TOH: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Cmloegcmluin (talk | contribs)
Created page with "An '''n-TOH''' stands for the nth tritave of odd harmonics. TOHs reject factors of 2 in JI ratios, having a prime minimum of 3 (similar to Bohlen-Pierce). (tables f..."
 
Cmloegcmluin (talk | contribs)
No edit summary
Line 1: Line 1:
An '''n-TOH''' stands for the nth tritave of odd harmonics.  
An '''n-TOH''' (pronounced /toʊ/, like "toe") stands for the nth tritave of odd harmonics.  


TOHs reject factors of 2 in JI ratios, having a [[prime minimum]] of 3 (similar to [[Bohlen-Pierce]]).
TOHs reject factors of 2 in JI ratios, having a [[prime minimum]] of 3 (similar to [[Bohlen-Pierce]]).


(tables forthcoming, as soon as I can use Edit instead of Edit Source after creating the page)
It is similar in concept to an octave of the [[harmonic series]], a special case of a [[Overtone scales|mode of the harmonic series]] where the mode is a power of 2. However, here the tuning spans (and repeats at) the [[tritave]], and includes only [[Oddharmonic series|odds]].
{| class="wikitable"
|+1-TOH
!step
!0
!1
|-
|pitch
|(1/1)
|3/1
|-
|reduced
|(1/1)
|3/1
|}
{| class="wikitable"
|+2-TOH
!step
!0
!1
!2
!3
|-
|pitch
|(3/3)
|5/3
|7/3
|9/3
|-
|reduced
|(1/1)
|5/3
|7/3
|3/1
|}
{| class="wikitable"
|+3-TOH
!step
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
|-
|pitch
|(9/9)
|11/9
|13/9
|15/9
|17/9
|19/9
|21/9
|23/9
|25/9
|27/9
|-
|reduced
|(1/1)
|11/9
|13/9
|5/3
|17/9
|19/9
|7/3
|23/9
|25/9
|3/1
|}

Revision as of 19:25, 1 April 2021

An n-TOH (pronounced /toʊ/, like "toe") stands for the nth tritave of odd harmonics.

TOHs reject factors of 2 in JI ratios, having a prime minimum of 3 (similar to Bohlen-Pierce).

It is similar in concept to an octave of the harmonic series, a special case of a mode of the harmonic series where the mode is a power of 2. However, here the tuning spans (and repeats at) the tritave, and includes only odds.

1-TOH
step 0 1
pitch (1/1) 3/1
reduced (1/1) 3/1
2-TOH
step 0 1 2 3
pitch (3/3) 5/3 7/3 9/3
reduced (1/1) 5/3 7/3 3/1
3-TOH
step 0 1 2 3 4 5 6 7 8 9
pitch (9/9) 11/9 13/9 15/9 17/9 19/9 21/9 23/9 25/9 27/9
reduced (1/1) 11/9 13/9 5/3 17/9 19/9 7/3 23/9 25/9 3/1