Diaschisma: Difference between revisions

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=== Significance ===

[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Parizek_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_tetracot_commas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started. ~~parizek1~~] – a [[comma pump]] progression that requires the diaschisma to be tempered out (i.e. equates two notes that are separated by a diaschisma).

[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Parizek_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_tetracot_commas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started. parizek diaschisma pump] – a [[comma pump]] progression that requires the diaschisma to be tempered out (i.e. equates two notes that are separated by a diaschisma).

[[File:Parizek diaschisma comma pump.png|thumb|Pařízek's diaschisma comma pump example in JI (notated with HEJI) and 12edo.]]

In the progression, the bassline moves as follows:

@@ Line 19: / Line 19: @@
 === Significance ===
-[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Parizek_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_tetracot_commas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started. parizek1] – a [[comma pump]] progression that requires the diaschisma to be tempered out (i.e. equates two notes that are separated by a diaschisma).
+[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Parizek_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_tetracot_commas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started. parizek diaschisma pump] – a [[comma pump]] progression that requires the diaschisma to be tempered out (i.e. equates two notes that are separated by a diaschisma).
 [[File:Parizek diaschisma comma pump.png|thumb|Pařízek's diaschisma comma pump example in JI (notated with HEJI) and 12edo.]]
 In the progression, the bassline moves as follows: