Warped diatonic: Difference between revisions
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A '''warped diatonic scale''' is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the [[ | A '''warped diatonic scale''' is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the [[5L 2s]] diatonic scale ("LLsLLLsLLsLLLs...") in its sequence of large and small steps, and such that the sizes of those steps are similar to those of the diatonic scale (namely, in the ballpark of 200 and 100 cents). | ||
Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale. | Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale. | ||
| Line 45: | Line 45: | ||
|- | |- | ||
| 8 | | 8 | ||
| [[ | | [[3L 2s]] | ||
| Sensi, Squares, Petrtri, A-Team, Father | | Sensi, Squares, Petrtri, A-Team, Father | ||
| LsLLsL | | LsLLsL | ||
| Line 51: | Line 51: | ||
|- | |- | ||
| 9 | | 9 | ||
| [[ | | [[4L 1s]] | ||
| Bug, superpelog | | Bug, superpelog | ||
| LLLsLL, LLsLLL | | LLLsLL, LLsLLL | ||
| Line 63: | Line 63: | ||
|- | |- | ||
| 10 | | 10 | ||
| [[ | | [[4L 2s]] | ||
| Decimal, lemba | | Decimal, lemba | ||
| LLsLLsLL | | LLsLLsLL | ||
| Line 75: | Line 75: | ||
|- | |- | ||
| 11 | | 11 | ||
| [[ | | [[4L 3s]] | ||
| Orgone, keemun, sixix | | Orgone, keemun, sixix | ||
| LsLLsL | | LsLLsL | ||
| Line 81: | Line 81: | ||
|- | |- | ||
| 11 | | 11 | ||
| [[ | | [[5L 1s]] | ||
| Machine, gorgo | | Machine, gorgo | ||
| LLLsLL, LLsLLL | | LLLsLL, LLsLLL | ||
| Line 87: | Line 87: | ||
|- | |- | ||
| '''12''' | | '''12''' | ||
| '''[[ | | '''[[5L 2s]]''' | ||
| '''Ordinary diatonic''' | | '''Ordinary diatonic''' | ||
| (infinitely long) | | (infinitely long) | ||
| Line 93: | Line 93: | ||
|- | |- | ||
| 13 | | 13 | ||
| [[ | | [[5L 3s]] | ||
| Father, A-Team, Petrtri | | Father, A-Team, Petrtri | ||
| LsLLsLL, LLsLLsL | | LsLLsLL, LLsLLsL | ||
| Line 99: | Line 99: | ||
|- | |- | ||
| 13 | | 13 | ||
| [[ | | [[6L 1s]] | ||
| Glacial, leantone, tetracot | | Glacial, leantone, tetracot | ||
| LLLsLL, LLsLLL | | LLLsLL, LLsLLL | ||
| Line 105: | Line 105: | ||
|- | |- | ||
| 14 | | 14 | ||
| [[ | | [[5L 4s]] | ||
| Superpelog, godzilla | | Superpelog, godzilla | ||
| LsLLsL | | LsLLsL | ||
| Line 111: | Line 111: | ||
|- | |- | ||
| 14 | | 14 | ||
| [[ | | [[6L 2s]] | ||
| Hedgehog | | Hedgehog | ||
| LLsLLLsLL | | LLsLLLsLL | ||
| Line 117: | Line 117: | ||
|- | |- | ||
| 15 | | 15 | ||
| [[ | | [[6L 3s]] | ||
| Triforce | | Triforce | ||
| LLsLLsLL | | LLsLLsLL | ||
| Line 123: | Line 123: | ||
|- | |- | ||
| 15 | | 15 | ||
| [[ | | [[7L 1s]] | ||
| Porcupine | | Porcupine | ||
| LLLsLL, LLsLLL | | LLLsLL, LLsLLL | ||
| Line 129: | Line 129: | ||
|- | |- | ||
| 16 | | 16 | ||
| [[ | | [[6L 4s]] | ||
| Lemba, antikythera | | Lemba, antikythera | ||
| LsLLsL | | LsLLsL | ||
| Line 135: | Line 135: | ||
|- | |- | ||
| 16 | | 16 | ||
| [[ | | [[7L 2s]] | ||
| Mavila | | Mavila | ||
| LLsLLLsLL | | LLsLLLsLL | ||
| Line 246: | Line 246: | ||
=== Warped antidiatonic === | === Warped antidiatonic === | ||
The scales at the top and bottom of this table are questionable as "warped antidiatonics", but the ones near | The scales at the top and bottom of this table are questionable as "warped antidiatonics", but the ones near {{nowrap|2''x'' + ''y'' {{=}} 9}} are good examples. | ||
{| class="wikitable" | {| class="wikitable" | ||
! {{nowrap|2''x'' + ''y''}} | ! {{nowrap|2''x'' + ''y''}} | ||
| Line 345: | Line 345: | ||
|} | |} | ||
= Example: Godzilla[9] = | == Example: Godzilla[9] == | ||
Godzilla[9] in [[19edo|19edo]] has steps of {{nowrap|3 3 1 3 1 3 1 3 1}}. That corresponds to LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are "recognized" as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like "do re mi fa sol", leading you to believe that "sol" is a 3/2 interval above "do", but in fact it's not—it's closer to 10/7. The "real" 3/2 is another small step above that, in the melodic position of a flatted "la". | Godzilla[9] in [[19edo|19edo]] has steps of {{nowrap|3 3 1 3 1 3 1 3 1}}. That corresponds to LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are "recognized" as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like "do re mi fa sol", leading you to believe that "sol" is a 3/2 interval above "do", but in fact it's not—it's closer to 10/7. The "real" 3/2 is another small step above that, in the melodic position of a flatted "la". | ||