User talk:CritDeathX: Difference between revisions

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:::::::::::::: Hmm... I think I have a simpler way to find the countersum and counterdifference tones (my makeshift terms for the treble-down counterparts of the sum and difference tones). For example, let's take a 5/3 Major Sixth. We already know that both the sum tone and the difference tone will be of the same pitch class courtesy of what we see in the numerators of your calculations: 5-3=2 (2/3), 5+3=8 (8/3). From there, we can construct a chord using the base interval plus the sum and difference tones surrounding it, this chord coming to 2:3:5:8. From there, we simply have to swap the numerators and denominators of each number in the chord, thus resulting in 1/2:1/3:1/5:1/8. Given that the middle two values correspond to the initial 5/3 interval, it is the two outer numbers that express the countersum and counterdifference tones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:43, 12 September 2020 (UTC)

:::::::::::::: I can already tell that the linear tones from bass-up operations correspond to a strikingly different sort of operation for treble-down ~~operations~~. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:50, 12 September 2020 (UTC)

:::::::::::::: I can already tell that the linear tones from bass-up operations correspond to a strikingly different sort of operation for their treble-down counterparts. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:50, 12 September 2020 (UTC)

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	:::::::::::::: Hmm... I think I have a simpler way to find the countersum and counterdifference tones (my makeshift terms for the treble-down counterparts of the sum and difference tones). For example, let's take a 5/3 Major Sixth. We already know that both the sum tone and the difference tone will be of the same pitch class courtesy of what we see in the numerators of your calculations: 5-3=2 (2/3), 5+3=8 (8/3). From there, we can construct a chord using the base interval plus the sum and difference tones surrounding it, this chord coming to 2:3:5:8. From there, we simply have to swap the numerators and denominators of each number in the chord, thus resulting in 1/2:1/3:1/5:1/8. Given that the middle two values correspond to the initial 5/3 interval, it is the two outer numbers that express the countersum and counterdifference tones. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:43, 12 September 2020 (UTC)		:::::::::::::: Hmm... I think I have a simpler way to find the countersum and counterdifference tones (my makeshift terms for the treble-down counterparts of the sum and difference tones). For example, let's take a 5/3 Major Sixth. We already know that both the sum tone and the difference tone will be of the same pitch class courtesy of what we see in the numerators of your calculations: 5-3=2 (2/3), 5+3=8 (8/3). From there, we can construct a chord using the base interval plus the sum and difference tones surrounding it, this chord coming to 2:3:5:8. From there, we simply have to swap the numerators and denominators of each number in the chord, thus resulting in 1/2:1/3:1/5:1/8. Given that the middle two values correspond to the initial 5/3 interval, it is the two outer numbers that express the countersum and counterdifference tones. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:43, 12 September 2020 (UTC)

	:::::::::::::: I can already tell that the linear tones from bass-up operations correspond to a strikingly different sort of operation for treble-down ~~operations~~. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:50, 12 September 2020 (UTC)		:::::::::::::: I can already tell that the linear tones from bass-up operations correspond to a strikingly different sort of operation for their treble-down counterparts. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:50, 12 September 2020 (UTC)