TOH: Difference between revisions
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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]]. | 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]]. | ||
[[File:TOH 1 through 4 on C.png|left|thumb|960x960px|The first four tritaves of odd harmonics, on C, notated using [[Richie's HEJI extensions]].]] | |||
{| class="wikitable" | {| class="wikitable" | ||
|+1-TOH | |+ style="font-size: 105%" | 1-TOH | ||
!step | ! step | ||
!0 | ! 0 | ||
!1 | ! 1 | ||
|- | |- | ||
| | | Pitch | ||
|(1/1) | | (1/1) | ||
|3/1 | | 3/1 | ||
|- | |- | ||
| | | Reduced | ||
|(1/1) | | (1/1) | ||
|3/1 | | 3/1 | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|+2-TOH | |+ 2-TOH | ||
! | ! Step | ||
!0 | ! 0 | ||
!1 | ! 1 | ||
!2 | ! 2 | ||
!3 | ! 3 | ||
|- | |- | ||
| | | Pitch | ||
|(3/3) | | (3/3) | ||
|5/3 | | 5/3 | ||
|7/3 | | 7/3 | ||
|9/3 | | 9/3 | ||
|- | |- | ||
| | | Reduced | ||
|(1/1) | | (1/1) | ||
|5/3 | | 5/3 | ||
|7/3 | | 7/3 | ||
|3/1 | | 3/1 | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|+3-TOH | |+ style="font-size: 105%" | 3-TOH | ||
|- | |- | ||
! Step | |||
! 0 | |||
! 1 | |||
! 2 | |||
! 3 | |||
! 4 | |||
! 5 | |||
! 6 | |||
! 7 | |||
! 8 | |||
! 9 | |||
|- | |- | ||
| | | Pitch | ||
|(1/1) | | (9/9) | ||
|11/9 | | 11/9 | ||
|13/9 | | 13/9 | ||
|5/3 | | 15/9 | ||
|17/9 | | 17/9 | ||
|19/9 | | 19/9 | ||
|7/3 | | 21/9 | ||
|23/9 | | 23/9 | ||
|25/9 | | 25/9 | ||
|3/1 | | 27/9 | ||
|- | |||
| Reduced | |||
| (1/1) | |||
| 11/9 | |||
| 13/9 | |||
| 5/3 | |||
| 17/9 | |||
| 19/9 | |||
| 7/3 | |||
| 23/9 | |||
| 25/9 | |||
| 3/1 | |||
|} | |} | ||
== Listening == | == Listening == | ||
https://soundcloud.com/cmloegcmluin/sets/third-tritave-odd-harmonics | https://soundcloud.com/cmloegcmluin/sets/third-tritave-odd-harmonics | ||
[[Category:Harmonic series]] | |||
[[Category:Tritave]] | |||
[[Category:Tables]] | |||
Latest revision as of 19:17, 13 March 2025
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.
| step | 0 | 1 |
|---|---|---|
| Pitch | (1/1) | 3/1 |
| Reduced | (1/1) | 3/1 |
| Step | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Pitch | (3/3) | 5/3 | 7/3 | 9/3 |
| Reduced | (1/1) | 5/3 | 7/3 | 3/1 |
| 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 |
Listening
https://soundcloud.com/cmloegcmluin/sets/third-tritave-odd-harmonics