. generated by 信号発生器 (signal generator) for iPhone.

Fig.4.1. base-2's tone generation from C ≒ 261.3. generated by Calculator for iPhone.

Links:

The new music theory, as music and mathematics are common denominator, of the novel Glass Bead Game.

https://www.kiyomnishio.com/post/the-new-music-theory-as-music-and-mathematics-are-common-denominator-of-the-novel-glass-bead-game-1

The new music theory, as music and mathematics are common denominator, of the novel Glass Bead Game (2)

https://www.kiyomnishio.com/post/the-new-music-theory-as-music-and-mathematics-are-common-denominator-of-the-novel-glass-bead-game

The new music theory, as music and mathematics are common denominator, of the novel Glass Bead Game (3)

https://www.kiyomnishio.com/post/the-new-music-theory-as-music-and-mathematics-are-common-denominator-of-the-novel-glass-bead-game-2

(The first post on kyonissho.com/kyos-blog was August 20, 2023.)

(C) Copyright 2023 Kyo Nissho (Kiyom Nishio). All rights reserved.